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science is bipolar, but that's okay

[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 effficient causality with before/after. Wholes accepted naively. Time treated as primitive quantity.
The equal sign of mathematical formulations on laws of nature taken as indicating closedness. 

2nd wa of looking at nature: Other p.o.v.: nature as modeled, with human agency as the exemplar of archetype. Effficient cause like simultaneous interaction. Formal cause as energeia; final cause as that toward which energeia (qua entelecheia) is directed.

Both POVs work together in modern science.

1st Looking at Math p.o.v., nature seems to be closed system. Think of equal sign. Each side a quantifiable. No room for metaphysics, so it seems, unless you want to do the Platonic metaphysics of number and of knowledge of number itself:

2nd Looking at agency POV, nature is open, incomplete; unifying form is evident to intellectus; to transcendence.

How the two interwoven. How folks who engage in polemics about limits and abilities of science often make something like category mistakes re these two POVs, ping-ponging between the two of them.

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