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When looking at Plato and Aristotle, where would we put them from the perspective of modern philosophy of science?
For Plato, the abstract ideal geometric forms had more reality than their Earthly manifestations. An object that looks pretty circular and that is contaminated (in Plato's view) by the dirt by worldly stuff (fingerprints, stains, moist, small things sticking out or in it) was just a manifestation of the more realistic idea of a circle.
For Aristotle, on the other hand, a round, circular object with all the stuff attached was the real thing.

Both are realist in their own domain of reality. Did Plato attach no value to the senses? Wasn't he an empiricist? If so, then how could he see the geometries? Was Aristotle an empiricist? Or did he think of a reality behind the perceived one? Were sense impressions all for Aristotle and were any ideals just fantasies not having a place in reality? If so would he think that a thought banana was the same as a real banana? Or are they just the same all over, despite their apparent differences?

Based on these two examples only, how would we call them? A platonist and an anti-platonist?

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    It is hard to consider them "from the perspective of modern philosophy of science". See Platonism in Metaphysics: "Platonism is the view that there exist such things as abstract objects — where an abstract object is an object that does not exist in space or time and which is therefore entirely non-physical and non-mental." See also Platonism in the Philosophy of Mathematics. Jun 16 at 11:59
  • Aristotle was much more interested into empirical knowledge; see A's contribution to biology and zoology. But we cannot "classify" A has an "empiricist" in the modern sense (Locke, Hume, etc.) Jun 16 at 12:01
  • @MauroALLEGRANZA I was thinking about Plato's view of the basic geometric forms and the mathematical sense of reality. There are two views on math. One says the objects in math are real, the other view is that the objects exist in the mind only.
    – user52804
    Jun 16 at 12:03
  • Yes, for Plato numbers are real object the we know with our mind (see Forms) while for Aristotle number are "abstracted" from our knowledge of empirical things. Jun 16 at 14:27
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Aristotle was not an empiricist in anything like the modern-day sense of the term. He had a "philosophy of science" radically incompatible with the empiricism of the early moderns or the mainstream philosophy of science today.

In particular, Aristotle held that science would consist in an axiomatic-deductive system, for which Euclidean geometry served as the exemplar. Along with this, his epistemological stance was that we know the theorems of the axiomatic-deductive system by virtue of grasping first principles and deducing those theorems.

Thus, Aristotle's philosophy of science consists in the search for first principles. This yields the traditional distinction between episteme and sofia and nous. Knowledge of first principles, which is yielded by nous, is more certain ("better known") than the episteme derived from the first principles. The ultimate first principles grasped by nous would be, for Aristotle, an a priori ontology that ultimately grounds every specific science.

But empiricists hold that we do not accept a scientific theory because we believe its axioms. Rather, we accept the theory because it yields a set of predictions superior to competing theories. We cannot then have ultimate knowledge of any first principles; we can only make strategic decisions that will refute a theory.

Empiricistic philosophy of science rejects the whole search for first principles and the possibility of an a priori ontology. The basic thrust of empiricism is that all scientific knowledge is hypothetical, and that the "first principles" of a science are as hypothetical as the theorems themselves. There is no problem of first principles in today's philosophy of science, rather, ontology becomes an a posteriori handmaiden of the empirical sciences.

It's true that Aristotle holds that knowledge of abstract objects is abstracted from empirical particulars. But I don't think Aristotle is anymore "down to earth" by today's standards than Plato. He had what is in my view a more sophisticated philosophy of science, but by today's standards it still looks exceedingly rationalistic. I don't mean to suggest that the rejection of Aristotlian ontology by empiricists is right or wrong, but merely to say that Aristotle's position on ontology and epistemology gives a far more robust place to mental faculties like nous and sofia for "seeing" mathematical forms than does present-day philosophy of science (rightly or wrongly).

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Traditionally Plato is considered as the prototypical idealist, whereas Aristotle is indeed considered more "down to earth," a dichotomy immortalized in the famous painting that depicts Plato pointing up and Aristotle pointing down.

Both Plato and Aristotle predate the rise of empiricism as an approach to the world in Western philosophy, although Aristotle is sometimes considered a kind of proto-empiricist.

If we do insist on judging them by this later standard, Plato is perhaps best considered anti-empiricist, since he believed that true knowledge comes through the mind, not the senses. At best the senses, for Plato, can remind us of the Truth, they do not convey it to us, nor teach it to us (see the Meno and the theory of recollection). Aristotle, conversely, is interested in the things of this material world, and their practical implications, but does not place any particular emphasis on sensory evidence --if anything, he takes it for granted.

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