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Foundations of mathematics
Overview
study of the basic mathematical concepts
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
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Where theorems are difficult, they should be first taught as exercises in geometrical drawing, until the figure has become thoroughly familiar; it will then be an agreeable advance to be taught the logical connections of the various lines or circles that occur. It is desirable also that the figure illustrating a theorem should be drawn in all possible cases and shapes, that so the abstract relations with which…
Bertrand Russell, Mysticism and Logic and Other Essays
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Any such select set is called the set of postulates, or premises, from which the reasoning proceeds. The reasoning is nothing else than the exhibition of the whole pattern of general conditions involved in the pattern derived from the selected postulates.
Alfred North Whitehead, Science and the modern world
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In modern expositions of the axioms of geometry certain conditions are laid down which the relation of congruence between segments is to satisfy. It is supposed that we have a complete theory of points, straight lines, planes, and the order of points on planes--in fact, a complete theory of non-metrical geometry. We then enquire about congruence and lay down the set of conditions--or axioms as they are called--which…
Alfred North Whitehead, The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919
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Philosophers who discussed Foundations of mathematics
- Nelson Goodman
- Henri Bergson
- Kurt Gödel
- Ludwig Wittgenstein
- Per Martin-Löf
- David Lewis (philosopher)
- Bertrand Russell
- Gottlob Frege
- Josiah Royce
- Jean Le Rond d'Alembert
- Ernst Cassirer
- Charles Sanders Peirce
- Edmund Husserl
- Louis Couturat
- Evert Willem Beth
- Richard Milton Martin
- Édouard Le Roy
- Ion Barbu
Related ideas
- First-order logic
- Independence (mathematical logic)
- Finite set
- George Berkeley
- Alan Turing
- Georg Cantor
- Gottfried Wilhelm Leibniz
- Philosophical realism
- Giuseppe Peano
- Skolem's paradox
- Springer Science+Business Media
- Infinite set
- Zeno of Elea
- Isaac Newton
- Forcing (mathematics)
- Zermelo–Fraenkel set theory
- Finitism
- Computability theory
- Infinitesimal
- Formalism (philosophy of mathematics)
- Kurt Gödel
- Posterior Analytics
- Ancient Greek philosophy
- L. E. J. Brouwer
Place in the tradition
Part of Bertrand Russell.
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