Category Archives: Propositions As Types Analogy

Survey of Precursors Of Category Theory • 1

A few years ago I began a sketch on the “Precursors of Category Theory”, aiming to trace the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice.  A Survey of … Continue reading

Posted in Abstraction, Ackermann, Analogy, Aristotle, C.S. Peirce, Carnap, Category Theory, Diagrams, Dyadic Relations, Equational Inference, Form, Foundations of Mathematics, Functional Logic, Hilbert, History of Mathematics, Hypostatic Abstraction, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Propositions As Types Analogy, Relation Theory, Saunders Mac Lane, Semiotics, Sign Relations, Surveys, Triadic Relations, Type Theory, Universals | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Propositions As Types : 1

Re: R.J. Lipton • Mathematical Tricks One of my favorite mathematical tricks — it seems almost too tricky to be true — is the Propositions As Types Analogy.  And I see hints the 2-part analogy can be extended to a 3-part … Continue reading

Posted in Abstraction, C.S. Peirce, Combinator Calculus, Combinatory Logic, Computation, Computational Complexity, Computer Science, Curry–Howard Isomorphism, Formal Language Theory, Graph Theory, Lambda Calculus, Logic, Logical Graphs, Mathematics, Peirce, Programming Languages, Propositions As Types Analogy, Type Theory | Tagged , , , , , , , , , , , , , , , , , | Leave a comment

Peirce’s Law

Peirce’s law is a logical proposition that states a non-obvious truth of classical logic and affords a novel way of defining classical propositional calculus. Continue reading

Posted in C.S. Peirce, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Peirce's Law, Proof Theory, Propositional Calculus, Propositions As Types Analogy, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , | 6 Comments