Probably the least controversial or 'speculative' sounding approach to metaphysics is the one that conceives of it basically as investigating the relationship between thought, mathematics and reality. Mathematics is so interesting because its boundaries (the boundary between mathematics and thought and the boundary between mathematics and reality, respectively) are so mysterious.

Consider first the boundary between mathematics and reality. Here we'll take reality to be simply the physical, objective world as physics understands it. On the one hand, we want to say that mathematics is a way of merely describing reality, as opposed to being really intrinsic to it. Human beings, with their power of cognition, come up with mathematical formulas in order to master nature. On the other hand, it seems we are required to think that in some meaningful sense mathematics really *structures *reality (rather than merely describing it). Our formulas would not work if they were not, in some way, basically isomorphic with the actual world that they are being applied to. Mathematical laws are discovered - they are part of reality itself - not simply made up.

Now on the other end, consider the boundary between mathematics and thought. On the one hand, we are tempted to say that mathematics simply *is *thought, or the highest form of thought. It is minds that do mathematics. On the other hand, math has quite a lot of synthetic content that seems to be arbitrary in a sense - it is not content that is merely true because of laws of thought, nor is it necessarily related to something physical.

Mathematics, then, is a sort of 'cognition' that can't easily be located inside minds nor outside in the world.

Structural Realism is the position (or constellation of somewhat differing positions, rather) that the physical universe is simply a special case of a mathematical structure. One could imagine subsuming both the world and the mind in a kind of mathematical infinity. This position is attractive and seems more and more likely the more we learn about computation. But can it amount to a complete explanation with no gaps?

It isn't so hard to imagine that human experience is at a certain level an illusion, and that we are wrong to feel that our ineffable and mysterious experiences cannot be quantized. What is much harder, though, is to describe the mathematical totality in a way that doesn't require further cosmogonical explanation. Even if there is an equation that could be unpacked to yield all of time and space, it must either have specificity (be one of multiple options) or not. It if does have specificity, we can wonder why *this *equation was chosen and not others. If it does not (if it is a sort of primordial A = A or Om), we are justified in wondering why it has produced the world at all.