Conhecimento simbólico na filosofia kantiana da aritmética

Abstract

This dissertation presents an investigation into what, according to Kant, is the role of symbolism in arithmetic. There are few references to arithmetic in the Kant s work, it was search for to assemble a preliminary picture regarding the role of the symbolism in it philosophy of the mathematics as a whole. Above all in the precritical period, but also in the notion of symbolic construction presented in the Critic of Pure Reason, they seem to survive inheritances of the Leibniz s thought, in matter, of the notion of symbolic knowledge, whose exam is also contemplated in this preliminary situation. The investigation had been lead, centrally, for the exam of the linking of the symbolism with two main elements present in the mature Kant s philosophy of the mathematics: intuition and concept. Kant establishes that the relationship between intuition and concept occur in the mathematics through construction, that is, of the exhibition beforehand of an intuition concept. This characterizes what is called ostensive construction. The symbolism gets prominence in which Kant denominates of symbolic or characteristic construction of concepts, by which the concepts are exhibited through signs that are for them. The emphasis in this symbolic aspect is justified by the crescent interests that had been demonstrated in this respect by the contemporary mathematics philosophy, once it points for a fundamental fact of the practical mathematics, to know, the symbolic manipulation. With the purpose of explaining which the own concepts construction of the arithmetic type occurred, then, to the exam the renewal of the studies concerning the Kant s mathematics philosophy, particularly the arithmetic, that point for the discussion of subjects linked with the symbolism and the intuition. It had been intended to show the relationship between the symbolic aspect and the arithmetic ostensive aspect in the extent of the mathematics Kant s philosophy and in connection with that, if we should consider instances that correspond to arithmetic concepts or signs that are for these concepts. All discussed interpretations, direct or indirectly, conclude the discussion between the different arithmetic notations and the correspondent concepts or objects represented by them.