Concept
Philosophy of mathematics
Overview
Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathematical objects are purely abstract entities or are in some way concrete, and in what the relationship such objects have with physical reality consists.
Major themes that are dealt with in philosophy of mathematics include:
Reality: The question is whether mathematics is a pure product of human mind or whether it has some reality by itself.
Logic and rigor
Relationship with physical reality
Relationship with science
Relationship with applications
Mathematical truth
Nature as human activity (science, art, game, or all together)
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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_General_ (or _Analytical_) geometry being entirely founded upon the transformation of geometrical considerations into equivalent analytical considerations, we must begin with examining directly and in a thorough manner the beautiful conception by which Descartes has established in a uniform manner the constant possibility of such a co-relation. Besides its own extreme importance as a means of highly perfecting…
Auguste Comte, The philosophy of mathematics
The book is titled for Philosophy of mathematics; names Philosophy of mathematics.
We may, if we please, call the proposition, “Three is two and one,” a definition of the number three, and assert that arithmetic, as it has been asserted that geometry, is a science founded on definitions. But they are definitions in the geometrical sense, not the logical; asserting not the meaning of a term only, but along with it an observed matter of fact. The proposition, “A circle is a figure bounded by a line…
John Stuart Mill, A System of Logic, Ratiocinative and Inductive
States what Philosophy of mathematics is; the author is tied to Philosophy of mathematics in the knowledge graph.
The notion of continuity depends upon that of _order_, since continuity is merely a particular type of order. Mathematics has, in modern times, brought order into greater and greater prominence. In former days, it was supposed (and philosophers are still apt to suppose) that quantity was the fundamental notion of mathematics. But nowadays, quantity is banished altogether, except from one little corner of Geometry…
Bertrand Russell, Mysticism and Logic and Other Essays
States what Philosophy of mathematics is; the author is tied to Philosophy of mathematics in the knowledge graph.
Philosophers who discussed Philosophy of mathematics
- Nelson Goodman
- Paul Benacerraf
- Hartry Field
- Hans Reichenbach
- Karl Popper
- Kurt Gödel
- Jaakko Hintikka
- Friedrich Waismann
- Ludwig Wittgenstein
- Moritz Schlick
- Frank P. Ramsey
- Philip Kitcher
- Crispin Wright
- Michael Dummett
- Willard Van Orman Quine
- Solomon Feferman
- George Boole
- Imre Lakatos
- David Lewis (philosopher)
- Blaise Pascal
- Alfred North Whitehead
- David Papineau
- Saul Kripke
- Gottlob Frege
Related ideas
- Eugene Wigner
- Empiricism
- Cognition
- Formal language
- First-order logic
- Falsifiability
- Finite set
- George Berkeley
- General relativity
- Alan Turing
- Georg Cantor
- Golden ratio
- Gödel's completeness theorem
- Proof assistant
- Philosophical realism
- Grammatical tense
- Hexadecimal
- Philosophy
- Differential equation
- Infinite set
- Counterexample
- Paul Benacerraf
- Imaginary number
- Integer
Opposing perspectives
Place in the tradition
Part of Outline of philosophy.
Narrower topics:
- Ancient Greek mathematics
- Applied mathematics
- Category theory
- Complex number
- Decimal
- Golden ratio
- Hexadecimal
- History and philosophy of science
- Imaginary number
- Manifold
- Mathematical analysis
- Numeral system
- Parallel postulate
- Part of speech
- Paul Erdős
- Saunders Mac Lane
- Square root of 2
- Theory (mathematical logic)
- Gregory Chaitin
- Intermediate value theorem
- Penelope Maddy
- Consilience
- James Franklin (philosopher)
- Samuel Eilenberg
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