مطالب

There are at least three elemental parts in Brouuer's philosophy ef mathematics that mqy have their origin in Kant. These three parts are (1) the intuition ef time, (2) the synthetic a priority of mathematical kn01vledge, and (3) the inter-suf?jectiviry ef mathematical constructions. Brouwer borrowed the notion ef the movement eftime as an a priori intuition ef time, explicit!J expressed, from Kant. In Brouuer's philosophy ef mathematics, the intuition ef time is the on/y a priori notion, on wbicb the whole ef mathematics is built. Houeuer, their notions o] the "intuition eftime" are not the same in the genealogy ef mind As far as the second item is concerned, Brouwer believes that all ef mathematical kn01vledge is a priori and synthetic. His arguments are differentfrom Kant's arguments. The concept of ''inter-suf?jectiviry" ef mathematics in Brotouer's philosophy is very involved, and there is no reference to Kant in this respect. One mqy interpret it f?y the Kantian transcendental subject or even the Husserlian transcendental phenomenology. Both interpretations seem to be consistent. My suggestion is to read Brauner ry himse!f.

I can predict from the aspects and signs of our times that the human race 1vill... progressivefy improve without af!)l more total reversals.... The profit which will accrue to the human race as it works its wqy fonvard will not be an ever increasing quantity ofmorality in its attitudes. Instead the legality of its attitudes willproduce an increasing number of actions governed 0 duty, tuha tever the particular motives behind these mqy be.... Violence will gradualfy become less on the part of those in pouer and obedience tou/ards the la1vs 1vill increase... and this 1vi!I ultimatefy extend to the external relations between the various peoples, until a cosmopolitan society is created. Such developments do not mean , however, that the basic moral capacity ofmankind will increase in the slightest, for this would require a kind ofnew creation or supernatural influence. For we must not expect too much of human beings in their progressive improvements. " (Reiss, 19 70, 18 7)

The a priori is the basic characteristic ofKant's theory of knowledge. Formaliz/ng the a priori, Kant appears to distinguish the a priorifrom the postriori and qffirms its purity. He insists that the a priori is prior to the a postriori and stqys independent!Jfrom it. The overall objectiue of this paper is, boueier; to present and to support this idea that the a priori, even prior, can be defined l?J its relation to experience; ifthe a priori is prior to the a postriori, and ifits validity is not depended on the a postriori, it is still not ivithout mry relation with it. The main thesis I u;iflfoll01v here is that the a postriori could be called the root of the a priori: the a priori has its principle in the a postriorijust because it is given to it. The a priori is given in the experience. Instead of conceiving the a priori as a formal or logical cond Ition of ol?Jectiviry, it uould be considered as immanent in the objea and apprehended during the very act of experience, although known implicit!J before experience occurs. If the a priori is indeed given in experience, we are not constrained to restrict it to the formal conditions of oijectiviry. However, before proceeding to substantiate this thesis, I 1vill reiien. Kant's analysis of the a priori quick/y. Then, I willpresent the main thesis and its proof to deformalize the a priori and implant it in the a postriori domain.