On 1/18/2013 1:08 PM, Bruno Marchal wrote:


On 17 Jan 2013, at 19:05, Stephen P. King wrote:

Dear Bruno,

I am discussing ontology, there is no such a process as Turing or 'realities' or objects yet at such a level. All is abstracted away by the consideration of cancellation of properties. Let me just ask you: Did the basic idea of the book, The Theory of Nothing by Russell Standish, make sense to you? He is arguing for the same basic idea, IMHO.

An expression like "cancellation of properties" needs already many things to make sense.

Dear Bruno,

Baby steps. The concept that Russell Standish discusses in his book, that is denoted by the word "Nothing": Do you accept that this word points to a concept?



You refer to paper which use the axiomatic method all the times, but you don't want to use it in philosophy, which, I think, doesn't help.

You seem to not understand a simple idea that is axiomatic for me. I am trying to understand why this is. Do you understand the thesis of Russell Standish's book and the concept of "Nothing" he describes?





Contingency is, at best, all that can be claimed, thus my proposal that existence is necessary possiblity.

Existence of what.

   Anything.

That's the object of inquiry.

OK, so go to the next step. Is the existence of a mind precede the existence of what it might have as thoughts?



"Necessary" and "possible" cannot be primitive term either. Which modal logics? When use alone without further ado, it means the modal logic is S5 (the system implicit in Leibniz). But S5 is the only one standard modal logic having no arithmetical interpretation.

   Wrong level. How is S5 implicit in Leibniz? Could you explain this?

With Kripke:

<>p, that is "possibly p", is true in the world alpha if p is true in at least one world accessible from alpha. []p, that is "necessary p", is true in the world alpha if p is true in all the worlds accessible from alpha.

The alethic usual sense of "metaphysically possible" and "metaphysically necessary" can be be given by making all worlds accessible to each other, or more simply, by dropping the accessibility relation:

<>p, that is "possibly p", is true in the world alpha if p is true in at least one world. []p, that is "necessary p", is true in the world alpha if p is true in all the worlds.

In that case you can verify that, independently of the truth value of p, the following propositions are true in all worlds:

[](p->q) -> ([]p -> []q)
[]p -> p
[]p -> [][]p
<>p -> []<>p

(p -> []<>p can be derived). You get the system S5, and reciprocally S5 (that is the formula above + the necessitation rule (p/ []p), and classical propositional calculus) is complete for all formula true (whatever values taken by the propositional variable) in all worlds.

To sump up, in Leibniz or Aristotle all worlds are presumed to accessible from each others (which makes sense from a highly abstract metaphysical view). In Kripke, or in other semantics, worlds (states, whatever) get special relations with other worlds (accessibility, proximity, etc.).

Good, we agree on those concepts, but we need to get back to the impasse we have over the concept of Nothing (which I am equating to the neutral ontological primitive) and my argument against your claim that numbers can be ontological primitives.

--
Onward!

Stephen


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