Hi Evgenii Rudnyi Interesting thoughts.
What I say below about analytic vs synthetic thinking is pre-Godelian and may no longer be true. That is, pure analytic thinking, because of the incompleteness theorem, may no long be considered possible. Ie that all thinking must be in part (or at least sometimes) synthetic. If you would like more of an explanation, read below. Roger Clough ---------------------------------------------------------------------- PRE-GODELIAN ANALYTIC VS SYNTHETIC THINKINg According to Aristotle and Kant, analysis -- that is, going from the general to the particular-- cannot give us anything truly new, for all it can do is rearrange or select things already known or assumed. So technically, Maxwell's Theory of Electromagnetism is not new knowledge, it is merely a rearrangemnent of what was known to be true at that time. I hasten to add that the truths or axioms that Maxwell combined in that master analysis were I think synthetically (intuitively) discovered by Maxwell previously. This is a topic I suppose for the philsophy or history of science. Clearly on the other hand, Einstein's Theory of Relativity truly contains new truths, because of his intuitive discovery or invention of relative time, which varies in such a way that no matter how you measure it, the speed of light is always the same. That was Einstein's magnificent breakthrough and it was discovered by him somehow not in current thinking but due to his intuition that the speed of light must be constant. That's called a synthetic truth. To put it briefly, analysis can teach us -- in principle, at least -- nothing we did not already know. Roger , rclo...@verizon.net 8/17/2012 Leibniz would say, "If there's no God, we'd have to invent him so everything could function." ----- Receiving the following content ----- From: Evgenii Rudnyi Receiver: everything-list Time: 2012-08-15, 04:45:30 Subject: G del on the Foundations of Mathematics After browsing Leibnitz' Monadology (Roger, thanks for the link), I have checked what else is available on marxists.org. It happens that marxists have quite a nice library available. I have even found an interesting paper of G?el. There he claims that Husserl will help us to find out what mathematics is. Evgenii Kurt G?el (1961) The modern development of the foundations of mathematics in the light of philosophy http://www.marxists.org/reference/subject/philosophy/works/at/godel.htm "In what manner, however, is it possible to extend our knowledge of these abstract concepts, i.e., to make these concepts themselves precise and to gain comprehensive and secure insight into the fundamental relations that subsist among them, i.e., into the axioms that hold for them? Obviously not, or in any case not exclusively, by trying to give explicit definitions for concepts and proofs for axioms, since for that one obviously needs other undefinable abstract concepts and axioms holding for them. Otherwise one would have nothing from which one could define or prove. The procedure must thus consist, at least to a large extent, in a clarification of meaning that does not consist in giving definitions." "Now in fact, there exists today the beginning of a science which claims to possess a systematic method for such a clarification of meaning, and that is the phenomenology founded by Husserl. Here clarification of meaning consists in focusing more sharply on the concepts concerned by directing our attention in a certain way, namely, onto our own acts in the use of these concepts, onto our powers in carrying out our acts, etc. But one must keep clearly in mind that this phenomenology is not a science in the same sense as the other sciences. Rather it is or in any case should be a procedure or technique that should produce in us a new state of consciousness in which we describe in detail the basic concepts we use in our thought, or grasp other basic concepts hitherto unknown to us. I believe there is no reason at all to reject such a procedure at the outset as hopeless. Empiricists, of course, have the least reason of all to do so, for that would mean that their empiricism is, in truth, an apriorism with its sign reversed." -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to email@example.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to firstname.lastname@example.org. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.