Karnataka II PUC Logic (KSEAB) key terms

The mental process of deriving a conclusion from one or more given statements called premises. Logic studies which inferences are correct, distinguishing valid from invalid reasoning.

A group of statements in which some, the premises, are offered as support for another, the conclusion. An argument claims that its premises justify accepting its conclusion.

A statement in an argument offered as evidence or reason for accepting the conclusion. Premises may be true or false; their role is to support.

The statement in an argument that the premises are intended to establish. It is what the arguer wants the audience to accept on the basis of the other statements.

A property of deductive arguments: the conclusion follows necessarily from the premises, so it is impossible for all premises to be true and the conclusion false. Validity concerns form, not factual truth.

A property of deductive arguments that are both valid and have all true premises. A sound argument guarantees a true conclusion, so soundness combines formal correctness with factual correctness.

An argument claiming that its conclusion follows with necessity from the premises. If the reasoning is valid, true premises cannot lead to a false conclusion.

An argument claiming that its premises make the conclusion probable rather than certain. Even with true premises a strong inductive argument may have a false conclusion.

A word or group of words that can serve as the subject or predicate of a categorical proposition, standing for a class. Terms are the building blocks of categorical propositions.

The set of attributes or qualities that a term implies, by which the objects it names are identified. Also called intension; it is what the term means rather than what it refers to.

The class of objects to which a term actually applies. Also called extension; it is the term's referential range rather than its meaning content.

A statement that explains the meaning of a term, either by giving its attributes, its members, or an equivalent expression. Good definitions avoid circularity and obscurity.

A declarative sentence that asserts something and is either true or false. Questions, commands, and exclamations are not propositions because they lack truth value.

A proposition that does not contain another proposition as a component and has no truth-functional connectives. In categorical logic it relates exactly two terms.

A proposition formed by combining simpler propositions with truth-functional connectives such as 'and', 'or', 'not', and 'if...then'. Its truth value depends on the truth values of its parts.

A proposition that asserts a relation of inclusion or exclusion between two classes, using a quantifier such as 'all', 'no', or 'some'. It has a subject term, a predicate term, and a copula.

The feature of a categorical proposition indicating whether it refers to all members of the subject class (universal) or only some (particular). Quantity determines the A, E, I, or O form together with quality.

The feature of a categorical proposition indicating whether it affirms or denies class inclusion. Affirmative propositions affirm; negative ones deny, giving the A, E, I, and O forms when combined with quantity.

A property of a term in a categorical proposition: it is distributed when the proposition says something about every member of the class the term names. Universal subjects and negative predicates are distributed.

A diagram showing logical relations among the four categorical forms with the same terms: contradiction, contrariety, subcontrariety, and subalternation. It lets one infer the truth or falsity of one proposition from another.

The relation between propositions that differ in both quantity and quality, such as A and O or E and I. Exactly one of a contradictory pair is true, so each implies the other's falsity.

An immediate inference that swaps the subject and predicate terms of a categorical proposition. It is valid only when neither term's distribution is changed, as with E and I propositions.

An immediate inference that changes a proposition's quality and replaces the predicate with its complement. It is valid for all four categorical forms and preserves truth value.

An immediate inference that replaces subject and predicate by their complements and then converts the result. It is valid for A and O propositions when distribution is preserved.

A deductive argument with exactly two premises and a conclusion, each a categorical proposition. In a categorical syllogism the three propositions together contain exactly three terms.

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

The arrangement of the middle term in the two premises of a categorical syllogism, giving four possible patterns. Each figure has its own valid moods.

The pattern of categorical forms (A, E, I, O) of the three propositions in a syllogism, listed in the order major premise, minor premise, conclusion. Figure and mood together identify a syllogism's form.

An error in reasoning that makes an argument logically defective, even if its conclusion happens to be true. Fallacies may be formal, depending on bad structure, or informal, depending on content and language.

The informal fallacy of assuming the very conclusion one is trying to prove, often by restating it as a premise. The argument moves in a circle and gives no independent support.

A truth-functional operator that joins simple propositions into compound ones, such as negation, conjunction, disjunction, conditional, and biconditional. Each has a fixed truth table.

The truth function of the conditional 'if p then q', false only when the antecedent is true and the consequent false. It does not require any causal or logical connection between the parts.

A systematic chart listing every possible combination of truth values for a proposition's components and the resulting value of the whole. It is used to test for tautology, contradiction, and validity.

A compound proposition that is true under every possible assignment of truth values to its components. Its truth table column contains only T's, showing it is logically true.

A valid argument form: if p then q; p; therefore q. Affirming the antecedent guarantees the consequent when the conditional is true.

A valid argument form: if p then q; not q; therefore not p. Denying the consequent forces denial of the antecedent when the conditional is true.

A step-by-step derivation of a conclusion from premises using stated rules of inference and replacement. Each step must be justified by a rule, unlike an informal argument sketch.

An inductive argument that concludes two things share a further property because they share several known properties. Its strength depends on the number and relevance of similarities.

A proposed explanation or tentative generalisation put forward for testing against evidence. In the scientific method it must be checkable by observation or experiment.

The procedure of forming hypotheses, deducing observable consequences, and testing them through observation or experiment. It combines inductive generalisation with deductive prediction and revision.

Word choice that arouses feelings or carries evaluative overtones rather than merely stating facts. In argument it can persuade by sentiment and obscure the actual evidence.

The property of an expression that has more than one possible meaning in a given context, whether through word sense or grammatical structure. It can make arguments appear valid when they are not.

The informal fallacy of shifting the meaning of a word between its occurrences in an argument. The reasoning seems to connect premises to conclusion only because one term changes sense.