Hi Stephen P. King
Who are these entities and how can they exist
a priori as does 2+2=4 ?
Roger Clough, rclo...@verizon.net
11/8/2012
"Forever is a long time, especially near the end." -Woody Allen
----- Receiving the following content -----
From: Stephen P. King
Receiver: everything-list
Time: 2012-11-07, 19:38:28
Subject: Re: Communicability
On 11/7/2012 12:44 PM, Bruno Marchal wrote:
>
> On 07 Nov 2012, at 17:13, Stephen P. King wrote:
>
>> On 11/7/2012 9:41 AM, Bruno Marchal wrote:
>>> Arithmetic explains why they are observers and how and why they make
>>> theories.
>> Dear Bruno,
>>
>> This is a vacuous statement, IMHO. Absent the prior existence of
>> entities capable of counting there is no such thing as Arithmetic.
>> Your belief to the contrary cannot be falsified!
>
> In the same sense that "2+2=4" cannot be falsified.
Dear Bruno,
You are missing my message. "2+2=4" is universally true only
because there does not exist a counter-example that can be agreed upon
by 3 or more entities. You continue to only think from the point of view
of a single entity. My reasoning asks questions from the point of view
of many entities
>
> It just mean that you have never grasp the proof of G?el's
> incompleteness theorem, which does that, almost in passing. This is
> proved in all good introduction text to logic.
Ha! OK, but you are wrong.
>
> We can prove, in Peano arithmetic, that there exist entities capable
> of counting.
If we follow the orthodox interpretation of Tennenbaum theorem
there can only be one entity that can count; the standard model of PA. I
am thinking of the uncountable infinity of non-standard models of PA
that have a condition imposed on them: each thinks that it alone is the
standard model as it cannot know that it is non-standard. In this way we
can get an infinity of standard models of PA instead of just one. I
think that this gives us a modal logical form of general relativity!
> By G?el's completeness those entities exists in the standard model of
> arithmetic (arithmetical truth), and in all model, and thus also in
> all non standard model.
Yes, but each model must be able to truthfully believe that it
alone is the standard model; it cannot see the constant that defines it
as non-standard from inside itself.
>
> So arithmetic assures the prior existence of entities capable of
> counting.
Sure.
>
> You have the Matiyasevich's book. A (more complex) proof is given
> there. It is more complex as it proves this for a much more tiny
> fragment of arithmetic.
It is impossible for me to write my ideas in Matiyasevich's
language. :_(
>
>
>> Forgive me, but I need to let others explain my argument as I have
>> run out of patience with my inability to form sentences that you will
>> understand. This article (which I cannot asses completely due to the
>> paywall) seems to make my claim well:
>> http://www.springerlink.com/content/052422q295335527/
>>
>> Nomic Universals and Particular Causal Relations: Which are Basic and
>> Which are Derived?
>>
>> "Armstrong holds that a law of nature is a certain sort of structural
>> universal which, in turn, fixes causal relations between particular
>> states of affairs. His claim that these nomic structural universals
>> explain causal relations commits him to saying that such universals
>> are irreducible, not supervenient upon the particular causal
>> relations they fix. However, Armstrong also wants to avoid Plato?
>> view that a universal can exist without being instantiated, a view
>> which he regards as incompatible with naturalism. This construal of
>> naturalism forces Armstrong to say that universals are abstractions
>> from a certain class of particulars; they are abstractions from
>> first-order states of affairs, to be more precise. It is here argued
>> that these two tendencies in Armstrong cannot be reconciled: To say
>> that universals are abstractions from first-order states of affairs
>> is not compatible with saying that universals fix causal relations
>> between particulars. Causal relations are themselves states of
>> affairs of a sort, and Armstrong? claim that a law is a kind of
>> structural universal is best understood as the view that any given
>> law logically supervenes on its corresponding causal relations. The
>> result is an inconsistency, Armstrong having to say that laws do not
>> supervene on particular causal relations while also being committed
>> to the view that they do so supervene. The inconsistency is perhaps
>> best resolved by denying that universals are abstractions from states
>> of affairs."
>
> I don't assume nature. And comp refutes naturalism, that's the point.
You are thinking too literally about that I am writing. comp
assumes Platonism, no? Why can we not see Platonism and Naturalism as
just opposite or "polar" views on Reality? Platonism looks Top-down and
Naturalism looks from the bottom-up.
>
>
> Bruno
>
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
--
Onward!
Stephen
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