Fallacies and scientific method

Philosophy · Logic, ethics and special topics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

A fallacy is an argument that looks sound but is not. A formal fallacy is a fault in the form of the argument, so it fails whatever the subject matter. An informal fallacy has a fault in the content: the premises are irrelevant, the language is ambiguous, or something is assumed without proof.

Science reasons by induction and tests its guesses. J. S. Mill, in 'A System of Logic' (1843), gave five methods of induction for finding the cause of a phenomenon by comparing cases. The scientific method moves from observation to a hypothesis that can be tested, then to experiment and a conclusion. A control group shows that the result is due to the one factor that was changed.

Rules to remember

Formal fallacies: affirming the consequent (If P then Q; Q; so P) and denying the antecedent (If P then Q; not P; so not Q).
Ad hominem: attacking the person, not the argument. Ad ignorantiam: 'not disproved, so true'. Appeal to inappropriate authority: citing someone who is not an expert in the field.
Begging the question (petitio principii): the conclusion is assumed in the premises; circular reasoning.
Equivocation: a word changes its meaning within the argument. Post hoc ergo propter hoc: 'after this, therefore because of this'. Hasty generalisation: a general claim from too small a sample.
Mill's methods: agreement (the one factor common to all cases); difference (the one factor that differs between two cases); the joint method of agreement and difference; residues (take away what known causes explain; the rest is due to the remaining factor); concomitant variations (two things vary together).
Scientific method: observation, hypothesis, experiment, conclusion. A scientific hypothesis must be testable.

Common mistake

Students mix up the two formal fallacies with the valid forms. Affirming the antecedent (modus ponens) and denying the consequent (modus tollens) are valid; affirming the consequent and denying the antecedent are not.

Worked example

'If a candidate cheats, he is disqualified. Bilal did not cheat. Therefore Bilal was not disqualified.' Name the fault in this argument.

Put it in form: If P (cheats) then Q (disqualified); not P; therefore not Q.
The first premise says cheating is enough for disqualification, not that it is the only ground. Bilal could be disqualified for another reason, such as arriving late.
So the premises can be true while the conclusion is false: the fault is in the form, not in the facts.
The second premise denies the 'if' part of the conditional, which is called the antecedent.

Answer: It is the formal fallacy of denying the antecedent.

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