Bruno Marchal wrote:
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 dont' really see any problem if we think of a conscious entity just like a proposition as information. Proposition p is information which can be either true or false. A conscious entity is also information. In this case, if the information is true then the entity 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.
The English language is treacherous. we have to be careful when we use the word "exist." I think there are several kinds of existence. In any case to assert that the square root of two exists is assigning to the square root of two an existence independent of any observer, thereby negating the primacy of first person.

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.
Yes I am saying that machines, propositions, databases, programs, and conscious minds are different words for the same thing: information. Thus information can be true, false or unknown.
3 If it is thinkable that p entails q, then if p thinks then q thinks.
One of the problem lies with the "it" word as in: "if 'it' is knowable" or  "If 'it' is thinkable". What or who is "it?" Here again the English or French languages can be treacherous.

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 :)
The first two statements are relatively easy to understand. The first one is more or less what Descartes said. The second one is a reflective form probably necessary for consciousness.
The third statement taken seriously is intringing. If entity p thinks that entity q is necessary for p's existence, then if p thinks then q thinks. In other words all necessary conditions for my own existence form a conscious entity. This is weird. It is as if I had my own personal Personal God or guardian angel.


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