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I join in the chorus strongly agreeing with Kolokotronis’ remark:

I am convinced that Aquinas was not by any means an Aristotelian, but the language and methods of Aristotle formed a common context for the discussions. Unfortunately his successors seem to have adopted Aristotelianism not merely as a framework within which to discuss Christianity with pagans, but rather accepted it as the way to explain God to themselves and other Christians. This manner of thinking about theology, scholasticism, had a profound effect on Western religious thought and compounded the already existing differences between Eastern and Western Christianity

Just the mention of Platonism in math and physics used to send our correspondents on Free Republic into a tailspin of accusations that betty boop and I were off the intellectual rails.

But I strongly suspect that is because Aristotle’s words (e.g. four causes) have been massaged to fit a modern view of science when he was actually almost entirely in sync with Plato.

One of those posters routinely posted a work of art which had Plato pointing up and Aristotle pointing down:

IMHO, that image is an accurate portrait of the difference as it effects one’s math or science.

In an article on parallel universes, physicist Max Tegmark described the difference in paradigms this way:

Parallel Universes

A mathematical structure is an abstract, immutable entity existing outside of space and time. If history were a movie, the structure would correspond not to a single frame of it but to the entire videotape. Consider, for example, a world made up of pointlike particles moving around in three-dimensional space. In four-dimensional spacetime — the bird perspective — these particle trajectories resemble a tangle of spaghetti. If the frog sees a particle moving with constant velocity, the bird sees a straight strand of uncooked spaghetti. If the frog sees a pair of orbiting particles, the bird sees two spaghetti strands intertwined like a double helix. To the frog, the world is described by Newton’s laws of motion and gravitation. To the bird, it is described by the geometry of the pasta — a mathematical structure. The frog itself is merely a thick bundle of pasta, whose highly complex intertwining corresponds to a cluster of particles that store and process information. Our universe is far more complicated than this example, and scientists do not yet know to what, if any, mathematical structure it corresponds.

The Platonic paradigm raises the question of why the universe is the way it is. To an Aristotelian, this is a meaningless question: The universe just is. But a Platonist cannot help but wonder why it could not have been different. If the universe is inherently mathematical, then why was only one of the many mathematical structures singled out to describe a universe? A fundamental asymmetry appears to be built into the very heart of reality.

The shift to an Aristotelian paradigm came with a big price. The most obvious is described in the last paragraph of the Tegmark excerpt, an isolation of science from the quest for knowledge per se. They no longer see the mission of science as Leibnitz said, to inquire into two matters:

Why is there something, rather than nothing?

And why are things the way they are, and not some other way?

The price to the faithful has been much, much higher because so often now, armed with Aristotelian logic, believers demand that God must be logical – and thus they anthropomorphize God, missing the power of God.