On Jan 15, 2004, at 7:25 PM, Doug Porpora wrote:
Well, only if reductionism succeeds. If reductionism fails, then, unlike universes, which, on my reading of Tegmark, are discrete and countable, thoughts are not only infinite but uncountably infinite. In that case, thoughts -- and persons -- comprise an even larger infinity than universes. And -- although this is another argument -- at least a part of the universe would not behave deterministically.
I don't see how "reductionism fails" entails "thoughts are uncountably infinite".
Is it because you are identifying thoughts with sentences and sentences are infinite? But not every sentence is a thought. Most sentences are not thinkable or believable. I'm not sure sentences are uncountably infinite, either.
(Here I'm interpreting your "reductionism fails" as "eliminative materialism and identity theory are false", which I tend to agree with; I notice you didn't mention functionalism however.)
If you tend to resist what I am suggesting, consider three things:
1. How do you even individuate thoughts so as to count them or correlate them with physical states? Is the belief that Mark Twain wrote Huckleberry Finn the same as or different from the belief that Samuel Clemens wrote Huckleberry Finn? Would that be one physical state you would seek to correlate with it or two? There are lots of well-discussed conceptual problems here.
To start off with, why should we commit ourselves to talking about beliefs as individuable entities in the first place? I prefer Dennett's intentional stance theory of beliefs - beliefs are abstract things we posit that explain or predict behavior.
To relate this to Tegmark/Schmidhuber, look at it like this: The physical (or Platonic/mathematical, it really doesn't matter) stuff is there; it's the underlying reality. If sub-sections of the stuff (i.e., us) see patterns in it and talk about these patterns as "individuals" and "beliefs", that's our business. It doesn't have any bearing on the nature of the underlying stuff. It's not a terribly important result that we can imagine infinite numbers of patterns (such as beliefs) -- after all, you can imagine an uncountably infinite number of strings composed of just 0 and 1.
John, I am not sure I understand everything you said. One thing I would say along lines I think you suggest: Determinism suggests a closed system. If you don't have a closed system, you don't get deterministic predictiveness. Human thought is both holistic and unclosable. Those features do not preclude mental causality, but they do preclude deterministic, causal laws.Could you explain what you mean here by "holistic and unclosable"?
-- Pete Carlton