The branch of philosophy that studies the nature of mathematical entities such as numbers and sets, and how, if at all, we can have knowledge of them. The Stanford Encyclopedia of Philosophy frames its central task as determining what the nature of mathematical entities consists in and how we can have knowledge of mathematical entities, a question that sets mathematics apart from the empirical sciences because mathematical truths seem to be established by proof rather than observation. The field is closely related to, but distinct from, the foundations of mathematics, the more technical project of grounding mathematical practice in a formal system.
Facts
Central QuestionWhat is the nature of mathematical entities such as numbers and sets, and how, if at all, can we have knowledge of them? 1 Key DebateMathematical platonism against nominalism and fictionalism: whether numbers, sets and other mathematical objects exist independently of the mind and of any physical instantiation, as platonists hold, or whether mathematical language is a useful fiction with no such independent objects behind it. A further, more recent debate concerns mathematical pluralism, the view that any consistent mathematical theory describes a free-standing mathematical universe and that no such theory is more true than any other, which unsettles the very idea of a single fact of the matter about which axioms are correct. 1 Disputed
Key DebateWhether a proof by exhaustive computer calculation, as in Appel and Haken's 1976 proof of the four color theorem, counts as genuine mathematical proof given that no human being can survey it, or marks a break from the traditional requirement that a proof be humanly checkable. 2 Kenneth Appel and Wolfgang Haken's 1976 proof of the four color theorem, verified by computer case-checking no mathematician could survey by hand, forced this question onto philosophers of mathematics. Connections
Associated With
Source Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)
Source Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)
Includes
Source Benacerraf's identification problem (Wikipedia)
Source Wikipedia: Carl Posy
Source Crispin Wright, Wikipedia
Source Danielle Macbeth, Wikipedia
Source Henri Bergson (Wikipedia)
Source Hilary Putnam (Wikipedia)
Source Imre Lakatos (Wikipedia)
Source Jesús Padilla Gálvez, Wikipedia
Source John McDowell (Wikipedia)
Source Wikipedia: Mark Colyvan
Source Wikipedia: Mary Leng
Source Max Black, Wikipedia
Source Michael Dummett (Wikipedia)
Source Paul Benacerraf (Wikipedia)
Source Wikipedia: Philip Kitcher
Source Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)
Source Quine-Putnam indispensability argument (Wikipedia)
Source Wikipedia: Roberto Torretti
Source Souleymane Bachir Diagne - Wikipedia
Source Hajime Tanabe, Wikipedia
Source Willard Van Orman Quine (Wikipedia)
Sources
1. Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)
Stanford Encyclopedia of PhilosophySection 1, opening paragraph
what the nature of mathematical entities consists in and how we can have knowledge of mathematical entities
Section 5.2
any consistent mathematical theory describes a free-standing mathematical universe, and that no such theory is more true than any other
- Associated With: Gottlob Frege
- Associated With: Bertrand Russell
Includes: Platonism, entry: Philosophy of Mathematics, Logic, and the Foundations of Mathematics, Section 3
On the platonistic conception, the subject matter of mathematics consists of abstract entities.
View the Source 2. Stanford Encyclopedia of Philosophy
Stanford University, Center for the Study of Language and Informations.v. Philosophy of MathematicsQuote, s.v. Philosophy of Mathematics
If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology.
Willard Van Orman Quine (Wikipedia)
Wikimedia FoundationIncludes: Willard Van Orman Quine, Infobox: main_interestsQuote, Includes: Willard Van Orman Quine, Infobox: main_interests
Logic, ontology, epistemology, philosophy of language, philosophy of mind, philosophy of mathematics, philosophy of science, set theory
Hilary Putnam (Wikipedia)
WikipediaIncludes: Hilary Putnam, Infobox: main_interestsQuote, Includes: Hilary Putnam, Infobox: main_interests
Philosophy of mind, of language, of science, and of mathematics Metaphilosophy Epistemology Jewish philosophy
Henri Bergson (Wikipedia)
WikipediaIncludes: Henri Bergson, Infobox: main_interestsQuote, Includes: Henri Bergson, Infobox: main_interests
Metaphysics, epistemology, philosophy of language, philosophy of mathematics, studies of immediate experience
Michael Dummett (Wikipedia)
WikipediaIncludes: Michael Dummett, Infobox: main_interestsQuote, Includes: Michael Dummett, Infobox: main_interests
Philosophy of mathematics Philosophy of logic Mathematical logic Philosophy of language Metaphysics History of analytic philosophy Voting theory Theology
Imre Lakatos (Wikipedia)
WikipediaIncludes: Imre Lakatos, Infobox: main_interestsQuote, Includes: Imre Lakatos, Infobox: main_interests
Philosophy of mathematics, philosophy of science, history of science, epistemology, politics
Hajime Tanabe, Wikipedia
Includes: Tanabe Hajime, Infobox: main_interestsQuote, Includes: Tanabe Hajime, Infobox: main_interests
Philosophy of science, philosophy of mathematics, philosophy of physics, metaphysics, philosophy of religion
Souleymane Bachir Diagne - Wikipedia
Includes: Souleymane Bachir Diagne, Infobox: main_interestsQuote, Includes: Souleymane Bachir Diagne, Infobox: main_interests
Philosophy of mathematics, Epistemology, Logic, Linguistics, Mathematics, Islamic philosophy
Crispin Wright, Wikipedia
Includes: Crispin Wright, Infobox: main_interestsQuote, Includes: Crispin Wright, Infobox: main_interests
Philosophy of mind Philosophy of language Philosophy of mathematics Frege Wittgenstein Epistemology
John McDowell (Wikipedia)
WikipediaIncludes: John McDowell, Infobox: main_interestsQuote, Includes: John McDowell, Infobox: main_interests
Metaphysics, epistemology, logic, philosophy of language, philosophy of perception, philosophy of mathematics, philosophy of mind, ethics, meta-ethics
Max Black, Wikipedia
Includes: Max Black, Infobox: main_interestsQuote, Includes: Max Black, Infobox: main_interests
Philosophy of language Philosophy of mathematics Philosophy of science Philosophy of art
Danielle Macbeth, Wikipedia
Includes: Danielle Macbeth, LeadQuote, Includes: Danielle Macbeth, Lead
Danielle Monique Macbeth (born 1954, Edmonton) is a Canadian philosopher whose work focuses on the philosophy of mathematics, the philosophy of language, metaphysics, and the philosophy of logic.
Wikipedia: Philip Kitcher
Includes: Philip Kitcher, Infobox: main_interestsQuote, Includes: Philip Kitcher, Infobox: main_interests
Philosophy of science, philosophy of biology, bioethics, philosophy of mathematics
Wikipedia: Roberto Torretti
Includes: Roberto Torretti, Infobox: main_interestsQuote, Includes: Roberto Torretti, Infobox: main_interests
History of philosophy, philosophy of physics, philosophy of mathematics
Jesús Padilla Gálvez, Wikipedia
Includes: Jesús Padilla Gálvez, Infobox: main_interestsQuote, Includes: Jesús Padilla Gálvez, Infobox: main_interests
Logic, ontology, epistemology, philosophy of language, philosophy of mathematics, philosophy of science, ethics.
Wikipedia: Mark Colyvan
WikipediaIncludes: Mark Colyvan, Infobox: main_interestsQuote, Includes: Mark Colyvan, Infobox: main_interests
Philosophy of logic, philosophy of mathematics, conservation biology
Wikipedia: Mary Leng
WikipediaIncludes: Mary Leng, LeadQuote, Includes: Mary Leng, Lead
Mary Leng is a British philosopher specialising in the philosophy of mathematics and philosophy of science.
Benacerraf's identification problem (Wikipedia)
Includes: Benacerraf's Identification Problem, LeadQuote, Includes: Benacerraf's Identification Problem, Lead
In the philosophy of mathematics, Benacerraf's identification problem is a philosophical argument developed by Paul Benacerraf against
Quine-Putnam indispensability argument (Wikipedia)
Includes: Quine-Putnam Indispensability Argument, LeadQuote, Includes: Quine-Putnam Indispensability Argument, Lead
The Quine-Putnam indispensability argument is an argument in the philosophy of mathematics for the existence of abstract mathematical objects such as numbers and sets, a position known as mathematical Platonism.
Paul Benacerraf (Wikipedia)
Includes: Paul Benacerraf, Infobox: main_interestsQuote, Includes: Paul Benacerraf, Infobox: main_interests
Philosophy of mathematics
Wikipedia: Carl Posy
WikipediaIncludes: Carl Posy, LeadQuote, Includes: Carl Posy, Lead
Posy's areas of research interest include the philosophy of mathematics, philosophical logic, the history of philosophy (particularly Kant and his predecessors).
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.