Logic and Fallacies
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Validity versus soundness, truth tables and syllogisms, and the informal fallacies by name with a concrete example for each. Learn to spot bad reasoning the moment it appears.
- Argument, in logic
- A set of statements in which some, the premises, are offered as support for another, the conclusion.
- Premise
- A statement offered as a reason to accept the conclusion.
- Conclusion
- The statement an argument is trying to establish.
- Deductive argument
- An argument whose premises are intended to guarantee the conclusion.
- Inductive argument
- An argument whose premises are intended to make the conclusion probable, not certain.
- Abductive reasoning
- Inference to the best explanation: accepting the hypothesis that would best account for the evidence.
- Validity
- A deductive argument is valid when it is impossible for all the premises to be true and the conclusion false.
- Soundness
- A deductive argument is sound when it is valid and all its premises are actually true.
- Can a valid argument have a false conclusion?
- Yes, if at least one premise is false. Validity only guarantees the conclusion given true premises.
- Can an invalid argument have a true conclusion?
- Yes. A conclusion can be true by accident even when the reasoning does not support it.
- Cogency
- An inductive argument is cogent when it is strong and its premises are true.
- Counterexample method
- Showing an argument form is invalid by constructing another argument with the same form, true premises, and a false conclusion.
- Modus ponens
- If P then Q. P. Therefore Q.
- Modus tollens
- If P then Q. Not Q. Therefore not P.
- Hypothetical syllogism
- If P then Q. If Q then R. Therefore if P then R.
- Disjunctive syllogism
- P or Q. Not P. Therefore Q.
- Reductio ad absurdum
- Proving a claim by assuming its negation and deriving a contradiction.
- Affirming the consequent
- If P then Q. Q. Therefore P. This is invalid.
- Denying the antecedent
- If P then Q. Not P. Therefore not Q. This is invalid.
- Undistributed middle
- A syllogism in which the middle term is not distributed in either premise, so it fails to connect the other terms.
- Illicit major
- A syllogism in which the major term is distributed in the conclusion but not in the premise where it appears.
- Illicit minor
- A syllogism in which the minor term is distributed in the conclusion but not in the premise where it appears.
- Existential fallacy
- Drawing a conclusion asserting that something exists from premises that make only universal claims.
- Categorical proposition
- A statement relating two classes, in one of four standard forms labeled A, E, I, and O.
- The A proposition
- The universal affirmative: All S are P.
- The E proposition
- The universal negative: No S are P.
- The I proposition
- The particular affirmative: Some S are P.
- The O proposition
- The particular negative: Some S are not P.
- Distribution of a term
- A term is distributed in a proposition if the proposition says something about every member of that class.
- Contradictories
- Two propositions that cannot both be true and cannot both be false, such as A and O, or E and I.