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."

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