Critical Reasoning 1.3 – Deduction and Induction

Course Policy & Disclaimer

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  • Violation entails legal responsibility.

The Turkey Vulture Example & Competing Theories of Truth

• Empirical fact presented:
  • The turkey vulture gets its name because its red, feather-less head resembles that of a wild turkey (photo credit: reddit link).
• Key questions posed:
  • Can facts be knowledge-dependent?
  • Can a statement’s truth depend on interpretation?
• Two theories of truth highlighted:
  • Truth-correspondence (adopted for the class)
  • A statement is true if it accurately corresponds to the world.
  • Example: If the naming origin of turkey vultures really involves their head’s resemblance, the statement is true by correspondence.
  • Truth-coherence
  • Truth hinges on consistency/entailment relations among propositions.
  • A proposition is true iff it coheres (is entailed by) a consistent web of propositions.
  • Under coherence, the turkey-vulture fact could be rejected if inconsistent with one’s overall proposition-set.
• Warnings against “bullshit” and “bald-faced lies”
  • These approaches bypass truth entirely, encouraging belief without regard to any theory of truth.
  • Ethical advice: avoid such thinking regardless of your preferred truth theory.

Session Objectives

• Understand key differences between deductive and inductive inferences.
• Identify and comprehend common forms of each inference type.

Comparing Two Argument Cases

• Assumption: premises are true in both cases.
• Case 1 – Inductive (fish):
  • \text{P1) } Both sharks and goldfish are kinds of fish.
  • \text{P2) } Sharks are carnivorous.
  • \text{C) } Therefore, goldfish are probably carnivorous.
  • Only probable support; other conclusions remain possible.
• Case 2 – Deductive (mongoose):
  • \text{P1) } The meerkat is a member of the mongoose family.
  • \text{P2) } All members of the mongoose family are omnivores.
  • \text{C) } Therefore, it necessarily follows that the meerkat is an omnivore.
  • 100 % support; impossible for conclusion to be false if premises are true.

Deduction vs Induction: Definitions & Inferential Strength

• Inductive inference:
  • Conclusion is claimed to probably follow from premises.
  • Inferential claim: “Given true premises, it is highly improbable that the conclusion is false.”
• Deductive inference:
  • Conclusion is claimed to necessarily follow from premises.
  • Inferential claim: “Given true premises, it is logically impossible that the conclusion is false.”
• Note: Arguments merely claim this strength; many fail in practice but still count as arguments.

Determining Argument Type

1. Linguistic Indicators (helpful but not foolproof)

• Deductive cues: necessarily, certainly, absolutely, definitely, must, cannot but…
• Inductive cues: probably, likely, plausibly, reasonably, it follows that …
• Caveat example:
  • “Tom is 99 and in a coma, so absolutely he cannot finish the marathon tomorrow.”
  • Despite ‘absolutely,’ it is still logically possible he finishes; thus argument is only inductive.

2. Strength of Inferential Link

• Core diagnostic: Does the conclusion have to be true (deductive) or just tend to be true (inductive) if premises are true?

3. Argument Forms (useful structural clues)

Deductive Forms

• Argument based on mathematics
  • “2 apples + 3 oranges ⇒ at least 5 pieces of fruit.” (2+3=5)
• Argument from definition
  • “Their speech was concise, so it was brief but comprehensive.”
• Categorical syllogism (uses "All, some, no")
  • “All humans are mortal. Prof Gregg is human. ∴ Prof Gregg is mortal.”
• Hypothetical syllogism (if … then …)
  • “If you get an A in logic, then you get a new iPhone. You got an A. ∴ You get a new iPhone.”
• Disjunctive syllogism (either … or …)
  • “Either Larry is in Sincheon or Songdo. He’s not in Sincheon. ∴ He’s in Songdo.”
• Fantasy example stressing form, not truth:
  • \text{P1) } All fairies can fly.
  • \text{P2) } Ferdinand is a fairy.
  • \text{C) } Ferdinand can fly.
  • Deductive & valid (truth of premises is separate issue; soundness covered later).

Inductive Forms

• Prediction (past → future)
  • Stock-market & weather-forecast examples (e.g., max 32^\circ C predicted for Sept 2, 3 pm).
• Argument from analogy
  • “Junyeol’s Hyundai Sonata gets great mileage, so yours will too.” (Similarity: same car model.)
• Generalization (sample → population)
  • “Three oranges from crate were tasty ⇒ all oranges in crate are tasty.”
• Argument from authority
  • “H-P earnings will rise; an investment counselor said so.”
  • Commercial: “Georgia Craft coffee is good because actor Daniel Henney said so.”
• Argument based on signs
  • Road sign shows sharp turns ⇒ road will indeed have sharp turns.
• Causal inference
  • Cause→effect: Watermelon left in freezer overnight ⇒ watermelon is frozen.
  • Effect→cause: Gate bent & pigeon sitting ⇒ pigeon’s weight bent gate.

Scientific Reasoning & Popper’s Falsificationism

• Science employs both inductive and deductive arguments depending on goal.

Inductive in Science: Discovery of Laws

• Example: Measuring fall times → notice t \propto \sqrt{d} ⇒ generalize law of falling-body times.

Deductive in Science: Applying Known Laws

• Example: Boyle’s law P \propto \frac{1}{V}
  • Halve gas volume ⇒ pressure doubles.
  • Though future-oriented, inference is deductive (law applies universally to the case).

Karl Popper’s Normative Claim: Falsification > Confirmation

• Good science should attempt to refute hypotheses via rigorous testing.
• Ideal test follows modus tollens structure: \text{P1) } P \rightarrow Q \ \text{P2) } \neg Q \ \therefore \neg P
  • If hypothesis predicts result Q, but ¬Q occurs ⇒ hypothesis rejected.
• Contrast with confirmation/affirming-the-consequent fallacy:
  
  \text{P1) } P \rightarrow Q \
  \text{P2) } Q \
  \therefore P \quad (\text{Invalid})
  
• Popper’s demarcation:
  • A theory is scientific if it exposes itself to possible empirical falsification.
  • Marxism & psychoanalysis criticized as unfalsifiable ("reinforced dogmatism").
  • Popper concedes that non-scientific theories can still be insightful.

Misconceptions & Additional Caveats

• Do not use “specific→general” versus “general→specific” as shortcut:
  • Inductive can move general→specific (emerald color example).
  • Deductive can move specific→general (prime-number list ⇒ all odds 2-8 are prime) or specific→specific (Flo the fish example).
• Indicators are helpful but insufficient; always test the actual logical relationship.

Exercises Prompt

• Students pair up; each pair assigned a question on section 1.3.
  • 5 minutes to develop answer and justification.
  • Class review follows.