On 21 Nov 2012, at 14:16, Roger Clough wrote:

Hi Bruno Marchal

Perhaps I have gotten things wrong, but
Godel's problem seems to me to be the self-reference
problem uncovered by B Russell, namely
that a class (if I am using the right word) cannot
itself be a member of that class.

For example suppose we have a list of siblings, john, jacob and jeremy.
Then the list itself cannot be a sibling.

OK, but the catalog of all catalog can be a catalog, like "polysyllabic" is polysyllabic. Let us say that an adjective is autological if it applies to itself, and heterological if not. Thus "polysyllabic" is autological, "short" is autological, but "monosyllabic" is heterological, and "long" is heterological. OK? Then can you tell me if "heterological" is autological, or heterological? (Lol!).

Gödel's theorem relies on a reasoning similar to Russell's paradox, or to Epimenides' paradox. The main difference is that Gödel's theorem is an impossibility theorem in math, where Russell and Epimenides are just informal paradoxes. If you want, you can see Gödel's theorem as those paradoxes made precise in the comp frame.

All those form of reasoning are different example of informal or formal diagonalization.

I will come back on this relationship on FOAR. I will show that the halting problem is really Russell's paradox, with recursively enumerable set of numbers, instead of arbitrary informal sets.

In the case of sets, we can build consistent theory of sets in which a set does belong to itself, like with Stephen's "Quine atom". Stephen is fond of those set theories, but I prefer not use set theory at all (ontologically) as it assumes *much* more than what we need to study comp and machines' beliefs.


[Roger Clough], [rclo...@verizon.net]
"Forever is a long time, especially near the end." -Woody Allen

----- Receiving the following content -----
From: Bruno Marchal
Receiver: everything-list
Time: 2012-11-20, 12:31:38
Subject: Re: Evolutionary logic Re: Some musings on is/ought and modal logic

On 20 Nov 2012, at 16:02, Alberto G. Corona wrote:

2012/11/11 Bruno Marchal <marc...@ulb.ac.be>

On 11 Nov 2012, at 01:29, Alberto G. Corona wrote:

It is an observable fact. is obviously true that if you live in a society where everyone take something as true , no matter what, then it is true for one of its members, you, for example.

That's correct. But that still does not make it true. Sometimes everybody can be wrong.

That磗 the reson why truth can only be defined in objective terms as a belief (except perhaps in the realm of mathematics).

Well, mathematicians can differ a lot, but arithmetic seems to be the sharable part of math.

When I say this is true, I磎 saying that I believe that this is true.

I don't think this is a good idea. This works well in many case, but on the fundamental question it is better to distinguish truth and belief. truth, by definition, cannot be made wrong, and is independent of our beliefs. Beliefs are typically wrong most of the time. "P" and "I believe P" have a very different meaning.

So truth in the realm of experience means "accepted as truth" in a certain context.

I would call that delusion. of course sometimes we can be lucky, and assert a genuine truth. But this we can never be sure of, except perhaps in arithmetic (but I do not use this in the reasoning I do).

We can磏t go further than that if we want to stay objective (or tautological).

I think we can, as we can have faith in truth, and just admit that we don't know it. We can still searching. defining truth by beliefs would lead to relativism.

Thay point of view would be pure relativism unless natural selection is considered.

Or many things weaker than that a priori. If you agree that 43 is prime, that is already a lot. I cannot start with natural selection, as I am agnostic on nature. I don't know what it is, if that exist, at which level, etc. It presuppose also arithmetic, and with comp I can argue that I cannot add anymore, except for the epistemological definitions. I do believe in natural selection, but not that it is something so fundamental. first person consciousness selection is more important, as it selects also the laws making natural selection possible.

The absolute requirement of existence of the minds which habites in the environmment of the laws of reality makes certain truths possible and certain alternatives impossible.

But such a sentences assumes a lot.

For example, that "electrons collapse in the nucleus is" can never be true for any living being.

Of course, this is a well known physical facts well explained by QM. But with comp, it is nothing but a complex problem, we have to derive QM from + and * before.

neither "Mothers don磘 love their children" for the very same reason in humans. Because these candidates for truth are incompatible with the existence of minds (1) and the human mind (2).

Hmm.. I can agree, but you are quick. Many mothers does not like their children. Some kill them. Some kill them all, as in a recent case nearby. It is a known phenomenon.

In the middle, there are many truths that can be accepted as truths in some contexts, no matter if they are later refuted. Our time is by no means any different from other times in history. Almost all that we known can be proved wrong in a way or other. except perhaps mathematics (and not even that, if we don磘 consider life ( autopoietic computation) as criteria for existence).

To summarize, to say that all may be wrong is not an impediment for a objective study of truth as as a evolutionary phenomenon and his closed identity with what exist and is perceived good .

I agree. That is why I think it is better to distinguih Truth from beliefs, and keep in mind that all scientific "truth" are only belief, by which it is meant that they can be false. truth is what we search (when we have the taste for it).

I mean, that this historic consideration is the only objective non speculative method of considering the notion of Truth, whatever if it is considered in capital letters or not. I may say that truth is an evolutionary (historical) path to Truth.

With comp something happen, which is that we can limit truth to arithmetical truth. It remains a big non-computable thing, but it is rather conceptually clear. Above arithmetics, with comp there are the mind tools and imagination, and dreams, cohering or not? They can be justified from inside arithmetical truth.

(1) What is objective is the study of beliefs (historical truths) and the testing of hypothesis of why these beliefs (truths) exist. and others do not.

OK, but this leads to other belief. And history can be revised. It is bad but it happens everyday, if you read many newspapers, you can see this.

(2)What is speculative, and has no firm ground, is to say "This is true" without concern for the fact that this is the expression of a belief.

Yes, but that is a reason to distinguish the truth and the belief. Not a reason to equate them.

 the people in (2) are a subject of study for the people in (1).

OK, but such study can only be based on some belief, that is theory or hypothesis. A belief is a questioning.

 modal logic is something instrumental for (1)
 pure logic is instrumental for (2)
people in (1) must explain the reductions from (1) to (2).

I gave here a way to do this last.

I explain how comp makes this already happening all the time in arithmetic.

I still did磏t do that formally.

I did, but then it does not help so much apparently, as it asks for some amount of works. But I am a mathematician, and I did not get more choice in the matter.



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