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.



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