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

On 1/17/2013 7:16 AM, Bruno Marchal wrote:

On 16 Jan 2013, at 23:45, Stephen P. King wrote:

On 1/16/2013 10:59 AM, Bruno Marchal wrote:

On 16 Jan 2013, at 13:13, Roger Clough wrote:

Hi Bruno Marchal

Specific properties, at least down here, are needed
if you accept Leibniz' dictum that identical entities cannot
exist in this contingent world, for they would have the same identity.

I'm inclined to say that that is also true in Platonia,
which would be a disaster, for you could not say 1 = 1.
A saving grace might be that one of those 1's is before,
and the other, after the equal sign.   That is, the numbers
are distinguished by context.

I agree with all what you say here. Tell this to Stephen.
Note that we are distinguished by context too.

Bruno
Hi,

There is no context or figure-ground relation at the primitive level as such would be a distinction that makes no difference. To who or what would such matter? Even consciousness cannot be primitive, as it is distinct from non-consciousness.. Property neutrality is a necessary condition for ontological primitivity.

The principle of Identity of Indiscernibles (of Leibniz) is exactly what I base my claim upon. In the absence of an agent to affect distinctions or to have a bias of a point of view, all properties vanish.

That is solipsism, and you have to assume a basic consciousness, which is what I search an explanation for. Also, it contradicts comp. Also, without assumeing something Turing universal, you will not been able to have computers in your reality, so a theory which assumes not elementary properties to its basic object will be mud unable to explain where the consciousness of the distinction come from.


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.

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.




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.



"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.).

Bruno






When we consider the nature of ontological primitives and understand that we are considering what must occur in the situation where there is no special or preternatural agent to distinguish a 1 from a 2, for example, then it follows that even the property of being a number becomes degenerate.

Then what you say make sense in a primitively physical universe, but you need to say "no" to the doctor to be coherent.

   Wrong level.



--
Onward!

Stephen


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