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
Intensional Meaning (Connotation)
Bundle of attributes/qualities a term implies.
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
Objective Approach
Term connotes whatever attributes must be had to fall under it (mind-independent).
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
Empty-extension series — attributes increase but extension stays empty.
E.g., unicorn → blue-eyed unicorn → blue-eyed, green-horned, 400-lb unicorn.
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:
Identify each key term.
Ask: What attributes (conventional connotation) does the author assume?
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.