Categorical logic is a branch of category theory within mathematics, adjacent to mathematical logic but more notable for its connections to theoretical computer science. In broad terms, categorical logic represents both syntax and semantics by a category, and an interpretation by a functor. The categorical framework provides a rich conceptual background for logical and type-theoretic constructions. The subject has been recognisable in these terms since around 1970.
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Famous quotes containing the words categorical and/or logic:
“We do the same thing to parents that we do to children. We insist that they are some kind of categorical abstraction because they produced a child. They were people before that, and they’re still people in all other areas of their lives. But when it comes to the state of parenthood they are abruptly heir to a whole collection of virtues and feelings that are assigned to them with a fine arbitrary disregard for individuality.”
—Leontine Young (20th century)
“Our argument ... will result, not upon logic by itself—though without logic we should never have got to this point—but upon the fortunate contingent fact that people who would take this logically possible view, after they had really imagined themselves in the other man’s position, are extremely rare.”
—Richard M. Hare (b. 1919)