On 23 Aug 2012, at 18:43, Stephen P. King wrote:
Hi Roger,
By Existence I mean all that is necessarily possible.
But necessary and possible are ultra fuzzy word. Aristotle invented
the modal logic to bring a bit of light, and, despite having been
mocked by logicians, modal logic appears naturally in computer science
and philosophy, through precise modal logic. So hat is your modal logic?
If you are using "necessary" in his alethic common sense, it means
through in all words, and possible means true in at least one world.
Then you are working implicitly in S5.
So do you agree with
If p is necessary then p is true
If p is possible then it is necessary that p is possible
if p is necessary then it is necessary that p is necessary
if p is true then it is necessary that p is possible
OK?
usually we would write: []p for "p is necessary"; "<>p" for "p is
possible", "p" for "p is true", etc.
With S5, Kripke accessibility relation is trivial, all worlds access
to each other. S5 does not appear in the arithmetical
"hypostases" (machines points of view on arithmetic).
By this definition mathematical points and theoretical domains
"exist". Existence is property neutral, neither defining or
excluding what is or what is not. It is not a property.
No where than in first order logic clearer that existence is not a
property. But at the meta level, you can reprsent it by "belonging to
a model", and of course such existence is always theory dependent.
Like the notion of nothing or everything, the notion of existence asks
you to be clear (axiomatically) about your "things".
It is what the philosophers attempted to mean by a "property bearer"
and could not escape the illusion of substance.
Here we agree.
It is Dasein but without the actuality, since this would contradict
its neutrality. Both the actual and the possible "exist"... It is
not contingent on observation or measurement or knowledge.
That's 1004 talk, sorry.
Bruno
On 8/23/2012 9:31 AM, Roger Clough wrote:
Hi Stephen P. King
It all depends on what you mean by existence.
If by existence you mean dasein (actually being there),
then mathematical points or theoetical domains do not exist.
Roger Clough, [email protected]
8/23/2012
Leibniz would say, "If there's no God, we'd have to invent him so
everything could function."
----- Receiving the following content -----
From: Stephen P. King
Receiver: everything-list
Time: 2012-08-22, 23:38:55
Subject: Re: Pratt theory
On 8/22/2012 4:04 PM, Richard Ruquist wrote:
Now this is interesting: "Points have necessary existence, all
being present simultaneously in the physical object A.�
15.States are possible, making a Chu space a kind of a Kripke
structure [Gup93]:�
only one state at a time may be chosen from the menu X of燼
lternatives.
Seems that divine intervention may be an assumption. I wonder who
does the choosing. May I suggest Godellian consciousness?
Dear Richard,
� No need for divine intervention! I am not sure what "Godellian
consciousness" is. Let me comment a bit more on this part of
Pratt's idea. The choice mechanism that I have worked out uses a
tournament styled system. It basically asks the question: what is
the most consistent Boolean solution for the set of observers
involved? It seems to follow the general outlines of pricing theory
and auction theory in� economics and has hints of Nash equilibria.
This makes sense since it would be modeled by game theory. My
conjecture is that quantum entanglement allows for the connections
(defined as bisimulations)� between monads to exploit EPR effects
to maximize the efficiency of the computations such that classical
signaling is not needed (which gets around the "no windows" rule).
This latter idea is still very much unbaked.
--
Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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