Deduction vs. Induction – Critical Reasoning 1.3

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• All lecture materials are produced exclusively for the Yonsei University course.
• Redistribution or use for non-enrolled individuals is prohibited; legal accountability applies.

Recap Example: Turkey Vultures

• Name origin: red, featherless heads resemble wild turkeys.
• Serves as a springboard to discuss how we decide whether a statement is true.

Competing Theories of Truth

• Truth-Correspondence (adopted for this class)
  • A statement is true iff it accurately reflects the world.
  • Ex: “Turkey vultures are named after the resemblance” is true if that historical fact holds in reality.
• Truth-Coherence
  • A statement is true when it logically fits (is entailed by / entails) other propositions in a coherent web.
  • If a claim clashes with the web, it is taken as false.
• Keep both sharply separate from
  • Bullshit (speaker tries to make truth irrelevant).
  • Bald-faced lies (speaker is indifferent to truth while assuming the audience also knows it is false).
• Guideline: regardless of your preferred theory, do not fall into truth-indifferent thinking.

Today’s Learning Goals

• Distinguish deductive vs inductive inferences.
• Recognize typical forms of each.

Two Diagnostic Cases

1. Fish Example (Induction)
   • \text{P1: sharks \& goldfish are fish}
   • \text{P2: sharks are carnivorous}
   • \therefore \text{goldfish are probably carnivorous}
   • Truth of premises makes the conclusion likely (>0 % but <100 %). Alternative outcomes remain possible.
2. Mongoose Example (Deduction)
   • \text{P1: meerkat ∈ mongoose family}
   • \text{P2: all mongoose → omnivore}
   • \therefore \text{meerkat is (necessarily) omnivore}
   • If premises hold, it is impossible for the conclusion to be false—100 % support.

Core Distinction

• Induction: premises confer probabilistic support; conclusion exceeds the premises’ information.
• Deduction: premises confer necessary support; conclusion is already “contained” in them.

Inductive Arguments in Detail

• Claim: “If premises true, conclusion probably true.”
• Inferential strength: “highly improbable the conclusion is false.”
• Many arguments claim probability but fail factually—still labeled inductive.

Deductive Arguments in Detail

• Claim: “If premises true, conclusion must be true.”
• Inferential strength: “logically impossible the conclusion is false.”
• Even surreal premises can create valid deduction:
  \text{P1: all fairies can fly}
  \text{P2: Ferdinand is a fairy}
  \therefore \text{Ferdinand can fly}
  (Soundness awaits later units on truth of premises.)

Practical Tests for Type Identification

1 — Indicator Words

• Deductive cues: “necessarily, certainly, absolutely, definitely.”
• Inductive cues: “probably, likely, plausibly, reasonable to conclude.”
• Caveat: Indicators mislead when authors misuse them (“absolutely he cannot finish the marathon…” is still only probabilistic; no contradiction involved).

2 — Inferential Strength (Most Reliable)

• Ask: If premises are true, must the conclusion be true, or only likely?
  • “Must” → Deduction.
  • “Likely” → Induction.

3 — Argument Form

• Certain structural templates strongly suggest deduction or induction (see below).

Canonical Deductive Forms

• Argument from Mathematics
  • E.g. “2 apples + 3 oranges ⇒ at least 5 pieces of fruit.”
• Argument from Definition
  • “Speech was ‘concise’; therefore it was brief yet comprehensive.”
• Categorical Syllogism (uses “All/No/Some”)
  • “All humans are mortal. Prof Gregg is a human. So Prof Gregg is mortal.”
• Hypothetical Syllogism (if … then …)
  • \text{If A→B, and A, then B} (modus ponens)
• Disjunctive Syllogism (either … or …)
  • “Either Larry is in Sincheon or Songdo. Not in Sincheon. ⇒ in Songdo.”

Canonical Inductive Forms

• Prediction
  • Past market/meteorological patterns → claims about future behaviour.
• Argument from Analogy
  • Similarity between two entities justifies transferring a property.
• Generalization
  • Sample exhibits trait X ⇒ entire population probably has X.
• Argument from Authority
  • Expert testimony/witness report supports claim.
• Argument Based on Signs
  • Physical/linguistic sign information → conclusion about surrounding reality.
• Causal Inference
  • From known cause → likely effect, or effect → likely cause.

Science: Both Styles Employed

• Discovery of a law = often inductive generalization.
  (Drop objects, note t \propto \sqrt{d} ⇒ propose general law.)
• Application of a known law = deductive.
  (Given Boyle’s law P \propto 1/V, halve V ⇒ deduce P doubles.)

Popper’s Falsificationism (Normative Scientific Logic)

• Good science should attempt to falsify hypotheses via rigorous tests (modus tollens):
  \text{P1: If H then R}
  \text{P2: Not R}
  \therefore \text{Not H}
• Rejects “confirmation via affirming the consequent,” which is a deductive fallacy:
  \text{If H then R; R; therefore H} (invalid).
• Criterion of demarcation: falsifiability.
  • Theories shielded by ad hoc modifications (e.g.
    some versions of Marxism or psychoanalysis) become unscientific.
• Non-scientific ≠ worthless; myths can inspire understanding, but they lack status as science.

Misleading Heuristic: “Specific → General”

• Not a safe classifier. Examples:
  1. Inductive, general→specific: “All found emeralds green ⇒ next emerald green.”
  2. Deductive, specific→general: “3, 5, 7 are prime ⇒ all odd numbers 2-8 are prime.”
  3. Deductive, specific→specific: “Flo is fish; Flo has fins ⇒ Flo’s fins are fish fins.”
• Deduction & induction can operate along any specificity direction.

Wrap-Up Exercises

• Pairwork: identify argument types & justify classification.
• Emphasis: articulate why inference is necessary or probable.

Quick Study Checklist

• Memorize typical indicator words but treat them cautiously.
• Practice spotting inferential strength and argument form.
• Recall that validity ≠ truth; focus now on the “must vs probably” distinction.
• In science‐related contexts, decide: Are we applying an established law (deductive) or searching for one (inductive)?
• Revisit Popper: understand why falsification employs a deductive pattern.