On 09 Nov 2012, at 00:01, Stephen P. King wrote:

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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 thecontingent to be necessary? As far as I have found, it cannot shownecessity 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 necessarypossibility; we have contingency built into our ontology in thatdefinition. ;-)In which modal logic?Hi Bruno,Why is there a formal modal logic implied in my remarks? I do notthink 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 intuitiveform 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, atmany different levels the necessity of the possible.OK, I'll bite your metaphorical bait. What does Gödel's theoremtell us about the necessity of the possible at most ontologicallyfundamental level?We even get that for all (true) sigma_1 sentences (the "atomicevents 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 differentlanguages!

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 possibleexistence 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 Prattconsiders a logical algebra to be atomic, in that it cannot bereduced to a structure with fewer components and cannot havecomponents added to it without altering its Satisfiability, but I donot 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, itis what p tells us that is True (or false) and I read theimplication 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 theantecedents and implicated precedents in its derivation. Logic doesnot and must not be considered to "anticipate" a truth. Truth is theend 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 thebox of the intelligible or sensible matter (Z1* and X1*). The modallogics becomes well defined, and allows, in Platonia, all theimperfections that you can dream of (which of course is notnecessarily a good news).All of these claims are coherent only after we assume that weexist 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 ofthe 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/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.