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From: Marchal <marchal.domain.name.hidden>

Date: Mon Jan 18 01:35:52 1999

Hi Jacques,

*>I know that any machine or formal system has a Godel proposition which
*

*>express it own non-provability, and therefore is true but not provable if
*

*>the system is consistant. But shouldn't we consider that the machine really
*

*>know something with certainty only if it can prove it ?
*

As far as a certain kind of knowledge is concerned I agree. I use

frequently the old definition of knowledge given by Platon in the

Theetete : (to know p) is (to prove p AND p is true). With the godelian

logic of provability, as you know, the consistent machine cannot prove

that by proving p, p is true. So this definition is not trivial. It makes

the knower not prouvably formalisable by the knower for exemple.

But we know much more than we can prove in the sense that we can also

make inference of p with p true. I think that a more general sort of

knowledge is given by a mixture of these two types of knowledge, proof

and inference.

In particular a consistent machine cannot prove his own consistency, but

nothing prevent it to infer it, or to bet on it.

Like Helmholtz I think that part of our conscious perception are really

produced by (unconscious, instinctive) inference processes.

And this explains also why people confuse belief and knowledge in many

situation.

Scientific knowledge is typically of the inference type.

*>It seems clear to me that the physical laws are mathematical.
*

*>But do you want to derive only the physical laws of OUR universe ?
*

Remember that by "mechanism" I mean the (personal) belief that you can

survive a discrete (finite, digital) substitution of yourself, at some

substitution level.

With mechanism, I don't think there is something like a universe obeying

physical laws, in which we inhabit.

All computationnal histories exist embedded in the necessary relations

between numbers.

Some computationnal histories are very deep (in Bennett sense, see the

book of LI & VITANYI recommended by Wei Dai), and relatively dense.

For these histories there is a notion of mean point of view, where there

are relatively different machines able to communicate classicaly about

their most probable continuation. They can also discover "indeterminism"

below their substitution level and other "physical things like that".

But physical laws themselves are the result of the interference of many

(a non denombrable set of) computationnal histories. The interference

comes from our unabililty to make distinctions between some

computationnal histories.

Like James I like OCCAM's razor. That is why, at least when I am in a

mechanist mood, I suspect there is no such thing we could call our

universe nor could there been really objective physical laws.

Bruno.

Received on Mon Jan 18 1999 - 01:35:52 PST

Date: Mon Jan 18 01:35:52 1999

Hi Jacques,

As far as a certain kind of knowledge is concerned I agree. I use

frequently the old definition of knowledge given by Platon in the

Theetete : (to know p) is (to prove p AND p is true). With the godelian

logic of provability, as you know, the consistent machine cannot prove

that by proving p, p is true. So this definition is not trivial. It makes

the knower not prouvably formalisable by the knower for exemple.

But we know much more than we can prove in the sense that we can also

make inference of p with p true. I think that a more general sort of

knowledge is given by a mixture of these two types of knowledge, proof

and inference.

In particular a consistent machine cannot prove his own consistency, but

nothing prevent it to infer it, or to bet on it.

Like Helmholtz I think that part of our conscious perception are really

produced by (unconscious, instinctive) inference processes.

And this explains also why people confuse belief and knowledge in many

situation.

Scientific knowledge is typically of the inference type.

Remember that by "mechanism" I mean the (personal) belief that you can

survive a discrete (finite, digital) substitution of yourself, at some

substitution level.

With mechanism, I don't think there is something like a universe obeying

physical laws, in which we inhabit.

All computationnal histories exist embedded in the necessary relations

between numbers.

Some computationnal histories are very deep (in Bennett sense, see the

book of LI & VITANYI recommended by Wei Dai), and relatively dense.

For these histories there is a notion of mean point of view, where there

are relatively different machines able to communicate classicaly about

their most probable continuation. They can also discover "indeterminism"

below their substitution level and other "physical things like that".

But physical laws themselves are the result of the interference of many

(a non denombrable set of) computationnal histories. The interference

comes from our unabililty to make distinctions between some

computationnal histories.

Like James I like OCCAM's razor. That is why, at least when I am in a

mechanist mood, I suspect there is no such thing we could call our

universe nor could there been really objective physical laws.

Bruno.

Received on Mon Jan 18 1999 - 01:35:52 PST

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