Critical Reasoning 2.2 – Intension and Extension of Terms

Context & Learning Goals

• Chapter: 2.2 — “The Intension and Extension of Terms.”

• Builds on:

  • Ch. 1 (deductive vs. inductive reasoning).

  • Sect. 2.1 (vagueness, ambiguity, and the need for linguistic clarity).

• Central task of logic: evaluate argument strength/weakness; this requires clarity about what our words refer to.

Quick Rewind to Ch. 1 — Deduction vs. Induction

• Deductive arguments (if valid + sound) yield conclusive support; conclusion cannot be false if premises are true.

• Inductive arguments (if strong + cogent) yield probabilistic/defeasible support.

• Question: “Are inductive arguments inferior?” → No.

  • Many inductive conclusions go beyond ‘reasonable doubt’ (e.g., the sun will rise tomorrow).

  • Sometimes deductive & inductive parity:

  • Deductive form: All fish have gills → If there is a fish in Gwangyo Lake, it will have gills.

  • Inductive form: All observed fish have gills → If there is a fish in Gwangyo Lake, it will have gills.

  • Determining truth of deductive premise (all existing fish) can depend on an inductive statistical survey of observed fish.

  • Therefore, extra guarantee of validity is offset by difficulty verifying universal premises; practical warrant may be equal.

Probability Digression

• Class deliberately keeps probability treatment minimal; deeper statistical material (e.g., Bayes) offered as optional final-unit poll.

• Example formulas briefly referenced:

  • Bayes’ theorem (generic): Pr(A|B)=\frac{Pr(B|A)\,Pr(A)}{Pr(B)}.

  • Joint probability rule: Pr(h1 \;\&\; h2)=Pr(h1)\times Pr\big(h2|h_1\big).

Source of Misunderstandings: Reference Misalignment

• From 2.1: ambiguity, vagueness, emotive rhetoric can hide whether two speakers talk about the same object/property.

• Remedy → Define our terms precisely.

Putnam’s “Twin-Earth” Thought Experiment

• Setup: Earth-Water (H₂O) vs. Twin-Earth-Water (XYZ, indistinguishable to senses).

• Question: Does the word “water” mean the same on both planets?

  • Hilary Putnam: No → “Meaning just ain’t in the head.” External facts + history partly constitute meaning (semantic externalism).

  • John Searle critique: Mental states can’t be identical if referents differ at molecular level.

• Lesson: To be sure we refer to the same thing, we must explicitly specify meaning.

Basic Linguistic Unit for Logic: The Term

• Term = any word/phrase that can serve as the subject of a statement.

  • Types: proper names, common names, descriptive phrases.

• Non-terms (cannot function as grammatical subjects): verbs, non-substantive adjectives (really, super…), adverbs, prepositions, conjunctions, nonsense strings ("cabbages into again the forest").

Use–Mention Distinction

• Use: word functions normally in sentence. E.g., I will follow you wherever you go.

• Mention: word is talked about. E.g., "Wherever" is an eight-letter word.

  • In mention, the subject is the quotation, not the word’s semantic content.

Two Kinds of Cognitive Meaning

1. Intensional Meaning (Connotation)

   • Bundle of attributes/qualities a term implies.

2. Extensional Meaning (Denotation)

   • Actual members of the class picked out by those attributes.

• Example — term “cat”:

  • Intension: four-legged, furry, meows, mammal, coughs up hairballs.

  • Extension: every cat (Grumpy Cat, Chu Chu, Ozzy, etc.).

Ethical & Practical Significance of Word Choice

• Words don’t merely label; they guide action & attitudes.

• Tirrell on derogatory terms:

  • Such terms possess negative normative force (weaken the target), positive power (fortify the in-group).

  • Example: “inyenzi” (cockroach) for Tutsi in Rwanda – linguistic groundwork that enabled genocide.

  • Five key features: insider/outsider status functions, essentialism, social embeddedness, action-engendering exit moves, etc.

  • Broader implication: studying linguistic violence helps gauge potential material violence in society.

Competing Accounts of How Terms Connote Attributes

1. Objective Approach

   • Term connotes whatever attributes must be had to fall under it (mind-independent).

2. Subjective Approach (adopted in class; akin to Descriptivism)

   • Connotation = attributes in speakers’ minds associated with the term.

   • Proper-name reference succeeds when descriptive content uniquely singles out individual.

   • SEP quote: speaker must think of N as the (unique) F and x must be the (unique) F.

   • Example: “You are the 41st face of Yonsei” requires sufficient descriptive precision.

Conventional Connotation Caveat

• Personal biases produce idiosyncratic associations (cat lover vs. cat hater).

• Conventional connotation = attributes competent speakers generally infer (four-legged, meows, mammal…).

Denotation Through Time & Empty Extension

• Denotation can vary:

  • “Currently living cats” – constantly changing token membership.

  • “Cat” (without temporal restriction) – relatively stable extension (all past/present/future cats).

• Empty extension: terms whose denoted class has no members (unicorns, leprechauns, dodo birds now, etc.).

• Important: A term with empty extension can still have rich intension (unicorn: horned, equine, mythical…).

Principle: Intension Determines Extension

• Even proper names possess some intension, else reference impossible.

  • Descriptive shorthand view: “Esteban” ≈ “my older brother in Pittsburgh.”

  • Causal-historical view: intension = entire causal chain from original baptism to current speaker’s tokening.

• Therefore, specifying qualities/descriptions (or causal chain) fixes which objects fall under the term.

Reference vs. Meaning Debate

• Is meaning just connotation? Just reference? Depends on theory.

• Descriptivism explains informative identities ("Superman = Clark Kent"). Two senses, same referent, discovered empirically.

Kripke’s Modal Challenge

• Names rigidly designate across possible worlds; descriptions may not.

• Example:

  • True modal claim: David Cameron might not have called for a referendum on Brexit.

  • If name’s meaning ≡ description “the PM who called for Brexit referendum,” substitution yields contradiction in same modal context.

  • Therefore, names ≠ definite descriptions in meaning/reference behavior.

Ordering Terms by Intension & Extension

• Increasing Intension (→ more specific): each successive term adds attributes.

• Decreasing Intension (→ less specific): each successive term removes attributes.

• Increasing Extension: class membership grows.

• Decreasing Extension: class membership shrinks.

• Default correlation:

  • ↑ Intension ⇔ ↓ Extension.

  • ↓ Intension ⇔ ↑ Extension.

Exceptions

1. Empty-extension series — attributes increase but extension stays empty.

   • E.g., unicorn → blue-eyed unicorn → blue-eyed, green-horned, 400-lb unicorn.

2. Same-extension series — extension constant while intension increases.

   • E.g., living human being → living human with genetic code → …with genetic code + brain → …with brain + height < 100 ft (all true of identical group, so extension unchanged).

Exercise Prompt (In-Class)

• Small-group activity:

  • Groups 4 – 6: reorder given sequences by decreasing intension.

  • Groups 7 – 9: reorder by increasing extension.

Key Takeaways & Study Tips

• Always clarify a term’s intension to know what it should denote.

• Watch for empty extensions; arguments about non-existent entities can still be meaningful but demand caution.

• Be alert to language’s normative power; linguistic choices can license or discourage actions.

• Understand contemporary debates:

  • Descriptivism (Frege/Russell) vs. Causal-historical/Kripkean theories.

  • Internalism vs. Externalism (Putnam Twin-Earth example).

• When analyzing arguments:

  1. Identify each key term.

  2. Ask: What attributes (conventional connotation) does the author assume?

  3. Verify whether audience shares that intension; if not, miscommunication or fallacy of equivocation may arise.

• Recognize patterns of intension/extension ordering; useful for classification, taxonomies, and evaluating generalizations.