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...the perpetual Plato/Aristotle dichotomy....

Hello Patrick! FWIW, to me, one of the most irritating habits of the modern mind is to see every question in terms of an either/or, true/false, yes/no, black/white decision. In many cases, this is an inappropriate way to look at problems; for often when we seem to have a case of choosing from among alternatives, what we really ought to be doing instead is recognizing the truth of what each "side" has to say. For in most cases, it seems to me there is truth on both sides. The differences in the alternative accounts mainly derive from differences in perspective. Rather than being mutually exclusive, the two accounts may be complementary. What truth either "side" has derives from the same source in any case. So it's not always a question of "either/or," but may be a question of "both."

Case in point: your observation WRT "the perpetual Plato/Aristotle dichotomy." Personally, I don't see there's a dichotomy at all. Aristotle was Plato's student for over a quarter of a century. They share much, yet in due course Aristotle shifted his attention away from the main concerns that preoccupied Plato: He was more interested in the study of creature than he was in the study of the ultimate foundations of microcosmic and cosmic reality. But this is not the same thing as saying that Aristotle doubted there was any such thing as ultimate foundations of reality. All it says is that his own interests were different from Plato's. So why do we feel that we most choose either Plato or Aristotle? The two of them together give us a profoundly rich and detailed picture of reality. We need them both.

Here's a very crude and perhaps silly example of what the false choice of "either Plato or Aristotle" can lead to. Take a doughnut and look at it. The Aristotelian would doubtless preoccupy himself with the "physical" part of the doughnut, and wouldn't look at the hole at all -- because there's "nothing to see there." Yet a doughnut is characteristically a doughnut because it has that hole! So you can't ignore the hole -- for the "whole" of the doughnut is comprised of the thing we can see and the thing we cannot see.

Case in point: your observation WRT "the perpetual Plato/Aristotle dichotomy." Personally, I don't see there's a dichotomy at all. Aristotle was Plato's student for over a quarter of a century. They share much, yet in due course Aristotle shifted his attention away from the main concerns that preoccupied Plato: He was more interested in the study of creature than he was in the study of the ultimate foundations of microcosmic and cosmic reality. But this is not the same thing as saying that Aristotle doubted there was any such thing as ultimate foundations of reality. All it says is that his own interests were different from Plato's. So why do we feel that we most choose either Plato or Aristotle? The two of them together give us a profoundly rich and detailed picture of reality. We need them both.

Precisely. The dichotomy is an existential one, not an ontological or even an epistemological one. You can function inductively or you can function deductively. Most people have a predisposition to value one or the other methods over the other. This is a comment on them, not the methods.

"So you can't ignore the hole -- for the "whole" of the doughnut is comprised of the thing we can see and the thing we cannot see."

That's a pretty good analogy, betty boop. Similar to different views of a child's block. Depending on your position, you can only see three sides at the most at one time. Someone viewing from a different position may see three different sides.

And again, someone viewing it straight on can only see one side as representing the whole.

I think the same analogy would describe how different people (beliefs) view the concept of God. Some view God as having only a single aspect. Others, who have moved from their position, view God as a Triunity -- each representing the whole.

I think it could also be expressed that as the volume of the cube can be known by multiplying length times breadth times height, so may the totality of God be known by the same equation. 1 X 1 X 1 = 1, not 3.

Thank y’all so much for this superb discussion! How compelling!

StJacques: I have always been fascinated by the ways the Cartesian Rationalists perceived mathematics as reflecting a perfection that exists beyond our existence, something that they felt could be rationally demonstrated without recourse to empirical validation. This perfection goes beyond science and I believe it does more to demonstrate the limits of science that anything else. Since mathematics is recognized as "the language of science" we must always ask ourselves "why is it that we are able to understand science"? And, if Descartes and Leibniz were correct, as I believe they were, the answer lies outside of science.

So very true! And well said.

With regard to the discussion about Einstein and “reality” I’d like to point out that in physics, "realism" refers to the idea that a particle has properties that exist even before they are measured. Einstein famously said:

Reality is an illusion, albeit a very persistent one.

In Einstein’s vision of relativity, gravity and space/time are like a duality. IOW, gravity can be described as an indentation of space/time. And it was his dream to transmute the basewood of matter to the pure marble of geometry, i.e. that the unified theory would be geometric. I believe we are getting closer to Einstein’s view at every turn and would like to offer for the discussion some of the work done by Harvard physicist Cumrun Vafa as evidence:

Cumrun Vafa profile

CERN Courier: Space goes quantum (topology and CY)

Geometric Physics

Mirror Symmetry and Closed String Condensation

For Lurkers, an introduction: Geometry and String Theory

Personally, I believe Einstein’s instincts were profound even though he philosophically stopped short of Plato's inquiry. He said ”To me it suffices to wonder at these secrets and to attempt humbly to grasp with my mind a mere image of the lofty structure of all that there is.” The word structure indicates that his interest ends with the geometry.

betty boop: Here's a very crude and perhaps silly example of what the false choice of "either Plato or Aristotle" can lead to. Take a doughnut and look at it. The Aristotelian would doubtless preoccupy himself with the "physical" part of the doughnut, and wouldn't look at the hole at all -- because there's "nothing to see there." Yet a doughnut is characteristically a doughnut because it has that hole! So you can't ignore the hole -- for the "whole" of the doughnut is comprised of the thing we can see and the thing we cannot see.

So very true. And whereas I’m confident that Aristotle did not ignore the doughnut hole – it is a sad result of modern scientific materialism that the existence of the hole is sometimes utterly denied in the name of science. Hence, the science consumer is force fed the ideology of metaphysical naturalism under the color of scientific materialism by such notables as Steven Pinker.

Using Einstein as an example, I agree with his sense that at bottom all fields will unify to a geometric solution. I agree simply because space/time is the host to all fields, a field being that which exists at all points in space/time. The mirror symmetry and duality which are built into nature illustrate the “unreasonable effectiveness of math”. In the CERN article, the speculation is that the fluctuations of topology and geometry are the origin of the strings themselves.

If that were the case and Einstein were still alive, it would be the end of the inquiry for him and virtually all scientific materialists – the Aristotle worldview with the modern added feature of denying the existence of the hole in the doughnut.

But the Tegmarks would pick up the inquiry from that point and ask why, in a classic Plato sense, it should be this way and not some other. And here I find Tegmark’s speculation particularly compelling, because all existents in any perceptible dimensionality can be described by mathematical structures. The universe, as many here have noted, is finite, i.e at minimum, countable and often, algorithmic (the doughnut) whereas the mathematical structures are non-corporeal, non-spatial and non-temporal (the doughnut hole).