Philosophy of mathematics
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| + | The '''philosophy of mathematics''' is the [[Branch (academia)|branch]] of [[philosophy]] that studies the assumptions, foundations, and implications of [[mathematics]], and to provide a viewpoint of the nature and [[methodology]] of mathematics and to understand the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts. | ||
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| + | The terms ''philosophy of mathematics'' and ''mathematical philosophy'' are frequently used interchangeably. The latter, however, may be used to refer to several other areas of study. One refers to a project of formalizing a philosophical subject matter, say, [[aesthetics]], [[ethics]], [[logic]], [[metaphysics]], or [[theology]], in a purportedly more exact and rigorous form, as for example the labors of [[scholasticism|scholastic]] [[theologian]]s, or the systematic aims of [[Gottfried Wilhelm Leibniz|Leibniz]] and [[Spinoza]]. Another refers to the working philosophy of an individual practitioner or a like-minded community of practicing [[mathematicians]]. Additionally, some understand the term "mathematical philosophy" to be an [[allusion]] to the approach to the foundations of mathematics taken by [[Bertrand Russell]] in his books ''[[The Principles of Mathematics]]'' and ''[[Introduction to Mathematical Philosophy]]''. | ||
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| ==See also== | ==See also== | ||
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| * [[Axiomatic set theory]] | * [[Axiomatic set theory]] | ||
| * [[Axiomatic system]] | * [[Axiomatic system]] | ||
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| * [[Foundations of mathematics]] | * [[Foundations of mathematics]] | ||
| * [[Golden ratio]] | * [[Golden ratio]] | ||
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| * [[History of mathematics]] | * [[History of mathematics]] | ||
| * [[Intuitionistic logic]] | * [[Intuitionistic logic]] | ||
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| * [[Mathematical proof]] | * [[Mathematical proof]] | ||
| * [[Metamathematics]] | * [[Metamathematics]] | ||
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| * [[Model theory]] | * [[Model theory]] | ||
| * [[Naive set theory]] | * [[Naive set theory]] | ||
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| * [[Proof theory]] | * [[Proof theory]] | ||
| * [[Rule of inference]] | * [[Rule of inference]] | ||
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| * [[Science studies]] | * [[Science studies]] | ||
| * [[Scientific method]] | * [[Scientific method]] | ||
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| * [[Truth]] | * [[Truth]] | ||
| *[[Ultimate ensemble]] | *[[Ultimate ensemble]] | ||
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| ===Related works=== | ===Related works=== | ||
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| * ''[[The Analyst]]'' | * ''[[The Analyst]]'' | ||
| * [[Euclid's Elements|Euclid's ''Elements'']] | * [[Euclid's Elements|Euclid's ''Elements'']] | ||
| * [[Original proof of Gödel's completeness theorem|Gödel's completeness theorem]] | * [[Original proof of Gödel's completeness theorem|Gödel's completeness theorem]] | ||
| * ''[[Introduction to Mathematical Philosophy]]'' | * ''[[Introduction to Mathematical Philosophy]]'' | ||
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| * ''[[New Foundations]]'' | * ''[[New Foundations]]'' | ||
| * ''[[Principia Mathematica]]'' | * ''[[Principia Mathematica]]'' | ||
Revision as of 11:39, 17 June 2017
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The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics, and to provide a viewpoint of the nature and methodology of mathematics and to understand the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts.
The terms philosophy of mathematics and mathematical philosophy are frequently used interchangeably. The latter, however, may be used to refer to several other areas of study. One refers to a project of formalizing a philosophical subject matter, say, aesthetics, ethics, logic, metaphysics, or theology, in a purportedly more exact and rigorous form, as for example the labors of scholastic theologians, or the systematic aims of Leibniz and Spinoza. Another refers to the working philosophy of an individual practitioner or a like-minded community of practicing mathematicians. Additionally, some understand the term "mathematical philosophy" to be an allusion to the approach to the foundations of mathematics taken by Bertrand Russell in his books The Principles of Mathematics and Introduction to Mathematical Philosophy.
See also
- Axiomatic set theory
- Axiomatic system
- Category theory
- Definitions of mathematics
- Formal language
- Formal system
- Foundations of mathematics
- Golden ratio
- History of mathematics
- Intuitionistic logic
- Logic
- Mathematical beauty
- Mathematical constructivism
- Mathematical logic
- Mathematical proof
- Metamathematics
- Model theory
- Naive set theory
- Non-standard analysis
- Philosophy of language
- Philosophy of science
- Philosophy of probability
- Proof theory
- Rule of inference
- Science studies
- Scientific method
- Set theory
- The Unreasonable Effectiveness of Mathematics in the Natural Sciences
- Truth
- Ultimate ensemble
Related works
- The Analyst
- Euclid's Elements
- Gödel's completeness theorem
- Introduction to Mathematical Philosophy
- New Foundations
- Principia Mathematica
- The Simplest Mathematics
Historical topics
