Realism

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What is it?
The view that the truths of mathematics are thus independent of human activities, i.e., they are objective.
Where is it found?
BLANCHETTE, PATRICIA A. (1998). Realism in the philosophy of mathematics. In E. Craig (Ed.), Routledge Encyclopedia of Philosophy. London: Routledge. Retrieved February 27, 2008, from http://www.rep.routledge.com.virtual.anu.edu.au/article/Y066
MOORE, A.W. (1998, 2004). Antirealism in the philosophy of mathematics. In E. Craig (Ed.), Routledge Encyclopedia of Philosophy. London: Routledge. Retrieved February 27, 2008, from http://www.rep.routledge.com.virtual.anu.edu.au/article/Y065
Horsten, Leon, "Philosophy of Mathematics", The Stanford Encyclopedia of Philosophy (Winter 2007 Edition), Edward N. Zalta (ed.), URL =
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Realism and Platonism
_Platonism_
Platonism is a form of math. realism in which the existence of independent math. objects is posited. Thus reasoning involving maths is exactly the same as reasoning involving concrete objects and both are held to exist independently of our thoughts regarding them.
_Problems for the Platonist_

_Problem Responses_
— prob. re: giving a clear account of math. intuition
— prob re: is this position actually Platonist (i.e. should knowledge of suitable propositions count as knowledge of the objects they contain)?

_Arguments for Platonism_

_Non-Platonist Realism_
Talking about objects in math is just a convenient way of speaking. Maths is really about general features of some less controversial/abstract kind of thing (e.g. collections, measurements, structures, etc.).
— structuralism still postulates the existence of abstract objects, just a different kind.
There is a point in Routledge concerning the need to phrase things in terms of possibility (in order for things to be true in a finite world?) that I don't really get.

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What do I think?

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Chris Wilcox