胡塞尔对弗雷格外延主义数论的批判
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摘要
西方arithmetic的本义和实质是数论(number theory),因为arithmetic奠基于数的内涵与本质。在把握数概念和把握为数学奠基的逻辑时,内涵主义与外延主义表现为两种不同的理性方式。胡塞尔从内涵把握的立场认为,弗雷格的外延主义数论和逻辑不能把握内涵意义本身,也不能为数学和科学奠基。
The original meaning and essence of western arithmetic is number theory,because arithmetic is based on the sense and essence of number.In grasping the concept of number and the logic which underlies mathematics,we find that the intensionalism and the extension nalism can be represented as two different kinds of rational ways.From the viewpoint of intension,Husserl held that in the case of Frege,the extensionalist number theory and the extensional logic cannot cover the intensional meanings,nor can they lay the foundations for mathematics and sciences.
The original meaning and essence of western arithmetic is number theory,because arithmetic is based on the sense and essence of number.In grasping the concept of number and the logic which underlies mathematics,we find that the intensionalism and the extension nalism can be represented as two different kinds of rational ways.From the viewpoint of intension,Husserl held that in the case of Frege,the extensionalist number theory and the extensional logic cannot cover the intensional meanings,nor can they lay the foundations for mathematics and sciences.
引文
[1]弗雷格.算术哲学[M].王路,译.北京:商务印书馆,1998.
[2]FREGE G.Gottlob Frege:collected papers on mathematics,logic,and philosophy[M].Oxford:Basil Blackwell,1984.
[3]FREGE G.Posthumous writings[M].Chicago:University of Chicago Press,1979.
[4]HUSSERLE.Philosophie der arithmetik[M].The Hague:Martinus Nijhoff,1970.
[5]FREGE G.Philosophical and mathematical correspondence[M].Chicago:University of Chicago Press,1980.
[6]胡塞尔.逻辑研究第一卷[M].倪梁康,译.上海:上海译文出版社,2006.
[7]DUMMETT M.Frege:philosophy of mathematics[M].Massachusetts:Harvard University Press,1991.
[8]HUSSERL E.Early writings in the philosophy of logic and mathematics[M].Dordrecht:Kluwer,1994:92.
[9]胡塞尔.欧洲科学的危机与超越论的现象学[M].王炳文,译.北京:商务印书馆,2008:170-171.
(1)汉语以“算术”翻译arithmetic是不妥当的,完全遮蔽了其本义。中国传统算术是经验性的,并偏重于算法(术),而西方arithmetic的算法(algorithm)也已经理论化了。由于“算术”与中文语境高度融合,我们只能沿用并在不引起歧义时尽可能用“数论”替代“算术”。
[2]FREGE G.Gottlob Frege:collected papers on mathematics,logic,and philosophy[M].Oxford:Basil Blackwell,1984.
[3]FREGE G.Posthumous writings[M].Chicago:University of Chicago Press,1979.
[4]HUSSERLE.Philosophie der arithmetik[M].The Hague:Martinus Nijhoff,1970.
[5]FREGE G.Philosophical and mathematical correspondence[M].Chicago:University of Chicago Press,1980.
[6]胡塞尔.逻辑研究第一卷[M].倪梁康,译.上海:上海译文出版社,2006.
[7]DUMMETT M.Frege:philosophy of mathematics[M].Massachusetts:Harvard University Press,1991.
[8]HUSSERL E.Early writings in the philosophy of logic and mathematics[M].Dordrecht:Kluwer,1994:92.
[9]胡塞尔.欧洲科学的危机与超越论的现象学[M].王炳文,译.北京:商务印书馆,2008:170-171.
(1)汉语以“算术”翻译arithmetic是不妥当的,完全遮蔽了其本义。中国传统算术是经验性的,并偏重于算法(术),而西方arithmetic的算法(algorithm)也已经理论化了。由于“算术”与中文语境高度融合,我们只能沿用并在不引起歧义时尽可能用“数论”替代“算术”。