> the existence of thoughts, imaginings, and concepts is pretty well universal amongst humans and possibly other organisms. Surely there is no need to imply it is a far-fetched notion!

Well, yeah, but a more basic question is what we mean by "exist." In a broad sense, they all obviously "exist." But except for the experience of perceiving it in your mind, does the *idea* of a 747 exist in the same way, or to the same degree, as a *physical* 747?

There seems to be more than one kind of existing, but "seems" isn't quite the same as "is." Advances in neuroscience certainly appear (that means "seem") to show that all thought is merely neurochemical activity, but I confess that that's so counterintuitive as to be unbelievable. Much like the fact that the earth goes around the sun seemed five hundred years ago.

Mathematics is another problem. While I can't find you a "three," I admit that evidence of "threeness" etc. is everywhere in nature. Mathematical quantities and relationships are certainly "real": not only do they exist in our minds, they can actually be manipulated to bring tangible results in the material world. And they include concepts like sqr -1 that, in and of themselves, seem to be irrational and impossible.

If words have any meaning at all, "2 + 2 = 4" is true for all time (where 2 and 4 represent integers that don't all melt together as when 2 raindrops plus 2 raindrops can equal 1 big raindrop on your windowsill, for example). Two dinosaurs and two dinosaurs equalled four dinosaurs even if there was no one around to notice.

So mathematical rules certainly seem to have been part of the Big Bang, even though they are essentially abstractions. Thus some abstractions can certainly "exist" and be "real," realer in fact than my mental image of a 747, which doesn't interact with the outside world at all.

But were mathematical rules equally independent of all things physical at the moment of the Big Bang, or did they arise from some unknown physical principle or material that blew itself out of existence in the first fraction of a nanosecond?

Beats me.

The point is that what's material is certainly "real," and immaterial mathematics is also certainly "real," though seemingly not in quite the same way. Maybe other things, like thoughts, are "real" in some other way or ways. Anything's possible, but the wisest course is to stick to what evidence there is and remain undecided about what's utterly unknown.