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.
quote:
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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