UPMSP Intermediate Logic flashcards

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

Validity

A property of deductive form: an argument is valid when it is impossible for all its premises to be true while its conclusion is false. It does not require actually true premises.

Soundness

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

Inductive strength

A degree property: premises make the conclusion probable without entailing it. A strong inductive argument can still reach a false conclusion despite true premises.

Argument versus explanation

An argument gives reasons intended to prove a claim whose truth is in question; an explanation assumes the claim is true and shows why or how it occurs.

Connotation and denotation

Connotation (intension) is the set of attributes a term implies; denotation (extension) is the class of objects it names. Increasing connotation typically decreases denotation.

Genus and difference

A definition by genus and difference places the term in a wider class (genus) and adds the distinguishing attribute (differentia), as in defining a triangle as a plane figure with three sides.

Stipulative definition

A definition that assigns a meaning to a term for a specific purpose or context rather than reporting established usage. It cannot be criticized as true or false, only as useful or not.

Equivocal term

A single word or phrase used with two unrelated meanings in different occurrences, which can generate the fallacy of four terms in a syllogism.

Distribution in A propositions

In 'All S are P' the subject term is distributed because the proposition asserts something about every S; the predicate term is undistributed because it covers only part of P.

Distribution in O propositions

In 'Some S are not P' the predicate is distributed because the proposition excludes the subject from the whole of P; the subject term remains undistributed.

Contradictories

Pairs A-O and E-I on the square of opposition: they always have opposite truth values, so if one is true the other is false and vice versa.

Obversion

A valid immediate inference for all four categorical forms: change the quality (affirmative to negative or reverse) and replace the predicate with its complement, keeping truth value.

Conversion

Swapping subject and predicate. Valid without change of quantity for E and I propositions; A converts only per accidens with existential import; O cannot be converted.

Existential import

The assumption that the subject class of a universal proposition has members. Traditional Aristotelian logic assumes it, allowing subalternation; modern Boolean logic does not.

Undistributed middle

A syllogistic fallacy in which the middle term is never distributed in either premise, so the premises fail to connect the minor and major terms.

Illicit major

A fallacy in which the major term is distributed in the conclusion but was undistributed in its premise, so the conclusion claims more than the premises support.

Mood and figure

Mood is the letter pattern of a syllogism's three propositions (for example EIO); figure is the position of the middle term as subject or predicate across the two premises.

Begging the question

A fallacy of presumption in which the conclusion is assumed, often subtly, among the premises, so the argument presupposes what it is supposed to prove.

Material implication

The truth-functional reading of the conditional: 'if p then q' is false only when p is true and q is false. It is equivalent to 'not-p or q'.

Modus tollens

A valid inference form: from 'if p then q' together with 'not q', conclude 'not p'. It is the contrapositive counterpart of modus ponens.

Tautology

A compound proposition true on every row of its truth table, such as 'p or not-p'. A valid argument's corresponding conditional is a tautology.

De Morgan's laws

Equivalences governing negation of compounds: not-(p and q) equals not-p or not-q; not-(p or q) equals not-p and not-q. They hold for quantifiers similarly.

Conditional proof

A proof technique that assumes the antecedent of the desired conditional, derives the consequent, then discharges the assumption to obtain the conditional.

Affirming the consequent

An invalid form: from 'if p then q' and 'q', concluding 'p'. The consequent may be true for reasons other than p.

Quantifier negation

Equivalences: not-all x Fx equals some x not-Fx, and no x Fx equals all x not-Fx. They permit moving negation past quantifiers by switching the quantifier.

Universal instantiation

From 'all x are F' infer that a named individual a is F. The step is valid for any constant, since the universal claim covers every member.

Existential instantiation

From 'some x is F' infer Fa using a new constant not previously used in the proof, since the claim identifies no specific individual.

Quantifier order

For multiple quantifiers, order changes meaning: 'for all x some y loves x,y' differs from 'some y is loved by all x'. Only one direction of implication holds.

Mill's method of difference

Compare two cases alike except that the effect occurs in one and not the other; the single differing factor is identified as the cause or a necessary condition.

Hypothetico-deductive method

Formulate a hypothesis, deduce testable predictions from it, perform tests, then retain, revise, or reject the hypothesis according to whether predictions hold.

Necessary versus sufficient

A necessary condition must be present for the effect but may not produce it alone; a sufficient condition guarantees the effect but may not be the only route to it.

Vyapti

In Nyaya, the invariable concomitance between reason (hetu) and inferable property (sadhya) that grounds inference, established through observation and causal analysis rather than mere counting.

Hetvabhasa

A Nyaya fallacy of inference: a reason that appears valid but fails, classified as deviating, contradictory, irrelevant, unproved, or unestablished depending on the defect.

Pancavayava

The five-membered Nyaya inference schema: thesis (pratijna), reason (hetu), example (udaharana), application (upanaya), and conclusion (nigamana).