On 03 Nov 2012, at 12:45, Roger Clough wrote:

Hi Bruno Marchal and Stephen,

http://www.angelfire.com/md2/timewarp/leibniz.html

"Leibniz declares that there are two kinds of truth:
truths of reason [which are non-contradictory, are always either
true or false],

We can only hope that they are non contradictory.
And although true or false, they are aslo known or unknown, believed of not believed, disbelieved or not disbelieved, etc.




and truths of fact [which are not always either true or false].

Why? They are contextual, but you can study the relation fact/context in the higher structure level.



Truths of reason are a priori, while truths of fact are a posteriori.
Truths of reason are necessary, permanent truths. Truths of fact are contingent, empirical truths. Both kinds of truth must have a sufficient reason. Truths of reason have their sufficient reason in being opposed to the contradictoriness and logical inconsistency of propositions which deny them. Truths of fact have their sufficient reason in
being more perfect than propositions which deny them."

Unfortunately, this is acceptable below Sigma_1 truth, but doubtable above, so even in the lower complexity part of arithmetic, things are not that simple.

Bruno





Roger Clough, rclo...@verizon.net
11/3/2012
"Forever is a long time, especially near the end." -Woody Allen


----- Receiving the following content -----
From: Bruno Marchal
Receiver: everything-list
Time: 2012-11-03, 07:13:24
Subject: Re: Numbers in the Platonic Realm


On 02 Nov 2012, at 23:12, Stephen P. King wrote:

On 11/2/2012 1:23 PM, Bruno Marchal wrote:
I can understand these symbols because there is at least a way
to physically implement them.

Those notion have nothing to do with "physical implementation".

So your thinking about them is not a physical act?

Too much ambiguous. Even staying in comp I can answer "yes" and "no".
Yes, because my human thinking is locally supported by physical
events.
No, because the whole couple mind/physical events is supported by
platonic arithmetical truth.
Dear Bruno,

Where is the evidence of the existence of a Platonic realm?

It is part of the assumption. We postulate arithmetic. I try to avoid
the use of "platonic" there, as I used the term in Plato sense. In
that sense Platonia = the greek No?, and it is derived from
arithmetic and comp.

All you need is the belief that 43 is prime independently of "43 is
prime".



The mere self-consistency of an idea is proof of existence

Already in arithmetic we have the consistence of the existence of a
prrof of the false, this certainly does not mean that there exist a
proof of the false. So self-consistency is doubtfully identifiable
with truth, and still less with existence.



but the idea must be understood by a multiplicity of entities with
the capacity to distinguish truth from falsehood to have any
coherence as an idea!

Not at all. 43 is prime might be true, even in absence of universe and
observer.



We cannot just assume that the mere existence of some undefined acts
to determine the properties of the undefined. Truth and falsity are
possible properties, they are not ontological aspects of existence.

Truth is no more a property than existence. It makes no sense.

Bruno


http://iridia.ulb.ac.be/~marchal/



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