On 05 Nov 2012, at 13:43, Roger Clough wrote:

Hi Bruno Marchal

OK, you say propositions might have a contradiction but you might not
yet have found the contradictions. That's a profound point.

Either we have not yet found the contradiction, or we have not the tool to prevent the existence of infinite non standard proof of a contradiction to exist (which is the Godelian reason for the consistency of inconsistency, contrary to what Stephen said in a recent post).

Nobody really believes that RA or PA can be contradictory. It is easy to prove the consistency of arithmetic in the usual math (informal set theory). Gödel's theorem does not cast any doubt on arithmetic, quite the contrary.




In other words, one can't ever be sure if a proposition is
necessarily true, because, as Woody Allen says, forever
is a long time.

Especially with non standard time.



And the variety and number of possible copntradictions
is possibly vast.

Transfinite, even.



Shades of Nietzsche ! Tell me it isn't so !

No, it is not so. No worry to have. I am glad we share some uneasiness with Nietzche. I take it for a great poet, but a bad philosopher.




I guess that's the same as saying that you can never be sure
of contingency either. I need to lie down for a while. This
is beginning to look like existentialism.

No worry. I am afraid that Stephen introduced some confusion here.

Bruno




Roger Clough, rclo...@verizon.net
11/5/2012
"Forever is a long time, especially near the end." -Woody Allen


----- Receiving the following content -----
From: Bruno Marchal
Receiver: everything-list
Time: 2012-11-04, 08:56:01
Subject: Re: The two types of truth


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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