>>21
Do laws of physics have neural correlates?
I'd say: No. Neural correlates are a matter of structure. My conjecture is that if you were to replace some neural structure with its functional equivalent, you will still remain conscious and have "the same" conscious experience. This view of functionalism (or more strongly computationalism) is what I believe is true.
Since you didn't define ``Infinity'' in any way, I'll just go ahead and give a concrete example that might or might not make sense to you: take all possible laws of physics and the worlds that follow them (ours being one). Such laws could be described by a computational abstraction (such as an Universal Turing Machine, or Peano Arithmetic, and they can implement each other as shown by the Church Turing Thesis (there are some rigorous proofs of this)) and are thus enumerable (as many as natural numbers, or countably infinite or ℵ
0). One conjecture is that our world is one such computable world (some physicists might disagree and involve higher infinities by invoking a continuum such as ℵ
1 or higher, I'm not doing this here as I'm undecided about wether a continuum can physically exist, and you who wants to deny the infinity of ℵ
0 would probably have even more problems with higher infinities). Now within this world, there exists self-aware substructures such as ourselves. By virtue of our implementation we are conscious (in some specific self-referential/transparent form) and might have qualia, but that's because of our structure, not because of anything else. The laws of physics may have ``qualia'', but that's absolutely irrelevant as their function is too low-level and simple and any ``qualia'' it may have are unlikely to be anything like ours, thus there's no way to actually relate to it. My understanding of qualia is how a particular structure (such as a consistent mathematical structure) feels from the inside (or what it's like to
be some structure). The brain is how our mind looks from the outside. I should also mention that a structure may embed another structure and so on recursively, but each structure is a separate thing (and if qualia exists, has separate qualia). For example, you have Peano Arithmetic or "Our Laws Of Physics" containing an embedding of a computational device (let's make it finite to please you) such as a CPU. Now this CPU is running some software. The software in this case is a theorem prover which contains rules for some iterative set theory or maybe Peano Arithmetic or maybe Robinson Arithmetic. The laws of physics or PA cannot say anything about the semantics of what they are running (in this case a CPU), no more than the CPU can say anything about the semantics of the theorem prover which implements PA or some set theory, no more than your neuron can understand the structure of the whole brain (you might have noticed that this also shows exactly what's wrong with the Chinese Room Argument). They all run at different levels and embody different functionalities and structures.
Either way, if you reject infinity in any form, that is almost the same as rejecting induction. That is, you reject that given some predicate P(k), that if you can prove that P(n) implies P(n+1), and if base case P(0) is trivially true, then P might not be true generally (you're rejecting the axiom schema of induction). For me it seems trivial to believe that if P(0) is true and if we proved that P(n) implies P(n+1), then we can follow it as P(0)->P(1)->P(2)->P(3)->... for all possible values of n (and this is where the infinity appears). For you, it might not be trivial, but why? If it's qualia, then qualia must have some ground-of-being as well, and I think the language of mathematics and logic is a suitable one to represent it (even if we may have inconsistent and thus fictional structures within current mathematics, but that's something which can be dealt within math itself, incompleteness theorems not withstanding).