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- Structuralism_(philosophy_of_mathematics) abstract "Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures of mathematical objects. Mathematical objects are exhaustively defined by their place in such structures. Consequently, structuralism maintains that mathematical objects do not possess any intrinsic properties but are defined by their external relations in a system. For instance, structuralism holds that all that the integer 1 is exhaustively defined by being the successor of 0 in the structure of the theory of natural numbers. By generalization of this example, any integer is defined by their respective place in this structure of the number line. Other examples of mathematical objects might include lines and planes in geometry, or elements and operations in abstract algebra.Structuralism is an epistemologically realistic view in that it holds that mathematical statements have an objective truth value. However, its central claim only relates to what kind of entity a mathematicalobject is, not to what kind of existence mathematical objects or structures have (not, in other words,to their ontology). The kind of existence mathematical objects have would clearly be dependent on that of thestructures in which they are embedded; different sub-varieties of structuralism make different ontological claimsin this regard.Structuralism in the philosophy of mathematics is particularly associated with Paul Benacerraf, Michael Resnik and Stewart Shapiro.".
- Structuralism_(philosophy_of_mathematics) wikiPageExternalLink structuralism.
- Structuralism_(philosophy_of_mathematics) wikiPageExternalLink m-struct.
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- Structuralism_(philosophy_of_mathematics) subject Category:History_of_mathematics.
- Structuralism_(philosophy_of_mathematics) subject Category:Mathematical_logic.
- Structuralism_(philosophy_of_mathematics) subject Category:Philosophy_of_mathematics.
- Structuralism_(philosophy_of_mathematics) subject Category:Set_theory.
- Structuralism_(philosophy_of_mathematics) subject Category:Structuralism_(philosophy_of_mathematics).
- Structuralism_(philosophy_of_mathematics) comment "Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures of mathematical objects. Mathematical objects are exhaustively defined by their place in such structures. Consequently, structuralism maintains that mathematical objects do not possess any intrinsic properties but are defined by their external relations in a system.".
- Structuralism_(philosophy_of_mathematics) label "Structuralism (philosophy of mathematics)".
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