Critical Reasoning 1.3 – Deduction and Induction

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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.

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.

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.

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.

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

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).

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.

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

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).

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.

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.

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