Le 05-août-06, à 02:07, George Levy a écrit :

Bruno Marchal wrote:I think that if you want to
make the first person primitive, given that neither you nor me can
really define it, you will need at least to axiomatize it in some way.
Here is my question. Do you agree that a first person is a knower, and
in that case, are you willing to accept the traditional axioms for
knowing. That is:

1) If p is knowable then p is true;
2) If p is knowable then it is knowable that p is knowable;
3) if it is knowable that p entails q, then if p is knowable then q is

(+ some logical rules).

I like where this may be leading.... This may be the first step to your roadmap. As you know I have been a supporter of first person primitive for a long time. My roadmap was simple. It is a chain rule a la Descartes. I mentionned it before. Let me repost it:
1 I think therefore I am  (Descartes)
2 I am therefore the world is (Anthropic principle)
3 The world is therefore the plenitude is. (Principe of sufficient reason: if something is observed to be arbitrary and without any cause, then all other alternatives must also be realized)

This is coherent with the theaetetical notion of comp, although you take "Anthropic" in a very large sense (perhaps too large).

1  I think what I think, therefore I am what I am. (Descartes augmented by defining my consciousness and being as a function of my thought process)
2 I am what I am, therefore the world is what it is. (Anthropic principle augmented by defining the world in more precise terms as a function of exactly who I am - There is a strange echo from the burning bush in Exodus)
3 The world is what it is, therefore the plenitude is.

I am not sure this helps.

Would it be possible to map your three axiomatic lines replacing "knowable" by "think" and "true" by "exist." ...

See my conversation with 1Z (Peter D. Jones). I will define "exist" by " "exist" is true".

Then we have:

1 If p thinks then p exists;

This does not make sense at all, I prefer to say honestly. It is not the proposition p which thinks, and I don't understand what would it means that a proposition exists. I guess you are perhaps saying here that If a Machine(entity) thinks then it exists. Then OK. But as you know I don't believe the reverse is true. In particular I belief that the square root of two exist (perhaps under the form of a total computable function), but I would not say that the square root of two thinks. I do think that the multiverse even got rich but devoid of consciousness (immaterial) comp-branches.

2 If p thinks then it is thinkable that p thinks;

All right with the interpretation that "p" is some entity, not a proposition. Perhaps you are identifying machines and propositions? This can be done .... with the Fi and Wi ...., and it needs many cautions.

3 If it is thinkable that p entails q, then if p thinks then q thinks.
1 If p thinks then p exists; (This maps nicely with Descartes as stated from a third person)
2 If p thinks then p think that p thinks; (This is nice reflective statement essential to consciousness)
3 If p think that p entails q, then if p thinks then q thinks. (The phrase "p entails q" reminds me vaguely of the Anthropic principle. I am not sure what to make of this. My children think???????)

Your way of talking is a bit confusing as you seem to see by yourself :)



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