UPMSP Intermediate Logic key terms

In Nyāya, the second valid means of knowing, in which a conclusion about something unperceived is drawn from a mark or reason known to be invariably connected with it, as fire is inferred from smoke.

The invariable, unconditional concomitance between a probans and its probandum, such as the universal relation between smoke and fire, which licenses an inferential step rather than a mere accidental co-occurrence.

The reason or probans in an Indian inference: the observed feature, such as smoke, offered as evidence for the conclusion, which must satisfy the five-membered syllogism's conditions of valid proof.

The five-membered Nyāya demonstration comprising pratijñā (thesis), hetu (reason), udāharaṇa (example), upanaya (application), and nigamana (conclusion), each member serving a distinct argumentative function.

The example member of a Nyāya inference, citing a familiar case where the reason and the conclusion are known to co-occur, thereby displaying the underlying invariable concomitance the argument relies on.

Deviation or the failure of invariable concomitance, occurring when a proposed reason is found in a case where the conclusion is absent; a hetu contaminated by it cannot ground a sound inference.

A valid, non-defective means of cognition in Indian epistemology, such as perception, inference, comparison, and testimony; the number and classification of pramāṇas differ among Nyāya, Mīmāṃsā, and Buddhist schools.

Perception, the direct cognition arising from contact between a sense faculty and its object, regarded by Nyāya as the foundational pramāṇa on which other means of knowledge ultimately depend.

The subject or locus of an Indian inference, the thing about which a property is being proved, as the hill is the pakṣa when one argues that it contains fire because it contains smoke.

A fallacious reason that is inconclusive because it deviates, being present both where the conclusion holds and where it fails, so it cannot establish the desired property.

A faulty reason that is counterbalanced: an equally strong reason can be advanced for the contradictory conclusion, so neither argument establishes its thesis.

The truth-evaluable content expressed by a declarative sentence, capable of being true or false and serving as the basic unit that propositional logic connects with truth-functional operators.

An operator such as negation, conjunction, disjunction, or the conditional whose output truth value is determined entirely by the truth values of the propositions it joins, regardless of their content.

A systematic display listing every possible assignment of truth values to the atomic components of a formula and the resulting value of the whole, used to test validity, consistency, and logical status.

A formula that comes out true under every assignment of truth values to its components, such as a disjunction of a proposition with its own negation; its negation is unsatisfiable.

A formula that is false under every assignment of truth values, for example the conjunction of a proposition with its own negation; such a formula can never be satisfied.

The relation holding between two formulas that receive the same truth value under every possible assignment, so that each entails the other and they may be substituted for one another in valid reasoning.

The valid argument form that affirms the antecedent: from a conditional and the affirmation of its antecedent, one may infer the consequent, as from 'if it rains, the ground is wet' and 'it rains' infer 'the ground is wet'.

The valid argument form that denies the consequent: from a conditional and the negation of its consequent, one may infer the negation of its antecedent, a pattern often confused with the invalid fallacy of denying the antecedent.

An error in the logical form of an argument, such as affirming the consequent, in which the premises fail to guarantee the conclusion even though their content may be true.

A formal syllogistic error in which the middle term is not distributed in either premise, so the premises fail to link the subject and predicate classes and the conclusion does not follow.

The property of a term in a categorical proposition indicating whether the proposition says something about every member of the class the term denotes; universal subjects and negative predicates are distributed.

A proposition asserting or denying that one class is wholly or partly included in another, standardly analysed into quantity (universal or particular) and quality (affirmative or negative) across the four A, E, I, O forms.

A diagram arranging the four categorical forms to display their logical relations: contradictories differ in truth value, contraries cannot both be true, subcontraries cannot both be false, and subalternation transmits truth downward.

The immediate inference that swaps the subject and predicate terms of a categorical proposition; it is valid without restriction only for E and I propositions, and by limitation for A propositions.

The immediate inference that changes a proposition's quality and replaces its predicate with its complement, yielding an equivalent proposition; unlike conversion it is valid for all four categorical forms.

The term appearing in both premises of a categorical syllogism but not in the conclusion, whose function is to connect the major and minor terms; its distribution is essential to validity.

A deductive argument of exactly three categorical propositions containing three terms, each appearing twice, whose validity depends on mood and figure rather than on the subject matter discussed.

The arrangement of the middle term in the premises of a categorical syllogism; there are four possible figures, each associated with a distinct set of valid moods.

The sequence of the categorical forms (A, E, I, O) of the three propositions in a syllogism, read in order from major premise through minor premise to conclusion.

A word or phrase that can serve as the subject or predicate of a proposition, standing for a class or an individual; terms are the units analysed in categorical logic before propositions are formed.

A statement that specifies the meaning of a term, most rigorously by genus and specific difference, thereby fixing the boundaries of the class the term denotes.

A definition that identifies the meaning of a term by listing the members of the class it denotes, either exhaustively or by example, rather than by stating the properties they share.

A logical operator that specifies how much of a domain a predicate applies to, the universal quantifier asserting that all objects satisfy a formula and the existential quantifier that at least one does.

In predicate logic, a symbol applied to one or more terms to express a property or relation, as opposed to the individual constants or variables that fill its argument places.

A variable occurring within the scope of a quantifier that binds it; its occurrences are placeholders governed by that quantifier rather than names of particular objects.

An inductive method that generalises from observed instances to an unobserved or total population, supporting the conclusion only with probability and vulnerable to counterexamples.

Five procedures for identifying causal connections from observed patterns, namely agreement, difference, joint agreement and difference, residues, and concomitant variation, each isolating a candidate cause by elimination.

A model of scientific inquiry in which a hypothesis is proposed, testable consequences are deduced from it, and those consequences are checked against observation, with failures counting against the hypothesis.

The property of an argument in which the premises, if true, guarantee the truth of the conclusion; validity concerns form and does not require the premises actually to be true.

The property of a deductive argument that is both valid and has all true premises, so that its conclusion is guaranteed true; soundness entails but is not entailed by validity.