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In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the subject term) are included in another (the predicate term). [1]
In traditional logic, a proposition (Latin: propositio) is a spoken assertion (oratio enunciativa), not the meaning of an assertion, as in modern philosophy of language and logic. A categorical proposition is a simple proposition containing two terms, subject (S) and predicate (P), in which the predicate is either asserted or denied of the subject.
A proposition that asserts or denies that all or some of the members of one category are included in another category, fundamental in syllogistic reasoning. categorical syllogism A form of deductive reasoning in Aristotelian logic consisting of three categorical propositions that involve three terms and deduce a conclusion from two premises ...
Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also notable for its connections to theoretical computer science. [1] In broad terms, categorical logic represents both syntax and semantics by a category, and an interpretation by a functor.
In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P. For the categorical proposition All S are P, the converse is All P are S. Either way, the truth of the converse is generally independent from that of ...
The square of opposition is often used to visualize the relations between the four basic categorical propositions in Aristotelian logic. It shows, for example, that the propositions "All S are P" and "Some S are not P" are contradictory, meaning that one of them has to be true while the other is false.
Contraposition is a type of immediate inference in which from a given categorical proposition another categorical proposition is inferred which has as its subject the contradictory of the original predicate. Since nothing is said in the definition of contraposition with regard to the predicate of the inferred proposition, it is permissible that ...
In traditional logic, where there are four named types of categorical propositions, only forms A (i.e., "All S are P") and E ("All S are not P") have an inverse. To find the inverse of these categorical propositions, one must: replace the subject and the predicate of the inverted by their respective contradictories, and change the quantity from ...