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數學哲學

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8/25/2013 7:57:39 PM

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The   philosophy   of   mathematics   is   the   branch   of   philosophy

that   studies   the   philosophical   assumptions,   foundations,

and   implications   of   mathematics.   The   aim   of   the   philosophy

of   mathematics   is   to   provide   an   account   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   as   synonyms.   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   taken   by

Bertrand   Russell   in   his   books   The   Principles   of

Mathematics   and   Introduction   to   Mathematical   Philosophy.

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