CHSE Odisha Elective Logic flashcards

35 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 principles of correct inference, distinguishing valid from invalid reasoning by examining the relation between premises and conclusion rather than the content of statements.

Validity

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

Soundness

An argument is sound when it is valid and all of its premises are actually true. Soundness guarantees a true conclusion, whereas validity alone does not.

Inductive strength

A graded property of inductive arguments: the premises make the conclusion probable. Strength increases with the amount and relevance of supporting evidence and decreases with counterevidence.

Distribution

A term is distributed when a proposition says something about every member of the class it denotes. Universal propositions distribute their subject; negative propositions distribute their predicate.

Existential import

The assumption that the subject class of a proposition has at least one member. Traditional logic assigns it to A and E propositions; modern Boolean logic does not.

A proposition

The universal affirmative categorical statement 'All S are P'. It distributes its subject only and, in traditional logic, asserts that the subject class is not empty.

O proposition

The particular negative categorical statement 'Some S are not P'. It distributes its predicate only and asserts that at least one member of S lies outside P.

Obversion

An immediate inference valid for all four categorical forms: change the quality of the proposition and replace the predicate term with its complement, leaving truth value unchanged.

Conversion

An immediate inference that swaps subject and predicate. It is valid for E and I propositions, valid per accidens for A when the subject exists, and invalid for O.

Contradictory opposition

The relation between A and O, and between E and I, on the square of opposition. Contradictories always differ in truth value: exactly one is true and the other false.

Subalternation

The square relation in which a universal implies its corresponding particular: A implies I and E implies O. It holds only when the subject class is not empty.

Middle term

The term occurring in both premises of a categorical syllogism and absent from the conclusion. It must be distributed in at least one premise for the syllogism to be valid.

Figure of a syllogism

The arrangement of the middle term in the premises. Four figures exist, distinguished by whether the middle term is subject or predicate in the major and minor premises.

Mood of a syllogism

The sequence of the three categorical proposition forms in a syllogism, given in the order major premise, minor premise, conclusion, using the letters A, E, I and O.

Undistributed middle

A formal fallacy in which the middle term of a categorical syllogism is not distributed in either premise, so the premises fail to link the subject and predicate classes.

Illicit process

A formal fallacy in which a term is distributed in the conclusion but not in the premise where it occurs. It appears as illicit major or illicit minor.

Affirming the consequent

A formal fallacy with the pattern P implies Q; Q; therefore P. The conditional does not license inferring the antecedent from the consequent, since other causes may produce Q.

Ad hominem

An informal fallacy that attacks the character, circumstances or motives of the person presenting an argument instead of addressing the argument's premises and reasoning.

Begging the question

The fallacy of petitio principii, in which the conclusion is assumed, explicitly or in disguised form, among the premises, making the argument circular rather than supportive.

Hasty generalisation

An informal fallacy that draws a general conclusion from a sample that is too small, unrepresentative or biased to support the claimed generalisation.

Material conditional

The truth function P implies Q, false only when P is true and Q is false. It is equivalent to not-P or Q and does not assert any causal connection.

Tautology

A well-formed formula that is true under every possible assignment of truth values to its sentence letters, such as P or not-P. Its truth-table column contains only T.

Contradiction

A well-formed formula that is false under every possible assignment of truth values, such as P and not-P. Its truth-table column contains only F.

Logical equivalence

Two statements are logically equivalent when they have identical truth values on every row of a joint truth table, so each entails the other.

Modus ponens

A rule of inference: from a conditional and its antecedent, infer the consequent. Formally, P implies Q together with P yields Q.

Modus tollens

A rule of inference: from a conditional and the negation of its consequent, infer the negation of its antecedent. Formally, P implies Q with not-Q yields not-P.

Conditional proof

A proof technique in which the antecedent of the desired conditional is assumed as an extra premise, the consequent is derived, and the assumption is then discharged to yield the conditional.

Reductio ad absurdum

An indirect proof technique: assume the negation of the conclusion, derive a formal contradiction, and conclude that the original conclusion follows from the premises.

Argument from analogy

An inductive argument: two things share several properties, one has a further property, so the other probably has it too. Strength depends on relevance and disanalogies.

Mill's method of difference

A causal method comparing two cases that differ in one circumstance: the circumstance present when the effect occurs and absent when it does not is the probable cause.

Falsifiability

Popper's criterion that a scientific hypothesis must forbid some observable outcome, so that a single contrary observation can refute it. Unfalsifiable claims are not empirical science.

Operational definition

A definition that specifies the concrete procedure or measurement used to identify or quantify a variable, allowing independent observers to record it consistently.

Well-formed formula

A symbolic expression built recursively from sentence letters using negation, conjunction, disjunction, conditional and biconditional, with parentheses fixing the scope of each connective.

Main connective

The connective in a well-formed formula that governs the whole expression and determines its form, its truth-table evaluation and the last step of its construction.