Karnataka II PUC Logic (KSEAB) flashcards

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

Argument

A group of propositions in which some, the premises, are offered as evidence for the truth of another, the conclusion. A single statement or a mere set of statements is not an argument.

Validity

A property of deductive argument form: it is impossible for all premises to be true while the conclusion is false. Validity does not guarantee that premises or conclusion are actually true.

Soundness

A deductive argument is sound when it is valid and all of its premises are true. Soundness guarantees a true conclusion, unlike validity alone, which only guarantees truth transmission.

Inductive strength

A degree property of inductive arguments: true premises make the conclusion probable. Strong arguments can still have false conclusions, so strength never gives deductive certainty.

Categorematic term

A term able to serve by itself as subject or predicate of a proposition, such as 'student' or 'red'. Syncategorematic terms like 'all' or 'not' need other words to function.

Extension and intension

Extension is the class of objects a term denotes; intension is the set of attributes that determines membership. For ordinary terms, widening intension narrows extension and narrowing intension widens extension.

Equivocal term

A term with the same spelling or sound but two or more distinct meanings, such as 'bank' (river edge, financial institution). Using it as though one meaning were intended is the fallacy of equivocation.

Contradictory terms

Two terms that exhaust the universe of discourse with no middle case, such as 'living' and 'non-living'. Contraries, by contrast, allow a middle case, as with 'hot' and 'cold'.

Proposition

What a declarative sentence asserts, capable of being true or false. Questions, commands, exclamations and wishes express no proposition because they have no truth value.

Truth-functional compound

A compound proposition whose truth value is fully determined by the truth values of its components and the connectives used, as with negation, conjunction, disjunction and the conditional.

Categorical proposition

A proposition that asserts or denies a predicate of a subject without conditions, as in 'All S is P'. It differs from conditional propositions, which assert dependence between antecedent and consequent.

Distribution of terms

A term is distributed when the proposition says something about every member of its class. A distributes subject only; E both; I neither; O predicate only.

Obversion

An immediate inference that changes the quality of a proposition and replaces the predicate with its complement. Valid for A, E, I and O without exception: All S is P becomes No S is non-P.

Conversion

An immediate inference that swaps subject and predicate. Valid unchanged for E and I; for A it holds only per accidens, yielding an I proposition; O cannot be converted at all.

Contradictories on the square

Pairs A–O and E–I, which always have opposite truth values: exactly one is true. This relation survives even when the subject class is empty, unlike subalternation.

Middle term

The term appearing in both premises of a categorical syllogism but never in the conclusion. It must be distributed in at least one premise to avoid the undistributed middle fallacy.

Figure of a syllogism

The arrangement of the middle term in the two premises. First figure has M as subject of the major and predicate of the minor; the other three figures shift these positions.

Undistributed middle fallacy

A formal syllogistic fallacy in which the middle term is not distributed in either premise, so the premises fail to connect subject and predicate. Example: all dogs are mammals; all cats are mammals; therefore all cats are dogs.

Illicit process

A formal fallacy in which a term distributed in the conclusion was undistributed in its premise. It is called illicit major or illicit minor according to which term is involved.

Begging the question

An informal fallacy of presumption in which the conclusion is assumed, explicitly or through a disguised equivalent, among the premises. The argument is circular and provides no independent support.

Material implication

The truth-functional conditional p → q, false only when p is true and q is false. A false antecedent makes it true, and it is equivalent to the disjunction ~p ∨ q.

Tautology

A well-formed formula true on every row of its truth table, such as p ∨ ~p. Its negation is a contradiction, false on every row; contingent formulas vary across rows.

De Morgan's laws

Equivalences that move negation through connectives: ~(p ∧ q) is equivalent to ~p ∨ ~q, and ~(p ∨ q) is equivalent to ~p ∧ ~q. They underlie many proofs by replacement.

Modus ponens

A rule of inference: from a conditional and its antecedent, infer the consequent (p → q, p, therefore q). Denying the antecedent is a different and invalid form.

Modus tollens

A rule of inference: from a conditional and the negation of its consequent, infer the negation of the antecedent (p → q, ~q, therefore ~p). Affirming the consequent is invalid.

Conditional proof

A proof technique: to establish p → q, assume p as an extra premise, derive q, then discharge the assumption and conclude the conditional. It mirrors the truth conditions of implication.

Reductio ad absurdum proof

An indirect proof that assumes the negation of the desired conclusion, derives a contradiction, and then infers the conclusion. In truth tables it appears as the premises-true, conclusion-false test.

Counterexample row

A single row of a truth table in which every premise is true and the conclusion is false. Its existence proves the argument form invalid; absence of such a row proves validity.

Mill's method of difference

A method of causal inquiry: if two otherwise similar cases differ in one antecedent circumstance and also differ in the effect, that circumstance is the cause or a necessary part of it.

Hypothetico-deductive method

A scientific procedure: frame a hypothesis, deduce observable consequences, then test them. Confirming instances support but never prove it; a single failed prediction can refute a universal hypothesis.

Hasty generalization

An inductive fallacy that draws a broad conclusion from a sample too small or unrepresentative. It is diagnosed by asking whether sample size and selection support the claimed scope.

Use versus mention

Using a word refers to what it names; mentioning it refers to the word itself, usually marked by quotation. Confusing the two generates equivocation and category mistakes in argument.