Tag 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. This post is … Continue reading

Posted in Abstraction, Ackermann, Analogy, Aristotle, Carnap, Category Theory, Diagrammatic Reasoning, Diagrams, Dyadic Relations, Equational Inference, Form, Foundations of Mathematics, Functional Logic, Hilbert, History of Mathematics, Hypostatic Abstraction, Iconicity, Kant, Logic, Mathematics, Mental Models, Peirce, Propositions As Types Analogy, Saunders Mac Lane, Surveys, Triadic Relations, Type Theory, Universals, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Propositions As Types : 1

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

Posted in Combinator Calculus, Combinatory Logic, Computation, Computer Science, Formal Language Theory, Graph Theory, Lambda Calculus, Logic, Logical Graphs, Mathematics, 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 Article, C.S. Peirce, Computation, Computer Science, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Peirce's Law, Programming, Proof Theory, Propositions As Types Analogy, Spencer Brown, Type Theory | Tagged , , , , , , , , , , , , , , | 4 Comments