aiguy:Plato held that ideal forms (including mathematical constructs) were real, but did he consider them to be the result of "intelligent" creation?

Plato was trying to deal with how the forms interact with the physical world. His answer seemed to be (at least in The Timaeus) a demiurge that was conscious of the forms, and then created the physical world after their patterns.
Then later in The Laws, Plato seemed to say that Mind was the most fundamental thing. Did he mean more fundamental than the Forms? Did the Forms reside in Mind? Not sure. I haven't read all of The Laws. I'll have to do that someday.

Mathematics is unreasonably effective when one ignores how many errors mathematicians make.

Are mathematicians all that "effective" and what makes them so effective?

Engineers Discover In Nature Exotic Structures Envisioned By Mathematicians

By the way, Wigner was a physics re-tread….he was an engineer by training who eventually became a Nobel prize winning physicist.

I'm glad to say, various schools are offering opportunities for engineers to get a retread as physics students…:cool:

Anyway, the point I was making was that neither "unspecified unintelligent cause" nor "unspecified intelligent cause" (ID) goes any distance at all in explaining why the universe is describable with mathematics. "Unspecified unintelligent cause" could be anything, of course - any sort of combination of causes that we currently understand, or a completely new sort of cause that we have never thought of. Likewise, "unspecified intelligent cause" could be anything too, from a "transcendent immaterial being" to an "unconscious algorithmic search mechanism naturally arising from the intrinsic interactive properties of dark matter" or something. Obviously, neither of these ideas go any distance to explaining anything about anything whatsoever, since we really can't say what we're talking about in either case.

aiguy:One could posit that some unknown, unintelligent process caused the universe, and this unintelligent process was mathematically describable, so the resulting universe was mathematically describable too. But this approach fails to identify what this process was, or say why it was mathematically describable in the first place.

This sounds very much like Pythagoras.

Alternatively, one could posit that some unknown intelligent entity caused the universe, and this entity was capable of understanding mathematics, and so the universe it created was mathematically describable too. But this approach fails to identify what this intelligent entity was, or say why it was capable of understanding mathematics in the first place.

I think Plato chose this approach.

Dembski: Factorability, however, has no physical significance.

That's not quite correct. Factoring is an outgrowth of counting and organizing. Factorization of quadratics can reveal underlying geometric relationships, e.g. a² + 2ab + b².

Our brains do not work in some magical manner that is independent of nature. Why would we expect to develop mental models that do not mimic nature?

But we do develop mental constructs that do not mimick nature. Salvador Cordova quoting Dembski:

Equations that are factorable are much easier for us to deal with than those that are not. Factorability, however, has no physical significance. A world indifferent to us has no stake in rendering itself intelligible to us by making the equations that describe it factorable through some mathematical device (like the Clifford algebra). And yet precisely such idiosyncratic manipulations of humanly constructed notations result in genuine and previously unsuspected physical insights.

There really is a problem here for naturalism. As Steiner notes, in every other area where human constructions are manipulated according to human convenience, naturalism expects and indeed confirms no profound in sight into the structure of the world. The rules of chess, for instance, do not yield insight into the structure of the atom. The study of palindromes (sentences that read the same backward as forward; e.g., "Madam, I'm Adam") tells us nothing about the first three minutes after the Big Bang.

One could posit that some unknown, unintelligent process caused the universe, and this unintelligent process was mathematically describable, so the resulting universe was mathematically describable too. But this approach fails to identify what this process was, or say why it was mathematically describable in the first place.

Alternatively, one could posit that some unknown intelligent entity caused the universe, and this entity was capable of understanding mathematics, and so the universe it created was mathematically describable too. But this approach fails to identify what this intelligent entity was, or say why it was capable of understanding mathematics in the first place.

I don't think there is any reason compelling anyone to prefer one of the alternatives over the other, but at least the former option leaves a simpler construct unexplained.

. Mathematics was not created independent of nature. Our brains do not work in some magical manner that is independent of nature. Why would we expect to develop mental models that do not mimic nature?

Paul Davies points out that if the laws of physics were not algorithmically compressible the universe would not be compehensible even if our minds were more powerful than the ones we have today.

"Algorithmically compressible" means we can express physical laws (approximations) with simple statements such as:

F=ma

The universe is thus highly amenable to computational analysis….

A computationally sensible universe is highly improbable when viewed in the space of possible universes — the cardinality of computable numbers is smaller than that of non-computable numbers…..

It is highly probable the universe would have been arranged in such a way that it would resist description by simple mathematical statements. Davies points out that only a narrow set of conditions in quantum cosmology would allow computable universes such as the one we live in.

We are able to apply data compression to our description of large numbers of natural phenomenon. If the datapoints were not amenable to this sort of compression, we couldn't have laws of physics, just a never ending catalogue of disconnected measurements……

If the universe were not fine tuned, the approxmately classical behavior on many levels would not be in evidence, and physics would be impossible. We would be unable to make inferences about anything…..

Without fine tuning, we would not have the approximately classical notions of motion and time, and the orbits of the planets (assuming they even existed) would be more like smeared out probability distributions that we see at the atomic level. Such world's would not be amenable to physical inquiry.

Davies book explains the details….I've only sketched out his ideas in these posts….Davies refutes the hypothesis that human minds in any universe would have been able to create the appropriate mathematics to explore such a universe. Only in certain possible universes will there be a convergence between mental processes and laws of physics…such a universe must be amenable to computation and algorithmic compression…

The idea that humans would adapt to whatever their circumstances is a Darwinian idea, it is not a scientific nor mathematically defensible idea

Mike: The belief that our universe was intelligently designed and is best understood through a design paradigm can be derived from many things among which is the "enormous usefulness of mathematics in the natural sciences."

Sure that subject observation might enforce someones preconceived notions. I, however, fail to see why this is anything put expected. Mathematics was not created independent of nature. Our brains do not work in some magical manner that is independent of nature. Why would we expect to develop mental models that do not mimic nature? I find it more amazing when our mental models turn out to be insufficient for the task of understanding nature. This is not to say we should treat instinct as a true reflection of nature, it is to say that our brains would not function at all if they were incapable of modeling nature in some rational way.

This reminds me of the "utility of abstraction" thread, its really another aspect of the exact same thing.