On Saturday, January 11, 2003, at 01:39 AM, Eric Hawthorne wrote:
There are excellent reasons to expect a formal system of symbols to correctly predict future time in reality: the operation of machines, chips, programs. Of enormous complexity, iterating for trillions of steps in time, the outcomes are consistent and predictable.This strict "anonymous symbols" interpretation is how one must treat formal logic and propositions expressed in formal logic too. Every time I read someone bemoaning how logic has difficulty with expressing "what is going to happen in future", I think, why would you expect a formal system of symbols to have anything to do with future time in reality?
As for someone "bemoaning how logic...future," temporal logic is an active research area. Arthur Prior has written much about the logic of time. Modal logic is essentially about this kind of reasoning.
Pace the point below about comets hitting planets, a formal symbol system is not going to predict something dependent on events we cannot see (yet) or model (yet). It would be unreasonable to expect a logic of time to somehow predict events from outside our "knowledge cone" (like a light cone, but for knowledge).
We analyze Reality in bits and pieces, in facets. We analyze planetary motions, and now we have logical symbol models which are enormously accurate and far-reaching in time. Granted, models of future planetary positions cannot predict events outside the model, such as collisions with comets not yet charted, and so on. But this is not a plausible goal of any model.
As far as I know, there is no good formulation of
a formal connection between a formal system and """"""reality""""" <-unbalanced quotes, the secret
cause of asymmetry in the universe. How's that for a
I don't understand your "secret cause of asymmetry in the universe" point. We understand some things about symmetry breaking in particle physics theories, via gauge theories and the like. If you want more than this, you'll have to expand on what you mean here.
Actually, science is just about such correspondences with external reality.
Is there? For example, "truth" is defined in formal logic with respect to, again, formal models with an infinite
number of formal symbols in them. It is not defined with respect
to some vague "correspondence" with external reality.
I haven't argued that logic alone is a substitute for science, measurement, experimentation, refutation, correction, adjustment, model-building.
Again, I don't understand what you mean by "there is still a huge disconnect there."
Someone was writing about "correspondence theory"
with this goal in mind many years back, and that sounded
interesting. I haven't read Tegemark et al. What do they say
about the formalities of how mathematics extends to correspond to, or to be? external reality? To me, there is
still a huge disconnect there.
If you are refuting Tegmark, you should read his articles first.
If you are saying that much still needs to be done, this is of course true, fortunately.