Maharashtra HSC Logic flashcards

34 cards. Read the term and the definition here. The deck at the top of this page is optional.

Logic

The normative science that studies the form and principles of valid inference, distinguishing correct from incorrect reasoning by evaluating the structure of arguments rather than the psychology of the reasoner.

Validity

A property of deductive arguments: it is impossible for all premises to be true while the conclusion is false. Validity concerns form, not the actual truth of the premises.

Soundness

A deductive argument is sound when it is valid and all its premises are actually true. Soundness therefore guarantees the truth of the conclusion.

Term connotation and denotation

Connotation is the set of attributes a term implies; denotation is the class of objects to which it applies. Increasing connotation normally narrows denotation.

Proposition

A declarative sentence that asserts something and is capable of being true or false. Questions, commands and exclamations express no proposition.

Argument

A group of propositions in which some, the premises, are offered as evidence or support for another, the conclusion. It must involve an inferential claim.

Premise and conclusion indicators

Words signalling premises include since, because, for and given that; words signalling conclusions include therefore, hence, thus and consequently. They help map an argument's structure.

Distribution of terms

A term is distributed when a proposition refers to all members of its class. A distributes only the subject, E both terms, I neither, O only the predicate.

Contradictory opposition

The relation between A and O, and between E and I. Contradictories always have opposite truth values: they cannot both be true or both be false.

Obversion

An immediate inference that changes quality and replaces the predicate with its complement. Valid for A, E, I and O, and it preserves truth value exactly.

Conversion

An immediate inference swapping subject and predicate. Simple conversion is valid for E and I; A converts only per accidens to I; O cannot be converted.

Middle term

The term appearing in both premises of a categorical syllogism but not in the conclusion. It must be distributed at least once for the syllogism to be valid.

Figure of a syllogism

The arrangement of the middle term in the premises. Four figures exist, determined by whether the middle term is subject or predicate in each premise.

Mood of a syllogism

The three-letter sequence naming the proposition types of the major premise, minor premise and conclusion in order, for example AAA or EIO.

Illicit process fallacy

A syllogistic error in which a term distributed in the conclusion was undistributed in its premise, either the major or the minor term.

Venn diagram test

A decision procedure for syllogisms: shade areas the premises declare empty, mark with X where existence is asserted, then check whether the conclusion is already represented.

Material conditional

A truth function that is false only when the antecedent is true and the consequent false. It is true whenever the antecedent is false, a feature called vacuous truth.

Tautology

A compound proposition that is true under every possible assignment of truth values to its components, for example p or not-p. Its truth table column is all T.

Logical equivalence

Two statements are logically equivalent when they have identical truth values on every row of a joint truth table, so their biconditional is a tautology.

De Morgan's laws

Rules relating negation to conjunction and disjunction: the negation of p and q equals not-p or not-q, and the negation of p or q equals not-p and not-q.

Modus ponens

A valid inference form: from a conditional and the affirmation of its antecedent, infer the consequent. Symbolically, p implies q, p, therefore q.

Modus tollens

A valid inference form: from a conditional and the denial of its consequent, infer the denial of the antecedent. Symbolically, p implies q, not-q, therefore not-p.

Conditional proof

A deduction technique: assume the antecedent of the desired conditional, derive the consequent, then discharge the assumption and assert the whole conditional.

Reductio ad absurdum

Indirect proof: assume the negation of the statement to be proved, derive a contradiction, and conclude that the original statement must be true.

Proof of invalidity

A method of showing an argument invalid by specifying one consistent truth-value assignment under which all premises are true and the conclusion is false.

Enumerative induction

Generalizing from observed instances to a claim about a whole class. Strength depends on sample size, randomness and representativeness of the observed cases.

Argument from analogy

Reasoning that two things alike in known respects are probably alike in a further respect. Strength rises with the number and relevance of shared features.

Mill's methods

Five inductive methods for identifying causes: agreement, difference, joint method of agreement and difference, concomitant variation, and residues.

Falsifiability

A property of empirical hypotheses: some conceivable observation would count as evidence against them. Unfalsifiable claims cannot be tested scientifically.

Affirming the consequent

A formal fallacy: from p implies q and q, inferring p. The consequent may hold for reasons other than the antecedent.

Begging the question

The fallacy of petitio principii, in which the conclusion is assumed, explicitly or implicitly, among the premises, making the reasoning circular.

Ad hominem

A fallacy of relevance that attacks the person making a claim rather than the claim's evidence, and so fails to address the argument itself.

Well-formed formula

A symbolic expression built by the recursive rules of propositional logic: statement letters are formulas, and connectives applied to formulas yield formulas.

Main connective

The connective in a formula with the widest scope; it determines the truth value of the whole formula and governs the form of a proof.