From Concepts To Signs——A Study On Early Husserl’s Thoughts About Arithmetic Philosophy And Its Intrinsic Logic

Traditionally, the academic world simply defined Philosophy of Arithmetic as psychologism. However, Husserl’s thoughts about philosophy of arithmetic are not so simply. It experienced different periods of development which include an intrinsic change of logic. Moreover, as the beginning of Husserl’s research on philosophy, it has a close connection with the foundation of phenomenology. Therefore, we need to critically investigate Husserl’s thoughts about philosophy of arithmetic more deeply. It is the main objective of this dissertation to show the whole appearance of Husserl’s thoughts about philosophy of arithmetic as far as possible and get its intrinsic logic of development into shape. Thus we can evaluate it objectively and provide foundation for a research on its relationship with the phenomenology.The main body of this dissertation is divided into three chapters, whose topics are "the authentic concepts of numbers and conceptual calculation", "the inauthentic concepts of numbers and symbolic calculation" and "the transition from the logic of concepts to the logic of signs".The first chapter mainly introduces Husserl’s analysis of the authentic concepts of numbers and its calculation. Husserl believed the whole numbers presupposed all the other number concepts and thus should be the beginning of the analysis of arithmetic. However, he not only objected to Frege’s logical definition of numbers but also didn’t agree with Kant that number concepts originate from the pure intuition. He emphasized that the number concepts can only be clarified by referring to the intuitive representation from which it is abstracted. Because the concept of multiplicity contains number concepts, Husserl first analyzed the origination and content of the concept of multiplicity. He found that the concept of multiplicity is abstracted from a psychological collective combination and in the process of abstraction each content or object is conceived as "something". Thus this process can be described as "something and something and something......". While number concepts are further determinations of the concept of multiplicity, both of them are based on the intuition of concrete multiplicities and compose of the concepts of collective combination and something. After clarifying the origination and content of number concepts, Husserl then revealed the psychological basis of addition and partition that are two kinds of conceptual calculation. At this time, Husserl still understood arithmetic as activities about number concepts.The second chapter turned to discussing the inauthentic concepts of numbers and symbolic calculation. The reason is that people can only authentically conceptualize the number less than twelve. Moreover, besides addition and partition, multiplication, exponentiation and division are all operations on signs based on operations on number concepts. Therefore, Husserl found that it is the signs or inauthentic representations that determine the characteristic, sense and purpose of arithmetic and thus turned to the research on the inauthentic representations of multiplicities and number concepts. Husserl thought the psychological basis of inauthentic representations of multiplicities is a kind of figural moment which is a quasi-qualitative character presented by the fusion of the individual contents and which serves as the sign of the inauthentic representations to make the instantaneous apprehensions of groups possible. Based on the inauthentic representations of multiplicities, number concepts are expanded to the inauthentic areas as well. This is because for every representation of multiplicity, there is a determinate number corresponding to it. However, there still needs systematic symbolization for number concepts, out of which arises a systematic including both the systematic of the number concepts and the systematic of number signs. It is the dual character of systematic and the strict one-to-one correspondence between the two systems that make the technical symbolic calculation possible.The third chapter presents the logic of the development of Husserl’s philosophy of arithmetic on the whole. From the authentic number concepts to the symbolic number concepts, Husserl always based number concepts on the representation of multiplicity. However, on one hand, Husserl had to confessed that the theory of representation couldn’t answer how the number zero and one, negative numbers, rational numbers, irrational numbers are represented. On the other hand, the constitution of the systematic shows that signs not only can be used independent of number concepts but also participate in the derivation of number concepts. Because of this, Husserl became aware of that it was impossible to reveal the origination of number concepts and arithmetic with the theory of representation alone, and that the symbolic method was the fundamental method of arithmetic. Therefore, Philosophy of Arithmetic includes two different understandings of arithmetic. The theory of representation which led Husserl proved to be incorrect finally. Husserl then turned to studying the logic of signs.Hence, although Husserl’s philosophical analysis of arithmetic includes immature or even false opinion, he found the problems of the theory of representation in this process and thus turned to studying the symbolic method and then the objective logic. In this sense, we can say that there included a beginning of leaving psychologism for logical investigations in Philosophy of Arithmetic.