Category Archives: History of Mathematics

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

What part do arguments from authority play in mathematical reasoning?

In forming your answer you may choose to address any or all of the following aspects of the question: Descriptive What part do arguments from authority actually play in mathematical reasoning? Normative What part do arguments from authority ideally play … Continue reading

Posted in Artificial Intelligence, Authority, Control, Control Theory, Cybernetics, Fixation of Belief, History of Mathematics, History of Science, Information, Information Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Intuition, Logic, Logic of Science, Mathematical Intuition, Mathematical Reasoning, Operations Research, Optimal Control, Optimization, Philosophy of Science, Scientific Method | Tagged , , , , , , , , , , , , , , , , , , , , , , | 2 Comments