On 11/8/2012 10:22 AM, Bruno Marchal wrote:
On 08 Nov 2012, at 14:45, Stephen P. King wrote:
On 11/8/2012 6:43 AM, Roger Clough wrote:
So how does Platonia's perfect necessary classes restrain or
contain this world of contingency ? Or does it ?
That is exactly my question! How does Platonism show the
contingent to be necessary? As far as I have found, it cannot show
necessity of the contingent. In the rush to define the perfect, all
means to show the necessity of contingency was thrown out. This is
why I propose that we define existence as necessary possibility; we
have contingency built into our ontology in that definition. ;-)
In which modal logic?
Why is there a formal modal logic implied in my remarks? I do not
think in a formal math form. I think visually and proprioceptively.
Ideas have 'texture' for me. ;-) Good theories have a different 'feel'
than wrong theories for me. Maybe this is just an intuitive form of
thinking but it has served me well so far.
What you say directly contradict Gödel's theorem, which shows, at many
different levels the necessity of the possible.
OK, I'll bite your metaphorical bait. What does Gödel's theorem
tell us about the necessity of the possible at most ontologically
We even get that for all (true) sigma_1 sentences (the "atomic events
in the UD execution) p -> <>p,
Can you see that this is just a statement in a particular language?
We should be able to refer to the very same ideas using different
languages! Truth is, after all, independent of any particular
representation! One thing: that "p -> <>p" reads to me as "the
necessary possible existence of p implies the existence of p". As to the
idea of atomicity in the UD. I understand a bit how Pratt considers a
logical algebra to be atomic, in that it cannot be reduced to a
structure with fewer components and cannot have components added to it
without altering its Satisfiability, but I do not know what 'atomicity'
means to you.
that is the truth of p implies the necessity of the possibility of p,
I do not see that at all! The truth of p is in its referent, it is
what p tells us that is True (or false) and I read the implication arrow
in the opposite direction as you. Logical necessitation (the logical
form of causality) looks at the antecedents and implicated precedents in
its derivation. Logic does not and must not be considered to
"anticipate" a truth. Truth is the end result of the process of logic,
not its beginning.
with p = either the box of the universal soul (S4Grz1), or the box
of the intelligible or sensible matter (Z1* and X1*). The modal logics
becomes well defined, and allows, in Platonia, all the imperfections
that you can dream of (which of course is not necessarily a good news).
All of these claims are coherent only after we assume that we exist
and can formulate theories. Comp floats high up in the Platonic realm on
the support of all of the minds that believe in it.
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