Re: possible worlds in logic.

Logic (and its possible worlds semantics) says nothing (precise) about external reality.
Logic only says something about the relationship of symbols in a formal language.

Remember that the reason non-sloppy mathematicians
use non-meaningful variable-names (i.e. terms) is
to avoid names that connote something in the world
and would lead one astray in understanding the precise
"formal" semantics of the mathematical formulae.

e.g. of problematic meaningful variable names:

one = 2.
two = 2.
four = 4.
therefore, one + two = four.

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 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
"quining" paragraph?

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.

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.
E.g. again, Godel's incompleteness
theorem is a theorem about the properties and limitations
of formal symbolic systems. The original theorem says nothing whatsoever about reality itself, whatever that may "informally" be,
nor about the limitations of human minds, unless we take minds
to be theorem provers working on formal symbolic systems.

Reply via email to