Analyzing meaning An introduction to semantics and pragmatics

🧭 Overview

🧠 One-sentence thesis

Linguistic meaning operates at three levels—word, sentence, and utterance—and successful communication depends on shared conventions for both normal usage and creative extensions, with semantics studying inherent linguistic meaning and pragmatics studying meaning derived from context and use.

📌 Key points (3–5)

• Three levels of meaning: word meaning, sentence meaning (semantic content), and utterance meaning (semantic content plus pragmatic inferences from context).
• Semantics vs pragmatics: semantics concerns inherent meaning of linguistic expressions; pragmatics concerns meaning that depends on how expressions are used in context.
• Shared conventions are essential: word meanings must be agreed upon by the speech community, yet can be stretched in rule-governed ways (Mark Twain's "good man in the worst sense" succeeds; Humpty Dumpty's arbitrary redefinition fails).
• Common confusion: sentence vs utterance—a sentence is a linguistic expression; an utterance is a speech event by a speaker in a specific context; the same sentence can produce different utterance meanings in different contexts.
• Form-meaning relationship: word forms are mostly arbitrary (except onomatopoeia); sentence meanings are compositional (predictable from word meanings plus syntax); utterance meanings are calculable from sentence meaning plus context via pragmatic principles.

🎭 Two ways to stretch meaning

✅ Successful extension (Mark Twain)

Mark Twain described someone as "a good man in the worst sense of the word."

• Twain uses good with nearly the opposite of its normal meaning (implying puritanical, self-righteous, judgmental, or hypocritical).
• Despite the unfamiliar usage, he successfully communicates his intended message.
• Why it works: the extension follows shared conventions for bending the rules; hearers can infer the intended meaning from context and shared pragmatic principles.

❌ Failed communication (Humpty Dumpty)

Humpty Dumpty claims "When I use a word, it means just what I choose it to mean—neither more nor less."

• He tries to use glory to mean "a nice knock-down argument."
• Alice cannot understand him; communication fails.
• Why it fails: arbitrary, individual redefinition violates the fundamental requirement that meanings be shared by the speech community.
• Don't confuse: creative extension (following shared pragmatic rules) vs arbitrary redefinition (ignoring community conventions).

🔬 Semantics and pragmatics

🔬 Two divisions of meaning study

Division	Focus	Example
Semantics	Inherent meaning of words and sentences as linguistic expressions in themselves	Dictionary meaning of good
Pragmatics	Aspects of meaning that depend on or derive from how expressions are used	Twain's negative implication when using good

• The distinction is useful but the exact boundary is difficult to draw and remains controversial.
• The two interact in complex ways, so studying them together is beneficial.

📐 Defining semantics more precisely

Semantics: the study of the relationship between linguistic form and meaning.

• Not just "the study of meaning" in isolation.
• This relationship is rule-governed, just like syntax.
• Language learners acquire:
  • Vocabulary (lexicon) with meanings
  • Rules for combining words into sentences (syntax)
  • Rules for interpreting the expressions formed when words are combined
• All components must be shared by the speech community for communication to work.

📊 Three levels of meaning

📝 Word meaning

• The meaning of individual vocabulary items.
• Must be learned and shared by the speech community.
• Example: the meaning of yellow allows us to identify objects that are yellow in color.

📄 Sentence meaning

Sentence meaning: the semantic content of the sentence; the meaning which derives from the words themselves, regardless of context.

• A sentence is a linguistic expression, a well-formed string of words.
• Sentence meaning is what the words literally say, independent of any particular use.
• Example: "Have you already eaten?" literally asks whether the addressee has eaten.

🗣️ Utterance meaning (speaker meaning)

Utterance meaning: the semantic content plus any pragmatic meaning created by the specific way in which the sentence gets used; "the totality of what the speaker intends to convey by making an utterance."

• An utterance is a speech event by a particular speaker in a specific context.
• When a speaker uses a sentence in a specific context, they produce an utterance.
• The same sentence can have different utterance meanings in different contexts.

🌏 Context-dependent interpretation example

The Teochew question "Have you already eaten?" illustrates context-dependence:

Context	Utterance meaning	Relation to sentence meaning
Greeting between friends	Equivalent to "hello" or "How do you do?"	Utterance meaning differs greatly from sentence meaning
Doctor asking patient before medicine	Genuine request for information about eating	Utterance meaning matches sentence meaning

• The literal (sentence) meaning is always "Have you already eaten or not?"
• The utterance meaning depends on who is speaking, to whom, and why.

🔗 Form-meaning relationships

🎲 Arbitrary relationship (most words)

• For most words, the relation between form (phonetic shape) and meaning is arbitrary.
• No inherent connection between the sound and what it refers to.
• Example: the word for 'dog' varies arbitrarily across languages—Armenian shun, Balinese cicin, Korean gae, Tagalog aso.

🔔 Partly conventional (onomatopoeia)

• Onomatopoetic words: forms intended to imitate sounds they refer to.
• Even these show conventional aspects; the same sound is represented differently across languages:
  • Dog barking: English bow-wow, Balinese kong-kong, Armenian haf-haf, Korean mung-mung or wang-wang
  • Cross-linguistic variation is not due to dogs barking differently in different places
  • Common pattern: labial, velar, or labio-velar consonants and low back vowels
• The form-meaning relation is non-arbitrary but still partly conventional.

🧩 Compositional relationship (sentences)

Compositional: the meaning of the expression is predictable from the meanings of the words it contains and the way they are combined.

• The relation between sentence form and meaning is generally compositional, not arbitrary.
• Example: knowing yellow describes a color class and submarine describes a vehicle class, plus English syntax, allows us to infer that yellow submarine refers to something in both classes.
• This principle is fundamental to almost every topic in semantics.

🚫 Exception: idioms

• Idioms are non-compositional: the meaning is not predictable from individual words.
• Examples: kick the bucket = 'die'; X's goose is cooked = 'X is in serious trouble'
• The meaning of the whole phrase must be learned as a unit.

🎯 Calculable relationship (utterances)

• Utterance meaning is neither arbitrary nor strictly compositional.
• Utterance meanings are derivable (calculable) from sentence meaning plus context via pragmatic principles.
• Not always fully predictable; sometimes multiple interpretations are possible for a given utterance in a situation.

🤔 What does "mean" mean?

⚠️ The circularity problem

• Defining semantics as "the study of meaning" uses one English word to define another.
• This creates circularity: a definition only works if the words in the definition are themselves well-defined.
• We must ask: What is the meaning of meaning? What does mean mean?

🔤 Object language vs metalanguage

• Object language: the language being analyzed (e.g., Swahili, English).
• Metalanguage: the language used to describe the object language (e.g., English used to describe Swahili).
• Problem: when both are natural languages, both exhibit vagueness and ambiguities.
• Solution: many linguists use formal logic as a semantic metalanguage.

✍️ Mention vs use

• Mentioned expressions (object language): written in italics, referred to as objects of study.
  • Example: "What is the meaning of meaning?"
• Used words (metalanguage): written in plain font, used in their normal sense.
• This distinction is crucial when using English to describe English.

🎯 Focusing on communicative intent

The excerpt limits its scope to:

• Kinds of meaning people intend to communicate via language.
• Not body language, dress, facial expressions, gestures (except in sign languages).
• Not unintended information a hearer may acquire.

🚫 Natural meaning vs linguistic meaning

• Natural meaning (philosopher Paul Grice's term): unintended information.
  • Example: smoke "means" fire; a rasping voice "means" laryngitis.
  • A suspect's inconsistent statement may reveal guilt to a detective, but guilt is not what the suspect intends to communicate.
• These types of inference are not the central focus.

🌍 The correspondence approach

An approach focusing on how speakers use language to talk about the world.

• Knowing word meanings allows us to identify the class of objects those words can refer to in a particular situation (universe of discourse).
• Knowing sentence meaning allows us to determine whether a sentence is true in a particular situation.
• Example: "It is raining" uttered at a particular time and place is true if it corresponds to the actual weather at that time and place.
• This is called the correspondence theory of truth.

📏 Meaning as truth conditions

• The meaning of a declarative sentence is the knowledge that allows speakers and hearers to determine whether it is true in a particular context.
• The principle of compositionality constrains word meanings: individual word meanings must compositionally determine correct sentence meanings.
• Some words (e.g., if, and, but) do not refer to things in the world; their meanings are defined by their contribution to sentence meanings.

🎬 Three questions about utterances

❓ What did the speaker say?

• What is the semantic content of the sentence?
• Philosopher Paul Grice used "What is said" to refer to sentence meaning.

💭 What did the speaker intend to communicate?

• Grice used the term implicature for intended but unspoken meaning.
• Aspects of utterance meaning that are not part of sentence meaning.

🎭 What is the speaker trying to do?

• What speech act is being performed?
• Speech acts are things people do by speaking (e.g., greeting, requesting information, making a promise).

🙏 Example: the word "please"

Consider: (a) "Please pass me the salt." (b) "Can you please pass me the salt?"

• Please does not contribute to sentence meaning (semantic content).
• Adding please to a true statement doesn't make it false; using it inappropriately is just odd.
• Please makes two contributions to utterance meaning:
  1. Identifies the speech act: indicates the utterance is a request
  2. Marks politeness: indicates the manner of performance and social relationship
• We cannot understand please without referring to speech acts.

🎯 Direct vs indirect speech acts

Type	Example	Form vs function
Direct request	"Please pass me the salt."	Grammatical form (imperative) matches intended speech act (request)
Indirect request	"Can you please pass me the salt?"	Grammatical form (interrogative) does not match intended speech act (request); requires pragmatic inference

• Direct: utterance meaning ≈ sentence meaning
• Indirect: utterance meaning must be inferred pragmatically

🧭 Overview

🧠 One-sentence thesis

Language connects speakers' words to the world through reference and denotation, but meaning cannot be fully explained by reference alone—it also requires understanding sense (dictionary meaning), structural relationships, and expressive content.

📌 Key points (3–5)

• Two approaches to meaning: denotational semantics (word-to-world link) vs. cognitive semantics (word-to-thought link); this book adopts the denotational approach.
• Sense vs. denotation: sense is dictionary meaning (context-independent), while denotation is what a word picks out in a specific context (context-dependent).
• Not all noun phrases refer: proper names and definite descriptions typically refer, but quantified phrases ("every student") and non-specific indefinites do not function as referring expressions.
• Common confusion: context-dependence does not equal ambiguity—"my father" refers to different people for different speakers but has one sense; ambiguity means multiple senses for the same expression.
• Three types of ambiguity: lexical (one word, multiple meanings), structural (same words, different syntactic structures), and referential (unclear which entity is meant).

🌍 How language connects to the world

🔺 The Semiotic Triangle

The excerpt presents three interconnected domains:

• Language: the words and phrases speakers use
• Mind: the speaker's thoughts, concepts, and mental representations
• World: the actual situations, things, and events being described

Key insight: No one-to-one correspondence exists between these three corners.

• A speaker's description rarely includes everything they know.
• What the speaker believes may not match the actual world.
• Strong associations link all three domains, but they remain distinct.

🎯 Denotational vs. cognitive semantics

Approach	Primary focus	Advantage mentioned
Denotational	Language ↔ World link	Hard to get direct evidence about minds; proven success at explaining compositionality
Cognitive	Language ↔ Mind link	Recognizes that mental representations matter

Denotational semantics: the approach that focuses on how linguistic expressions relate to the world, using truth and reference as foundational concepts.

Why denotational?

• Native speakers can reliably judge whether sentences are true in specific situations.
• This provides concrete evidence for semantic analysis.
• Both approaches recognize all three corners matter; they differ in emphasis.

🏷️ Types of referring expressions

🏷️ What counts as referring

Referring expression: an expression (normally a noun phrase) which a speaker uses to direct the hearer's attention to something, or enable the hearer to identify something.

Example: Brazilians used "o rei" (the king) to refer to Pelé—the phrase directed hearers' attention to that specific soccer player.

🔒 Rigid designators

Some expressions always pick out the same entity regardless of context:

• Proper names: Abraham Lincoln, King Henry VIII, Mao Zedong
• Natural kind terms (when referring to the species/substance as a whole): octopus, camel, methane, gold

Example: "The octopus has eight tentacles" refers to the species in general, not any particular octopus.

👉 Deictic elements (indexicals)

Words whose reference depends on the speech situation itself:

• I = current speaker
• you = current addressee
• here = place of speech event
• now = time of speech event
• he/she (when pointing) = person being indicated

🔗 Anaphoric elements

Anaphoric element: one whose reference depends on the reference of another noun phrase (the antecedent) within the same discourse.

Example: "Susan refuses to marry George because he smokes."

• The pronoun "he" takes "George" as its antecedent.
• The pronoun's reference is determined by what the antecedent refers to.

❌ What does NOT refer

Quantified noun phrases like "every student," "all students," "some people":

• Evidence from reflexives: "Everyone trusts himself" ≠ "Everyone trusts everyone"
• Evidence from contradiction: "Some people are Estonian and some people are not Estonian" can be true, but "John is Estonian and John is not Estonian" cannot
• Evidence from collective predicates: "The student body outnumbers the faculty" is fine, but "#Every student outnumbers the faculty" is semantically odd

Pronouns with quantifier antecedents: "Every boy should respect his mother"—the pronoun "his" does not refer to any specific individual.

📝 Definite vs. indefinite descriptions

Definite descriptions ("this book," "the sixteenth President," "my eldest brother"):

• Normally used when the hearer can identify a unique referent
• Can also be used generically without referring to a specific individual

Indefinite descriptions ("a cowboy"):

• Specific: "My sister has just married a cowboy" (refers to a particular person)
• Non-specific: "My sister would never marry a cowboy" (no particular individual in mind)
• Ambiguous: "My sister wants to marry a cowboy" could mean either

Don't confuse: Specific indefinites are referring expressions; non-specific indefinites are not.

📖 Sense vs. denotation

📖 The crucial distinction

Frege identified two kinds of meaning:

Sense (Sinn): aspects of meaning that do not depend on context—the kind of meaning you find in a dictionary.

Denotation (Bedeutung): meaning that does depend on context; for referring expressions, this is typically the referent.

For content words, denotation = the set of all things the word could describe:

• Denotation of "yellow" = set of all yellow things
• Denotation of "tree" = set of all trees
• Denotation of "snore" = set of all creatures that snore

🌐 Context-dependence of denotation

"The Prime Minister" has one sense but different denotations:

• In Singapore, 1975 → Lee Kuan Yew
• In England, 1975 → Harold Wilson
• In England, 1989 → Margaret Thatcher

"Talks" has different denotation sets in different universes:

• Our world: people, some computers, some parrots
• Wonderland: playing cards, chess pieces, a white rabbit, a cat, a dodo
• Narnia: beavers, badgers, wolves, some trees

Key principle: Sense is a fact about the language; denotation is a fact about the world or situation.

🔄 Same denotation, different sense

"The largest land mammal" and "the African bush elephant":

• Same denotation in our current world
• Different denotations in other contexts (e.g., 30 million BC, when Paraceratherium existed)
• Therefore, different senses

Rule: If two expressions can have different denotations in any context, they have different senses.

Converse: Synonymous expressions (same sense) must always have the same denotation in every possible situation.

• Example: "my mother-in-law" and "the mother of my spouse" should refer to the same person for any monogamous speaker in any context.

💎 Non-referring expressions still have sense

These phrases have no referent in our current world but are not meaningless:

• "the present King of France"
• "the largest prime number"
• "the diamond as big as the Ritz"
• "the unicorn in the garden"

Why this matters: Sense is derived by the normal rules of the language, even when denotation fails.

🔀 Three types of ambiguity

📚 Lexical ambiguity

One word with multiple senses:

• "hand": body part / clock pointer / bunch of bananas / cards held by a player / hired worker
• "beat": to strike / to defeat / to whisk (eggs)
• "charges": attacks / demands payment
• "organ": body part / musical instrument

Example: "A boiled egg is hard to beat" (defeat vs. whisk)

Don't confuse with context-dependence: "my father" refers to different people for different speakers, but this is not ambiguity—it has one sense with context-dependent denotation.

🏗️ Structural ambiguity

Same words, different syntactic structures, different meanings:

• "Two cars were reported stolen by the Groveton police" (who stole them? or who reported?)
• "One morning I shot an elephant in my pajamas"
  • Structure 1: [shot an elephant] [in my pajamas] (I was wearing pajamas)
  • Structure 2: shot [an elephant in my pajamas] (elephant was wearing pajamas)

What this reveals: Meanings are assigned to syntactic objects, not just strings of words—syntactic structure contributes crucially to meaning.

👤 Referential ambiguity

Unclear which entity is meant:

• "Adams wrote frequently to Jefferson while he was in Paris" (who was in Paris—Adams or Jefferson?)
• "My student has won a Rhodes scholarship" (which of my 14 students?)

Historical example: King Croesus asked the oracle whether to fight the Persians. The oracle said he would "destroy a mighty empire"—ambiguous reference meant it could be either the Persian empire or his own (it turned out to be his own).

😮 Expressive meaning

😮 A different kind of meaning

Words like "ouch" and "oops" present a challenge:

• They convey meaning but do not refer to things in the world
• They do not help determine truth conditions
• They do not form part of sentences—they stand alone as one-word utterances

Expressive meaning: the kind of meaning conveyed by expressives, which reflects the speaker's feelings or attitudes at the time of speaking.

How expressive meaning differs from descriptive meaning: The excerpt introduces this topic but the provided text cuts off before listing the specific differences.

🧭 Overview

🧠 One-sentence thesis

Knowing the meaning of a declarative sentence means knowing what the world would have to be like for that sentence to be true, and this truth-conditional approach allows us to identify important logical relationships between propositions such as entailment and presupposition.

📌 Key points (3–5)

• Truth conditions define meaning: A sentence's meaning is determined by the situations in which it would be true, not by whether we know its actual truth value.
• Three types of propositions: Analytic sentences (always true), contradictions (never true), and synthetic sentences (truth depends on the situation).
• Entailment vs. presupposition: Entailment is a semantic relation where one proposition's truth guarantees another's; presupposition is pragmatically encoded information treated as part of the common ground.
• Common confusion: Presuppositions survive under negation and questioning, while entailments do not—this is the key test to distinguish them.
• Accommodation as repair: Hearers can add presupposed information to the common ground even when it wasn't previously shared, if it seems uncontroversial.

🎯 Truth conditions and proposition types

🎯 What truth conditions mean

"To know the meaning of a [declarative] sentence is to know what the world would have to be like for the sentence to be true."

• A sentence by itself is neither true nor false; truth value depends on the situation.
• Example: "King Henry VIII snores" is false in 2023 (he died in 1547) but may have been true in 1525.
• Knowing a sentence's meaning means knowing the kinds of situations where it would be true, not necessarily knowing whether it is true.

📊 Three categories of propositions

Type	Definition	Example	Informativeness
Analytic (tautology)	Always true in all circumstances	"Today is the first day of the rest of your life"	Not informative about the world
Contradiction	False in all circumstances	"Your children are not your children" (literal reading)	Cannot be true
Synthetic	May be true or false depending on situation	Most everyday statements	Requires world knowledge to evaluate

• Analytic sentences and contradictions have communicative value through pragmatic inference, not semantic content.
• An adequate semantic analysis should explain why certain sentences are analytic or contradictory.

🔗 Meaning relations between propositions

🔗 Entailment: logical necessity

Proposition p entails proposition q when: (a) whenever p is true, q must be true; (b) whenever q is false, p must be false; (c) this follows from the meanings alone, not context.

• Example: "Edward VIII has abdicated the throne" entails "Edward VIII is no longer King."
• Entailment is a very strong inference—if you're certain p is true and p entails q, you can be equally certain q is true.

Tests for entailment:

• Asserting p while denying q creates a contradiction: "#I broke your jar, but the jar didn't break."
• Expressing doubt about q while asserting p sounds unnatural: "#I broke your jar, but I'm not sure whether it broke."
• Stating both p and q separately is redundant: "#I broke your jar, and the jar broke."

🔄 Synonymy: mutual entailment

• Two sentences that mutually entail each other are synonymous (paraphrases).
• Example: "Hong Kong is warmer than Beijing" and "Beijing is cooler than Hong Kong" have the same truth conditions.
• They must have the same truth value in any imaginable situation.

⚔️ Incompatibility: cannot both be true

Two types:

1. Contradictory: Must have opposite truth values in all circumstances

   • Example: "Ringo Starr is my grandfather" vs. "Ringo Starr is not my grandfather"
   • Any proposition and its negation are contradictory

2. Contrary: Cannot both be true, but can both be false

   • Example: "Al is taller than Bill" and "Bill is taller than Al" cannot both be true
   • But both can be false (if they're the same height)

🔓 Independence

• Two sentences are independent when neither entails the other and they are neither incompatible nor synonymous.
• Knowing one's truth value doesn't tell you the other's truth value.

🎭 Presupposition: common ground information

🎭 What presupposition is

Presupposition: information linguistically encoded as being part of the common ground at the time of utterance.

• Common ground: everything both speaker and hearer know or believe, and know they share.
• Certain words or constructions (triggers) signal that information is already shared.
• Example: Using "more" in "Take some more tea" presupposes the person has already had some tea.

Don't confuse with entailment:

• Entailments hold only for assertions; they disappear under negation or questioning.
• Presuppositions hold whether you assert, deny, or question the sentence.

🧪 Tests for identifying presuppositions

Family of sentences test:

• If a positive statement triggers a presupposition, related forms (negative, question, if-clause, modal) trigger the same presupposition.
• Example: "Susan has stopped dating that Albanian monk" presupposes she was dating him.
  • Negative: "Susan has not stopped..." → same presupposition
  • Question: "Has Susan stopped...?" → same presupposition
  • If-clause: "If Susan has stopped..." → same presupposition
• Entailments do NOT survive these transformations.

"Hey, wait a minute!" test:

• A presupposition not in the common ground can be challenged with "Wait a minute, I didn't know that!"
• Simple assertions cannot be challenged this way (speakers don't usually assert what the hearer already knows).
• Example: "The mathematician who proved Goldbach's Conjecture is a woman."
  • Appropriate: "Hey, wait a minute. I had no idea someone proved it."
  • Inappropriate: "#Hey, wait a minute. I had no idea that was a woman."

🔑 Common presupposition triggers

Trigger type	Example	Presupposition
Definite descriptions	"the King of France"	There exists a unique King of France
Possessives	"my cat"	The speaker has a cat
Factive predicates	"regret," "know," "realize"	The complement clause is true
Implicative predicates	"manage to"	The subject tried
Aspectual predicates	"stop," "continue"	The event was ongoing
Temporal clauses	"Before I moved to Texas..."	The speaker moved to Texas
Counterfactuals	"If you had written..."	You did not write

🛠️ Accommodation: repairing mismatches

• When a presupposition trigger doesn't match the common ground, two outcomes are possible:
  1. Presupposition failure: Hearer objects (like Dorothy rejecting "Are you a good witch or bad witch?")
  2. Accommodation: Hearer accepts and adds the information to common ground

When accommodation happens:

• The presupposed information is uncontroversial
• It's consistent with existing common ground
• The hearer would immediately accept it if asserted
• Example: "My cat got stuck on the roof" → hearer accommodates that you have a cat

Important point:

• Speakers often encode new information as presuppositions, expecting accommodation.
• Presuppositions need not be "mutually known" beforehand—they must be "non-controversial" (something the hearer would accept from you).

⚖️ Semantic effects of presupposition failure

• Presupposition failure is primarily a pragmatic problem (makes utterances inappropriate/infelicitous).
• But it can also create semantic problems: difficulty assigning truth values.

Truth-value gaps:

• "The present King of France is bald" (when there is no King of France)
• Is this false? But then "The present King of France is not bald" should be true—yet it seems equally "un-true."
• Some presupposition failures create truth-value indeterminacy.

Not all failures create gaps:

• "The vice president regrets falsifying his dental records" (when he never did)
• This seems clearly false, not indeterminate.
• The negative version has at least one reading that is true.
• Complications arise with how negation is interpreted (affected by intonation and other factors).

🎓 Evaluating semantic analyses

🎓 Benchmarks for success

An adequate semantic analysis should:

• Explain why certain sentences are analytic (always true)
• Explain why certain sentences are contradictions (never true)
• Predict which sentence pairs will be synonymous
• Predict which pairs will be incompatible (contradictory or contrary)
• Account for entailment and presupposition patterns

🎓 Foundation for further study

• Truth-conditional semantics is the foundation for analyzing word meanings and sentence composition.
• The goal is to explain how a sentence gets its meaning—why a given form has the particular meaning it does.
• Both semantic relations (entailment) and pragmatic relations (presupposition) are essential for understanding how meaning works.

🧭 Overview

🧠 One-sentence thesis

Formal logic provides a precise metalanguage for semantic analysis by defining valid patterns of inference through propositional and predicate logic, enabling us to explain how sentence meanings determine truth conditions and predict meaning relations like entailment and paraphrase.

📌 Key points (3–5)

• Why use logic as a metalanguage: Logic avoids ambiguity, provides precise rules for determining entailment and paraphrase, allows testing of semantic hypotheses, models compositionality, and is recursive (unlimited formulae from finite rules).
• Valid inference vs. true conclusions: A valid logical form guarantees a true conclusion only if the premises are true; false premises or invalid reasoning can each lead to false conclusions independently.
• Propositional logic: Deals with inferences determined solely by logical operators (¬, ^, _, →, ↔) and truth values, not by content-word meanings; explains certain tautologies, contradictions, and meaning relations.
• Predicate logic: Represents meanings of content words (predicates and arguments) and quantifiers (∀ 'all', ∃ 'some'); explains inferences that depend on word meanings and quantifier scope.
• Common confusion—scope ambiguities: When multiple quantifiers or negation interact, the order (wide vs. narrow scope) changes meaning; e.g., "Some man loves every woman" has two distinct readings depending on which quantifier takes priority.

🎯 Why formal logic matters

🎯 Avoiding natural language problems

• Every human language has ambiguity, vagueness, and figures of speech—useful for communication but problematic for precise semantic description.
• Using formal logic as a metalanguage avoids these issues: logical notation is unambiguous and precise.
• Example: English "or" can be inclusive (and/or) or exclusive (but not both), but logical operators _ and XOR are clearly distinguished.

🔍 Testing semantic hypotheses

• If we hypothesize that a sentence means p, logic lets us derive what else must follow (e.g., q).
• If native speakers feel no inconsistency in asserting the sentence but denying q, this mismatch suggests p is not the correct meaning.
• Logic provides objective methods to distinguish valid from invalid inference patterns.

🔄 Recursivity and compositionality

• Logic is recursive: a small set of symbols and rules generates unlimited formulae.
• This matches human language: finite vocabulary and grammar produce infinite meaningful sentences.
• Example: The negation operator ¬ can apply repeatedly: p, ¬p, ¬(¬p), etc.
• Logic is a powerful tool for modeling compositionality—how sentence meanings arise from word meanings plus syntactic structure.

🧮 Propositional logic

🧮 Basic operators and truth tables

Propositional operators: Symbols that combine propositions to form new propositions; their meanings are fully specified by truth values.

One-place operator:

• ¬ (negation, 'not'): ¬p is true when p is false, and false when p is true.

Two-place operators:

Operator	Symbol	True when	Example
Conjunction	^ ('and')	Both p and q are true	"It is raining ^ the north wind is blowing" is true only if both conditions hold
Inclusive disjunction	_ ('or')	Either p or q or both are true	"It is raining _ it is snowing" is true if at least one holds
Exclusive disjunction	XOR	Either p or q but not both	"White wine XOR red wine" (common in English "or")
Material implication	→ ('if…then')	False only when p is true but q is false	"If it rains → I will take you to a movie" is false only if it rains but no movie
Biconditional	↔ ('if and only if')	p and q have the same truth value	Abbreviation for (p → q) ^ (q → p)

Don't confuse: The material implication → is defined purely by truth values; it may not always match English "if" intuitions (discussed further in Chapter 19).

📊 Evaluating complex formulae

• Truth tables evaluate formulae by calculating truth values step-by-step from left to right.
• Example: To prove p _ (¬p) is a tautology:
  1. List all possible truth values for p (T, F).
  2. Calculate ¬p (F, T).
  3. Calculate p _ (¬p) using the _ truth table: (T, T).
  4. Result: always true → tautology (logically true regardless of p's meaning).
• Example: p ^ (¬p) yields (F, F) → contradiction (never true).

⚖️ Meaning relations via truth tables

• Tautologies (always T): Formulas true in all circumstances due to logical structure alone.
• Contradictions (always F): Formulas false in all circumstances.
• Entailment: If (p → q) is a tautology, then p entails q.
• Paraphrase: If (p ↔ q) is a tautology, then p and q are paraphrases (mutual entailment).
• Example: ((p _ q) ^ (¬p)) → q is a tautology, so "Either Joe is crazy or lying, and he is not crazy" entails "Joe is lying."

🔑 Valid inference patterns

🔑 Famous rules (tautologies)

Rule	Formula	Meaning	Example
Modus Ponens (affirming the antecedent)	((p→q) ^ p) → q	If p→q is true and p is true, infer q	If John is Estonian → he likes this book; John is Estonian; ∴ he likes this book
Modus Tollens (denying the consequent)	((p→q) ^ ¬q) → ¬p	If p→q is true and q is false, infer ¬p	If dolphins are fish → cold-blooded; not cold-blooded; ∴ not fish
Disjunctive Syllogism	((p _ q) ^ (¬p)) → q	If p or q is true and p is false, infer q	Dolphins are fish _ mammals; not fish; ∴ mammals
Hypothetical Syllogism	((p→q) ^ (q→r)) → (p→r)	Chain implications	If rodent → mammal; if mammal → warm-blooded; ∴ if rodent → warm-blooded

⚠️ Valid form ≠ true conclusion

• Valid reasoning guarantees a true conclusion only if premises are true.
• Example: Modus Tollens with false premise "Salmon are not cold-blooded" → false conclusion "Salmon are not fish" (but reasoning is still valid).
• Conversely, a true conclusion does not prove valid reasoning.
• Common fallacy—denying the antecedent: ((p→q) ^ ¬p) → ¬q is invalid.
  • Example: "If bats are birds → have wings; bats are not birds; ∴ bats do not have wings" (false conclusion from true premises).
  • Don't confuse: This looks similar to Modus Tollens but negates the wrong part.

🧩 Predicate logic basics

🧩 Predicates and arguments

Predicate: The element of meaning that determines what property, event, or relationship is being described (expressed by verbs, adjectives, nouns, prepositions).

Arguments: The individuals of whom the property or relationship is claimed to be true.

• Different predicates require different numbers of arguments:
  • One-place: HUNGRY(j), SNORE(h), MAN(s)
  • Two-place: LOVE(j,m), NEAR(n,p), ADMIRE(a,v)
  • Three-place: GIVE, SHOW, OFFER, SEND
• Notation: Predicates in CAPITALS, proper names in lowercase initials, agent/experiencer listed first.
• Example: "John loves Mary" → LOVE(j,m); "Abraham Lincoln was tall and homely" → TALL(a) ^ HOMELY(a).
• Some predicates take propositions as arguments: "Henry thinks Anne is beautiful" → THINK(h, BEAUTIFUL(a)).

🔢 Quantifiers: ∀ and ∃

Universal Quantifier ∀: 'for all individuals x'; used with → for universal generalizations.

Existential Quantifier ∃: 'there exists one or more individuals x'; used with ^ for existential claims.

English	Logical form	Interpretation
All students are weary	∀x[STUDENT(x) → WEARY(x)]	Choose any x; if x is a student, then x is weary
Some men snore	∃x[MAN(x) ^ SNORE(x)]	There exists at least one x that is both a man and snores
No crocodile is warm-blooded	¬∃x[CROCODILE(x) ^ WARM-BLOODED(x)]	There does not exist an x that is both a crocodile and warm-blooded

Why the difference?

• ∀ pairs with → because "all students are weary" does not claim everything is a student; it claims if something is a student, then it is weary.
• If we used ∀x[STUDENT(x) ^ WEARY(x)], it would mean "everything in the universe is a student and is weary" (wrong).
• ∃ pairs with ^ because "some men snore" claims there exists something that has both properties.

🔗 Bound vs. free variables

• Bound variable: Introduced by a quantifier (∀x or ∃x); all occurrences within the scope (square brackets) refer to the same arbitrary selection.
• Free (unbound) variable: Not introduced by a quantifier or outside its scope; the formula is an open proposition with no truth value until a value is assigned.
• Example: ∀x[x + x = 2x] is true (bound); x – 7 = 4x has no truth value (free).
• Universe of discourse: The set of individuals currently available for discussion; quantifiers range over this set.

🎲 Quantifiers in non-subject positions

• Quantified NPs can be objects, oblique arguments, etc., but the quantifier always appears at the beginning of the formula.
• Examples:
  • "John loves all girls" → ∀x[GIRL(x) → LOVE(j,x)]
  • "Susan has married a cowboy" → ∃x[COWBOY(x) ^ MARRY(s,x)]
  • "Ringo lives in a yellow submarine" → ∃x[YELLOW(x) ^ SUBMARINE(x) ^ LIVE_IN(r,x)]
• Indefinite NPs ("a cowboy") are often translated as existential quantifiers.

🔀 Quantifier principles and scope

🔀 Two key principles

Principle	What it licenses	Example
Universal instantiation	Anything true of all members of a class is true of any specific member	All men are mortal; Socrates is a man; ∴ Socrates is mortal
Existential generalization	If a specific individual has two properties, then something exists with both properties	Arthur is a lawyer; Arthur is honest; ∴ Some lawyer is honest

🌀 Scope ambiguities

• When multiple quantifiers or negation interact, scope (which operator takes logical priority) creates ambiguity.
• Wide scope: The quantifier that appears farthest left in the formula; takes logical priority.
• Narrow scope: Embedded within another quantifier's scope.

Example: "Some man loves every woman"

1. ∃x[MAN(x) ^ (∀y[WOMAN(y) → LOVE(x,y)])]
   • Wide scope ∃: There exists a specific man who loves every woman (one man loves all).
2. ∀y[WOMAN(y) → (∃x[MAN(x) ^ LOVE(x,y)])]
   • Wide scope ∀: For any woman, there exists some man who loves her (different men for different women).

Example: "All that glitters is not gold"

1. ∀x[GLITTER(x) → ¬GOLD(x)] — Everything that glitters is non-gold.
2. ¬∀x[GLITTER(x) → GOLD(x)] — Not everything that glitters is gold (some glittering things are not gold).

Don't confuse: Changing scope changes meaning; test by finding contexts where one reading is true and the other false.

🎓 Conclusion and limitations

🎓 What we've covered

• Propositional logic: Accounts for inferences determined by logical operators (^, _, ¬, →, ↔); explains certain tautologies, contradictions, entailments, and paraphrases based on logical structure alone.
• Predicate logic: Represents meanings of content words (predicates and arguments) and quantifiers; explains inferences involving word meanings and quantifier scope.
• Valid inference: Logic defines valid patterns (Modus Ponens, Modus Tollens, etc.) but does not guarantee true conclusions unless premises are true.

🚧 What logic doesn't cover

• Lexical entailments: Inferences like "John killed the wasp" → "The wasp died" depend on the meanings of kill and die, not logical structure.
• Predicate logic provides notation for representing such meanings but does not itself address these inferences.
• Logic deals with general patterns of reasoning, not individual word meanings (though it provides a framework for expressing them).

🔮 Looking ahead

• Unit IV will discuss how to interpret logical propositions using set theory and how this helps understand compositionality.
• Future chapters will explore how logical operators relate to natural language words (e.g., does English "or" match _ or XOR? Does "if" match →?).
• Presupposition failure (Chapter 3) can sometimes block truth-value assignment, interacting with logical analysis.

🧭 Overview

🧠 One-sentence thesis

Lexical ambiguity—when a single word has multiple senses—must be distinguished from vagueness and indeterminacy through diagnostic tests, and context normally enables hearers to select the intended sense automatically.

📌 Key points (3–5)

• What lexical ambiguity is: A single word-form with multiple distinct senses that can refer to very different kinds of things (e.g., case = container or legal proceeding).
• How to distinguish it from similar patterns: Ambiguity involves antagonistic senses (only one at a time), unlike vagueness (borderline cases, context-dependent) or indeterminacy (underspecified features like gender in cousin).
• Common confusion—polysemy vs. homonymy: Polysemous senses are related and share features (e.g., foot = body part or unit of length); homonymous senses are unrelated coincidences (e.g., row = pull oars vs. line of things).
• Why context matters: Hearers use context to automatically select the intended sense; knowledge about the world plays a crucial role in disambiguation.
• How new senses emerge: Figurative extensions (metaphor, metonymy) can become conventional and eventually lexicalized as established senses.

🔍 Core concepts

🔍 What lexical ambiguity means

Lexical ambiguity: A situation where a single word may have more than one sense.

• Not just "different referents"—the word must have truly distinct meanings with different truth conditions.
• Example: The bull charges is ambiguous because charges can mean 'attacks' or 'demands payment'; the sentence's truth value depends on which sense is chosen.
• Contrast with a word like cousin, which can refer to males or females but has only one sense.

🔍 Construals and word choice

• Words reflect different construals (ways of thinking about things), not complete descriptions.
• Example: I am wiping the table (specifies manner) vs. I am cleaning the table (specifies change of state).
• Example: paperweight vs. quartz crystal can refer to the same object but encode different properties.
• Key principle: We analyze linguistically coded information, not all encyclopedic knowledge about the world.

🧪 Diagnostic tests for ambiguity

🧪 The identity test (ellipsis parallelism)

• How it works: Ellipsis requires parallel interpretations; if "crossed" readings are blocked, the word is ambiguous.
• Example: John saw her duck, and so did Bill allows only parallel readings (both saw an action OR both saw a bird), not mixed readings.
• What it shows: The parallelism constraint blocks incompatible senses, proving they are distinct.
• Example with indeterminacy: John is my cousin, and so is Mary allows different genders because cousin is not ambiguous, just underspecified.

🧪 The contradiction test

• How it works: If X but not X can be true (not a contradiction), then X is ambiguous.
• Example: An aged mother saying "They are not children any more, but they are still my children" is not contradictory because children has two senses (pre-adolescent vs. offspring).
• Equivalent formulation: If a sentence can be both truly affirmed and truly denied in the same context, it must be ambiguous.
• Don't confuse: Sentences like #She is my cousin and she is not my cousin are contradictions, showing cousin is not ambiguous.

🧪 Zeugma and puns

• Zeugma: Clash of senses in coordinate structures feels odd or humorous.
• Example: Mary and her visa expired on the same day (person vs. document).
• Example: He carried a strobe light and the responsibility for the lives of his men (physical vs. abstract).
• Puns: Sentences requiring two senses simultaneously, like The batteries were given out free of charge.
• What this shows: Distinct senses are antagonistic—they cannot both apply at once in normal usage.

🧪 Sense relations test

• Distinct senses have different synonyms and antonyms.
• Example: light (opposite of heavy) vs. light (opposite of dark).
• Caution: Not always reliable because context can restrict possible synonyms even for vague/indeterminate words.

🌫️ Vagueness and indeterminacy

🌫️ What vagueness is

Vagueness: The limits of a word's possible denotations cannot be precisely defined.

• Three characteristics:
  1. Context-dependent truth conditions (someone tall in a gymnastics club may not be tall on a basketball team)
  2. Borderline cases (Is a $50 bottle of wine expensive? Unclear)
  3. "Little-by-little" paradoxes (losing one hair doesn't make you bald, but losing many does—impossible to say which specific hair caused baldness)
• Example: city clearly applies to Montreal but not to Kingsville; unclear for Red Deer or Moose Jaw.
• Key point: More knowledge won't resolve vagueness (unlike ignorance).

🌫️ What indeterminacy is

Indeterminacy: A word is underspecified with respect to certain features but has a single sense.

• Example: cousin doesn't specify gender; kick doesn't specify which foot.
• How to tell: The identity test allows mixed references (John is my cousin, and so is Mary), unlike true ambiguity.
• Translation note: Indeterminacy is language-specific; English uncle is indeterminate for features that Mandarin distinguishes with separate words (father's elder brother, father's younger brother, etc.).

🌫️ Vagueness vs. indeterminacy

Feature	Vagueness	Indeterminacy
Borderline cases	Yes (e.g., Is $50 expensive?)	No (someone is or isn't your cousin)
Context changes truth	Yes (same person tall in one context, not in another)	No (cousin in one context = cousin in all)
Translation	Tends to be preserved (scalar adjectives are vague cross-linguistically)	Language-specific (different languages specify different features)
Example words	tall, bald, expensive, big	cousin, carry, kick

🔀 Polysemy vs. homonymy

🔀 The basic distinction

• Polysemy: One word with multiple related senses; "an intelligible connection" between senses.
• Homonymy: Different words that happen to sound the same; senses are unrelated.
• Why it matters: Polysemous senses are stored in a single lexical entry; homonyms have separate entries.

🔀 Guidelines for distinguishing them

a. Shared features

• Polysemous senses share at least one salient component.
• Example: foot (body part) and foot (unit of length ≈12 inches) share approximate size; foot (body part) and foot (base of tree/mountain) share position/location.
• Homonymous senses share nothing: row (pull oars) vs. row (line of things).

b. Figurative extension

• If one sense seems to be a figurative extension of another, likely polysemous.
• Example: run in This road runs from Rangoon to Mandalay is based on metonymy (act of running → path traversed).

c. Primary vs. secondary senses

• For polysemy, one sense is typically primary (first mentioned by native speakers, most common translation).
• For homonymy, neither sense is primary.

d. Etymology

• Used in dictionaries but not reliable for synchronic analysis.
• Etymological fallacy: Historical meaning may differ from current meaning (e.g., curious came from Latin 'careful' but now means something else).

🔀 Systematic polysemy

• Regular patterns of related senses that recur across many words.
• Example: Many change-of-state verbs have transitive and intransitive senses (break, melt, split), where transitive = 'cause to [intransitive]'.
• Example: Instrumental nouns can become verbs (hammer, saw, brush, comb → 'use the instrument').
• Important: Even systematic patterns must list secondary senses in the lexicon because not all predicted senses actually occur (e.g., no verbal use for scalpel, tweezers).

🎭 Context and disambiguation

🎭 One sense at a time principle

• In normal usage, context makes clear which sense is intended.
• Hearers automatically filter out unintended senses unconsciously.
• Example: "Several rare ferns grow on the steep banks of the burn where it runs into the lake" contains five ambiguous words, but context eliminates unlikely readings (rare ≠ 'undercooked', steep ≠ 'unjustifiably high').
• Exception: Puns intentionally activate multiple senses, which is why they seem unusual or humorous.

🎭 Role of world knowledge

• Knowledge about the world (not just linguistic context) enables disambiguation.
• Example: "Baked since 1919" on bread packaging—we know bread can't stay in the oven that long, so we select the habitual reading, not durative.
• Implication: Disambiguation is harder with culturally unfamiliar material or translations.

🎭 Problems for translation

• Distinct senses unlikely to share the same translation equivalent in another language.
• Type 1 problem: Wrong sense chosen in source language.
  • Example: Chinese restaurant menu translating 炸灌腸 as 'deep-fried enema' instead of 'deep-fried sausage'.
• Type 2 problem: Translation equivalent is ambiguous in target language when original was not.
  • Example: French apprivoiser 'to tame' translated as Portuguese cativar, which can also mean 'capture, enslave, charm', creating ambiguity not present in the original.

🎨 Figurative extensions

🎨 Coercion and figures of speech

Coercion: The process by which context creates non-established (temporary) senses.

• Motivated by assumption that speaker intends something intelligible.
• If no established sense works, hearer creates an extended meaning.
• Example: Mark Twain's "a good man in the worst sense of the word" forces interpretation of good as something negative (puritanical, self-righteous).

🎨 Common tropes (figures of speech)

Trope	Definition	Example
Metaphor	Implied comparison between unlike things	—
Hyperbole	Exaggeration for emphasis	I have eaten more salt than you have eaten rice
Euphemism	Inoffensive term for explicit one	passed away for died
Metonymy	Substitution of closely associated term	crown for monarch
Synecdoche	Part for whole, whole for part	—
Litotes	Understatement via negating opposite	not bad = 'good'
Irony	Intended meaning opposite of literal	—

🎨 From figurative to established senses

Three stages:

1. Novel/creative metaphors: Calculated fresh each time based on context.
2. Conventional metaphors (clichés): Frequently used, remembered rather than calculated, still felt as figurative (fishing for compliments, burning the candle at both ends).
3. Lexicalized senses: Become established senses stored in the lexicon.
   • Example: grasp 'hold in hand' → 'understand'
   • Example: freeze 'become ice' → 'remain motionless'
   • Example: broadcast 'scatter seeds' → 'transmit via radio/TV'

Final stage: Original literal sense may disappear, leaving only the figurative sense.

• Example: night owl now means only 'person who stays out late', not the bird.

Translation note: Novel metaphors may survive translation (general patterns are widespread), but conventional metaphors rarely work across languages (specific contextual motivations are lost).

📦 Facets of meaning

📦 What facets are

Facets: "Fully discrete but non-antagonistic readings of a word"—distinguishable components of a global whole.

• Different from polysemy because facets are non-antagonistic (can apply simultaneously).
• Example: book includes both physical object (tome) and information content (text).
• Typically both facets apply together; context can highlight just one.

📦 Evidence for facets vs. polysemy

Key test: No zeugma effects

• Example: This is a very interesting book, but it is awfully heavy to carry around (text + tome together—acceptable).
• Example: My religion forbids me to eat or wear rabbit (meat + fur together—acceptable).
• Contrast with true polysemy: #The ham sandwich at table seven was stale and left without paying (zeugma—unacceptable).

Other examples of facets:

• bank: premises, personnel, institution
• Britain: land mass, populace, political entity
• chicken, duck: animal, meat

📦 Facets vs. metonymy

• Some authors analyze facets as systematic polysemy via metonymy.
• Examples that might be metonymy: I'm parked out back (person for vehicle), The ham sandwich left without paying (food for customer).
• Problem: Metonymic senses ARE antagonistic (#The ham sandwich was stale and left without paying), but facets are not.
• Conclusion: Facets may be a distinct phenomenon, not reducible to figurative extension.

🧭 Overview

🧠 One-sentence thesis

Lexical sense relations—such as synonymy, antonymy, hyponymy, and meronymy—reveal word meanings by examining how specific word senses relate to one another through substitution, opposition, hierarchy, and part-whole connections.

📌 Key points (3–5)

• What sense relations are: relationships between specific word senses (not whole words), such as same meaning, opposite meaning, generic-specific, and part-whole.
• Why paradigmatic relations matter: they involve words that are mutually substitutable in the same syntactic positions, making them useful for probing meaning.
• How to identify relations: use entailment tests and sentence-level diagnostics rather than intuition about isolated words.
• Common confusion—antonym types: "opposite" does not mean one thing; complementary pairs (alive/dead) allow no middle ground, while gradable pairs (big/small) name points on a scale.
• Application: sense relations underpin traditional dictionary definitions, especially the classical genus + differentia structure.

🔗 Core paradigmatic relations

🔗 What paradigmatic means

• Paradigmatic sense relations hold between words that can substitute for each other in the same syntactic slot.
• Example: "Look at that big/large/small/enormous mosquito!" shows substitutability.
• Contrast with syntagmatic relations, which involve words that co-occur in construction (e.g., which nouns big can modify).
• This chapter focuses on paradigmatic relations; syntagmatic relations (selectional restrictions) appear in Chapter 7.

🧪 Testing sense relations

• Reliable judgments come from sentence-level tests, not isolated word comparisons.
• Use entailment, contradiction, and paraphrase to diagnose relations.
• Semantic similarity and syntactic substitutability limit the useful comparisons (comparing big with multilingual is uninformative).

🔄 Synonymy and its limits

🔄 Definition of synonyms

Two words are synonymous (for a specific sense) if substituting one for the other does not change the meaning of a sentence.

• Example: "John frightened the children" ↔ "John scared the children" (semantically equivalent; each entails the other).
• This shows frightened and scared are synonyms.

⚠️ Perfect synonymy is rare

• Even true meaning equivalents often differ in collocation.
• Example: bucket and pail are synonymous in "John filled the bucket/pail," but the idiom "kick the bucket" does not work with pail.
• Example: big and large are equivalent in "a big/large house," but big sister (= elder sister) ≠ large sister.
• Don't confuse: synonymy in one context does not guarantee synonymy in all contexts.

⚖️ Types of antonyms

⚖️ What "opposite" means

• Antonyms are not "as different as possible" (e.g., big vs. multilingual).
• True antonyms share most meaning components and differ only in one feature value (e.g., both big and small express size; both dead and alive express vitality).
• The excerpt identifies several antonym subtypes.

🔲 Complementary pairs (simple antonyms)

Complementary pairs exhaust the range of possibilities and allow no middle ground.

• Examples: open/shut, alive/dead, male/female, on/off.
• Diagnostic test: replacing one with the other produces contradictory sentences (opposite truth values in every situation).
  • "The switch is on" vs. "The switch is off" → one must be true, the other false.
  • Negation of one entails the other: "not open" → "closed."
• No natural middle: "⁇The switch is neither on nor off" is odd.
• Common confusion: simple antonyms can be coerced into gradable uses in figurative expressions (half-dead, more dead than alive), but these are not fully natural; compare "?half-alive," "#How dead is that mosquito?"

📏 Gradable (scalar) antonyms

Gradable antonyms name opposite ends of a scale and produce contrary (not contradictory) sentences.

• Examples: big/small, hot/cold, diligent/lazy.
• Diagnostic test: replacing one with the other yields sentences that cannot both be true but may both be false (contrary).
  • "My son-in-law is extremely diligent" vs. "extremely lazy" → both can be false ("neither extremely diligent nor extremely lazy").
• Key properties:
  • Have intermediate terms (warm, tepid, cool between hot and cold).
  • Values are relative, not absolute (a small elephant > a big mosquito).
  • Often vague.
  • Comparative forms are natural (hotter, colder).
  • Comparatives form converse pairs: "A is longer than B" ↔ "B is shorter than A."
  • One member often has privileged status: "How old/⁇young are you?"
• Don't confuse with incompatibles: turnip and platypus produce contrary sentences but are not antonyms (they don't name a single scale).

🔁 Converse pairs

Converse pairs name an asymmetric relation with reversed argument positions.

• Examples: parent/child, above/below, employer/employee, advisor/advisee.
• Test: reversing both the word and the argument order produces paraphrases.
  • "Michael is my advisor" ↔ "I am Michael's advisee."
  • OWN(x,y) ↔ BELONG_TO(y,x).

↔️ Reverse pairs

Reverse pairs (typically verbs) denote motion or change in opposite directions.

• Examples: push/pull, come/go, fill/empty, heat/cool, strengthen/weaken.
• Diagnostic: some allow a restitutive reading of again (restoring original state, not repeating action).
  • "The nurse heated the instruments, then cooled them again" (= restored to cool state).

🌳 Hyponymy and taxonomy

🌳 Hyponymy: generic-specific relations

A hyponym is a more specific term; the superordinate (hyperonym) is more generic.

• Test: a simple positive statement with the hyponym entails the same statement with the superordinate.
  • "Seabiscuit was a stallion" → "Seabiscuit was a horse."
  • "Fred stole my bicycle" → "Fred took my bicycle."
  • "This pot is made of copper" → "This pot is made of metal."
• Negation reverses the entailment direction:
  • "Not a horse" → "Not a stallion."

🏷️ Taxonomy: a special hyponymy

Taxonomy is a classifying relation; X is a taxonym of Y if "An X is a kind/type of Y" sounds natural.

• Examples: "A beagle is a kind of dog," "Gold is a type of metal."
• Less natural: "?A stallion is a kind of horse," "⁇Sunday is a kind of day."
• Taxonomic sisters share the same superordinate and must be incompatible (a single thing cannot be both a squirrel and a mouse).
• Often involves natural kind terms (species, substances) that resist paraphrase by superordinate + modifier:
  • "⁇Beagle means a dog," "⁇Gold means a metal."
• Important: linguistic taxonomy may differ from scientific classification.
  • Example: Malay labah-labah 'spider' is defined as "a kind of serangga (insect)," even though spiders are not zoologically insects.
  • Semantic analysis studies the object language, not scientific facts.

🧩 Meronymy: part-whole relations

🧩 What meronymy is

A meronymy is a pair expressing a part-whole relationship; the word naming the part is the meronym.

• Examples: hand, brain, eye are meronyms of body; door, roof, kitchen are meronyms of house.
• Test: "The parts of an X include the Y, the Z, …" sounds natural.

🔍 Parts vs. pieces

• A part has three properties that a piece lacks:
  1. Autonomous identity: you can buy automobile parts that were never in a car; a piece must come from a whole.
  2. Motivated boundaries: parts have natural boundaries (joints, material changes, potential separation); piece boundaries are arbitrary.
  3. Definite function: parts have a role relative to the whole; pieces do not.
• We study lexical structure (relations between words), not the things themselves.

📖 Defining words via sense relations

📖 Classical definition structure

Traditional definitions use the nearest superordinate term (genus proximum) plus distinguishing modifiers (differentia specifica).

• This creates a phrasal synonym: mutually substitutable and equivalent in meaning.
• Example: ewe = "an adult female sheep" (superordinate: sheep; modifiers: adult, female).
• Samuel Johnson's definition: "Lexicographer: A writer of dictionaries; a harmless drudge that busies himself in tracing the origin and detailing the signification of words."
• More examples:
  • fir: "a kind of tree [with evergreen needles]."
  • rectangle: "a [right-angled] quadrilateral."

🔀 Alternative definition types

When classical structure is difficult, dictionaries use:

Type	Description	Example
Synonym	Use a synonym or near-synonym	grumpy: "moodily cross; surly"
Antonym	Define via negation of antonym	free: "not controlled by obligation…"
Extensional	Spell out denotation (list members)	New England: "the NE U.S. comprising Maine, New Hampshire…"
Full sentence	COBUILD style	confidential: "Information that is confidential is meant to be kept secret"

💡 Why this works

• Hyponymy plays a central role (superordinate term).
• Other sense relations (synonymy, antonymy, meronymy) supplement the definition toolkit.
• Studying sense relations provides a systematic method for probing and defining word meanings.

🧭 Overview

🧠 One-sentence thesis

Word meanings can be broken down into smaller components that create entailments and selectional restrictions, and identifying these components helps explain sense relations and syntactic behavior, especially for verb classes.

📌 Key points (3–5)

• Lexical entailments: one word's meaning "contains" another's (e.g., ewe entails sheep), creating sentence-level entailment relations.
• Selectional restrictions: semantic constraints that rule out odd combinations like #This sausage appreciates Mozart, functioning as presuppositions.
• Binary feature analysis: an influential but limited approach that represents meanings as bundles of +/− features (e.g., [+adult], [+male]).
• Common confusion: selectional restrictions vs. collocational restrictions—the former are semantic (meaning-based), the latter are conventional usage patterns that can be repaired by synonym substitution.
• Verb classes: verbs sharing systematic meaning components (e.g., "change of state" for break verbs) show parallel syntactic behavior, while idiosyncratic components distinguish individual verbs within a class.

🔗 Lexical entailments

🔗 What lexical entailments are

Lexical entailment: when the meaning of one word creates an entailment relation between sentences containing that word and sentences containing another word.

• Strictly speaking, entailment is a relation between sentences, not words.
• When we say "ewe lexically entails sheep," we mean: any sentence with ewe entails the corresponding sentence with sheep.
• The meaning of the entailed word (sheep, kill, unmarried) is "part of" or "contained in" the meaning of the entailing word (ewe, assassinate, bachelor).

Example: John assassinated the Mayor entails John killed the Mayor because the meaning of kill is part of the meaning of assassinate.

🧪 How to test for lexical entailments

Test 1: Natural vs. incoherent statements

• Sentences that affirm the entailment feel natural: It's a dog and therefore it's an animal.
• Sentences that deny the entailment feel incoherent: #It's not an animal, but it's just possible that it's a dog.

Test 2: Denying the entailed component leads to contradiction

• #John killed the Mayor but the Mayor did not die.
• #It's a dog but it's not an animal.
• #John is a bachelor but he is happily married.

Test 3: Asserting the entailed component leads to redundancy (pleonasm)

• #It's a dog and it's an animal. (feels redundant)
• ⁇Kick it with one of your feet. (redundant because kick already implies using a foot)
• ⁇He was murdered illegally. (redundant because murder already implies illegality)

Don't confuse: Contradiction (denying an entailment) vs. dissonance (violating a selectional restriction)—the former is logically inconsistent, the latter is linguistically odd but not contradictory.

🚫 Selectional restrictions

🚫 What selectional restrictions are

Selectional restrictions: semantic constraints on specific word combinations that rule out linguistically unacceptable sentences.

• They are part of the meanings of specific words, not just facts about the world.
• Violations create dissonance rather than contradiction.
• Example: #This sausage doesn't appreciate Mozart is linguistically odd because appreciate (in this sense) requires an animate, sentient subject.

🚫 How selectional restrictions differ from world knowledge

Linguistic constraint (selectional restriction):

• #I know an old woman who swallowed a participle/prime number.
• Hearer reaction: "You can't say that."

Improbable fact (world knowledge):

• Our kitten drank a bottle of claret.
• Hearer reaction: "No! Really?" (astonishment, not linguistic rejection)

🔒 Selectional restrictions as presuppositions

Unlike entailments, selectional restrictions hold even in questions, negations, and other non-assertive contexts:

Context	Entailment behavior	Selectional restriction behavior
Negation	Can be denied: John didn't kill the Mayor; the Mayor is not even dead.	Still holds: #John didn't drink his sandwich.
Question	Can be questioned: Is that a dog, or even an animal?	Still holds: #Did John drink his sandwich?

This behavior shows that selectional restrictions are a type of presupposition.

🆚 Selectional restrictions vs. collocational restrictions

Selectional restrictions (semantic):

• German essen (people eat) vs. fressen (animals eat)—cannot be repaired by synonym substitution.
• Kimaragang paalansayad (pregnant, but only for water buffalo)—the restriction is part of the word's meaning.

Collocational restrictions (conventional usage):

• John died/passed away/kicked the bucket (all acceptable)
• My rose bush died/#passed away/#kicked the bucket (only died is acceptable)
• dirty joke vs. #unclean joke (can be repaired by synonym)
• unclean spirit vs. #dirty spirit (can be repaired by synonym)

Collocational restrictions reflect "normal" usage patterns; violations feel odd but can typically be fixed by replacing one word with a synonym, suggesting they are not strictly due to lexical meaning per se.

🧩 Componential analysis with binary features

🧩 The binary feature approach

This influential mid-20th-century approach treats word meanings as bundles of distinctive semantic features, similar to how phonemes are defined by phonetic features.

Example: Horse terms

Word	[adult]	[male]
horse	⌀	⌀
stallion	+	+
mare	+	−
foal	−	⌀
colt	−	+
filly	−	−

(⌀ = unspecified)

Example: Human terms

Word	[adult]	[male]
human	⌀	⌀
man	+	+
woman	+	−
child	−	⌀
boy	−	+
girl	−	−

✅ Advantages of binary features

Neat explanations for some sense relations:

• Synonyms: pairs that share all the same components.
• Complementary pairs: differ only in polarity for one feature (e.g., [+/− alive], [+/− awake]).
• Hyperonyms and hyponyms: hyperonym components are a proper subset of hyponym components (e.g., child [+human, −adult] vs. boy [+human, −adult, +male]).
• Taxonomic sisters: distinguished by the "extra" components each hyponym adds to the hyperonym.
• Reverse pairs: differ in one component (typically direction), with dimension, manner, and reference point held constant.

❌ Limitations of binary features

Problem 1: Many distinctions are not binary

• Species names within the cat family (lion, tiger, leopard, jaguar, cougar, wildcat, lynx, cheetah)—what binary features distinguish them?
• Color terms, types of metal, etc.—the number of features needed would approach the number of lexical items.

Problem 2: Two-place predicates

• Recognize entails a change of state in the first argument.
• Offend entails a change of state in the second argument.
• A simple feature matrix cannot specify which argument a particular feature applies to.

Problem 3: Structured components

• Some meanings require ordered components, not just an unordered bundle.
• Kinship: 'mother's brother's spouse' (one sense of aunt) ≠ 'spouse's mother's brother' (no English term).
• Verbs: 'want to cause to die' (murderous) ≠ 'cause to want to die' (similar to mortify).

Problem 4: Efficiency question

• Binary features are efficient within restricted semantic domains.
• For the entire lexicon, the inventory of features might need to be almost as large as the lexicon itself.

🏃 Verb meanings and verb classes

🏃 Why verbs are special

Verb meanings directly influence syntactic structure, so syntactic evidence can supplement traditional semantic methods.

🔨 Two foundational verb classes

Charles Fillmore (1970) distinguished two classes based on shared syntactic and semantic properties:

Class	Example verbs	Shared semantic component
hit class	hit, slap, strike, bump, stroke	surface contact
break class	break, bend, fold, shatter, crack	change of state

🧪 Syntactic tests for verb classes

Test 1: Causative-inchoative alternation

• Break verbs allow it: John broke the window (transitive/causative) ↔ The window broke (intransitive/inchoative).
• Hit verbs do not: John hit the tree ↔ *The tree hit.

Test 2: Body-part possessor ascension

• Hit verbs allow it: I hit his leg ↔ I hit him on the leg.
• Break verbs do not: I broke his leg ↔ *I broke him on the leg.

Test 3: Conative alternation

• Hit verbs allow it: Mary hit the piñata ↔ Mary hit at the piñata.
• Break verbs do not: Mary broke the piñata ↔ *Mary broke at the piñata.

Test 4: Middle alternation

• Break verbs allow it: This glass breaks easily.
• Hit verbs do not: *This fence hits easily.

🔬 Semantic evidence for verb classes

The syntactic tests converge, but crucially there is independent semantic evidence:

Evidence that break verbs entail change of state:

• I hit the window with a hammer; it didn't faze the window, but the hammer shattered. (acceptable, though surprising)
• *I broke the window with a hammer; it didn't faze the window, but the hammer shattered. (contradiction)

Evidence that hit verbs entail surface contact:

• *I hit the window without touching it. (contradiction)
• I broke the window without touching it. (acceptable)

Don't confuse: Without this direct semantic evidence, we risk circular reasoning (e.g., "break verbs permit the alternation because they contain 'change of state,' and we know they contain 'change of state' because they permit the alternation").

🗂️ Four verb classes and their components

Levin (1993) extended Fillmore's work, identifying four classes with distinctive syntactic patterns:

Class	Body-part ascension	Conative alternation	Middle	Shared components
touch	yes	no	no	contact
hit	yes	yes	no	motion, contact
cut	yes	yes	yes	motion, contact, change
break	no	no	yes	change

Key insight: Each diagnostic test is sensitive to specific meaning components:

• Body-part possessor ascension: possible only for verbs with the "surface contact" component.
• Conative alternation: possible only for verbs with both "contact" and "motion."
• Middle construction: possible only for verbs with "caused change of state."

🧬 Systematic vs. idiosyncratic components

Systematic components:

• Shared by an entire verb class.
• Have syntactic consequences (affect argument realization).
• Define class membership.
• Example: "change of state" for all break verbs.

Idiosyncratic components:

• Specific to individual verb roots.
• Distinguish one verb from another within the same class (e.g., punch vs. slap).
• Do not affect syntactic behavior.

Example of lexical decomposition for break verbs:

• Formula: [[x ACT] CAUSE [BECOME [y <state>]]]
• The idiosyncratic aspect (e.g., broken, split) is associated with the state predicate.

Important principle (Levin):

"The important theoretical construct is the notion of meaning component, not the notion of verb class. Verb classes arise because a set of verbs with one or more shared meaning components show similar behavior."

Don't confuse: The verb class is an "artificial construct"—a useful tool for identifying systematic meaning components, but not the ultimate goal.

🎯 Conclusion and open questions

🎯 Systematic vs. idiosyncratic meaning

The distinction between systematic (class-defining) and idiosyncratic (verb-specific) components appears in multiple theories:

• Fillmore (1970) and Levin (1993) for verbs.
• Katz & Fodor (1963) for content words in general: "semantic markers" (systematic) vs. "distinguisher" (idiosyncratic).

Reasons to make this distinction:

• Syntax is sensitive to some meaning components but not others.
• Grammatically relevant components are shared by whole classes.
• Rules of systematic polysemy must be stated in terms of systematic aspects of meaning.

❓ Unresolved issues

No consensus on:

• What the systematic aspects of meaning are.
• How they should be represented.

Competing views:

• Some scholars deny that components exist, treating word meanings as "atoms" (unanalyzable units).
• Under the atomic view, lexical entailments might be expressed as meaning postulates (e.g., ∀x[STALLION(x) → MALE(x)]).
• Many scholars believe meanings are built from smaller elements, but much work remains to determine what those elements are and how they combine.

🧭 Overview

🧠 One-sentence thesis

Grice's theory explains how speakers communicate meaning beyond the literal words they use by relying on shared conversational principles that allow hearers to infer intended messages through systematic reasoning.

📌 Key points (3–5)

• The Cooperative Principle: conversation works because participants assume each other is being cooperative and following shared maxims (Quality, Quantity, Relation, Manner).
• How implicatures arise: when a speaker appears to violate a maxim, hearers assume cooperation and infer additional meaning to resolve the apparent violation.
• Two types of conversational implicature: particularized (context-dependent) and generalized (typically triggered by certain expressions regardless of context).
• Common confusion: apparent violations vs. real violations—implicatures arise when hearers interpret apparent violations as intentional and meaningful, not when maxims are genuinely broken.
• Key diagnostic properties: conversational implicatures are defeasible (cancellable), suspendable, reinforceable, and calculable—unlike entailments and presuppositions.

🤝 The Cooperative Principle and maxims

🤝 What the Cooperative Principle assumes

The Cooperative Principle: a background assumption that participants in rational conversation share awareness of certain norms, even if they don't always follow them slavishly.

• Not a moral code: speakers can communicate by obeying or breaking the maxims, as long as the hearer recognizes which strategy is being used.
• Shared awareness is key: what matters is that both speaker and hearer know the principle exists and expect each other to know it.
• Radio wave analogy: the Cooperative Principle is like a carrier wave—it provides the baseline against which meaningful variations (implicatures) can be detected.

📋 The four maxims

Maxim	Sub-maxims	What it requires
Quality	1. Do not say what you believe false<br>2. Do not say what you lack evidence for	Be truthful
Quantity	1. Be as informative as required<br>2. Don't be more informative than required	Give the right amount of information
Relation	Be relevant	Stay on topic
Manner	1. Avoid obscurity<br>2. Avoid ambiguity<br>3. Be brief<br>4. Be orderly	Be clear and organized

🌍 Cross-linguistic validity

• The excerpt notes that Grice's principles appear to hold across all languages.
• Cultural differences affect which specific implicatures arise, but not whether the maxims operate.
• Example: speakers in different cultures obey Grice's principles given their own cultural values and assumptions.

🔄 How implicatures work

🔄 Apparent violation with no real violation

Pattern: the speaker seems to violate a maxim, but the implicature restores cooperation.

Example: "I am a stranger here myself" (in response to "Where is the post office?")

• Appears to violate Relation (relevance)
• Hearer reasoning: "Bill seems irrelevant, but I assume he's being cooperative → strangers don't know locations → he's explaining why he can't help → this IS relevant after all"
• Implicature: "I cannot tell you where the post office is"

Example: "There is a garage around the corner" (in response to "I am out of petrol")

• Appears to violate Relation
• Implicature: "You can buy petrol there"

Example: "He has been paying a lot of visits to New York lately" (in response to "Smith doesn't seem to have a girlfriend")

• Appears to violate Relation
• Implicature: "Maybe he has a girlfriend in New York"

⚖️ Conflict between maxims

Pattern: violating one maxim to obey another.

Example: "Where does C live?" → "Somewhere in the South of France"

• Appears to violate Quantity (not informative enough)
• But obeying Quality (can't be more specific without lacking evidence)
• Implicature: "I do not know exactly where C lives"

🎭 Flouting maxims

Pattern: deliberate, obvious violation intended to be recognized as such.

Flouting: a deliberate and obvious violation of a maxim, meant to trigger an implicature.

Example: Philosophy professor's reference letter—"Mr. X's command of English is excellent, and his attendance at tutorials has been regular"

• Flouts Quantity and Relation (omits expected information about philosophy competence)
• Implicature: "Mr. X is not competent in philosophy"

Example: Concert review—"Miss X produced a series of sounds that corresponded closely with the score of Home sweet home"

• Flouts Manner (unnecessarily complex way to say "she sang")
• Implicature: "The performance was poor"

🎨 Special cases of flouting

Tautologies (flouting Quantity—semantically uninformative):

• "War is war"
• "Boys will be boys"

Metaphors, irony, figures of speech (flouting Quality—literally false):

• "You are the cream in my coffee"
• "Queen Victoria was made of iron"
• "A fine friend he turned out to be!" (ironic)

📊 Types of implicatures

📊 Particularized conversational implicature

Particularized conversational implicature: an inference that depends on particular features of the specific context.

• The examples discussed above (stranger, garage, New York visits) are all particularized.
• Different contexts would trigger different implicatures from the same sentence.

🔢 Generalized conversational implicature

Generalized conversational implicature: an inference typically associated with a type of proposition, not dependent on particular context features.

Key difference: these arise unless something in the context prevents them, rather than requiring special context to trigger them.

🔢 Sequential meaning with "and"

Example: "She gave him the key and he opened the door"

• Semantic content: logical AND (conjunction)
• Implicature: "and then" (temporal sequence)
• Motivated by Manner (Be orderly)
• Reasoning: if events didn't happen in that order, the speaker would have violated the orderliness maxim

📏 Scalar implicatures

Pattern: using a weaker term on a scale implicates "not the stronger term."

Example: "The water is warm"

• Scale: frigid < cold < cool < lukewarm < warm < hot < scalding
• Implicature: "not hot"
• Motivated by Quantity: if the speaker knew it was hot but only said warm, they wouldn't be appropriately informative

Example: "It is possible that we are related"

• Implicature: "It is not necessarily true that we are related"

Example: "Some of the boys went to the rugby match"

• Implicature: "Not all of the boys went"

Example: "John has most of the documents"

• Implicature: "John does not have all of the documents"

🔀 Disjunction implicature

Example: "That man is either Martha's brother or her boyfriend"

• Implicature: "The speaker does not know which alternative is correct"
• Motivated by Quantity: if the speaker knew which, they should have said so

🏷️ Indefinite article implicatures

Alienable possessions:

• "I walked into a house" → implicates "not my house"
• "Arthur is meeting a woman tonight" → implicates "not his wife or close relative"

Inalienable possessions (opposite pattern):

• "I broke a finger yesterday" → implicates "my finger"

Don't confuse: the same grammatical form (indefinite article) triggers opposite implicatures depending on whether the noun is alienable or inalienable.

🔖 Conventional implicature

Conventional implicature: part of the conventional meaning of a word or construction, not context-dependent or pragmatically explainable, but not contributing to truth conditions.

Key properties:

• Not context-dependent
• Must be learned word-by-word
• Do not affect truth conditions
• Different from conversational implicatures (which are calculable from context)

Example: "therefore"

• "He is an Englishman; he is, therefore, brave"
• Conventional implicature: being brave follows from being an Englishman
• But the sentence isn't false if this consequence doesn't hold

Example: "but" vs. "and"

• Truth-conditional meaning is identical
• "but" conventionally implicates contrast or counter-expectation
• If no contrast exists, the sentence isn't false

Example: "still"

• "Alfred has still not come"
• Says: Alfred has not come
• Conventionally implicates: his arrival is expected

Example: "too"

• "I was in Paris last spring too"
• Conventional implicature: some other specific person was in Paris last spring

Example: "even"

• "Even Bart passed the test"
• Conventional implicature: Bart was among the least likely to pass

🧪 Diagnostic tests for conversational implicatures

🧪 Five key properties

Property	What it means	Test
Defeasible/Cancellable	Can be explicitly negated without contradiction	Add "but not [implicature]"
Suspendable	Speaker can refuse to commit without anomaly	Add "if not [stronger claim]" or "but I'm not sure whether [implicature]"
Reinforceable	Can be overtly stated without redundancy	Add "and [implicature]"
Calculable	Can be worked out from literal meaning + maxims + context + background knowledge	Trace the reasoning
Nondetachable	Replacing words with synonyms preserves the implicature (except Manner violations)	Use paraphrase

✅ How to apply the tests

Step 1: Confirm there is a linguistic inference

• Would a truthful, well-informed speaker's utterance of p give reason to believe q?
• If based only on world knowledge (not sentence meaning), there's no linguistic inference to test

Step 2: Apply multiple tests

• Any single test may give unreliable results
• Use several tests and choose the analysis that best explains all the data

Step 3: Compare against entailment and presupposition profiles

🔬 Test examples

Entailment example: "John killed the wasp" → "The wasp died"

• ❌ Not cancellable: "#John killed the wasp, but the wasp did not die" (contradiction)
• ❌ Not suspendable: "#John killed the wasp, but I'm not sure whether the wasp died"
• ❌ Not reinforceable: "?#John killed the wasp, and the wasp died" (redundant)
• ❌ Not preserved in questions: "Did John kill the wasp?" doesn't imply the wasp died
• ❌ Not preserved under negation: "John did not kill the wasp" doesn't imply the wasp died

Conversational implicature example: "There is a garage around the corner" (context: out of petrol) → "You can buy petrol there"

• ✅ Cancellable: "There is a garage around the corner, but they aren't selling petrol today"
• ✅ Suspendable: "There is a garage around the corner, but I'm not sure whether they sell petrol"
• ✅ Reinforceable: "There is a garage around the corner, and you can buy petrol there"
• ❌ Not preserved in questions: "Is there a garage around the corner?" doesn't imply you can buy petrol
• ❌ Not preserved under negation: "There is no garage around the corner" doesn't imply anything about petrol

Presupposition example: "John has stopped chewing betel nut" → "John used to chew betel nut"

• ❌ Not cancellable: "#John has stopped chewing betel nut, and in fact he has never chewed it"
• ✅ Suspendable: "John has stopped chewing betel nut, if he ever did chew it"
• ❌ Not reinforceable: "?#John has stopped chewing betel nut, and he used to chew it"
• ✅ Preserved in questions: "Has John stopped chewing betel nut?" implies he used to
• ✅ Preserved under negation: "John has not stopped chewing betel nut" implies he used to

⚠️ Complications and special cases

⚠️ Negation complications

Problem: Negation can introduce ambiguity and complexity, especially with quantifiers.

Example: "Most of the boys didn't go to the soccer match"

• This seems to entail (not just implicate) "not all went"
• But other "family of sentences" tests (questions, conditionals) show it's an implicature
• Lesson: preservation under negation is not always a reliable indicator

🎭 Metalinguistic negation

Metalinguistic negation: a special kind of negation used to contradict something the addressee said or implied, typically with special intonation and followed by a correction.

Key feature: negates the implicature or appropriateness, not the propositional content.

Example: "John hasn't stopped chewing betel nut, he never did chew it"

• With special "contradiction" intonation
• Cancels the presupposition (which normal negation preserves)
• This is presupposition-cancelling negation

Example: "That wasn't a bad year, it was horrible"

• "bad" entails "not horrible," so this would be a contradiction with normal negation
• Metalinguistic negation rejects "bad" as too weak (violating the implicature "not horrible")

Example: "Most of the boys didn't go to the soccer match, all of them went"

• Rejects "most" as not strong enough
• Negates the implicature "not all"

Important for testing: When testing whether an inference is preserved under negation, use normal logical negation, not metalinguistic negation.

🔍 "Hey, wait a minute" test for presuppositions

How it works: If a speaker presupposes something not in the common ground, the hearer can appropriately object.

Example: "John has stopped chewing betel nut"

• ✅ Appropriate: "Hey, wait a minute, I didn't know that John used to chew betel nut!"
• ❌ Inappropriate: "#Hey, wait a minute, I didn't know that John has stopped chewing betel nut!"

The test shows that "used to chew" is presupposed (can be challenged as new information), while "has stopped" is asserted (expected to be new).

📋 Summary comparison table

Feature	Entailment	Conversational Implicature	Presupposition
Cancellable	No	Yes	Sometimes (only with negation of trigger clause)
Suspendable	No	Yes	Sometimes
Reinforceable	No	Yes	No
Preserved under negation	No	No	Yes (except metalinguistic negation)
Preserved in questions	No	No	Yes

🧭 Overview

🧠 One-sentence thesis

Post-Gricean pragmatics has revealed that the boundary between semantics and pragmatics is more complex than originally assumed, because pragmatic inferences can affect truth-conditional meaning through explicatures and certain generalized conversational implicatures.

📌 Key points (3–5)

• Core challenge: Grice's simple division (sentence meaning + implicatures = speaker meaning) breaks down when pragmatic reasoning is needed to determine truth conditions.
• Explicatures vs. implicatures: Explicatures are pragmatic inferences that complete or expand sentence meaning to yield a truth-evaluable proposition; implicatures are separate propositions communicated in addition to sentence meaning.
• Logical operators vs. English words: English and, or, and if are not polysemous; their varied interpretations arise from pragmatic inference, not multiple lexical senses.
• Common confusion: Don't confuse semantic ambiguity (multiple dictionary senses) with pragmatic enrichment (single sense + context-driven inference); the Modified Occam's Razor principle favors single-sense analyses when possible.
• Numeral words are special: Cardinal numbers allow both "at least n" and "exactly n" readings in ways that other scalar terms do not, suggesting underspecification rather than standard scalar implicature.

🔤 Logical operators and English connectives

🔤 The ambiguity question for and

• The puzzle: English and sometimes seems commutative (like logical ∧) but often carries sequential ("and then") or causal ("and therefore") meanings that logical conjunction lacks.
• Example: She gave him the key and he opened the door strongly suggests temporal sequence; reversing the clauses changes the interpretation dramatically.
• Two competing analyses:
  1. Polysemy: and has multiple distinct senses (logical, sequential, causal).
  2. Gricean: and has only one sense (logical ∧); additional interpretations arise via conversational implicature.

🧹 Arguments against polysemy for and

The excerpt presents five arguments favoring the Gricean single-sense analysis:

Argument	Why it matters
Cross-linguistic pattern	Almost all languages show the same "ambiguity" for their conjunction—unlikely if it were true lexical polysemy
No reverse-order conjunctions	No language has a word meaning "and earlier" (e.g., They had a baby shmand got married = baby came after marriage)
Too many "senses"	Temporal, causal, and other contextual uses would require an implausibly large number of distinct senses
Juxtaposition shows the same effect	They had a baby. They got married. (two separate sentences) also suggests sequence, so the interpretation is not contributed by and itself
Defeasibility	They got married and had a baby, but not necessarily in that order cancels the sequential reading—strong evidence for conversational implicature

Conclusion: English and has the semantic content of logical ∧; the sequential "and then" use is a generalized conversational implicature motivated by the maxim of manner (order of mention reflects order of events).

🔀 The ambiguity question for or

• The puzzle: English or can be inclusive (p ∨ q, "and/or") or exclusive (XOR, "either…or but not both").
• Inclusive reading likely: Every year the Foundation awards a scholarship to a student of Swedish or Norwegian ancestry.
• Exclusive reading likely: I can't decide whether to order fried noodles or pizza.

🧹 Arguments against polysemy for or

• Grice's analysis: The semantic content of or is inclusive (∨); the exclusive reading arises via conversational implicature from the maxim of quantity.
  • If the speaker says p or q but knows both are true, saying p and q would be more informative.
  • So p or q implicates "not both" in contexts where the speaker is expected to know if both hold.
• Intrinsically exclusive alternatives: Examples like Mary is in Prague or Stuttgart don't distinguish the two senses, because world knowledge makes both alternatives mutually exclusive; inclusive and exclusive or yield the same truth value here.
• Negation test (Gazdar 1979): If or were polysemous, negating it should yield ambiguity. But Mary doesn't have a son or daughter does not allow a reading that is true when Mary has both—only the inclusive-or reading survives under negation, suggesting or is semantically inclusive.
• Defeasibility: I will order either fried noodles or pizza; in fact I might get both cancels the exclusive reading.

Modified Occam's Razor: "Senses are not to be multiplied beyond necessity"—favor single-sense analyses with pragmatic enrichment unless clear evidence demands polysemy.

🧩 Explicatures: completing propositional content

🧩 What explicatures are

Explicature: a pragmatic inference that adds information to the overtly expressed meaning in order to yield a complete, truth-evaluable proposition.

• Grice assumed that sentence meaning ("what is said") plus implicatures equals speaker meaning, and that truth values depend only on sentence meaning.
• But many sentences do not express a complete proposition even after resolving pronouns, deixis, and ambiguity.

🔧 Two types of explicature

🔧 Completion (filling in)

• Semantic under-determination: the sentence fails to express a complete proposition; missing information must be supplied.
• Examples:
  • Steel isn't strong enough → [strong enough for what?] → Steel isn't strong enough to stop this kind of anti-tank missile.
  • The princess is late → [late for what?] → The princess is late for the party.
  • Tipper is ready → [ready for what?] → Tipper is ready to dance.
• These are not syntactic ellipsis; the sentences are grammatically complete but semantically incomplete.
• The potential for such constructions is lexically specific: The king has arrived is fine, but The king has reached is ungrammatical without an object.

🔧 Expansion (fleshing out)

• Semantic expansion: the sentence expresses a complete proposition, but not the one the speaker intends to communicate; the meaning must be narrowed or expanded.
• Example: A mother says to her crying child, You're not going to die → she means You're not going to die from this cut, not a promise of immortality.
• More examples:
  • I have eaten breakfast → [today]
  • I have eaten caviar → [before, at some point in my life]
  • I have nothing to wear → [nothing appropriate for this specific event]
• The same sentence structure can be expanded differently based on context and world knowledge.

🆚 Explicature vs. implicature

Key distinction (Bach 1994):

• Implicature: a separate proposition, conceptually independent of what is said; inferred from the saying of the sentence.
  • Has its own truth value, independent of the sentence's truth value.
  • A true statement can trigger a false implicature.
• Explicature: built up from the explicit content by adding implicit material; the sentence's truth value cannot be determined until the explicature is supplied.
  • Does not have an independent truth value.
  • Pragmatic reasoning affects truth-conditional content.

Example: I have nothing to wear is literally true (the speaker owns clothes) but the explicature I have nothing appropriate to wear to this wedding may be false if the speaker does own something appropriate but forgot about it.

Don't confuse: Explicatures complete or expand the proposition expressed; implicatures are additional propositions communicated alongside the main proposition.

🌉 Implicatures and truth conditions

🌉 Conventional implicatures are not truth-conditional

• Words like but and therefore carry conventional implicatures (contrast, inference) that are part of their conventional meaning.
• Yet Frege and Grice argued these do not affect truth conditions.
• So conventional meaning is not always truth-conditional.

🌉 Some generalized conversational implicatures are truth-conditional

• The puzzle: The sequential "and then" reading of and is a generalized conversational implicature (not lexical ambiguity), yet it affects truth conditions.
• Example pair:
  • If the old king has died of a heart attack and a republic has been declared, then Tom will be quite content.
  • If a republic has been declared and the old king has died of a heart attack, then Tom will be quite content.
  • These can have different truth values in the same context, due solely to the sequential interpretation of and.
• Another example: If he had three beers and drove home, he broke the law; but if he drove home and had three beers, he did not break the law.
  • This is not a contradiction, which it would be if and meant only logical ∧.

🌉 Relevance Theory response

• Proponents of Relevance Theory argue that the sequential "and then" use is an explicature, not a generalized conversational implicature.
• Most inferences that neo-Griceans call generalized conversational implicatures are treated as explicatures in Relevance Theory.

🌉 Generalized implicatures can still communicate falsehoods

• The Picasso "Guernica" example: An envoy is asked if he has the original documents; he replies Not all of them.
  • Literal meaning: true (he has zero, which is indeed "not all").
  • Scalar implicature: "I have some of them" (false).
• He was "not lying but not telling the truth, either"—the sentence meaning was true, but the implicature was false.
• This shows that generalized conversational implicatures can have truth values independent of the sentence's truth value, which is hard to reconcile with treating them as explicatures.

🔢 Why numeral words are special

🔢 Two readings for numerals

• Numeral words like two, three allow both:
  • "At least n" reading: Do you have two children? in a context discussing a subsidy for families with two or more children.
  • "Exactly n" reading: Do you have two children? in most ordinary contexts.
• Neither reading seems to be derived as an implicature from the other.

🔢 Evidence that numerals differ from other scalar terms

Test	Other scalars	Numerals
Cancellation pattern	A: Did many guests leave? B: Yes, in fact all of them. (natural)	A: Do you have two children? B: No, three. (more natural than Yes, three)
Mathematical statements	N/A	2 + 2 = 3 is not true under "at least 3" reading
Round vs. precise numbers	N/A	I have $200, if not more (OK); I have $201.37, if not more (odd)
Reversible scales	He ate some, if not all (not none)	That bowler can break 100 (or score 150); That golfer can break 100 (or score 90)
Collective vs. distributive	Most students surrounded the stadium, perhaps all (OK)	Four students carried this sofa, if not more (odd—collective reading blocks "at least")

🔢 Analysis

• Most pragmaticists treat numeral words as underspecified or indeterminate between "at least n" and "exactly n."
• The intended reading is supplied by explicature based on context.
• This is a kind of systematic flexibility, but not polysemy in the traditional sense.

Example: If Mrs. Smith has three children, there will be enough seatbelts can have different truth values depending on which reading of three is chosen.

🎯 Conclusion

🎯 The revised picture

• Grice's simple model: sentence meaning + implicatures = speaker meaning; truth conditions depend only on sentence meaning.
• Reality is more complex:
  • Some pragmatic inferences (explicatures) are needed to determine truth conditions.
  • Some generalized conversational implicatures affect truth conditions.
  • Some conventional meaning (conventional implicatures) does not affect truth conditions.
• The boundary between semantics and pragmatics is not as clean as early work assumed.

🎯 What we've learned

• Pragmatic inferences contribute to truth-conditional content in multiple ways.
• The Modified Occam's Razor principle helps avoid unnecessary polysemy claims.
• Numeral words show special behavior that sets them apart from other scalar terms.
• The debate between neo-Gricean and Relevance Theory approaches continues, particularly regarding the status of generalized conversational implicatures.

🧭 Overview

🧠 One-sentence thesis

Indirect speech acts accomplish actions (like requests or invitations) through implicature rather than through the literal meaning of the words spoken, and recognizing them is especially challenging in cross-cultural communication and language learning.

📌 Key points (3–5)

• What indirect speech acts are: actions performed by implicature, not by the literal meaning of the words.
• How they differ from direct speech acts: direct speech acts are accomplished by literal meaning; indirect ones require the hearer to infer the intended action.
• Common confusion: a question that literally asks for information may actually be an indirect request (e.g., asking about scrambled eggs may be interpreted as requesting them).
• Why they matter: misunderstandings are common even within the same culture, but especially frequent in cross-cultural communication and pose challenges for language learners and translators.
• Foundation: they are a special type of conversational implicature, building on Austin's theory of speech acts and Searle's analysis of how hearers recognize and identify them.

🎭 What speech acts are

🎭 Speech acts as actions

A speech act is an action that speakers perform by speaking: offering thanks, greetings, invitations, making requests, giving orders, etc.

• Speaking is not just describing the world; it is doing things with words.
• Examples of actions: thanking, greeting, inviting, requesting, ordering.
• The excerpt emphasizes that utterances can perform actions beyond their descriptive content.

🔀 Direct vs indirect speech acts

Type	How it works	Example
Direct speech act	Accomplished by the literal meaning of the words	A command stated as a command
Indirect speech act	Accomplished by implicature, not literal meaning	A question that functions as a request

• Direct: the literal meaning performs the action.
• Indirect: the hearer must infer the intended action from context and implicature.
• Don't confuse: the same sentence form (e.g., a question) can be either direct (genuinely asking for information) or indirect (requesting action).

🌍 The cross-cultural challenge

🌍 Tannen's Crete example

The excerpt opens with a story:

• Tannen asked her Greek hosts whether they ever scrambled eggs and why she hadn't seen grapes.
• Her hosts interpreted these questions as indirect requests (hints) and provided scrambled eggs and grapes.
• Tannen intended only to make conversation, not to request anything.

Why the misunderstanding happened:

• The hosts believed she was implicating desires without stating them directly.
• Literally, her utterances were questions (requests for information).
• The hosts inferred an indirect speech act: requests to provide eggs and grapes.

🌐 Why indirect speech acts are hard

• Misunderstandings are common even within the same culture.
• They are "especially characteristic of cross-cultural communication."
• Major focus areas: applied linguistics, second language acquisition, translation.
• Even advanced language learners struggle with recognizing and correctly identifying indirect speech acts.

🧩 Theoretical foundations

🧩 Austin's performatives

The excerpt introduces Austin's 1955 lectures (published 1962) on a special class of declarative sentences:

Performatives: declarative sentences which cannot be assigned a truth value, because they do not make any claim about the state of the world.

Austin's examples:

• "I do" (in a marriage ceremony)
• "I name this ship the Queen Elizabeth" (when smashing the bottle)
• "I bet you sixpence it will rain tomorrow"
• "I hereby sentence you to 10 years in prison"
• "I now pronounce you man and wife"
• "I declare this meeting adjourned"

Key insight:

• These sentences are not true or false; they perform actions.
• Saying "I now pronounce you man and wife" does not describe a pronouncement—it is the pronouncement.
• Austin later generalized his account of performatives to apply to all speech acts.

🔍 Searle's two fundamental questions

Searle builds on Austin's theory and addresses:

1. How do hearers recognize that an utterance is an indirect speech act (i.e., that the intended action is not the literal one)?
2. How do hearers correctly identify the intended speech act once they know it is indirect?

Searle's key insight:

• Indirect speech acts are a special type of conversational implicature.
• This connects them to Gricean pragmatics and the mechanisms of implicature discussed in earlier chapters.

🌏 Cross-linguistic issues

• The excerpt mentions that §10.4 addresses whether Searle's theory works for all languages.
• This suggests that indirect speech acts may vary across languages and cultures, raising questions about the universality of Searle's account.

🔗 Connection to implicature

🔗 Indirect speech acts as implicature

• The excerpt explicitly states that indirect speech acts are "a special type of conversational implicature."
• Like other implicatures, they involve communicating more than the literal meaning.
• Unlike typical implicatures (which add information), indirect speech acts change the action being performed.

Example from Tannen's story:

• Literal meaning: "Do you ever scramble eggs?" (question, request for information)
• Implicated meaning (as interpreted by hosts): "I would like scrambled eggs" (request for action)
• The implicature changes the speech act from a question to a request.

⚠️ Don't confuse with other implicatures

• Most implicatures add information or nuance to a statement.
• Indirect speech acts use implicature to perform a different action than the literal meaning would perform.
• Example: "Can you pass the salt?" literally asks about ability, but indirectly requests the action of passing salt.

🧭 Overview

🧠 One-sentence thesis

Austin's analysis of performatives reveals that all utterances have an illocutionary force beyond their propositional content, fundamentally changing how we understand sentence meaning.

📌 Key points (3–5)

• Performatives do not describe but perform: sentences like "I now pronounce you man and wife" change the world rather than make claims about it, so they cannot be assigned truth values.
• Felicity conditions replace truth conditions: performatives succeed or fail based on whether proper procedures, authority, and circumstances are met, not on whether they are true or false.
• Explicit vs implicit performatives: explicit performatives have special grammatical features (first person, present tense, performative verbs, "hereby"), but the same speech acts can be performed implicitly (e.g., "Shut the door!" vs "I hereby order you to shut the door").
• Common confusion: not all declarative sentences make claims about the world—performatives look like statements but function as actions.
• All utterances are performatives: since any speech act can be paraphrased as an explicit performative, virtually all utterances should be analyzed as having illocutionary force in addition to propositional content.

🎭 What performatives are

🎭 Doing things with words

Performatives: a special class of declarative sentences that do not describe something but rather perform an action; the speaker changes the world rather than making a claim about it.

• When someone says "I now pronounce you man and wife," they are not reporting that a marriage has occurred—they are making the marriage occur.
• Similarly, "I hereby sentence you to 10 years in prison" does not describe a sentencing; it is the sentencing.
• Because performatives perform actions rather than describe states of affairs, it doesn't make sense to ask whether they are true or false.

Example: A judge saying "I hereby declare this meeting adjourned" ends the meeting; the utterance itself is the act of adjournment, not a report about adjournment.

🎯 Illocutionary force

• Austin distinguished three types of acts:
  • Locutionary act: the act of speaking itself
  • Illocutionary act: the act the speaker intends to perform "in speaking" (e.g., promising, ordering, declaring)
  • Perlocutionary act: the actual result achieved "by speaking" the utterance
• The illocutionary force is what the speaker intends to accomplish by speaking.

Don't confuse: The illocutionary force (what the speaker intends to do) is different from the perlocutionary effect (what actually happens as a result).

✅ Felicity conditions

✅ When performatives succeed or fail

Since performatives cannot be true or false, Austin proposed that we evaluate them based on felicity conditions—the conditions under which a performative speech act will be successful, valid, and appropriate.

Condition type	What must be satisfied	Violation name	Effect of violation
A.1	An accepted conventional procedure must exist, including uttering certain words by certain persons in certain circumstances	Misfire	Act not successfully performed or invalid
A.2	The particular persons and circumstances must be appropriate for invoking the procedure	Misfire	Act not successfully performed or invalid
B.1	The procedure must be executed correctly by all participants	Misfire	Act not successfully performed or invalid
B.2	The procedure must be executed completely	Misfire	Act not successfully performed or invalid
C.1	Participants must have the required thoughts or feelings and intend to conduct themselves accordingly	Abuse	Act is performed and valid but insincere or inappropriate
C.2	Participants must actually conduct themselves as required subsequently	Abuse	Act is performed and valid but insincere or inappropriate

🚫 Misfires vs abuses

• Misfires (violations of A–B): the intended act is not successfully performed or is invalid.
  • Example: If someone not licensed to perform marriages says "I now pronounce you man and wife," the couple does not become legally married—the performative fails.
• Abuses (violations of C): the speech act is still performed and valid, but done insincerely or inappropriately.
  • Example: If someone says "I promise to return this book by Sunday" with no intention of doing so, it still counts as a promise—but an insincere one that the speaker intends to break.

🔍 Explicit vs implicit performatives

🔍 Properties of explicit performatives

Explicit performatives have distinctive grammatical features:

• Indicative mood and simple present tense with a non-habitual interpretation
  • Unlike normal event verbs in simple present (which typically require habitual reading), performative verbs in simple present refer to the act being performed right now.
• Performative verbs: verbs that can be used either to describe or to perform the intended speech act
  • Examples: sentence, declare, confer, invite, request, order, accuse
• Active voice with first person subject (most common)
  • "I hereby sentence you…"
  • "I now pronounce you…"
• Passive voice with second or third person subject (possible with certain verbs)
  • "You are hereby sentenced to 10 years in prison."
  • "Passengers are requested not to talk to the driver."
  • "Permission is hereby granted to use this software."
• Optional performative adverb "hereby"
  • This adverb can only be used with performatives, not with non-performative statements.

🔄 Paraphrasing performatives

• Explicit performatives can often be paraphrased using sentences that lack the special features listed above—these are implicit performatives.
  • "I hereby order you to shut the door" → "Shut the door!" (imperative)
  • "I hereby invite you to join me for dinner" → "Would you like to join me for dinner?" (question)
• Since the same speech act can be performed with either expression, it would be odd to classify one as a performative but not the other.

Don't confuse: The grammatical form (declarative, imperative, interrogative) does not determine whether an utterance is a performative—what matters is the illocutionary force, the act being performed.

🌐 All utterances as performatives

• Conversely, most speech acts can be paraphrased using an explicit performative:
  • "Is it raining?" → "I hereby ask you whether it is raining."
  • Simple statements → "I hereby inform you that…"
  • Commands → "I hereby order/command you to…"
• If the same speech act can be performed with either expression, it seems odd to classify one as a performative but not the other.
• Conclusion: Virtually all utterances should be analyzed as performatives, whether explicit or not.

💡 Implications for meaning

💡 Beyond propositional content

• If all utterances are performatives, then the label "performative" alone doesn't distinguish a special class—but the analysis yields important insights.
• Key insight: In addition to their propositional content (what the sentence says about the world), all utterances have an illocutionary force (what the speaker is doing by speaking).
• This fundamentally changes how we understand sentence meaning: meaning is not just about truth conditions but also about the action the speaker intends to perform.

🧩 Questions and commands

• The excerpt notes that questions and commands cannot be assigned truth values—a question is not the sort of thing that can be true or false, yet questions are clearly meaningful.
• The performative analysis helps explain this: questions and commands have illocutionary force (asking, ordering) even though they lack propositional content that can be evaluated as true or false.
• The semantic analysis of questions and commands is acknowledged as an interesting and challenging area, but not addressed in detail in the excerpt.

Don't confuse: The excerpt's initial definition of meaning as "what the world would have to be like for the sentence to be true" applies only to declarative sentences that make claims about the world—it does not directly apply to performatives, questions, or commands.

🧭 Overview

🧠 One-sentence thesis

The meaning of a complex expression is determined by the meanings of its constituent parts and the way they are combined, though certain contexts (like propositional attitude verbs) create referential opacity where this principle appears to fail.

📌 Key points (3–5)

• Compositionality principle: the meaning of a whole expression is predictable from the meanings of its parts and how they combine.
• Substitutivity principle: replacing a constituent with another that has the same denotation should not change the denotation of the whole expression.
• Referential opacity: complements of propositional attitude verbs (believe, hope, want) violate substitutivity—co-referential expressions are not freely substitutable.
• Common confusion: denotation vs. sense in opaque contexts—Frege proposed that in opaque contexts, expressions denote their customary sense rather than their normal denotation.
• De dicto vs. de re ambiguity: definite and indefinite NPs in opaque contexts can refer either to a specific individual (de re) or to a property/type (de dicto).

🧩 The Principle of Compositionality

🧩 What compositionality means

Principle of Compositionality: the meaning of a complex expression is determined by the meanings of its constituent expressions and the way in which they are combined.

• This principle explains how we understand newly-created sentences.
• It applies not only to sentences but to any multi-word expression (except idioms).
• A stronger version requires a one-to-one correspondence between syntactic rules (building constituents) and semantic rules (providing interpretations).

🔍 Why compositionality matters

• Without compositionality, we could not produce or understand an infinite number of sentences from a finite vocabulary.
• The excerpt states: "language accomplishes [something] astonishing. With a few syllables it expresses a countless number of thoughts."
• Compositionality requires that parts of a sentence correspond to parts of the thought/proposition it expresses.

🧱 Two simple compositional patterns

🧱 Subject NP + intransitive VP

• Example: "King Henry VIII snores"
  • Subject NP: King Henry VIII (a proper name, rigid designator, refers to a specific individual)
  • VP: snores (expresses a property; its denotation is the set of all things that snore in the current situation)
• How they combine: the sentence is true if and only if the individual named by the NP is a member of the denotation set of the VP.
• This rule works for many simple declarative sentences.

🧱 Adjective + common noun

• Example: "yellow submarine"
  • yellow has denotation set Y (all yellow things)
  • submarine has denotation set S (all submarines)
• How they combine: the phrase denotes the intersection of Y and S—all things that are both yellow and submarines.
• Even though this phrase is smaller than a sentence and has no truth value, its denotation is still compositional.

🔄 Frege on substitutivity and denotation

🔄 The substitutivity principle

• If two expressions have the same denotation (are co-referential), replacing one with the other should not change the denotation of the larger expression.
• Example: "Abraham Lincoln" and "the 16th president of the United States" refer to the same individual.
  • "the wife of Abraham Lincoln" = "the wife of the 16th president of the United States" (both refer to Mary Todd Lincoln)
  • "the man who killed Abraham Lincoln" = "the man who killed the 16th president of the United States" (both refer to John Wilkes Booth)

🔄 Non-referring expressions

• If a constituent lacks a denotation, the larger expression also lacks a denotation.
• Example: In a world where Superman does not exist:
  • "the mother of Superman" fails to refer
  • "the man who Superman rescued" fails to refer
• This supports the claim that denotation is compositional.

🔄 Sentences have denotations too

• Frege argued that the denotation of a declarative sentence is its truth value (not the proposition it expresses).
• The proposition is the sentence's sense.
• Why truth value, not proposition?
  • "The Prince and the Pauper was written by Mark Twain" and "…by Samuel Clemens" have the same truth value, but a speaker could believe one without believing the other → they express different propositions.
  • "Abraham Lincoln ended slavery" and "The 16th president ended slavery" could have different truth values in different situations → different propositions.
• Parallel with NPs: both truth values and NP denotations depend on the situation, can vary across situations, and are preserved under substitution of co-referential expressions.

🚫 Referential opacity and propositional attitudes

🚫 What are propositional attitude verbs?

Propositional attitude verbs: verbs that take a propositional argument (complement clause) and denote the mental state or attitude of an experiencer toward that proposition.

• Examples: believe, hope, want, know, think, expect
• Example: "John believes [that the airplane was invented by an Irishman]"

🚫 Referential opacity defined

Referential opacity: a context where denotation does not appear to be compositional, because the principle of substitutivity fails.

• The complements of propositional attitude verbs are opaque contexts.
• Example: "Mary knows that The Prince and the Pauper was written by Mark Twain" can be true while "Mary does not know that it was written by Samuel Clemens" is also true—even though the two names refer to the same person.
• Another example: "Copernicus believed [the earth revolves around the sun]" is true, but "Copernicus believed [the planetary orbits are ellipses]" is false—even though both complement clauses are true statements (same truth value).

🚫 Frege's solution: denotation shifts to sense

• In opaque contexts, a clause or NP denotes its customary sense rather than its normal denotation.
• For complement clauses: their denotation is the proposition they express, not their truth value.
• This explains why substitutivity fails: expressions with different senses are not freely substitutable, even if they have the same normal denotation.
• Analogy: similar to the shift when a word is mentioned rather than used:
  • Used: "Maria is a pretty girl" (refers to a person)
  • Mentioned: "'Maria' is a pretty name" (refers to the word itself)
  • "Samuel Clemens adopted the pen name 'Mark Twain'" is true, but "Mark Twain adopted the pen name 'Samuel Clemens'" is false.

🚫 Why non-referring expressions can still yield truth values

• Example: "Ponce de León hoped to find the fountain of youth"
• Even though "the fountain of youth" does not refer to anything, the sentence can be true or false.
• Why? The complement clause denotes the proposition it expresses (its sense), not its truth value.
• All constituents have well-defined denotations in this shifted sense, so the sentence's truth value can be derived compositionally.

🔀 De dicto vs. de re ambiguity

🔀 Two readings for definite NPs in opaque contexts

• Definite NPs in opaque contexts can be interpreted in two ways:
  • De re ('about the thing'): refers to a specific individual
  • De dicto ('about what is said'): identifies a property or type of individual

🔀 Examples with definite NPs

Sentence	De re reading	De dicto reading
"I hope to meet with the Prime Minister next year"	Refers to the specific person currently serving as PM (e.g., after he retires)	Refers to whoever will hold the office of PM next year (we don't yet know who)
"I wanted my husband to be a Catholic"	Refers to the specific man I married (but he was too old to convert)	Refers to the property of being married to me and being Catholic (but I ended up marrying a Sikh)

🔀 Examples with indefinite NPs

• Indefinite NPs show a similar ambiguity, often called specific vs. non-specific.
• Example: "The opposition party wants to nominate a retired movie star for President"
  • Specific (de re): they have a particular individual in mind (e.g., Ronald Reagan)
  • Non-specific (de dicto): they want someone with the property of being a retired actor, but don't have a specific person in mind
• Example: "The Dean believes that I am collaborating with a famous linguist"
  • De re: I am collaborating with Noam Chomsky; the Dean knows this but doesn't realize Chomsky is a famous linguist → sentence is true
  • De dicto: the Dean believes I am collaborating with someone who is a famous linguist → sentence is false (in the scenario where the Dean doesn't know Chomsky is a linguist)

🔀 True semantic ambiguity

• These are not just pragmatic differences—the two readings have different truth conditions.
• Don't confuse: this is not about vagueness or context-dependence; the same sentence in the same situation can be true under one reading and false under the other.

🧭 Overview

🧠 One-sentence thesis

Model Theory provides a formal framework for testing how word meanings combine compositionally by explicitly describing situations (models) and stating rules that predict sentence truth-values from syntactic structure and word denotations.

📌 Key points (3–5)

• What Model Theory does: constructs formal rule systems that replicate speakers' ability to determine sentence truth-values in specific contexts by isolating compositional rules from complicating factors (ambiguity, vagueness, pragmatics).
• What a model specifies: (i) the domain (set of all individuals in the situation) and (ii) denotation sets for basic vocabulary items (predicates, proper names).
• How rules work: semantic interpretation rules operate in parallel with syntactic rules, specifying how to compute the denotation of complex expressions from their parts.
• Common confusion: a model does not explain how speakers determine word senses (e.g., why someone is called "man"); it assumes denotations are given and focuses only on how they combine.
• Why set theory matters: interpretations are stated in terms of set membership and relations (intersection, union, subset), which correspond to logical operations (and, or, implication).

🎯 The Model Theory approach

🎯 What Model Theory isolates

Model Theory: a formal approach that constructs rule systems to replicate speakers' ability to identify denotations and determine sentence truth-values in a given context.

• Language involves many complicating factors: lexical ambiguity, vagueness, figurative meanings, implicatures, world knowledge.
• To make progress on compositionality, Model Theory isolates the rules for combining word meanings from these other factors.
• Analogy: medical researchers control for diet, age, exercise when studying genetic factors in disease.
• A model provides an explicit test situation with controlled variables.

📦 What a model must specify

Two required components:

1. Domain (U): the set of all individual entities in the situation
2. Denotations: the semantic values of basic vocabulary items
   • Predicates (verbs, adjectives, common nouns)
   • Proper names
   • Not non-denoting words like not, and, if

Example: a simple model with three individuals (King Henry VIII, Anne Boleyn, Thomas More):

• Domain: U = {King Henry VIII, Anne Boleyn, Thomas More}
• ⟦MAN⟧ = {King Henry VIII, Thomas More}
• ⟦WOMAN⟧ = {Anne Boleyn}
• ⟦SNORE⟧ = {King Henry VIII}
• ⟦Henry⟧ = King Henry VIII

🔧 What Model Theory does not do

• Does not represent how speakers determine that King Henry VIII counts as a "man" or that Anne Boleyn counts as a "woman."
• Does not account for word senses themselves—only for how denotations combine.
• This is not denying the importance of word meanings; it's a strategic choice to make progress on compositionality without solving all problems about word meanings simultaneously.
• The approach has proven extremely successful and productive.

🧮 Set theory foundations

🧮 Basic set concepts

Set: a clearly-defined collection of things, represented with braces {}.

Key properties:

• Identity by membership: two sets with the same members are the same set
• Order irrelevant: {a,b,c} = {b,a,c} = {c,a,b}
• Cardinality: the number of members; written |B| for set B
• Empty set (∅): the unique set with no members; |∅| = 0
• Singleton: {Paul Kroeger} ≠ Paul Kroeger (a set containing one person vs. the person)

Example: {King Henry VIII, Thomas More} is a set with two members (cardinality = 2).

🔗 Relations and functions

Ordered pair: ⟨x,y⟩ where order matters; ⟨x,y⟩ ≠ ⟨y,x⟩ (unlike sets).

Relation: a set of ordered pairs; the domain is all first elements, the range is all second elements.

Function: a relation where each domain element maps to exactly one range element (each first element appears in only one pair).

Example of a function:

• B = {⟨2,3⟩, ⟨3,2⟩, ⟨4,7⟩, ⟨5,2⟩, ⟨6,7⟩, ⟨7,4⟩}
• Domain: {2,3,4,5,6,7}; Range: {2,3,4,7}
• B(2) = 3, B(3) = 2, etc.

Characteristic function: maps elements to {1,0} where 1 = "True" (member) and 0 = "False" (not a member).

⚙️ Set operations

Four key operations/relations:

Operation	Notation	Definition	Corresponds to
Intersection	A ∩ B	elements in both A and B	logical AND (∧)
Union	A ∪ B	elements in A or B or both	logical OR (∨)
Complement	B–A	elements in B but not in A	logical NOT (¬)
Subset	A ⊆ B	all elements of A are in B	logical implication (→)

Don't confuse: "A ∩ B" and "A ∪ B" are names of sets; "A ⊆ B" is a proposition (claim that could be true or false).

Formal definitions (where U is the universal set):

• x ∈ (A ∩ B) ↔ (x ∈ A AND x ∈ B)
• x ∈ (A ∪ B) ↔ (x ∈ A OR x ∈ B)
• x ∈ (B–A) ↔ (x ∈ B AND x ∉ A)
• (A ⊆ B) ↔ for all x, if x ∈ A then x ∈ B

📐 Truth relative to a model

📐 Evaluating sentence truth

Notation: ⟦x⟧ represents the denotation (semantic value) of x in the current model.

Basic rule for simple sentences:

• Sentence structure: [NP VP]
• Truth condition: ⟦S⟧ = 'true' iff ⟦NP_subj⟧ ∈ ⟦VP⟧
• In words: a sentence is true if the subject's referent is a member of the VP's denotation set.

Example: Henry snores

• True iff King Henry VIII ∈ ⟦SNORE⟧
• In Model 1, ⟦SNORE⟧ = {King Henry VIII}, so the sentence is true.

📊 Interpreting complex sentences

The truth conditions can be stated using set operations:

Sentence type	Example	Set interpretation
OR statement	Anne is a man or woman	Anne ∈ (⟦MAN⟧ ∪ ⟦WOMAN⟧)
AND statement	Henry is a man who snores	Henry ∈ (⟦MAN⟧ ∩ ⟦SNORE⟧)
Universal	All men snore	⟦MAN⟧ ⊆ ⟦SNORE⟧
Negative existential	No women snore	⟦WOMAN⟧ ∩ ⟦SNORE⟧ = ∅

Why this works: the definitions of set operations (intersection, union, etc.) involve the same logical connectives (AND, OR) that appear in the logical forms.

🏗️ Compositional interpretation rules

🏗️ One-place predicates

General rule for propositions with one-place predicates:

• If α refers to an entity and P is a one-place predicate, then:
• ⟦P(α)⟧ = 'true' iff ⟦α⟧ ∈ ⟦P⟧

Example: SNORE(h)

• True iff ⟦h⟧ ∈ ⟦SNORE⟧
• True iff King Henry VIII ∈ {King Henry VIII}
• Result: true in Model 1

🔗 Two-place predicates (transitive verbs)

Denotation sets for transitive predicates are sets of ordered pairs.

General rule:

• If α, β refer to entities and P is a two-place predicate, then:
• ⟦P(α,β)⟧ = 'true' iff ⟨⟦α⟧, ⟦β⟧⟩ ∈ ⟦P⟧

Example: Henry loves Anne

• LOVE(h,a)
• True iff ⟨King Henry VIII, Anne Boleyn⟩ ∈ ⟦LOVE⟧
• In Model 1ʹ, ⟦LOVE⟧ = {⟨King Henry VIII, Anne Boleyn⟩, ⟨Anne Boleyn, King Henry VIII⟩}
• Result: true

🔄 Transitive VP rule

To apply the basic sentence rule to transitive sentences, we need a rule for transitive VPs.

Syntax: VP → V_trans NP_obj

Semantics: The VP denotation is the set of all individuals x such that the ordered pair ⟨x, object⟩ is in the verb's denotation set.

⟦VP⟧ = {x: ⟨x, ⟦NP_obj⟧⟩ ∈ ⟦V_trans⟧}

Example: loves Anne Boleyn

• ⟦loves Anne Boleyn⟧ = {x: ⟨x, Anne Boleyn⟩ ∈ ⟦LOVE⟧}
• This is a set of individuals (all those who love Anne)
• Now the basic sentence rule can apply: Henry loves Anne is true iff Henry ∈ this set

Why this matters: the transitive VP rule "feeds" the basic sentence rule, modeling stepwise derivation.

🎨 Adjective modification rule

Syntax: Nʹ → A N

Semantics: The Nʹ denotation is the intersection of the adjective and noun denotation sets.

⟦A N⟧ = ⟦A⟧ ∩ ⟦N⟧

Example: happy man

• ⟦happy man⟧ = ⟦HAPPY⟧ ∩ ⟦MAN⟧
• = {King Henry VIII, Anne Boleyn} ∩ {King Henry VIII, Thomas More}
• = {King Henry VIII}

For Henry is a happy man:

• Assuming copula and indefinite article contribute nothing semantically
• ⟦is a happy man⟧ = ⟦HAPPY⟧ ∩ ⟦MAN⟧
• Sentence is true iff Henry ∈ (⟦HAPPY⟧ ∩ ⟦MAN⟧)

Pattern: same as yellow submarine discussed earlier—the modified noun denotes the intersection of two sets.

🎓 Compositional analysis summary

🎓 The stepwise process

The excerpt demonstrates compositional analysis for simple sentences by:

1. Starting with a model that specifies domain and denotations
2. Stating a basic rule for simple sentences (NP + VP)
3. Adding rules for transitive VPs and adjective modification
4. Showing how rules apply stepwise to derive truth conditions from word meanings and syntactic structure

Example workflow for Henry is a happy man:

• Step 1: Apply adjective rule → ⟦happy man⟧ = ⟦HAPPY⟧ ∩ ⟦MAN⟧
• Step 2: Apply basic sentence rule → true iff ⟦Henry⟧ ∈ ⟦happy man⟧

🔮 Looking forward

The excerpt notes that future chapters will:

• Focus more on understanding phenomena than formalizing rules
• Cover quantifiers, conditionals, tense, modality, etc.
• Maintain the assumption that descriptions must be compatible with this kind of compositional analysis
• Address contexts where purely denotational treatment is inadequate (e.g., propositional attitude verbs)

Key assumption: all semantic descriptions must be compatible with compositional analysis—meanings of complex expressions must be derivable from their parts and how they combine.

🧭 Overview

🧠 One-sentence thesis

Quantifier words like all, some, and no express relationships between two sets, and understanding their scope is essential for determining the truth conditions of sentences containing them.

📌 Key points (3–5)

• What quantifiers denote: relations between two sets (e.g., all = subset relation, some = non-empty intersection, no = empty intersection).
• Two types of quantifiers: cardinal quantifiers (e.g., some, four, no) specify cardinality of intersection; proportional quantifiers (e.g., all, most, every) specify proportions of one set included in another.
• Restricted quantifier notation: a three-part format (operator, restriction, nuclear scope) that handles quantifier meanings more uniformly than standard predicate logic.
• Common confusion: cardinal vs. proportional—cardinal quantifiers are symmetric (some A are B entails some B are A), but proportional quantifiers are not (all A are B does not entail all B are A).
• Scope ambiguities: when quantifiers interact with negation, other quantifiers, modals, or propositional attitude verbs, the sentence can have multiple readings depending on which element takes wider scope.

🔗 Quantifiers as set relations

🔗 The core insight

Quantifier words name relations between two sets.

• The principle of compositionality leads to this conclusion: if All men snore is true when the set of men is a subset of the set of entities that snore, then all must contribute the subset relation itself.
• This may seem odd at first—all means 'subset'—but it follows logically from how meanings compose.

🧮 Common quantifier meanings

Quantifier	Example	Set relation
all	All students are brilliant	S ⊆ B (subset)
no	No students are brilliant	S ∩ B = ∅ (empty intersection)
some (plural)	Some students are brilliant	|S ∩ B| ≥ 2 (intersection cardinality ≥ 2)
a/some (singular)	A student is brilliant	S ∩ B ≠ ∅ (non-empty intersection)
four	Four students are brilliant	|S ∩ B| = 4 (intersection cardinality = 4)
most	Most students are brilliant	|S ∩ B| > ½|S| (more than half)
both	Both students are brilliant	S ⊆ B and |S| = 2 ('all two of them')

• Each quantifier specifies how the two sets relate to each other.
• Example: Most students are brilliant is true when the number of students who are brilliant is greater than half the total number of students.

🔄 Three-place quantifiers

• Some quantifiers express relations among three sets.
• Example: Half as many guests attended as were invited compares the cardinality of (guests ∩ attended) to the cardinality of (guests ∩ invited).

📢 Adverbial quantifiers

• Quantifier meanings can also be expressed by adverbs like always, sometimes, never, usually.
• These are called "unselective quantifiers" because they can quantify over different kinds of things:
  • Over times: Napoleon always relied upon surprise = 'at all times'
  • Over individuals: A triangle always has three sides = 'all triangles'
• Don't confuse: Dogs usually have brown eyes quantifies over individual dogs, not over moments in time (a dog's eye color doesn't change moment to moment).

🌍 Cross-linguistic variation

• Not all languages use quantifying determiners; adverbial quantifiers are more common cross-linguistically.
• Other strategies include quantificational verb roots, affixes, particles.
• Some languages may have limited syntactic means for expressing certain quantifier meanings.

📝 Logical representation

📝 Standard predicate logic

• The logical forms from Chapter 4 reflect the set-relation analysis:
  • All men snore: ∀x[MAN(x) → SNORE(x)] (uses implication → for subset)
  • No women snore: ¬∃x[WOMAN(x) ∧ SNORE(x)] (empty intersection)
  • Some man snores: ∃x[MAN(x) ∧ SNORE(x)] (non-empty intersection)
• The use of → for all follows from the definition of subset: (A ⊆ B) ↔ ∀x[(x ∈ A) → (x ∈ B)].
• The use of ∧ for some and no follows from the definition of intersection: x ∈ (A ∩ B) ↔ (x ∈ A) ∧ (x ∈ B).

📝 Limitations of standard notation

• Standard predicate logic is first-order logic: predicates represent properties of individual entities.
• Some quantifiers like most cannot be expressed in first-order logic because cardinality is a property of sets, not individuals.
• What would be needed: second-order logic, which deals with properties of sets.
• Example: Four men snore can be expressed but requires a clumsy formula with multiple existential quantifiers and inequality statements.

📝 Restricted quantifier notation

A three-part format: [operator x: restriction] scope

• Operator: the quantifier word itself (e.g., most, all, no)
• Restriction: the material from the NP containing the quantifier (defines the first set)
• Nuclear scope: the rest of the sentence (defines the second set)

Example: Most students are brilliant

• Logical form: [most x: STUDENT(x)] BRILLIANT(x)
• Interpretation: |STUDENT ∩ BRILLIANT| > ½|STUDENT|

📝 Uniform interpretation procedure

With restricted quantifier notation, we can apply a consistent rule:

1. The quantifying determiner → operator
2. The rest of the NP containing the determiner → restriction
3. The rest of the sentence → nuclear scope

Example: All brave men are lonely

• Determiner: all → operator
• Rest of NP: brave men → restriction: MAN(x) ∧ BRAVE(x)
• Rest of sentence: are lonely → scope: LONELY(x)
• Result: [all x: MAN(x) ∧ BRAVE(x)] LONELY(x)
• Interpretation: (MAN ∩ BRAVE) ⊆ LONELY

📝 Quantified objects and obliques

• The same procedure works for quantified NPs in any argument position.
• Example: John loves all pretty girls
  • [all x: GIRL(x) ∧ PRETTY(x)] LOVE(j,x)
  • (GIRL ∩ PRETTY) ⊆ {x: ⟨j,x⟩ ∈ LOVE}
  • "The set of pretty girls is a subset of the set of things John loves."

📝 Compound quantifier words

• Words like everyone, someone, nothing, everywhere include a quantifier root plus a classifier (person, thing, place).
• Include the classifier as a predicate in the restriction.
• Example: Everyone loves Snoopy → [all x: PERSON(x)] LOVE(x,s)

⚖️ Two classes of quantifiers

⚖️ Cardinal vs. proportional

Type	Definition	Examples	Key property
Cardinal	Specify cardinality of intersection	no, some, four, several	Symmetric relations
Proportional	Specify proportion of one set in another	all, every, most, few out of five	Non-symmetric relations

⚖️ Symmetry test

• Cardinal quantifiers express symmetric relations:

  • Three senators are Vietnam veterans entails Three Vietnam veterans are senators
  • Some drug dealers are federal employees entails Some federal employees are drug dealers
  • This follows because intersection is commutative: A ∩ B = B ∩ A

• Proportional quantifiers express non-symmetric relations:

  • All brave men are lonely does NOT entail All lonely men are brave
  • Most Popes are Italian does NOT entail Most Italians are Popes
  • Don't confuse: the proportion of A that is B can be very different from the proportion of B that is A.

⚖️ Ambiguous quantifiers

• Many and few are ambiguous between cardinal and proportional senses.
• Example: Few people in America have an IQ over 145, but many students at Cal Tech are in that range.
  • This is not a contradiction if we use the proportional senses.
  • Cardinal senses would create a contradiction.
• Both senses are vague and context-dependent.
• Example: in a country where 80% normally vote, "few people voted" might apply to 60% turnout; in a city where 20% normally vote, "many people voted" might apply to 40% turnout.

⚖️ Existential there construction

• Only cardinal quantifiers can occur as the pivot in existential there sentences.
• Grammatical: There are several/some/no/many/six unicorns in the garden.
• Ungrammatical: *There are all/most unicorns in the garden.
• This distributional difference helps distinguish the two classes.

⚖️ Discourse familiarity requirement

• Proportional quantifiers presuppose a contextually relevant and identifiable set (the restriction set).
• Example: Most people attend the Baptist church requires context to specify which set of people.
• Example: All students are required to pass phonetics requires context to specify which students (e.g., in a particular program).
• Cardinal quantifiers do not require this:
  • Many people attend the Baptist church is acceptable without special context.
  • No aircraft are allowed to fly over the White House is acceptable without special context.

⚖️ Articles as quantifiers

• The indefinite article a(n) can be analyzed as an existential quantifier (non-empty intersection) → cardinal quantifier.
• The definite article the can be analyzed as a special universal quantifier ('all of them' or 'all one of them') → proportional quantifier.
• This analysis predicts that a(n) but not the can occur in existential there:
  • There is a unicorn in the garden. ✓
  • *There is the unicorn in the garden. ✗ (under existential reading)
• The presupposition of unique identifiability triggered by the may follow from the discourse familiarity requirement for proportional quantifiers.

🔀 Scope ambiguities

🔀 What scope means

• When a quantifier combines with negation, another quantifier, a modal, or a propositional attitude verb, the sentence can have multiple readings.
• The difference depends on which element has wider scope (which "applies first" in the interpretation).

🔀 Quantifier + negation

Example: I did not find many valuable books

• Reading (a): [many x: BOOK(x) ∧ VALUABLE(x)] ¬FIND(speaker,x)
  • "There were many valuable books which I did not find."
  • Quantifier has wide scope over negation.
• Reading (b): ¬[many x: BOOK(x) ∧ VALUABLE(x)] FIND(speaker,x)
  • "There were not many valuable books which I found."
  • Negation has wide scope over quantifier.
• These have different truth conditions: if a library has 600 valuable books and I found 300, reading (a) could be true while reading (b) is false.

Example: All that glitters is not gold

• Reading (a): [all x: GLITTER(x)] ¬GOLD(x) — "Everything that glitters is non-gold"
• Reading (b): ¬[all x: GLITTER(x)] GOLD(x) — "Not everything that glitters is gold"
• The (b) reading is the intended meaning of the proverb, but the (a) reading is also grammatically possible.
• Don't confuse: many speakers are unaware of the ambiguity because only one reading is consistent with world knowledge, and the (b) reading is generally preferred.

🔀 Two quantifiers

Example: Many linguists have read every paper by Chomsky

• Reading (a): [many x: LINGUIST(x)] ([every y: PAPER(y) ∧ BY(y,c)] READ(x,y))
  • "There are many linguists such that each of them has read every paper."
  • Many has wide scope.
• Reading (b): [every y: PAPER(y) ∧ BY(y,c)] ([many x: LINGUIST(x)] READ(x,y))
  • "For each paper, there are many linguists who have read it."
  • Every has wide scope.
• Reading (b) could be true while (a) is false: each paper might be read by many people, but no single person has read all papers.

Example: Every student knows two languages

• Reading (a): each student knows some pair (possibly different pairs for different students)
• Reading (b): there is a specific pair of languages that every student knows

🔀 Quantifier + modal

Example: Every student might fail the course

• Reading (a): ∀x[STUDENT(x) → ◊FAIL(x)] — "For each student, it is possible that they fail"
• Reading (b): ◊∀x[STUDENT(x) → FAIL(x)] — "It is possible that all students fail"
• The symbol ◊ means 'possibly true'; □ means 'necessarily true'.

Example: Some sanctions must be imposed

• Reading (a): ∃x[SANCTION(x) ∧ □BE-IMPOSED(x)] — "There are some sanctions that are necessarily imposed"
• Reading (b): □∃x[SANCTION(x) ∧ BE-IMPOSED(x)] — "It is necessary that some sanctions be imposed"

🔀 Quantifier + propositional attitude verb

Example: John thinks that he has visited every state

• Reading (a): [all x: STATE(x)] (THINK(j, VISIT(j,x)))
  • "For each state, John thinks he has visited it."
  • Could be true if John answers "I think so" for each individual state but has no idea how many states exist.
• Reading (b): THINK(j, [all x: STATE(x)] VISIT(j,x))
  • "John thinks that he has visited all states."
  • Could be true if John believes there are 48 states and knows he visited all of them, even if he hasn't visited Alaska or Hawaii.

🔀 De dicto vs. de re as scope ambiguity

• If we treat the indefinite article as an existential quantifier, de dicto/de re ambiguity can be analyzed as scope ambiguity.

Example: Susan wants to marry a cowboy

• Wide scope (de re): ∃x[COWBOY(x) ∧ WANT(s, MARRY(s,x))]

  • "There is a specific cowboy Susan wants to marry."
  • Could be true even if Susan doesn't know he's a cowboy.

• Narrow scope (de dicto): WANT(s, ∃x[COWBOY(x) ∧ MARRY(s,x)])

  • "Susan wants it to be the case that she marries a cowboy."
  • Could be true even if Susan has no specific individual in mind.

• Don't confuse: some scholars argue that de dicto/de re ambiguity cannot always be reduced to scope relations, but the scope analysis handles many cases.

🧭 Overview

🧠 One-sentence thesis

Intensional contexts are linguistic environments where the truth value of a sentence cannot be determined solely from the denotations of its parts but must also depend on the senses (intensions) of one or more constituents.

📌 Key points (3–5)

• What intensional contexts are: contexts where denotation of a complex expression cannot be predicted just by looking at the denotations of its constituents; we must look at senses as well.
• Three diagnostic properties: (1) substitutivity fails—replacing coreferential expressions can change truth value; (2) sentences may have truth values even when constituents lack denotation; (3) NPs may exhibit de re vs. de dicto ambiguity.
• Main types covered: propositional attitude verbs (believe, want), non-intersective adjectives (typical, skillful, former, alleged), tense, modality, counterfactuals, and intensional verbs (seek, want).
• Common confusion: not all adjectives combine via simple set intersection—intersective adjectives like yellow do, but subsective (skillful), privative (former), and non-subsective (alleged) adjectives require reference to the sense of the noun they modify.
• Why it matters: intensional contexts show that compositionality holds for natural language, but only when we account for both denotation and sense (intension).

🔍 Propositional attitude verbs and substitutivity failure

🔍 The substitutivity problem

• Normally, replacing one expression with another that has the same denotation should not change the truth value of a sentence.
• Example: Mark Twain and Samuel Clemens refer to the same individual, yet:
  • "Mary believes that The Prince and the Pauper was written by Mark Twain" can be true while
  • "Mary believes that The Prince and the Pauper was written by Samuel Clemens" is false.
• Both sentences can be true simultaneously without logical inconsistency.
• This seems to violate the Principle of Compositionality—at least when applied to denotations alone.

🧩 Frege's solution: intension vs. denotation

Intension: a technical synonym for sense; the proposition expressed by a sentence, as opposed to its truth value.

• Frege proposed that the denotation of complement clauses under propositional attitude verbs is not their truth value but the proposition they express.
• The speaker in "Mary believes that…" is making a claim about Mary's beliefs, not about the actual authorship of the book.
• The truth value of the whole sentence depends on what propositions Mary believes, not on the actual facts.
• Key insight: the denotation of the complement clause is its sense (intension), not its truth value.
• Compositionality is preserved: we calculate the denotation of the whole sentence based on the intension of the complement clause.

🔀 De re vs. de dicto ambiguity

• Propositional attitude verbs create a second special property: ambiguity in how noun phrases are interpreted.
• Example: "I hope to meet with the Prime Minister next year."
  • De re reading: refers to the specific individual who is Prime Minister at the moment of speaking.
  • De dicto reading: refers to whoever will hold the property of being Prime Minister at the specified future time.
• Another example: "I think that your husband is a lucky man."
  • De re: because I saw him winning at the casino (refers to the specific individual married to you now).
  • De dicto: any man married to you would be considered fortunate (refers to the property of being married to you).
• Under the de dicto reading, the truth value depends on the sense (the property) rather than the denotation (the specific individual).

🎨 Non-intersective adjectives

🎨 Intersective adjectives: the baseline

Intersective adjectives: adjectives that obey the rule ⟦Adj N⟧ = ⟦Adj⟧ ∩ ⟦N⟧.

• Example: yellow submarine denotes the intersection of all yellow things and all submarines.
• The denotation set contains all things that are both yellow and submarines.
• Valid inference pattern: "Arnold is a carnivorous biped" and "Arnold is a mammal" → "Arnold is a carnivorous mammal."
• Examples of intersective adjectives: Brazilian, blonde, carnivorous.

🔧 Subsective adjectives: not simple intersection

Subsective adjectives: adjectives that satisfy ⟦Adj N⟧ ⊆ ⟦N⟧ but not ⟦Adj N⟧ = ⟦Adj⟧ ∩ ⟦N⟧.

• The denotation of the phrase is a subset of the denotation of the head noun, but not a simple intersection.
• Example: "Bill Clinton is a typical politician" and "Bill Clinton is a Baptist" does not validly entail "Bill Clinton is a typical Baptist."
• Another example: "Francis is a skillful surgeon" and "Francis is a violinist" does not entail "Francis is a skillful violinist."
  • Even if surgeon and violinist have the same denotation set in some context (e.g., all surgeons are violinists), skillful surgeon and skillful violinist do not.
• Why substitutivity fails: two expressions with the same denotation (surgeon and violinist) are not mutually substitutable when modified by skillful.
• How they work: subsective adjectives combine with the sense of the noun, not just its denotation.
  • Informal definition of skillful: combines with a noun N to denote individuals who belong to the set of all Ns and are extremely good at the activity named by N.
• Don't confuse: all intersective adjectives are subsective, but saying an adjective is subsective implicates it is not intersective.

❌ Privative adjectives: excluding the head noun

Privative adjectives: adjectives that satisfy ⟦Adj N⟧ ∩ ⟦N⟧ = ∅ (the denotation sets are disjoint).

• A "former N" cannot be a member of the denotation set of N.
• Example: a former Member of Parliament is no longer a Member of Parliament.
• Other examples: counterfeit, spurious, imaginary, fictitious, fake, would-be, wannabe, past, fabricated.
• Similar prefixes: ex-, pseudo-, non-.
• Informal definition of former: combines with a noun N to denote individuals who belonged to the set of all Ns at some time in the past, but no longer do.

❓ Non-subsective adjectives: neither subset nor disjoint

• These adjectives are neither subsective nor privative.
• Example: alleged terrorist—an alleged terrorist may or may not actually be a terrorist.
• The adjective alleged does not have a clear denotation set on its own (what would "the set of all alleged things" mean?).
• Informal definition of alleged: combines with a noun N to denote individuals (x) such that some other individual claims that x belongs to the set of all Ns.
• Other examples: potential, possible, arguable, likely, predicted, putative, questionable.

📏 Context-dependent adjectives: intersective but vague

• Adjectives like tall, old, big seem non-intersective at first glance.
• Invalid inference: "Win is a tall 14-year-old" and "Win is a basketball player" does not entail "Win is a tall basketball player."
• However, these adjectives are actually intersective; they are just context-dependent and vague.
• The boundaries of their denotation sets are determined by context, including but not limited to the head noun.
• Example: "My two-year-old son built a really tall snowman" vs. "The fraternity brothers built a really tall snowman"—the standard of tallness differs even though the head noun is the same.
• Evidence for intersectivity: these adjectives take for-phrases to indicate comparison class (tall for an East coast mountain), whereas truly non-intersective adjectives like skillful take as-phrases (skillful as a surgeon).

🔄 Ambiguous adjectives: intersective or subsective

• Some adjectives are ambiguous between an intersective and a subsective sense.
• Example: "Marya is a beautiful dancer."
  • Intersective: Marya is beautiful and a dancer.
  • Subsective: Marya dances beautifully.
• Non-contradictory interpretation: "Marya is not beautiful, but she is a beautiful dancer."
• Example: "Floyd is an old friend."
  • Intersective: Floyd is old and a friend.
  • Subsective: Floyd has been a friend for a long time.
• Example: "He is a poor liar."
  • Intersective: He is poor and a liar.
  • Subsective: He is not skillful in telling lies.

🗣️ Predicative use of adjectives

• Many adjectives can function as clausal predicates: "John is happy/sick/rich/Australian."
• Intersective adjectives generally can be used as predicates: "Otacilio is a Brazilian poet; therefore he is Brazilian."
• When an ambiguous adjective is used as a predicate, generally only the intersective sense is available.
  • "Marya is a beautiful dancer; therefore she is beautiful" is not valid (unless the intersective sense is intended).
  • "He is a poor liar; therefore he is poor" is most naturally interpreted as a pun.
• Non-subsective adjectives like former and alleged cannot be used as predicates: "*That terrorist is former/alleged" is ungrammatical.
• Some non-subsective adjectives can be predicates in the right context: "His illness is imaginary," "This money is counterfeit."

⏳ Other intensional contexts

⏳ Modality and tense

• Modality (markers of possibility and necessity like might, could, must) creates intensional contexts.
• Contrast with negation: to determine the truth value of a negated proposition, we only need the truth value of the original proposition.
  • Example (spoken in 2006): "Barack Obama is the first black President of the United States" [False] → "Barack Obama is not the first black President…" [True].
  • Same for "Nelson Mandela is the first black President…" [False] → "Nelson Mandela is not the first black President…" [True].
• With modals, knowing the truth value is not enough; we need to evaluate the meaning.
  • "Barack Obama could be the first black President…" (spoken in 2006) [True].
  • "Nelson Mandela could be the first black President…" (spoken in 2006) [False].
• Tense also creates intensional contexts.
  • Example (spoken in 2014): "Hillary Clinton is the Secretary of State" [False] and "Lady Gaga is the Secretary of State" [False] have the same truth value.
  • But "Hillary Clinton was/has been the Secretary of State" [True] and "Lady Gaga was/has been the Secretary of State" [False] have different truth values.
  • Knowing the present tense is true does not allow us to determine the future tense: "Henry is Anne's husband" [True] does not tell us whether "In five years, Henry will still be Anne's husband."

🔁 Substitutivity failure in modals and counterfactuals

• Example (spoken in 1850): "I do not believe that James Brooke is the White Rajah of Borneo" could be true, but "I do not believe that James Brooke is James Brooke" would certainly be false.
  • During 1842–1868, James Brooke and the White Rajah of Borneo referred to the same individual.
• Counterfactual example: "Martin Luther King might have become the first black President of the United States" is debatable, but "Martin Luther King might have become Barack Obama" is irrational.
• Replacing one clause with another of the same truth value can change the truth value of a counterfactual:
  • "If Beethoven had died in childhood, we would never have heard his magnificent symphonies" [True].
  • "If Beethoven had died in childhood, Columbus would never have discovered America" [False].

🔎 Intensional verbs: searching and desiring

Intensional verbs: verbs like seek, want, look for that create intensional contexts.

• These verbs license de re vs. de dicto ambiguities in their direct objects.
• Example: "I'm looking for a black cocker spaniel."
  • De re: looking for a specific dog (e.g., it got lost).
  • De dicto: wants to acquire a dog that fits that description, but no specific dog in mind.
• Example: "John wants the same job as you."
  • De re: John is interested in the same type of work as you.
  • De dicto: John wants to be doing whatever you are doing.
• Referential opacity: substitution of a coreferential NP can affect truth value.
  • "Lois Lane is looking for Superman" [True], but "Lois Lane is looking for Clark Kent" [arguably False], even though Superman is Clark Kent.
• Direct objects may fail to refer, yet the sentence can still have a truth value:
  • "Arthur is looking for the fountain of youth" can be true even though the fountain of youth does not exist.
  • "John wants a unicorn for Christmas" can be true even though unicorns do not exist.

🌍 Subjunctive mood as a marker of intensionality

🌍 Subjunctive in Spanish and Greek

• In some languages, intensional contexts require special grammatical marking, often the subjunctive mood.
• The distribution of the subjunctive is complex and varies even between closely related dialects.
• Not all uses of the subjunctive can be explained by intensionality alone, but intensionality is one key factor.

🇪🇸 Spanish relative clauses

• Spanish uses indicative vs. subjunctive mood to distinguish de re vs. de dicto readings.
• Example: "María busca a un profesor que enseña griego" (indicative) can only be de re (a specific professor).
• Example: "María busca a un profesor que enseñe griego" (subjunctive) can only be de dicto (any professor who teaches Greek).
• Neither sentence is ambiguous in the way the English translation is.

🇬🇷 Modern Greek relative clauses

• Modern Greek uses the particle na to mark subjunctive mood.
• Example: "We want to hire a secretary [who knows Japanese]" (indicative) can only be de re (a specific person, e.g., Jane Smith).
• Example: "We want to hire a secretary [who na knows Japanese]" (subjunctive) can only be de dicto (hard to find one, not sure if we will succeed).
• Definite NPs cannot contain subjunctive relative clauses: "Roxanne wants to marry a/*the man who na has a lot of money."
• Objects of verbs of creation with future time reference require subjunctive: "I have to write an essay [that (na) is longer than 15 pages]."
• Pattern: subjunctive is used when the noun phrase refers to a property rather than a specific individual.

🧮 Lambda abstraction and functions

🧮 Functions vs. sets

• Truth conditions can be expressed in terms of functions rather than set membership.
• The two approaches (sets vs. functions) are essentially equivalent.
• The functional representation is often simpler, more general, and more convenient for many constructions.
• The membership of a set can always be expressed as its characteristic function.

λ Lambda notation for defining functions

• Standard function notation uses named functions: f₁(x) = x – 4, so f₁(13) = 9.
• Lambda notation defines anonymous functions: λx. x – 4 = 9.
• When the function is applied to an argument, substitute that argument for the bound variable introduced by λ.
• Example: λx. 3x² + 1 = 28.

🔧 Lambda abstraction: propositions to predicates

• Lambda (λ) is an operator that changes propositions into predicates by replacing some element with a bound variable.
• Example: from "Caesar loves Brutus" we can derive:
  • [λy. Caesar loves y] = the property of being loved by Caesar.
  • [λx. x loves Brutus] = the property of being someone who loves Brutus.
• Applying these predicates to an argument:
  • λy. LOVE(c,y) = LOVE(c,b) = "Caesar loves Brutus."
  • λx. LOVE(x,b) = LOVE(c,b) = "Caesar loves Brutus."
  • λx. LOVE(x,c) ∧ HATE(x,b) = LOVE(a,c) ∧ HATE(a,b) = "Antony loves Caesar and hates Brutus."

🔢 Characteristic functions and semantic values

• Predicates derived by lambda abstraction can be interpreted as characteristic functions:
  • λx. SNORE(x) = 1 if n snores, 0 otherwise.
• Semantic value of "Henry snores": λx. SNORE(x) = SNORE(h) = 1 if Henry snores, 0 otherwise.
• Transitive predicates take two arguments: [λy. [λx. LOVE(x,y)]].
• For "Caesar loves Brutus":
  • Apply the verb to the object: λy. [λx. LOVE(x,y)] = [λx. LOVE(x,b)] = "is someone who loves Brutus."
  • Apply the VP to the subject: λx. LOVE(x,b) = LOVE(c,b) = "Caesar loves Brutus."

🌐 Intensions as functions from possible worlds

• In formal semantics, intensions (senses) are often defined as functions from possible worlds to denotations.
• A "possible world" is any way the universe might conceivably be without changing the structure of the language.
• Knowing the meaning (sense) of a word like yellow allows us to identify the set of all yellow things in any particular context.
• The sense of yellow is a mapping from each possible world to the expression's denotation in that world.
• Using lambda abstraction: the intension of speak = [λw. [λx. SPEAK(x) in w]], where w is a variable over possible worlds.
• The intension of yellow = [λw. [λx. YELLOW(x) in w]].
• These functions take a possible world as argument and return the set of all yellow things (or speaking things) in that world.

🎯 Conclusion

🎯 Summary of intensional contexts

• Intensional (or opaque) contexts are linguistic environments where the truth value of a sentence cannot be determined from the denotations of its parts alone.
• Many intensional contexts require knowledge about denotations in other situations:
  • Past/future tense: denotations at other times.
  • Possibility and counterfactuals: denotations in other possible worlds.
  • Non-intersective adjectives like former and potential: similar effects.
• Key principle: knowing the sense of an expression allows speakers to identify the denotation in various situations.
• What all these phenomena share: the denotation of a complex expression cannot be compositionally determined from the denotations of its parts alone; we must refer to senses as well.
• Compositionality holds for natural language, but only when we account for both denotation and sense (intension).

🧭 Overview

🧠 One-sentence thesis

Situation type (Aktionsart) and grammatical aspect both describe how situations are distributed over time, with situation type distinguishing states from events and telic from atelic events, while grammatical aspect markers indicate how a situation's internal structure is viewed.

📌 Key points (3–5)

• States vs. events: states are homogeneous over time (nothing changes within the described span), while events are dynamic and involve change.
• Linguistic tests matter: distinctions like state/event are supported by tests such as "What happened?" questions, progressive forms, and simple present interpretations.
• Telic vs. atelic events: telic events have a natural endpoint (measured out by an argument), while atelic events do not.
• Common confusion: agentive/volitional vs. non-agentive is not the same as event vs. state—most states are non-agentive, but not all non-agentive predicates are states.
• Aspect vs. Aktionsart: grammatical aspect (marked by morphemes) tells us about distribution over time, while Aktionsart (situation type) is the inherent temporal structure of the situation being described.

🔍 Core distinction: States vs. Events

🔍 What states are

State: a situation which is homogeneous over time; construed as being the same at every instant within the time span being described.

• Informally: nothing "happens"; a video of a state looks like a snapshot.
• Examples: "this tea is cold," "George is my brother," "my puppy is playful."
• Don't confuse: saying a state is homogeneous does not mean it will never change (tea can be reheated, puppies grow up)—it means the change is not part of the situation currently being described.

🔍 What events are

Event: a situation which is not homogeneous over time; involves some kind of change.

• Also called dynamic or internally complex.
• Examples: "my tea got cold," "my puppy is playing," "George hit my brother," "Susan will write a letter."
• A video of an event will not look like a snapshot because something changes.

🧪 Linguistic tests for situation type

🧪 Test 1: "What happened?" question

• Only eventive situations can appropriately answer "What happened?"
• Eventive: "Mary kissed the bishop," "the sun set," "Peter sang Cantonese folk songs."
• Stative (unacceptable): "Sally was Irish," "the grapes were rotten," "George loved sauerkraut."

🧪 Test 2: Progressive form (be V-ing)

• Only eventive situations can naturally use the progressive.
• Eventive: "Mary is kissing the bishop," "The sun is setting," "Peter is singing Cantonese folk songs."
• Stative (unacceptable or coerced): "This room is being too warm" (unacceptable), "Sally is being Irish" (unacceptable), "William is having a headache" (unacceptable).
• Coerced interpretations: some states can take progressive with special meaning—"George is loving all the attention he is getting this week" (temporary situation), "Arthur is being himself" (behaving in a certain way, eventive reading).

🧪 Test 3: Simple present tense interpretation

• Eventive situations in simple present → habitual interpretation.
• Stative situations in simple present → statement about present time, no habitual reading.
• Eventive: "Peter sings Cantonese folk songs" (he does it regularly), "The sun sets in the west."
• Stative: "This room is too warm" (just now), "William has a headache" (not "he gets headaches frequently").

🧪 What NOT to confuse: Agentive vs. non-agentive tests

• Tests like imperative use, agent-oriented adverbials ("deliberately"), and Control complements ("try to...") distinguish agentive/volitional from non-agentive, not state from event.
• Most states are non-agentive, but not all non-agentive predicates are states (e.g., "die," "melt," "fall," "bleed" are non-agentive events).
• Some states can be volitional: "Be careful!" (imperative), "He is trying to be good" (Control complement).
• Key point: use the right tests for the right question.

🎯 Telic vs. Atelic events

🎯 What telic events are

Telic event: an event that has a natural endpoint.

• Easy to know when the event is over.
• Examples: dying (patient is dead), arriving, eating a sandwich (sandwich is gone), crossing a river, building a house (house is built).
• Many telic events involve a change of state in a particular argument (patient or theme).
• This argument "measures out" the event: once the result state is achieved, the event is over.
• Some telic events are measured out by an argument that does not undergo change of state (the excerpt mentions "read a..." but is cut off).

🎯 What atelic events are

• The excerpt does not provide a full definition or examples of atelic events (the text is incomplete).
• By contrast with telic: atelic events would be those without a natural endpoint.

📐 Broader context: Tense, Aspect, and Aktionsart

📐 Tense vs. Aspect

Dimension	What it tells us	Example
Tense	Location in time	Lithuanian: "dirb-au" (I worked, past), "dirb-u" (I work, present), "dirb-s-iu" (I will work, future)
Aspect	Distribution over time	English: "my wife wrote a letter" vs. "my wife was writing a letter"

📐 Situation aspect (Aktionsart) vs. Grammatical aspect

• Situation aspect (Aktionsart): the inherent temporal structure of the situation being described (state vs. event, telic vs. atelic).
• Grammatical aspect: meanings expressed by grammatical markers (morphemes) that indicate how a situation's internal structure is viewed.
• Both contribute information about time, but in different ways.
• The chapter focuses on aspect; the next chapter will cover tense.

📐 Why situation type matters

• Situation type (Aktionsart) can have a significant effect on the interpretation of both tense and aspect markers.
• The same issues encountered in studying word meanings apply here: entailments vs. selectional restrictions and presuppositions, implicature and coercion, polysemy, idiomatic senses, etc.
• The excerpt mentions that situation type plays an important role in syntax as well as semantics.

📐 Topic Time (preview)

• The excerpt mentions that §20.3 will introduce the notion of Topic Time (the time under discussion), which will be important for understanding both tense and aspect.
• This concept is not yet explained in the provided text.

🧭 Overview

🧠 One-sentence thesis

Grammatical aspect markers contribute to the truth conditions of sentences by specifying the temporal relationship between the time about which a claim is made (Topic Time) and the time of the situation being described, while situation type (Aktionsart) reflects inherent properties of the situation itself.

📌 Key points (3–5)

• Situation type vs. grammatical aspect: Aktionsart is an inherent property of the situation; grammatical aspect is a feature of the speaker's description—how they choose to view or present the situation.
• Klein's three-way time distinction: Time of Utterance (TU = time of speaking), Topic Time (TT = the time span the speaker is making a claim about), and Time of Situation (TSit = when the event/state occurs).
• Perfective vs. imperfective: perfective indicates TSit fits inside TT (the whole situation is contained within the time being talked about); imperfective indicates TT fits inside TSit (the time being talked about is only part of the situation).
• Common confusion: tense vs. aspect—tense relates TT to TU (when we're talking about relative to now); aspect relates TSit to TT (how the situation relates to the time we're talking about).
• Why it matters: aspect markers affect truth conditions—the same event described with different aspects can be true or false in the same real-world situation.

🔍 Situation type (Aktionsart)

🔍 Stative vs. eventive situations

Situation type (Aktionsart): an inherent property of the situation itself, independent of how the speaker describes it.

Key test: habitual adverbials

• Eventive situations can naturally combine with habitual adverbials like "every Saturday" or "on a regular basis."
• Stative situations cannot naturally combine with these adverbials without changing the meaning.
• Example: "Peter sings Cantonese folk songs (every Saturday)" → eventive; "William has a headache" → stative (adding "every Saturday" would change the meaning to recurring headaches, not a statement about the present).

Don't confuse with agentive/volitional tests

• Tests like imperatives, "deliberately," or control predicates (try, persuade) distinguish agentive vs. non-agentive, not state vs. event.
• Most states are non-agentive, but not all non-agentive predicates are states (e.g., die, melt, fall).
• Some stative predicates can be volitional (e.g., "Be careful!" or "He is trying to be good").

🎯 Telic vs. atelic events

Telic event: an event that has a natural endpoint; atelic event: an event that does not have a natural endpoint.

Telic events

• Have a natural endpoint—it's easy to know when the event is over.
• Examples: dying (patient is dead), eating a sandwich (sandwich is gone), building a house (house is built).
• Often involve a change of state in an argument (patient or theme) that "measures out" the event.
• Some telic events are measured out by an argument that doesn't change (e.g., "read a novel"—when half read, the event is half over).
• Motion events can be measured out by the path traversed (e.g., "run five miles," "fly to Paris").

Atelic events

• Have no natural endpoint; can continue indefinitely until the actor stops or something intervenes.
• Examples: singing, walking, bleeding, shivering, looking at a picture.
• No argument "measures them out"; no specified change of state.

Two key tests

Test	Atelic events	Telic events
Duration phrases ("for ten minutes")	Natural ✓	Unnatural ✗
Boundary phrases ("in ten minutes")	Unnatural ✗	Natural ✓

Example: "For ten minutes Peter sang in Cantonese" (natural) vs. "For ten minutes Peter broke three teeth" (unnatural); "In ten minutes Peter broke three teeth" (natural) vs. "In ten minutes Peter sang in Cantonese" (unnatural or means "began to sing").

🧩 How the whole VP determines situation type

• Situation type is not purely lexical—the whole VP (or clause) often determines it.
• Quantified objects: "eat ice cream" (atelic) vs. "eat a pint of ice cream" (telic); "sing folk songs" (atelic) vs. "sing 'The Skye boat song'" (telic).
• Delimited paths: "walk" (atelic) vs. "walk to the beach" (telic).

⏱️ Durative vs. punctiliar situations

Durative situations: extend over a time interval; punctiliar (instantaneous) situations: construed as happening in an instant.

Test: progressive + iterative interpretation

• Punctiliar situations in the progressive normally require an iterative (repeated) interpretation: "He is tapping on the door" = repeatedly tapping.
• Durative situations do not: "He is reading your poem" = one continuous reading event.

📊 Five major situation types

Type	Static	Durative	Telic	Examples
State	+	+	–	be warm, have a headache
Activity	–	+	–	dance, sing, carry a sword
Accomplishment	–	+	+	eat a pint of ice cream, build a house, run to the beach
Achievement	–	–	+	break, die, recognize, arrive, find
Semelfactive	–	–	–	blink, wink, tap, snap, clap

• Activities: atelic events.
• Achievements: telic, instantaneous, normally involve a change of state.
• Accomplishments: durative telic events; require time to reach their endpoint; often involve a process resulting in a change of state.
• Semelfactives: instantaneous events without a change of state; atelic because nothing measures them out.
• Additional distinction: stage-level (temporary) vs. individual-level (permanent) states.

⏰ Klein's three-way time framework

⏰ The three cardinal time points

Klein distinguishes three significant times:

• TU (Time of Utterance): the time of speaking; can be treated as a point.
• TSit (Time of Situation): the time of the event or situation being described; a time interval.
• TT (Topic Time): the time span to which the speaker's claim is confined—"the time span that we are talking about"; a time interval.

🗣️ Why Topic Time matters

The problem with traditional definitions

• Traditional definitions say tense "locates situations in time" relative to the present moment.
• But consider: "The cab driver was Latvian" or "He was dead" or "The Grand Canyon was enormous."
• Does past tense mean the cab driver is no longer Latvian, John is no longer dead, or the Grand Canyon is no longer enormous? No.

Klein's solution

• Tense locates or restricts the speaker's assertion, not the situation itself.
• Tense indicates the location of the time period about which the speaker is making a claim.
• Example: "There was a book on the table. It was/#is in Russian."—the judge's question establishes a specific topic time (when you looked into the room), and any reply must be relevant to that topic time, even if the book is still in Russian at the time of speaking.

📍 How Topic Time is determined

• Can be specified by time adverbs: "yesterday," "next year."
• Can be specified by temporal adverbial clauses: "When I got home from the hospital."
• Can be determined by context, especially in narrative sequences.
• In narratives: event-type verbs in simple past move TT forward; stative predicates in simple past inherit TT from the previous main-line event.

🔑 Klein's definitions of tense and aspect

Tense: indicates a temporal relation between TT and TU.

Aspect: indicates a temporal relation between TT and TSit.

Example: "When I got home from the hospital, my wife wrote a letter" vs. "…my wife was writing a letter."

• The temporal adverbial clause specifies TT.
• Perfective ("wrote"): the writing occurred completely within TT—began after arriving home, completed shortly thereafter.
• Imperfective ("was writing"): the writing extended beyond the limits of TT—began before arriving home, may not be completed at time of speaking.

🎥 Grammatical aspect (viewpoint aspect)

🎥 What grammatical aspect is

Grammatical aspect (viewpoint aspect): a feature of the speaker's description of the situation—part of the claim being made—rather than a property of the situation itself.

Smith's camera metaphor

• Perfective aspect = wide angle view: the situation fits inside the time frame of the speaker's perspective.
• Imperfective aspect = zoom or close-up view: focusing on just a part of the situation, with the whole extending beyond the boundaries of the speaker's perspective.

Crucial insight: aspect affects truth conditions

• Aspect markers contribute to whether a sentence is true or false.
• Example: "The Syrians built a nuclear weapon" (false in 2010) vs. "The Syrians were building a nuclear weapon" (reportedly true in 2010, due to intervention).
• Different aspect markers = different claims about the world.

🔬 Klein's formal definitions

First approximation

• Perfective: TSit ⊆ TT (situation time fits inside Topic Time).
• Imperfective: TT ⊆ TSit (Topic Time fits completely inside situation time).

Example: the tunnel-digging scenario

• "While the guards were at the Christmas party, the prisoners were digging a tunnel (but they never finished it)."—imperfective: TT is contained within TSit; the boundaries of TSit extend beyond TT; can be true even if the tunnel was never completed.
• "While the guards were at the Christmas party, the prisoners dug a tunnel (#but they never finished it)."—perfective: TSit is contained within TT; the entire event took place within the time span of the party; would not be true if the tunnel was not completed.

Why the difference matters

• Digging a tunnel is a telic situation (accomplishment); its endpoint (culmination) is an integral part of the event.
• Perfective description requires the endpoint to be reached within TT.
• Imperfective description may be true even when a perfective description of the same event would be false.

🌳 Typology of grammatical aspect (Comrie's hierarchy)

aspects
├── perfective
└── imperfective
    ├── habitual
    └── continuous
        ├── progressive
        └── non-progressive

Perfective

• Often the default or unmarked way of describing a past event.
• Simply asserts that the event happened.
• In English: simple past tense (lack of overt aspect marking indicates perfective).
• Aspect is distinct from tense—many languages distinguish perfective vs. imperfective in the future as well as the past.

Habitual

• Describes a recurring event or on-going state that is a characteristic property of a certain period of time.
• English: simple present ("Mary plays tennis") or "used to" for past habituals ("Mary used to play tennis").

Progressive

• Non-habitual imperfective used only for describing events, not states.
• English: "be + V-ing" ("Mary is playing tennis").

Continuous

• Non-habitual imperfective not restricted to events; can be used for both states and events.
• (In some languages, "continuous" is applied to markers used primarily for states.)

Example: Spanish

• Has a general imperfective form (ambiguous between habitual and continuous): "Juan llegaba" = 'Juan was arriving/used to arrive.'
• Also has a more specific progressive: "Juan estaba llegando" = 'Juan was arriving.'

🇨🇳 Mandarin Chinese imperfective markers

Two markers: zài (progressive) vs. –zhe (continuous)

Feature	zài	–zhe (main clause)
With events	✓ Natural	✗ Generally unacceptable
With states	✗ Unacceptable	✓ Primary use
Selectional restriction	Events only	States only (in main clauses)

Examples with events

• "Zhāngsān zài tiào" = 'Zhangsan is jumping.' ✓
• "*Zhāngsān tiào-zhe" = (intended: 'Zhangsan is jumping.') ✗

Examples with states

• "*Wo zài xǐhuān Měiguó" = (intended: 'I am liking America.') ✗
• "Tā zài chuáng-shàng tǎng-zhe" = 'He is lying on the bed.' ✓

Verbs with dual senses

• Some verbs allow both stative and eventive readings: "chuān" = 'wear' (stative) or 'put on' (eventive); "ná" = 'hold' (stative) or 'pick up' (eventive).
• zài selects the eventive reading; –zhe selects the stative reading.
• Example: "Tā zài chuān pí-xié" = 'He is putting on leather shoes' vs. "Tā chuān-zhe pí-xié" = 'He is wearing leather shoes.'

Additional restrictions on –zhe

• Only individual-level (temporary) states can be marked with –zhe; generally incompatible with stage-level (permanent) states.
• Example: "*Tā cōnghuì-zhe" (for: 'He is intelligent.') ✗
• Present time reference is not part of the meaning: "Nǐ dāngshí mí-zhe Mǎkèsī, Ēngésī, Lièníng" = 'At that time you were fascinated by Marx, Engels and Lenin.'

Don't confuse: main clause vs. subordinate clause uses

• In adverbial clauses, –zhe occurs freely with both stative and eventive predicates and is grammatically obligatory (cannot be replaced by zài).
• Example: "Tā kū-zhe pǎo huí jiā qù le" = 'He ran home crying.'
• The function of a tense or aspect marker in subordinate clauses may be quite different from its function in main clauses.

🔄 Perfect and prospective aspects

Perfect (retrospective) aspect: indicates that the situation time is prior to Topic Time (TSit < TT).

Prospective aspect: indicates that the situation time is later than Topic Time (TT < TSit).

• English perfect: auxiliary "have" + past participle (e.g., "has eaten," "has arrived").
• English prospective: "going to V" construction ("the ship is going to sail"), "about to V," "on the point of V-ing."
• Don't confuse: perfect vs. perfective—these are different categories.

🔢 Minor aspect categories

Phase aspects

• Inceptive: the beginning of the situation falls within the topic time; often translated as "begin to X."
  • (Inchoative is sometimes used for this meaning, but more commonly restricted to changes of state: "become fat," "get old," "get rich.")
• Terminative/completive: the end of the situation falls within the topic time.
• Continuative: "continue to X" or "keep on X-ing."

Repetition aspects

• Iterative (repetitive): events that occur repeatedly; often translated with "over and over," "more and more," "here and there."
• Distributive: a sub-type of iterative; an action done by or to members of a group, one after another.

🔗 Interactions between situation type and grammatical aspect

🔗 Why certain combinations are impossible

The imperfective + semelfactive problem

• The definition of imperfective (TT ⊆ TSit) implies that the situation time must have some duration.
• A semelfactive event is construed as instantaneous—it has no duration.
• When a semelfactive is described in the imperfective (e.g., "he was tapping on the window"), it cannot refer to a single instantaneous event.
• The only interpretation available is iterative (repeated): the tapping happened over and over.

General principle

• The definitions of grammatical aspects predict that certain aspects will not be available for certain situation types.
• When such combinations occur, the interpretation must shift (e.g., to iterative) to make the combination semantically coherent.

🧭 Overview

🧠 One-sentence thesis

Grammatical aspect (viewpoint aspect) describes the speaker's choice of how to frame a situation's relationship to the topic time, while Aktionsart (situation aspect) classifies the inherent temporal structure of events and states themselves, and mismatches between the two trigger coercion effects that shift interpretation.

📌 Key points (3–5)

• Aktionsart vs. grammatical aspect: Aktionsart is the inherent temporal contour of a situation (state, activity, accomplishment, achievement, semelfactive); grammatical aspect is the speaker's chosen viewpoint (perfective, imperfective, progressive).
• Aspectual sensitivity: certain tense/aspect markers impose selectional restrictions on which situation types they can describe (e.g., progressive normally requires events, not states).
• Coercion effects: when a predicate's natural Aktionsart clashes with the aspectual requirements of a marker or adverbial, the interpretation shifts to resolve the conflict (e.g., a semelfactive in the imperfective becomes iterative).
• Common confusion: perfect vs. perfective—the perfect (e.g., "has sailed") is not the same as perfective aspect; the perfect relates a past event to a later reference time.
• Imperfective paradox: in English, imperfective descriptions of accomplishments (e.g., "was writing a letter") do not entail the perfective completion ("wrote a letter"), unlike states and activities.

🏗️ Situation types (Aktionsart)

🏗️ States vs. events

Aktionsart (situation aspect): a way of classifying situations based on their temporal contour—the shape of their "run time."

• State: homogeneous over time; nothing changes within the described time span.
• Event: involves some kind of change.
• Example: "be happy" (state) vs. "wake up" (event).

⏱️ Duration and telicity

Two primary features distinguish event classes:

Feature	Meaning	Example
Duration	Does the event take time, or is it instantaneous?	"swim" (durative) vs. "snap fingers" (instantaneous)
Telicity (boundedness)	Does the event have a natural endpoint?	"swim" (atelic) vs. "swim the English channel" (telic)

📊 Five main situation types

Type	Duration	Telic?	Change?	Example
State	durative	no	no	"know the answer"
Activity	durative	no	yes	"play tennis"
Accomplishment	durative	yes	yes	"build a house"
Achievement	instantaneous	yes	yes	"arrive"
Semelfactive	instantaneous	no	yes	"knock (once)"

• Don't confuse: "play tennis" (activity, no endpoint) vs. "play a sonata" (accomplishment, has endpoint).

👁️ Grammatical aspect (viewpoint aspect)

👁️ What grammatical aspect marks

Grammatical aspect (viewpoint aspect): the speaker's choice of how to describe a situation; it indicates the relation between the situation's run time (TSit) and the Topic Time (TT).

• Topic Time (TT): the time span about which the speaker is making a claim.
• Time of Utterance (TU): the time of speaking.
• Situation Time (TSit): the run time of the event or state being described.

🔲 Perfective aspect

• Definition: indicates that TSit ⊆ TT (the situation time is contained within the topic time).
• The speaker presents the situation as a bounded whole.
• Example: "I played tennis yesterday" (the entire event of playing is within the topic time).

🔳 Imperfective aspect

• Definition: indicates that TT ⊆ TSit (the topic time is contained within the situation time).
• The speaker looks at the situation "from the inside," without asserting boundaries.
• Example: "I was playing tennis" (the topic time falls somewhere within the ongoing event).

🔄 Progressive aspect

• A subtype of imperfective found in English, Mandarin, and other languages.
• Typically used only for events, not states.
• Example: "I am writing" (event in progress).
• Don't confuse: progressive (a type of imperfective) vs. perfect (e.g., "has written," which relates a past event to a later time).

⚙️ Aspectual sensitivity and coercion

⚙️ What is aspectual sensitivity?

Aspectual sensitivity: selectional restrictions imposed by tense/aspect markers on the types of situations they can describe.

• Example: English progressive normally selects for events, not states.
• Ungrammatical: *"I am knowing the answer."
• This restriction is not absolute; context can override it.

🔀 Coercion effects

When a predicate's Aktionsart clashes with the aspectual requirements of a marker or adverbial, the interpretation shifts:

Clash	Coercion result	Example
Semelfactive + imperfective	Iterative (repeated events)	"He was tapping on the window" (multiple taps)
Accomplishment + "for X time" (short duration)	Activity (process only)	"I read The Lord of the Rings for a few minutes" (didn't finish)
Accomplishment + "for X time" (long duration)	Iterative activity	"John played the sonata for eight hours" (over and over)
Achievement + "for X time"	Habitual state	"For months, the train arrived late" (repeatedly)
State + "suddenly"	Change of state (achievement)	"Suddenly I knew the answer" (moment of realization)

• Don't confuse: the basic meaning of a predicate vs. its coerced interpretation in context.

🧩 The imperfective paradox

• With states and activities, imperfective entails perfective:
  • "Arnold was wearing a wig" → "Arnold wore a wig" ✓
• With accomplishments, imperfective does NOT entail perfective:
  • "Felix was writing a letter" ↛ "Felix wrote a letter" ✗
• Why? The imperfective can describe the process phase of an accomplishment without asserting that the endpoint was reached.
• This suggests accomplishments have two phases: (1) process/activity, (2) culmination/change of state.

🌍 Cross-linguistic variation

🌍 Non-culminating accomplishments

• In some languages (Tagalog, Hindi, Mandarin, Thai), perfective accomplishments do not entail culmination.
• Example (Tagalog): "I removed the stain, but I ran out of soap, so I couldn't remove it" is not a contradiction.
• Possible explanation: in these languages, an accomplishment VP can refer to just the first phase (the process) without asserting the second phase (the culmination).

🇫🇷 French passé simple vs. imparfait

• Passé simple: requires bounded situations (events or bounded states).
• Imparfait: requires unbounded situations (ongoing states or activities).
• Coercion example: a stative predicate in the passé simple gets an inchoative (beginning of state) or bounded-duration reading.
• Example: "Anne fut triste" → "Anne became sad" or "Anne was sad for a while."

🔑 Key distinctions

🔑 Perfect vs. perfective

• Perfective aspect: TSit ⊆ TT (situation contained within topic time).
• Perfect: relates a past situation to a later reference time (e.g., "the ship has sailed" = past event with present relevance).
• Don't confuse: "the ship sailed" (perfective) vs. "the ship has sailed" (perfect).

🔑 Minor aspect categories

• Inceptive: beginning of a situation falls within topic time ("begin to X").
• Terminative/completive: end of a situation falls within topic time.
• Continuative: "continue to X" or "keep on X-ing."
• Iterative/repetitive: events occurring repeatedly ("over and over").
• Distributive: action done by/to members of a group, one after another.

🧭 Overview

🧠 One-sentence thesis

Relative tense marks the temporal location of an event not against the time of speaking but against a contextually determined perspective time, allowing languages to express relationships like "past in the past" or "future in the past."

📌 Key points (3–5)

• What relative tense measures: the temporal relation between Topic Time (TT) and a Perspective Time (PT), rather than between TT and the Time of Utterance (TU).
• How it differs from absolute tense: absolute tense anchors to the time of speaking; relative tense anchors to some other reference point (often the time of the main clause).
• Where it appears: most commonly in subordinate clauses (e.g., Imbabura Quechua subordinate verbs, English/Latin participles), but also in indirect speech complements and occasionally in main clauses.
• Common confusion: relative tense can produce forms that look like absolute tense when the perspective time equals the time of speaking (e.g., English be going to in present contexts).
• Complex tense: some languages grammatically specify both the location of PT (relative to TU) and TT (relative to PT), creating "absolute-relative" or complex tense forms like the English Pluperfect.

🔄 Core mechanism of relative tense

🔄 What relative tense indicates

Relative tense: indicates the temporal relation between Topic Time (TT) and a Perspective Time (PT), where PT is determined by context rather than being fixed to the time of speaking.

• In absolute tense, TT is located relative to TU (the utterance time).
• In relative tense, TT is located relative to PT, which may be in the past, present, or future relative to TU.
• The perspective time is often set by the main clause or by discourse context.

Example: In Imbabura Quechua, a subordinate verb marked for relative past refers to a situation that existed before the situation named by the main verb, regardless of when the main verb situation occurred relative to now.

🔄 Terminology for relative tenses

The excerpt uses three standard labels:

Relative tense type	Alternative name	Meaning
Relative past	Anterior	Event before the perspective time
Relative present	Simultaneous	Event at the same time as the perspective time
Relative future	Posterior	Event after the perspective time

Don't confuse: "Anterior" does not mean "ancient" or "very old"; it simply means "earlier than the reference point."

🌍 Relative tense in subordinate clauses

🌍 Imbabura Quechua subordinate verbs

• Main clause verbs in Imbabura Quechua have absolute tense reference (anchored to the time of speaking).
• Most subordinate verbs use a distinct set of tense affixes that receive a relative tense interpretation.
• The subordinate verb is marked for relative past, present, or future according to whether it refers to a situation before, during, or after the main verb situation.

Example: When the main verb is past tense, the subordinate verb marked for "future" may still refer to a time before the utterance time—it is future only relative to the main verb's time.

• Sentence (18a): "I believed that Mary was living (at that time) in Agato" → subordinate verb marked relative present (simultaneous with believing).
• Sentence (18b): "I believed that Mary had lived (at some previous time) in Agato" → subordinate verb marked relative past (before the believing).
• Sentence (18c): "I believed that Mary would (some day) live in Agato" → subordinate verb marked relative future (after the believing), even though the believing itself is in the past.

🌍 Participles in English and Latin

Comrie points out that participles in many languages get a relative tense interpretation.

• English present participle (flying): simultaneous meaning.
  • Example (19a): "Last week passengers flying with Qantas were given free tickets" → the flying was simultaneous with last week.
  • Example (19b): "Next week passengers flying with Qantas will be given free tickets" → the flying will be simultaneous with next week.
• Latin future participle (trāiectūrus): posterior meaning.
  • Example (20): "Being about to cross the Rhine, he did not send over the provisions" → the crossing is future relative to the not-sending.
• Latin past participle (commorātus): anterior meaning.
  • Example (21): "Having delayed a little while, he orders them to give the signal" → the delaying is past relative to the ordering.

Don't confuse: The tense of the participle is relative to the main clause time, not to the time of speaking. A present participle can refer to past time (19a) or future time (19b) depending on the main clause.

🗣️ Relative tense in indirect speech

🗣️ Direct vs. indirect speech

• Direct speech: purports to be an exact quotation; deictics (I, you, here, tomorrow) are anchored to the original speaker and the original speech event.
• Indirect speech: does not quote exactly; deictics shift to the perspective of the current speaker and the current speech event.

Example (26):

• Direct: "Yesterday Arthur told me, 'I will meet you here again tomorrow.'"
• Indirect: "Yesterday Arthur told me that he would meet me there again today."

Notice the shifts: I → he; you → me; here → there; tomorrow → today; will meet → would meet.

🗣️ Russian: true relative tense in indirect speech

In Russian, the tense of the verb in indirect speech is identical to the tense used by the original speaker.

• All other deictic elements (pronouns, place/time adverbs) shift to the current speaker's perspective, just as in English.
• The verb tense does not shift; it remains anchored to the time of the original speech event.

Example (27b): "John said that he will leave (lit.) on the following day" → the verb is still future tense (as in the original utterance), even though the reporting verb is past.

This is relative tense: the reference point is the time of the reported speech event (the perspective time), not the current time of speaking.

🗣️ English: complex "sequence of tenses"

English verbs in indirect speech behave differently from Russian.

• When the matrix (main clause) verb is future, the complement verb tense matches the original speaker's tense (like Russian).
  • Example (28b): "If I ask him tomorrow, he will say that he is studying" (present progressive, as in the original).
• When the matrix verb is past, the complement verb is often "back-shifted" to a corresponding past form.
  • Example (28a): "Yesterday he said that he was studying" (past progressive, even though the original used present progressive).

Don't confuse: This is not simply a shift in deictic reference point. The rules are more complex and partly grammatical (not fully predictable from semantics).

🗣️ Back-shifting patterns in English

The excerpt illustrates several patterns:

Matrix verb tense	Original tense	Complement tense	Example
Future	Present progressive	Present progressive	(28b) is studying
Past	Present progressive	Past progressive	(28a) was studying
Future	Present perfect	Present perfect or Future perfect	(29b) has/will have eaten
Past	Present perfect	Past perfect	(29a) had eaten
Future	Simple future	Simple future	(30b) will get
Past	Simple future	Conditional (would)	(31b) would get
Future	Simple past	Simple past	(32b) got
Past	Simple past	Simple past or Past perfect	(33b) got/had gotten

Key observation: When the matrix verb is past and the complement contains an auxiliary, the auxiliary is normally back-shifted to the corresponding past form (examples 29a, 31b).

🗣️ Optional back-shifting

Back-shifting is sometimes optional, especially when:

• The complement describes a situation still true at the time of speaking (example 34: "the mayor revealed that he is/was terminally ill").
• The complement describes a generic or timeless truth (example 34c: "the Babylonians did not know that the earth circles/circled the sun").

However, even in these contexts, back-shifting is sometimes obligatory (example 35: "I knew you liked/*like her").

Don't confuse: The "sequence of tenses" in English is not the same as relative tense in Russian. English rules are partly grammatical and cannot be fully explained by the semantic content of the tense forms alone.

🔗 Complex (absolute-relative) tense

🔗 What complex tense marks

Complex tense (also called "absolute-relative" tense): grammatically specifies both the location of Perspective Time (PT) relative to the Time of Utterance (TU) and the location of Topic Time (TT) relative to PT.

• This contrasts with simple relative tense, where PT is determined by context, not by grammar.
• English has several complex tense constructions: Pluperfect (had eaten), Future Perfect (will have eaten), and "future in the past" (would V).

🔗 English Pluperfect: "past in the past"

The Pluperfect (had eaten) can express "past in the past": an event in the past relative to a perspective time that is itself in the past.

Example (23a): "I reached the base camp Tuesday afternoon; Sam had arrived the previous evening."

• PT = Tuesday afternoon (in the past relative to now).
• TT = Monday evening (in the past relative to PT).
• Diagram: [TT: Mon. eve.] PT TU → "past in the past."

Example (23b): "Einstein was awarded the Nobel prize in 1922, for a paper that he had published in 1905."

• PT = 1922 (past relative to now).
• TT = 1905 (past relative to 1922).

🔗 English Future Perfect: "past in the future"

The Future Perfect (will have eaten) can express "past in the future": an event in the past relative to a perspective time that is in the future.

Example (24a): "I expect to reach the base camp on Tuesday afternoon; Sam will have arrived the previous evening."

• PT = Tuesday afternoon (in the future relative to now).
• TT = Monday evening (in the past relative to PT).
• Diagram: TU [TT: Mon. eve.] PT → "past in the future."

🔗 "Future in the past"

The construction would V can express "future in the past": an event in the future relative to a perspective time that is in the past.

Example (24b): "Einstein published four ground-breaking papers in 1905, including the one for which he would win the Nobel prize in 1922."

• PT = 1905 (past relative to now).
• TT = 1922 (future relative to 1905).
• Diagram: PT [TT: 1922] TU → "future in the past."

Don't confuse: Even though 1922 is in the past relative to now, the sentence uses would win because 1922 is in the future relative to the perspective time (1905).

🔗 Morphological complexity

Comrie notes that cross-linguistically, most forms expressing complex tense are morphologically complex (combinations of two or more morphemes), like English Pluperfect and Future Perfect.

• Occasional exceptions exist, e.g., the mono-morphemic pluperfect -ara in literary Portuguese.

🔗 Ambiguity of Pluperfect and Future Perfect

The excerpt notes (in passing) that the Pluperfect and Future Perfect forms are ambiguous: they can mark either complex tense (as discussed here) or perfect aspect (discussed in Chapter 22).

• The choice of temporal adverbs can disambiguate: adverbs specifying the time of the situation itself → complex tense; adverbs specifying a topic time before which the event occurred → perfect aspect.

⏱️ Temporal Remoteness markers

⏱️ What Temporal Remoteness systems mark

Some languages have verbal affixes that distinguish more than one degree of past and/or future time reference, e.g., "immediate past" vs. "near past" vs. "distant past."

• These systems are sometimes called "metrical tense" or "graded tense."
• They are especially well-known among Bantu languages.

Example: ChiBemba (Bantu) has a symmetric set of four past and four future markers:

• Remote past: "they worked (before yesterday)"
• Removed past: "they worked (yesterday)"
• Near past: "they worked (today)"
• Immediate past: "they worked (within the last 3 hours)"
• Immediate future: "they'll work (within the next 3 hours)"
• Near future: "they'll work (later today)"
• Removed future: "they'll work (tomorrow)"
• Remote future: "they'll work (after tomorrow)"

⏱️ Units of measurement

Temporal Remoteness systems frequently make distinctions like "today" vs. "yesterday" vs. "before yesterday."

• Hodiernal: the "today" category (from Latin hodie 'today').
• Hesternal: the "yesterday past" category (from Latin heri 'yesterday').

In some languages, remoteness is measured in other units (months, years), and the unit can shift depending on context.

Some languages make other distinctions, e.g., remembered past vs. non-remembered past.

⏱️ Symmetry and asymmetry

• Symmetrical systems (like ChiBemba and Grebo): equal numbers of past and future categories.
• Asymmetrical systems (more common): more distinctions in the past than in the future.
  • Nurse (2008): in a sample of 210 Bantu languages, about half have only a single future category, but 80% have more than one degree of past marking.

⏱️ Secondary meanings

When languages have multiple contrastive future markers, one or more often take on secondary meanings relating to degree of certainty (remote future marking less certainty).

• Similar secondary meanings are associated with past markers in some languages (remoteness indicating reduced certainty).

⏱️ Debate: tense or not?

Recent research argues that in at least some languages, Temporal Remoteness markers indicate the location of Situation Time (TSit) rather than Topic Time (TT) relative to the time of speaking.

• If true, these markers would not fit Klein's definition of tense (which requires a relation between TT and TU).
• The label "Temporal Remoteness" is general enough to include both types.

🎯 Conclusion

🎯 Klein's framework recap

• Absolute tense: temporal relation between TT and TU.
• Aspect: temporal relation between TT and TSit.
• Relative tense: temporal relation between TT and PT (perspective time, determined by context).

🎯 Factors affecting tense-aspect usage

The observed uses of tense-aspect markers depend not only on their semantic content but also on:

• Aspectual sensitivity (restriction to specific situation types).
• Potential for different semantic functions in different situation types.
• Coercion effects.
• Potential for different uses in main vs. subordinate clauses.
• Presuppositions triggered by the marker.
• Implicatures adding extra meaning.
• Potential polysemy and/or idiomatic senses.

Example: The simple present tense in English illustrates several of these factors (discussed elsewhere in the source material).

🧭 Overview

🧠 One-sentence thesis

The perfect aspect exhibits multiple distinct readings (existential, universal, resultative, "hot news") whose relationship—whether true semantic ambiguity or context-dependent interpretations of a single meaning—remains debated, with cross-linguistic evidence showing that different languages carve up this semantic space in different ways.

📌 Key points (3–5)

• Core debate: whether the various readings of the perfect (existential, universal, resultative, recent past) represent true polysemy (multiple meanings) or a single general meaning that yields different interpretations in different contexts.
• Evidence for polysemy: different truth conditions, different translation equivalents across languages, different aspectual requirements (e.g., universal reading requires atelic situations, resultative requires telic events).
• Cross-linguistic variation: some languages (e.g., German, modern Greek) use present tense for the universal reading; others (e.g., Hungarian, Najdi Arabic, Mandarin) have distinct forms for only the existential/experiential perfect.
• Common confusion: the same aspectual form can produce different interpretations depending on situation type (Aktionsart), so correlation with situation type alone doesn't prove polysemy—single meanings can interact with event structure to yield varied readings.
• Key constraint patterns: languages impose different requirements (e.g., Baraïn perfect requires result state still hold; Mandarin -guo requires result state no longer hold).

📊 Arguments for polysemy of the perfect

📊 Truth-conditional differences

The various readings do not all have the same truth conditions.

• Example from the excerpt: "I have been in Hyderabad since 1977" is ambiguous:
  • Universal reading: the speaker was in Hyderabad at all times from 1977 to present (false if they left even briefly)
  • Existential reading: the speaker was in Hyderabad at at least one time between 1977 and present
• These can have opposite truth values in the same context, suggesting genuine semantic ambiguity rather than vagueness.
• Why it matters: if a single sentence can be true under one reading and false under another, this is strong evidence for distinct meanings.

🌍 Cross-linguistic translation patterns

Different languages use different forms to express the various perfect readings:

Reading	Some languages' strategy	Example languages
Universal	Use simple present tense instead of perfect	German, modern Greek
Existential/experiential	Have a distinct dedicated form	Hungarian, Najdi Arabic, Mandarin

• This suggests the readings are conceptually distinct enough that languages can grammaticalize them separately.
• Don't confuse: this is about which form languages use, not whether the meanings exist—all languages can express these concepts somehow.

🎭 Aspectual requirements differ by reading

Universal reading (only with atelic situations):

• States: "I have loved Charlie Chaplin ever since I saw Modern Times"
• Activities: "Fred has carried the food pack for the past 3 hours"
• Habituals: "I have attended All Saints Cathedral since 1983"
• Imperfective accomplishments: "I've been writing a history of Nepal for the past six years"

Resultative reading (only with telic events):

• Achievements or accomplishments that produce a result state
• Example: "He has left Andi (and has not returned)"

Blocked combinations:

• "#Fred has arrived at the summit for the past 3 hours" (telic + universal = ungrammatical)
• "#I have written a history of Nepal for the past six years" (telic perfective + universal = ungrammatical)

Important caveat: This correlation doesn't by itself prove polysemy, since we've seen other cases where a single tense/aspect marker produces different interpretations with different situation types.

🎪 Pragmatic play on meanings

The Groucho Marx joke demonstrates antagonism between expected and unexpected readings:

"I've had a perfectly wonderful evening, but this wasn't it."

• The humor relies on the listener first interpreting "have had" as "hot news" perfect (about the current evening)
• Then the speaker reveals they meant the existential perfect (at some point in their life they had a wonderful evening, but not tonight)
• This kind of wordplay typically requires genuinely distinct meanings, not just contextual variation.

🗂️ Case study: Baraïn perfect (Chadic)

🗂️ Four readings, one gap

Baraïn perfect expresses four of the five common perfect uses:

Reading	Baraïn example	Key feature
Resultative	"He has left Andi"	Result state persists
Universal	"He has lived in Mongo for ten years"	Situation continues
Recent past	"He has just left this moment"	Temporal proximity
Present state	"Rama has stayed in Melfi"	Current location

Notable absence: The existential/experiential perfect is expressed with the perfective marker instead, not the perfect.

Example: "How many times have you been to N'Djamena?" uses perfective, not perfect.

⏱️ The result-state requirement

The perfect in Baraïn, in all four of its uses, entails that the situation is still true or the result state still holds at the time of speaking.

Semelfactives blocked: Events without result states cannot use the perfect:

• "#He has coughed once" (with perfect) is ungrammatical
• "He coughed once" (with perfective) is fine

Contrast with perfective:

• Perfect: "He left but he has returned" → he is still here now
• Perfective: "He left and he returned" → he is not here now (implicature that result state ended)

🔄 Permanent changes require perfect

Events that produce permanent result states normally must use perfect:

• "My arm was removed" (perfect) → normal statement
• "My arm was removed once" (perfective) → implies extraordinary reversal (someone reattached it)
• "He died" (perfect) → normal statement
• "?He was dead" (perfective) → implies miraculous resurrection

Key insight: The perfective implicates (but doesn't entail) that the result state no longer holds—this is a conversational inference from choosing not to use the perfect. In narrative contexts, this implicature disappears.

Proof of entailment vs. implicature:

• Perfective: "He died, but he has been resurrected" → acceptable (implicature cancelled)
• Perfect: "#He has died, but he has been resurrected" → ungrammatical (entailment cannot be cancelled)

🀄 Case study: Mandarin experiential -guo

🀄 Polar opposite of Baraïn

While the perfect in Baraïn can express all of the standard perfect readings except the experiential, -guo expresses only the experiential perfect. While the perfect in Baraïn requires that the result state of the event still holds true at the time of speaking, -guo requires that the result state no longer holds true at the time of speaking.

Terminology: Various authors call -guo "indefinite past aspect" or "experiential aspect"—it indicates the situation has been experienced at least once at some indefinite time in the past.

🔀 Distinguishing aspectual -guo from compound verb -guò

Don't confuse these two homophonous forms:

Feature	Aspectual suffix -guo	Compound verb -guò
Tone	Always toneless (neutral tone)	Optional 4th tone
Meaning	Experiential aspect	'finish, complete'
Can be followed by -le?	No	Yes
Example context	General experience	Completion of specific recent event

Example of compound verb: "I have already eaten" (meaning: finished the recent meal) uses -guò with tone, not aspectual -guo.

⛔ The discontinuity requirement

There must be a "discontinuity" between Situation Time and Topic Time: TSit ∩ TT = ∅

With result states: The result state must be over before Topic Time.

Examples showing this is an entailment (not just implicature):

• "I have broken my leg" (-guo) → it has healed since (#and is still broken now)
• "He has been to China last year" (-guo) → #and is still there now (ungrammatical)
• "He once loved Miss Huang" (-guo) → #and still loves her now (ungrammatical)

Contrast with perfective -le:

• Perfective allows: "He went to China last year (and is still there now)"
• Perfective allows: "He has fallen in love with Miss Huang (and still loves her now)"

🎯 Definiteness matters

The discontinuity requirement is partially dependent on definiteness of the affected argument:

Definite patient: discontinuity required

• "Lisi has broken this laptop before" → strongly implies the laptop has been fixed

Indefinite patient: no discontinuity requirement

• "Lisi has broken a laptop before" → no commitment about whether it's been fixed

This same pattern appears with "repeatability" effects (discussed below).

🔁 Repeatability vs. discontinuity

Claim in some literature: The situation marked by -guo must be repeatable.

Counter-evidence: The operative factor is discontinuity, not repeatability:

• "You also have been young before" (-guo) → acceptable (being young is a state that can end while person is alive)
• "You have also been old before" (-guo*) → ungrammatical (being old cannot end while person is alive—violates discontinuity)

Definiteness interaction:

• "Columbus has discovered America before" (-guo*) → ungrammatical (definite, permanent result)
• "Columbus has discovered a small island before" (-guo) → acceptable (indefinite)

The fact that -guo can be used for actions of dead people (when patient is indefinite) further shows there's no true repeatability requirement—such examples are unnatural in English experiential perfect.

📐 Interaction with situation types

With states: -guo indicates the state no longer exists

• "Miss Zhang has been fat" → she is not fat now
• "Beef in America has also been expensive" → but not now
• "He has lived in China for three years before" → but does not live there now
• Permanent states blocked: "*Local farmers knew that chrome dregs were poisonous" (with -guo) is ungrammatical

With atelic events (activities, non-culminating accomplishments): -guo indicates termination, similar to perfective

• "Lisi has played tennis before"
• "I wrote Wang's letter but didn't finish it" (acceptable with -guo)
• "#I wrote Wang's letter and am still writing it" (ungrammatical with -guo)

With telic predicates (achievements, accomplishments):

When patient is definite and result is permanent:

• "*He has killed that person" (with result compound verb shā-sǐ-guo) → ungrammatical
• "He tried to kill that person (without success)" (with simple verb shā-guo) → acceptable; -guo signals non-achievement of result

When patient is indefinite:

• "He has killed three people" (with result compound verb) → acceptable
• "Someone has drowned in this river before" → acceptable

Special case—partial affectedness:

• "The dog just ate your apple" (perfective) → whole apple consumed
• "The dog just took a bite of your apple" (-guo) → partial consumption; culmination not achieved

🧪 Result compound verbs (RCV)

When a verb includes a result compound (e.g., shā-sǐ 'kill-die'), culmination is entailed. With -guo:

• Definite patient + RCV → ungrammatical (permanent result violates discontinuity)
• Indefinite patient + RCV → acceptable (discontinuity requirement relaxed)
• Simple verb (no RCV) + -guo → explicitly signals result state not achieved

Example: "I almost died quite a few times" uses sǐ-guo (die-EXPER) in a figurative sense where the result state (being dead) was not achieved.

🔍 Conclusion and theoretical implications

🔍 Klein's unifying analysis

What all of these various uses have in common is the fact that (all or part of) the Situation Time precedes Topic Time.

• This is Klein (1992)'s proposed defining feature of perfect aspect.
• The various "readings" might then be contextual interpretations of this single temporal relationship, influenced by:
  • Situation type (Aktionsart)
  • Definiteness of arguments
  • Pragmatic context
  • Language-specific additional constraints

🔍 The polysemy question remains open

The excerpt presents evidence on both sides but doesn't definitively resolve whether the perfect is:

1. Truly polysemous: multiple related but distinct meanings
2. Semantically general: one abstract meaning that interacts with context to produce varied interpretations

Evidence for polysemy: truth-conditional differences, cross-linguistic grammaticalization patterns, aspectual restrictions, pragmatic wordplay

Evidence for generality: the correlation with situation type could reflect compositional semantics rather than lexical ambiguity; we've seen other cases where single markers yield different interpretations with different event structures

Cross-linguistic lesson: Languages make different choices about how to carve up this semantic space—some (like Baraïn) exclude experiential, some (like Mandarin -guo) express only experiential, some (like English) allow all readings with a single form.

🧭 Overview

🧠 One-sentence thesis

This excerpt is a bibliography section listing academic sources on semantics, pragmatics, linguistic theory, and related topics, organized alphabetically by author surname.

📌 Key points (3–5)

• What this section contains: A reference list of academic works (journal articles, books, dissertations, conference proceedings) cited elsewhere in the text.
• Scope of topics: Covers evidentiality, modality, tense and aspect, conditionals, presupposition, implicature, speech acts, cross-linguistic semantics, and formal semantic theory.
• Format: Standard academic citation format with author names, publication years, titles, venues, and DOIs/URLs where applicable.
• Common confusion: This is not substantive content—it is a support section for locating cited works; no theories or arguments are presented here.

📚 Nature of the content

📚 What a reference section is

A bibliography or reference list: an alphabetical inventory of sources cited in the body of a work, providing publication details for retrieval.

• The excerpt does not explain concepts, present arguments, or offer data.
• It serves as a lookup tool: each entry points to a published work that the main text has cited.
• Example: "Faller, Martina. 2002. Semantics and pragmatics of evidentials in Cuzco Quechua" tells the reader where to find Faller's dissertation on evidentiality.

🔍 How to use this section

• When the main text cites "Faller 2002," the reader consults this list to find the full publication details.
• URLs and DOIs enable direct access to online versions of the works.
• Don't confuse: The reference list itself does not teach the theories—it only identifies where those theories are published.

🗂️ Topics represented in the citations

🗂️ Major thematic clusters

The cited works span several core areas of linguistic semantics and pragmatics:

Topic area	Example citations
Evidentiality	Faller (2002, 2003, 2006), Aikhenvald (2020, 2021, 2328, 2329)
Modality	Kratzer (1981, 1991, 1995, 1999), von Fintel (2004, 2006, 2011, 2012), Matthewson (2010, 2016)
Tense and aspect	Klein (1992, 1994, 2009), Reichenbach (1947), Partee (1973), Nurse (2008)
Conditionals	Lewis (1973b), Stalnaker (1968), Iatridou (1991), von Fintel (2011, 2012)
Presupposition and implicature	Grice (1975, 1978, 1981), Horn (1972, 1989, 1992, 1997, 2004), Levinson (1983, 1995, 2000), Potts (2005, 2007a, 2007b, 2007c, 2012, 2015)
Speech acts	Searle (1969, 1975), Austin (1969, 1982, 1193, 1349)
Cross-linguistic semantics	Matthewson et al. (2007), von Fintel & Matthewson (2008), various language-specific grammars
Formal semantics	Heim & Kratzer (1998), Gamut (1991a, 1991b), Hodges (1997, 2013)

🌍 Cross-linguistic and typological works

• Many entries describe specific languages: Quechua (Faller), Mandarin Chinese (Li & Thompson, Xiao & McEnery), Korean (Sohn, Martin), Tok Pisin (Verhaar, Smith, Wohlgemuth), Tagalog (Schachter & Otanes), and others.
• Typological surveys: Greenberg (1963), Haspelmath (1995), van der Auwera & Ammann (2013).
• These works provide empirical grounding for semantic theories by showing how different languages encode meaning.

🧩 Theoretical frameworks

• Formal semantics and logic: Frege (1892, 1918–1919), Montague-style semantics (Gamut, Heim & Kratzer), model theory (Hodges).
• Pragmatics: Gricean implicature (Grice 1975, 1978, 1981), relevance theory (Sperber & Wilson 1986), speech act theory (Searle, Austin).
• Lexical semantics: Fillmore (1970, 1977, 2000), Levin (1993, 2015), Pustejovsky (1995).
• Don't confuse: The reference list does not explain these frameworks—it only lists where they are published.

🔗 How this section supports the main text

🔗 Citation function

• Every claim, definition, or example in the main text that draws on prior research should be traceable to an entry here.
• Example: If the main text discusses "Kratzer's modal base," the reader can find Kratzer (1981, 1991) in this list to read the original proposal.

📖 Further reading

• The reference list implicitly serves as a reading guide: a student interested in evidentiality can follow up on Faller, Aikhenvald, and Murray; one interested in aspect can consult Klein, Smith, Comrie, and others.
• URLs and open-access links (e.g., semanticsarchive.net) make many works directly accessible.

⚠️ Limitations

• This excerpt contains no explanatory content: no definitions, no arguments, no data.
• It is purely a bibliographic tool.
• To learn the actual theories, one must consult the cited works themselves or the main text that references them.

🧭 Overview

🧠 One-sentence thesis

This excerpt is a bibliographic reference section (name index and language index) from a linguistics textbook, containing no substantive theoretical or analytical content to review.

📌 Key points (3–5)

• The excerpt consists entirely of name index entries listing authors and page numbers where they are cited.
• A language index lists languages discussed in the book with corresponding page references.
• No definitions, explanations, arguments, or theoretical content are present in this excerpt.
• The material is purely navigational apparatus for the book, not substantive content.

📚 What this excerpt contains

📚 Name index structure

The excerpt provides an alphabetical list of scholars cited in the book, with page numbers indicating where their work is referenced.

• Covers authors from Abbott to Zwicky (A–Z).
• Includes linguists, philosophers, and semanticists working on topics like aspect, modality, tense, speech acts, and cross-linguistic semantics.
• Example entries: "Comrie, Bernard" with extensive page references; "Grice, H. Paul" with references to pages discussing his work.

Note: This is reference apparatus only; it does not explain any author's theories or contributions.

🌍 Language index structure

The excerpt lists languages mentioned in the book, with page numbers showing where each language is discussed.

• Covers languages from Arabic to Swahili.
• Includes both widely-studied languages (English, French, German, Mandarin) and less commonly described languages (Baraïn, ChiBemba, Jarawara, St'át'imcets).
• Some entries include cross-references, e.g., "Chinese, 5, 96, 98... see also Mandarin."

Note: This is also purely navigational; no linguistic facts about these languages are provided in this excerpt.

⚠️ Limitations of this excerpt

⚠️ No substantive content

• The excerpt does not define concepts, present arguments, or explain mechanisms.
• It is metadata: an index to help readers locate discussions elsewhere in the book.
• Any attempt to extract theoretical content would require inventing information not present in the excerpt.

⚠️ What cannot be reviewed

Because the excerpt contains only names and page numbers, the following cannot be provided:

• Definitions or explanations of linguistic concepts.
• Comparisons of theoretical approaches or paradigms.
• Examples illustrating mechanisms or phenomena.
• Common confusions or distinctions between concepts.

Conclusion: This excerpt serves as a finding aid for the book's main content, which is located in the chapters referenced by these page numbers.