Deduction vs. Induction – Critical Reasoning 1.3

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

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.

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.
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.

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

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.

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.)

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).

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

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

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.”

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.

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.)

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.

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.

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.