Philosophy of Mathematics： Naturalism vs. Category Theory  

作　　者：Milan Tasic 

机构地区：[1]University of Nis

出　　处：《Journal of Philosophy Study》2013年第10期929-944,共16页哲学研究（英文版）

摘　　要：Although E Maddy （1997） says on naturalism： ＂This is not, in itself, a philosophy of mathematics [...]＂ （161）, already by its name, or by those whose interest has called on it （Quine, Putnam et al.） ... it anyhow reveals desire to be it. Insofar as otherwise, the semantic potential of the word leaves far behind it （after all scarce） results it achieved from the relation of an exact （mathematical） expression and （overly rich） intuitive reality of Being. We plead here already from the perspective of the slogan ＂One and All＂ of the first philosopher： Tales, when by the number （which one forebodes） one could go to such an extent into areas of reality （Pythagoras）, or when （especially in the human sphere） is being over again actual final cause of Aristotle the philosophy and the mathematics to accomplish far more fruitful encounter with the Being. Alain Badiou （1988） has already pointed that： ＂Mathematics is ontology,＂ and the category theory in mathematics, having covered by itself other fields of this science, continues to find applications in a series of＂non-traditional＂ domains of reality. In that correlation the philosophy can express its （primary） needs for truth, justice, beauty, ... as well as for the overall development in the sense of purpose--also because of an undreamed power of the technological development （of hardwares and softwares） today. Namely, the naturalism in mathematics, which developed an abundant reflection on the place （importance of） the mathematical idiom in sciences--in the balance of criticism--has come rather to meager provisions, such as： ＂preestablished harmony of thinking,＂ ＂ontic commitment,＂ （Quine 1960） ＂the hygiene of mind,＂ （Maddy 1996） ＂success argument,＂ （Putnam 1975） ＂pragmatic argument,＂ （Resnik 1981） etc., which only are few places from the encounter of an exact expression such as is mathematical one and the reality of natuural sciences. Instead of philosophy of ma

关 键 词：NATURALISM indispensability argument ontology MATHEMATICS CATEGORY final cause biocosmology 

分 类 号：N02[自然科学总论—科学技术哲学] O1-0[理学—数学]