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Author Topic:   Is mathematics a science?
Posts: 6531
From: Oklahoma
Joined: 09-28-2003

Message 46 of 48 (240668)
09-05-2005 6:41 PM
Reply to: Message 43 by Brad McFall
09-03-2005 8:26 AM

Re: "/&/ "as genes? math or biology? normal rxns??
Sorry that it's taken me so long to get back to you, Brad.

I really do think that whatever that "math" is it is pure in itself no matter how it sorts difference of natural and artifical selection in the statistical normal distribution approximation.

While my contention is that modern mathematics is pure symbol manipulation, I certainly do not dispute that it is the mental concepts given to the symbols by the human mathematicians that make the practice of mathematics possible. I should also admit that it is, in the end, the correspondence between certain concepts in mathematics and concepts in the sciences (especially the physical sciences) that largely determine which fields of mathematics and the directions of research are "useful". As it should be, since the main motivation for mathematics (at least for non-mathematicians) is its utility.

This message is a reply to:
 Message 43 by Brad McFall, posted 09-03-2005 8:26 AM Brad McFall has responded

Replies to this message:
 Message 48 by Brad McFall, posted 09-06-2005 8:20 PM Chiroptera has not yet responded

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Message 47 of 48 (240674)
09-05-2005 6:54 PM
Reply to: Message 45 by Brad McFall
09-05-2005 8:23 AM

Re: to speak a langugage or not, is that a question?
I appreciate you taking the time to reply to me specifically but, as usual, I didn't understand a word of what you said.
This message is a reply to:
 Message 45 by Brad McFall, posted 09-05-2005 8:23 AM Brad McFall has not yet responded

Brad McFall
Member (Idle past 3136 days)
Posts: 3428
From: Ithaca,NY, USA
Joined: 12-20-2001

Message 48 of 48 (240930)
09-06-2005 8:20 PM
Reply to: Message 46 by Chiroptera
09-05-2005 6:41 PM

Re: "/&/ "as genes? math or biology? normal rxns??
Here is the "mental concept" am concerned about.

Can Weyl be mistaken that "quantity" is not much longer an issue but instead that the whole scholarship he attempts to close, should be reopened, as the " quantity of genes" is adumbrated. Is there not something to Mr.Jack's query as to if there is something else a foot?? I for one was completely struck to sit in a graduate seminar in ecology and evolution@CUin 86 to hear a new professor Will Provine used contra Johnson in 96 ask formerly without response from other profs, as to what a "gene" was. How we "quantify" them seems to invert the relative importance of metric and geometry in Weyls' thought in this context but I should rather speak of yours or mine. Quatification can have purposes in mind, not pure- granted. Thanks so much for your clear response. You and others in this thread have gained real respect from me time around.

On the character of mathematical cognition

From time immemorial mathematics has been looked upon as the science of quantity, or of space and number. (Though we also find this definition with Leibniz, the mathesis thus delineated is to him but a part of the more comprehensive ars combinatoria.) Today this view appears much too narrow in consideration of such fields as projective geometry or group theory. Consequently we need not worry particularly over an exact determination of what is meant by quantitative. In fact, the development of mathematics itself rasies doubts as to whether quantity is a well-determined and philosophically important category. Geometry, inasmuch as it is concerned with real space, is no longer considered a part of pure mathematics; like mechanics and physics, it belongs among the applications of mathematics. Under the influence of the general arithmetic of hypercomplex numbers and later of the axiomatic investigations, of set theory and symbolic logic, the distinction between mathematics and logic is gradually obliterated.

page 62 Weyl Philosophy of Mathematics and Natural Science.

I think we are tempted to think of bioinformatics as an implementation applicable to Weyl's perspective but I think this is mistaken as it entails TOO much Greek Society reference which just does not exist in post-modern culture. I thought Weyl failed to follow through the Katian LOGICAL horizon organonically. Yes, I need to justify that last sentence biologically but there is no distortion in my so thus thought such applied albeit it be.

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