Concept
Categorical logic
Overview
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.
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.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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When we think of mathematics, we have in our mind a science devoted to the exploration of number, quantity, geometry, and in modern times also including investigation into yet more abstract concepts of order, and into analogous types of purely logical relations. The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities.
Alfred North Whitehead, Science and the modern world
Close in meaning to Categorical logic; the term itself is not named.
People have discovered how to make reasoning symbolic, as it is in Algebra, so that deductions are effected by mathematical rules. They have discovered many rules besides the syllogism, and a new branch of logic, called the Logic of Relatives,[11] has been invented to deal with topics that wholly surpassed the powers of the old logic, though they form the chief contents of mathematics.
Bertrand Russell, Mysticism and Logic and Other Essays
Close in meaning to Categorical logic; the term itself is not named.
The modern development of mathematical logic dates from Boole's _Laws of Thought_ (1854). But in him and his successors, before Peano and Frege, the only thing really achieved, apart from certain details, was the invention of a mathematical symbolism for deducing consequences from the premisses which the…
Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy
Close in meaning to Categorical logic; the term itself is not named.
Related ideas
- Interpretation (logic)
- Dana Scott
- Intuitionistic logic
- Logical connective
- Mathematics
- Intuitionism
- Mathematical logic
- Model theory
- Set theory
- Theoretical computer science
- Metalogic
- Type theory
- Quantifier (logic)
- Classical logic
- Higher-order logic
- Category theory
- Disjunction and existence properties
- Cartesian closed category
Place in the tradition
Part of Outline of logic.