Philosophy of mathematics and computer science and philosophy of science's active role in

1、 Philosophy of mathematics and computer science and philosophy of sciences active role inSummary This right exists in the philosophy of mathematics and philosophy of science, and philosophy of mathematics and computer science between the impact and penetration to analyze the relationship and use it

2、as a basis for proposing an active role of this knowledge and conceptual development general model, that we should not only attach great importance in different fields, the important link that exists between, and should be clearly affirmed the dynamic nature of this relationship. Text 1 Introduction

3、 This article has two interrelated objectives: first, that philosophy of mathematics in the 20th century, with two very different areas, namely, the philosophy of science and computer science (including artificial intelligence), resulting in a significant interaction, but also , these three areas af

4、fected by this interaction benefited greatly; Second, as for the further analysis of this interrelationship, this paper proposes an active role (dynamic interaction) concept, the authors believe that this in fact on behalf of the concept of knowledge and development of a universal model. In order to

5、 facilitate the discussion, the following first of the active role in this concept of a more specific characterization. In my opinion, this mainly includes the following four characteristics: (1) In the two previously unrelated areas considered to be among the link may be found in some surprise; (2)

6、 both have such a link, or more precisely, by this interaction, has greatly benefited; (3) This is not a static but a dynamic relationship, in particular, the previous position in the secondary area is likely to turn to occupy the leading position, and vice versa; (4) to maintain contact with each o

7、ther at the same time, opposing two sides should maintain a certain degree of relative independence, which in fact is the major and minor changes in the status of a necessary condition. Philosophy of mathematics and philosophy of science in this century, the interaction can be seen as the active rol

8、e of the first example: In the first half of this century, philosophy of mathematics is clearly dominant in both the position of, for example, Vienna School is from the philosophy of mathematics (which at the time index is mainly basic research) to draw a lot of important basic ideas in order to dev

9、elop their own philosophy of science from the theory, the latter and has a large period of time has been regarded as the philosophy of science in the field of orthodoxy; however, since the age of 60 years, have gradually replaced the philosophy of science philosophy of mathematics in the two occupy

10、a dominant position, for example, is mainly due to the impact of the philosophy of science that had led to the revolutionary philosophy of mathematics in modern change. For the philosophy of mathematics and philosophy of science of this dynamic role will be to make a detailed analysis in section II.

11、 Second, between the philosophy of mathematics and computer science we can see the same active role. In fact, some of the founders of computer science, namely, such as the Von Neumann (Von Neumann) and Thulin (A. Turing) and so on, have been directly involved in the previous philosophy of mathematic

12、s (basic) research, and, in the Second World a number of post-war years, computer scientists from the philosophy of mathematics has been trying to draw a number of important ideas, which in the future artificial intelligence research has been further applications; however, modern developments in com

13、puter science, especially in The so-called proving, in turn on the philosophy of mathematics research has raised new questions, and to some extent affected the philosophy of mathematics of modern development, so that the role of both primary and secondary relations also have undergone substantial ch

14、anges. For the philosophy of mathematics and computer science between the dynamic role of the specific analysis that is the main content section III. Clearly, the above two examples also show that: active role of the concept has a certain universality, and thus can be regarded as knowledge and conce

15、ptual development of a model. Should be raised is, active role is not a new concept, especially in the Chinese traditional philosophy, we can find many similar ideas. For example, the I in the following discussion is obviously the above on the active role main characteristics of the analysis of dire

16、ct parallel: Whether the relative health, ease of complementary and length by comparison, Gao Xia-phase tilting, sound phase and, after hand in hand. (Chapter 2) Bad Come into an opportunity, Fu Xi evil of the volt. Knows the right of extreme? Its non-positive. (Chapter 58) Counter-movement of the T

17、ao, the weak Road use. (Si Shizhang) In addition, the removal of ancient Chinese philosophy in the early embryo, the number of modern scholars, have through their own research has raised a similar idea. For example, is particularly important that the United States women scholars Douglas Gertz (E. Gr

18、osholz) once the field of mathematics in the interaction between different branches, including the logic and arithmetic (1981), logic and topology (1985), geometry and Algebra (1991), etc., to conduct a more systematic study. Glass Gertzs conclusion: this interaction for the development of mathemati

19、cs has a very active role; in particular, if the interaction at the same time, the relevant branch to maintain a certain degree of independence, then this interaction would The most useful, on the contrary, if an area full of trying to go into another area, you may hinder further development. Thus,

20、despite the Glass Gertz, and failed to clearly put forward the active role of the concept, but also failed to clearly identify the role of both primary and secondary relations between the dynamic (change) in nature, but the above analysis can still be seen as for her the corresponding point of view

21、the need to deepen and rational development. 2 philosophy of mathematics and philosophy of science of the dynamic role of Known to all, on the philosophy of science as the birth of an independent discipline is concerned, in large part be attributed to logical positivism (more precisely, that is, the

22、 Vienna School), who is the philosophy of mathematics in this played a very important role. Specifically, the contribution of the Vienna school that we can go up from two different levels of analysis: First, the Vienna Circle philosophy presented on the nature of a new perspective and highlighted th

23、e philosophy of logical analysis method for the special importance of the fact, since the development of a new kind of philosophical traditions, that is, analytic philosophy, the latter English-speaking countries who had long-dominant position. For example, the position of the Vienna Circles declara

24、tion , that the worlds scientific concepts: Vienna School in this book there is a clear reflection on: The task of philosophy is the clarification of issues and propositions, rather than make a special philosophy proposition. This method is to clarify the method of logical analysis. (11 p.8) Second,

25、 only through the work of the Vienna school of philosophy of science truly become a separate subject. That is to say, only through this school, work, philosophy of science has gained a clear meaning, and have an established research questions and methodology. The fact is that, despite the philosophy

26、 of science content and scope of a historical evolution and development process, but the Vienna school of philosophy of science has been dominant in Western academia, occupy the position of long-term and hence be seen as the orthodox philosophy of science point of view. The philosophy of mathematics

27、 philosophy of science on the impact of, clearly we should concentrate on the above-mentioned second aspect, but because of the Vienna school in the philosophy of science in the field of work is the general philosophical position with their closely linked and, therefore, Only the latter as a backgro

28、und to carry out analysis, we can well understand this school of philosophy of science working in the field of nature and philosophy of mathematics a significant impact in this regard. For example, only from this point of view to carry out analysis, we can well understand the Vienna Circle in the fi

29、eld of philosophy of science for their own set targets, as the latters position in fact is its basic philosophy of the concrete in this area expression, or, that is, their basic philosophical position directly determined. Specifically, the metaphysical objection (or, for the basic position of empiri

30、cisms insistence), and an emphasis on the logical approach is undoubtedly the Vienna Circle (more generally, that is, logical positivism) the two most important features of the This basic philosophical position also directly determine its presence in the philosophy of science in the field of the mai

31、n objective, that is, go through one level of technology, until those in the lowest tier of directly related to the direct grant (immediately given) concepts and propositions to the scientific concepts and to clarify the meaning of propositions (By contrast, if the item can not be a word to be const

32、ructed by means of a direct grant, then the items that contain this term should be regarded as propositions on the meaningless, that is should be seen as metaphysical pseudo-proposition to exclude from the scientific field); In addition, as a whole, this also means that we should be directly given a

33、s the foundation on which to build or re-construct all the science (this is the so-called unified science). Obviously, we can clearly see in this philosophy of mathematics an important implication: it is the logical doctrine of basic research, namely how to construct a logic-based or re-constructed

34、from all the mathematical work for the Vienna school provides a direct example of or model. However, as the logical activists to go into all the mathematical logic encountered serious difficulties in the work of the Vienna school building unified science efforts have also not been easy, and therefor

35、e caused further theoretical thinking, in particular the people began to in-depth to examine the following issues: the scientific basis of the experience of what it is is an individual experience, or observation of public record? In addition, the so-called observation propositions and theoretical pr

36、opositions and there really between what kind of relationship, or, in what sense, the theoretical proposition can be confirmed by the corresponding observation? Is easy to see, as opposed to the specific construction of scientific theories, the above thought into a higher level, because it is no lon

37、ger concerned about a particular scientific theory of any specific building, but a scientific theory general structure. Thus, it is actually on behalf of the Vienna Circle philosophy of science, the concept of a major change. The latter can be simply stated as: the philosophy of science that is so-c

38、alled meta-scientific. Thus, it is also clear from another point of view of the important influence of the philosophy of mathematics, because, in the final analysis, yuan (meta) This concept is directly borrowed from the philosophy of mathematics over: it is directly originated from Hilbert special

39、basic research, namely the so-called meta-mathematics. To sum up can be seen from the philosophy of mathematics concepts and ideas did in the Vienna Circle philosophy of science research has played a very important role. Thus, the philosophy of mathematics and philosophy of science on the mutual rel

40、ations are concerned, we should say, in the first half of this century, the philosophy of mathematics to hold a dominant position. 40 years since the beginning of the philosophy of mathematics has entered a period of pessimism and stagnation; the same time, the philosophy of science already graduall

41、y got rid of the tradition of logical positivism into a thriving new period of development. Taken from this perspective, led to the development of the latter, one of the important reasons is that: although the philosophy of science had long before at the basis of Marxist philosophy of mathematics, u

42、nder the direct influence, but even in such circumstances, the scientific philosophy remains a certain amount of relative independence, in particular, has always been the philosophy of science has its own specific research questions. Since the latter is the basic philosophy of mathematics the proble

43、m is not quite the same, therefore, it is the philosophy of science on these issues gradually started his own independent development. For example, in the first logical positivist and Popper (K. Popper) about what is scientific and non-scientific propositions demarcation of the standard debates, tha

44、t is, whether this is the verifiability or falsifiability of? Subsequently, in the wider sense, we can also see the logic of empiricism and historicism school debate on the nature of science. Finally, the so-called new historicism school is also a variety of viewpoints on the previous widely critici

45、zed, and through the integration of different points of view put forward on the rationality of scientific development and new insights. Thus, from the whole, the philosophy of science had been away from the tradition of logical positivism which has entered a new period of development. Because the ph

46、ilosophy of science emerged in the modern study of so many new concepts, ideas, problems and methods, therefore, that for the beleaguered mathematical philosophers had a tremendous appeal. For example, in the latter one of the scholars working in the field will sooner or later realize that such a nu

47、mber of issues, that is, as we should those in the modern study of philosophy of science played an important role in promoting the concept or idea into the field of philosophy of mathematics? Again, some problems have been proved in-depth understanding of the nature of science has a special signific

48、ance, which, in the philosophy of mathematics, we should also be to discuss whether the same or similar problems? For example, it is such an atmosphere, Kelun Wa (M. Crowe, 1975), Moerdunsi (H. Mehrtens, 1976), and Dao-Ben (J. Dauben, 1984) and so once successively Kuhn (T . Kuhn) on the theory of s

49、cientific revolution in mathematics can be applied is analyzed. In addition, more generally, Thomas Rizk (T. Tymoczko) of the following remarks can be seen as even more concentrated in this direction represents the mathematical philosopher working on a common attitude: It seems the philosophy of sci

50、ence is indeed in advance among the philosophy of mathematics why not move it ? (7 p.127) Even though the direction of research in the initial promotion and migration are mainly the work of some, however, as time passes and in-depth study, which comes from the impact of the philosophy of science of

51、the modern development of the philosophy of mathematics had a very important influence, and with the philosophy of mathematics with its own dynamic factors (the latter mainly refers to the basic doctrine of the philosophy of mathematics for the in-depth critique as well as on how it should be to eng

52、age in conscious reflection on the philosophy of mathematics studies), in fact, created a revolution in the philosophy of mathematics. 15 17 Thus, the mathematical relationship between philosophy and the philosophy of science, this is clearly an important change: the philosophy of mathematics philos

53、ophy of science has been replaced by the two occupy a dominant position. Finally, it should be mentioned that, Lakatos (I. Lakatos) the work can broadly be seen as the real turning point in the above-mentioned changes. Specifically, in the early 60s, Lakatos passed to Poppers falsification philosoph

54、y of science popularization and application of Marxism to the field of mathematics and thus developed a theory of his own philosophy of mathematics, which is in fact the first thought is the philosophy of science be applied to the field of philosophy of mathematics. In addition, the removal of the a

55、bove-mentioned work, Lakatos again in the opposite direction on the work, that is based on the logic of the development of mathematics as the basic conceptual framework for the development of new scientific and philosophical theories: Scientific Research program methodology . 14 Thus, Lakatos not on

56、ly contributed to the above-mentioned changes in the first, more from this cross-over study to get the biggest gains. To sum up we can see that in this century philosophy of mathematics and philosophy of science in terms of development, in large measure through active role to be achieved. Reposted e

57、lsewhere in the paper for free download 3 Philosophy of Mathematics and Computer Sciences active role in The philosophy of mathematics for computer science major impact of the performance of the following facts: Some from the philosophy of mathematics (mathematics for basic research) concepts and th

58、eories in the historical development of computer science has played a very important role. For example, this could be the first-mentioned (a first-order) predicate calculus theory: This is determined by Frege (G. Frege), published in 1879, the concept of language was first given, while the latter ha

59、s often been read basic research into the actual starting point for mathematics; However, this mainly to the strict mathematical-based (more generally, that is, thinking strictly of) the conceptual tools created by computer science has become the most important theoretical tool for In particular, a special form of predicate calculus (the clausal form) has even been proved artificial intelligence (that is, if th