The Human Question

This relates to that analysis of mechanism where a person discovers a machine/or/device and tries to analyze it without guessing its purpose....he would describe it in lawful language. The new point is that engineering (techne/ars in Greek/Latin) is able to use nature for achieving human purposes precisely by thinking of nature as an instrument.  In order to give a supervening purpose to nature, it must describe it in a manner that is, in a sense, ateleological.  And that language is naturally mathematical.  A cook counts how many eggs; a cosmetologist talks about hair length, a farmer talks in geometrical language about how to plow the field. Could we include hypothetical reasoning w/ mathematical? That's probably not 100% on target, but I do think I'm on to something...

Math soliter is descriptive, not explanatory. And the description has to do with quantity (DUH!) But the quantity deals first of all with form in the sense of shape. (note atomists) But when applied to the explanation of natural phen, math can refer to quality in the sense of disposition, as in force, for example, as well as action and passion... after a fashion... too late to finish... wife sez blogging not my buz at this hour...

How mathematical operations require the infinite: they don't require an explicit affirmation of the infinite any more than reasoning requires an explicit affirmation of the principle of non-contradiction.  But they do require an openness to the applicability of the form of the operation to more numbers. And if numbers had a limit, X+1, where the operation would not work, then our knowledge about the form of the proposition would not be genuine knowledge.  We wouldn't even be able to know how to apply the operation to known numbers IF we denied that it could apply to others.  An openness to an unbounded applications is necessary in principle for us to be able to know what we do about numbers within the bounds that we have found them so far.

[Sketch of a longer post:] Really, I mean bifocal. Science as we know it is always doing the following two things together (or at least when it is functioning well): looking at nature in terms of analogies with human agency and in terms of what can be quantified. To do just one of these two is to depart from science and, well, to embarrass oneself (and I can't do either of the two, which is even more embarrassing). 1st way of looking at nature: Mathematical p.o.v. nature as placeable within Cartesian coordinates and describable according to quantitative laws of nature. Such descriptions take atom like wholes for granted and ignore final or formal causality. Or rather you might say that they reduce formal = pythagorean shape whatever lawful description can be used, etc. Temptation is to look at material substrate as ultimately being this intert monistic stuff (sorta like pure extension of Descartes) The treat material universe monistically monistic stuff or atom. Replace ...

One interesting point of departure for the study of human nature is our ability to know (or suppose that we know) laws of nature. For quite a while these laws have been formulated in mathematical and geometric terms. But math and geometry involve a kind of awareness of the infinite: the infinities that pertain to math and geometry, that is. But what kind of awareness is that? Is it simply a combination of NOT plus FINITE? But how could that mean anything if finite things are all we know? There is some sort of transcendence of experience going on here. Or rather, a transcendence of all possible experience. At this point it seems to be a good idea to reread the Phaedo.