The article East Asian mathematics covers the mostly independent development of mathematics in China, Japan, Korea, and Vietnam.
When professional philosophers investigate philosophical questions concerning mathematics, they are said to contribute to the philosophy of mathematics.
Teaching the mathematics course that was required for those who wished to become elementary school teachers led to an interest in mathematics education.
An apparent problem with naturalism is that there do not seem to be sharp boundaries between science and non-science and between mathematics and non-mathematics.
Moreover, Quine and Putnam maintain that these standards sanction platonist mathematics because mathematics and its platonist construal are an indispensable part of our best scientific theories.
Second, the reliance on a philosophy of mind introduces features that are absent from classical mathematics as well as from other forms of constructive mathematics: unlike those, intuitionistic mathematics is not a proper part of classical mathematics.
aesthetics: aesthetic judgment | Brouwer, Luitzen Egbertus Jan | Duhem, Pierre | mathematics, philosophy of | mathematics, philosophy of: intuitionism | mathematics, philosophy of: naturalism | mathematics: constructive | scientific knowledge: social dimensions of
abstract objects | mathematics, philosophy of | mathematics, philosophy of: indispensability arguments in the | nominalism: in metaphysics | ontological commitment | Platonism: in metaphysics | Platonism: in the philosophy of mathematics | plural quantification | Quine, Willard Van Orman
Frege, Gottlob: controversy with Hilbert | Gödel, Kurt | Hilbert, David: program in the foundations of mathematics | mathematics, philosophy of | mathematics, philosophy of: fictionalism | Platonism: in the philosophy of mathematics | Wittgenstein, Ludwig: philosophy of mathematics
abstract objects | fictionalism | mathematics, philosophy of | mathematics, philosophy of: indispensability arguments in the | mathematics, philosophy of: nominalism | nominalism: in metaphysics | nonexistent objects | Platonism: in metaphysics | Platonism: in the philosophy of mathematics | psychologism
Goodman, Nelson: aesthetics | imagination | mathematics, philosophy of | mathematics, philosophy of: nominalism | measurement: in science | models in science | Platonism: in the philosophy of mathematics | reference | scientific realism | scientific theories: structure of | theoretical terms in science | truth: deflationary theory of
category theory | Dedekind, Richard: contributions to the foundations of mathematics | identity: of indiscernibles | mathematics, philosophy of | mathematics, philosophy of: nominalism | physics: structuralism in | Platonism: in the philosophy of mathematics | structural realism | style: in mathematics
Brouwer, Luitzen Egbertus Jan | epsilon calculus | Frege, Gottlob: controversy with Hilbert | Gödel, Kurt | Gödel, Kurt: incompleteness theorems | Hilbert, David | mathematics, philosophy of | mathematics, philosophy of: formalism | mathematics, philosophy of: intuitionism | Principia Mathematica | proof theory: development of | Russell, Bertrand
algebra | Frege, Gottlob | Hilbert, David | Hilbert, David: program in the foundations of mathematics | mathematics, philosophy of | mathematics, philosophy of: structuralism | mathematics: explanation in | Russell, Bertrand | Russell’s paradox | set theory: early development | set theory: Zermelo’s axiomatization of | style: in mathematics
Church-Turing Thesis | Gödel, Kurt | Hilbert, David: program in the foundations of mathematics | logic, history of: intuitionistic logic | logic: second-order and higher-order | mathematics, philosophy of | mathematics, philosophy of: intuitionism | proof theory | proof theory: development of | recursive functions | set theory | set theory: independence and large cardinals | Turing machines | Wittgenstein, Ludwig: philosophy of mathematics
Brouwer, Luitzen Egbertus Jan | finitism | Gödel, Kurt | logic, history of: intuitionistic logic | logic: classical | logic: modal | logic: provability | logicism and neologicism | mathematics, philosophy of | mathematics, philosophy of: formalism | mathematics, philosophy of: intuitionism | mathematics: constructive | Platonism: in the philosophy of mathematics | proof theory: development of | set theory: constructive and intuitionistic ZF
Brouwer, Luitzen Egbertus Jan | Gödel, Kurt | Hilbert, David | Hilbert, David: program in the foundations of mathematics | logic: classical | logic: intuitionistic | logic: provability | logic: relevance | mathematics, philosophy of: formalism | mathematics, philosophy of: intuitionism | mathematics: constructive | Principia Mathematica | proof theory | proof theory: development of | set theory: constructive and intuitionistic ZF | Wittgenstein, Ludwig: philosophy of mathematics
abstract objects | cognitivism vs. non-cognitivism, moral | constructive empiricism | fictionalism: modal | imagination | impossible worlds | logic and ontology | mathematics, philosophy of: fictionalism | mathematics, philosophy of: indispensability arguments in the | mathematics, philosophy of: naturalism | models in science | moral anti-realism | moral realism | naturalism | nominalism: in metaphysics | nonexistent objects | Platonism: in metaphysics | Platonism: in the philosophy of mathematics | propositions | realism
Cantor, Georg | Frege, Gottlob: controversy with Hilbert | Hilbert, David | Hilbert, David: program in the foundations of mathematics | Kant, Immanuel: philosophy of mathematics | logic, history of: intuitionistic logic | logic: classical | logic: intuitionistic | mathematics, philosophy of | mathematics, philosophy of: formalism | mathematics, philosophy of: intuitionism | mathematics: constructive | Platonism: in metaphysics | Platonism: in the philosophy of mathematics | set theory: early development | Weyl, Hermann | Wittgenstein, Ludwig: philosophy of mathematics
abstract objects | Brouwer, Luitzen Egbertus Jan | dependence, ontological | epsilon calculus | existence | logic: intuitionistic | logic and ontology | mathematics, philosophy of | mathematics, philosophy of: fictionalism | mathematics, philosophy of: formalism | mathematics, philosophy of: indispensability arguments in the | mathematics, philosophy of: nominalism | mathematics, philosophy of: structuralism | mathematics: constructive | mathematics: explanation in | mathematics: non-deductive methods in | naturalism | nominalism: in metaphysics | object | ontological commitment | Platonism: in metaphysics | Platonism: in the philosophy of mathematics | Quine, Willard van Orman: New Foundations | realism | realism: challenges to metaphysical | reism | scientific realism | set theory | set theory: early development | structural realism | truth | type theory | Wittgenstein, Ludwig: philosophy of mathematics
mathematics
noun cognition
- a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
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abstract objects | Brouwer Luitzen Egbertus Jan | dependence ontological | epsilon calculus | existence | logic intuitionistic | logic and ontology | mathematics philosophy of | mathematics philosophy of fictionalism | mathematics philosophy of formalism | mathematics philosophy of indispensability arguments in the | mathematics philosophy of nominalism | mathematics philosophy of structuralism | mathematics constructive | mathematics explanation in | mathematics non-deductive methods in | naturalism | nominalism in metaphysics | object | ontological commitment | Platonism in metaphysics | Platonism in the philosophy of mathematics | Quine Willard van Orman New Foundations | realism | realism challenges to metaphysical | reism | scientific realism | set theory | set theory early development | structural realism | truth