On 09 Nov 2012, at 00:01, Stephen P. King wrote:
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:
Hi meekerdb
So how does Platonia's perfect necessary classes restrain or
contain this world of contingency ? Or does it ?
Hi Roger,
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?
Hi Bruno,
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.
It might suit well your 1p-intuition. Good for you. But you can use
that for public communication. Necessity and possibility have been
controversial notion from Aristotle to Feys and Kripke (say). After
Kripke, we can give a mathematical meaning, and btw, the first
remarkable fact is that those modal notion have transfinities of
mathematical meaning, but then we can be more precise.
You define existence, which is simlple and rather well handled in
elementeray logic, by very complex controversial notion. So I can't
understand them.
Like for "primitive", that you want having objects without properties.
This just makes no sense for me.
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
fundamental level?
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?
In arithmetic. All the modalities like [] and <> are entirely defined,
either directly by an expression in arithmetic, or by appeal to well
defined infinities of arithmetical expressions.
We should be able to refer to the very same ideas using different
languages!
Perhaps, but then you must give the dictionary.
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".
?
"p -> []<>p" is for, p being any sigma_1 arithmetical proposition: p
implies box diamond p", with the box being defined in the Z1* or X1*
logic, and playing the role of observable with "probability 1".
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.
The usual one in logic. Atomic formula are the formula from which we
build the non atomic. In propositional calculus the atomic formula are
p, q, r, ... In arithmetic, the atomic formula are (t = s) with t and
s beings terms; etc.
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.
I thought it was typo, above. The you read "->" in the opposite sense
of all the logicians. If you dare doing things like that, it will not
help you to be understood. It is better to use the accepted
conventions, or at least, if you change one, to make that clear and
explicit before all things.
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.
This sentence has no meaning. When doing logic, we abstract from
truth. We let truth come back in the model theory, but then it is
defined mathematically, and of course it is not "the truth".
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.
This is does not make sense. Logicians put all their assumption the
table, and our existence does not figure in them.
Comp floats high up in the Platonic realm on the support of all of
the minds that believe in it.
?
You said that you are a beginners and want to learn, but you keep
showing that you don't even want to learn logic. It is a technical
subject. Nobody will criticize a formula in differential geometry with
a philosophical argument. same for logic, especially when applied to
philosophy.
Bruno
http://iridia.ulb.ac.be/~marchal/
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