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

Date: Sat, 26 Jun 2004 17:30:52 +0200

Hi George, Stephen, Kory, & All.

I am thinking hard finding to find a reasonable way to explain the

technical part of the thesis, without being ... too much technical.

The field of logic is rather hard to explain, without being

a little bit long and boring in the beginning :(

At least I found a very good Mathematical Logic Web page:

http://www.ltn.lv/~podnieks/index.html

The page contains also a test to see if you are platonist (actually it tests

only if you are an arithmetical realist!). Try it!

From that page I will be able to mention easily set of axioms, and rules.

For example below are the non logical axioms of Peano Arithmetic.

Does it makes intuitive sense ?

I suggest you try to find the logical axioms and the inference rules in

Podnieks page. This will define a precise exemple of loebian machine,

exactly those I will interview about the geometry of their

maximal consistent extensions (their comp histories) to see if it looks

like quantum logic as comp predict.

AxP(x) should be read: For any (natural number) x we have P(x), for

example: Ax((x = 0) or not (x = 0)) is a intuitively true proposition.

==============

The specific (non-logical) axioms of the first order arithmetic:

x=x,

x=y -> y=x,

x=y -> (y=z -> x=z),

x=y -> x+1=y+1,

~(0=x+1),

x=y -> x+1=y+1,

x+0=x,

x+(y+1)=(x+y)+1,

x*0=0,

x*(y+1)=(x*y)+x,

+ the following infinite set of formula:

B(0) & Ax(B(x)->B(x+1)) -> AxB(x), where B is any formula.

Any comments ?

Bruno

PS I have finished my french paper, and I will write the paper for

Amsterdam. The goal is always the same: how to be clear, short and

understandable .... (given the apparent "enormity" of the result!)

http://iridia.ulb.ac.be/~marchal/

Received on Sat Jun 26 2004 - 11:33:02 PDT

Date: Sat, 26 Jun 2004 17:30:52 +0200

Hi George, Stephen, Kory, & All.

I am thinking hard finding to find a reasonable way to explain the

technical part of the thesis, without being ... too much technical.

The field of logic is rather hard to explain, without being

a little bit long and boring in the beginning :(

At least I found a very good Mathematical Logic Web page:

http://www.ltn.lv/~podnieks/index.html

The page contains also a test to see if you are platonist (actually it tests

only if you are an arithmetical realist!). Try it!

From that page I will be able to mention easily set of axioms, and rules.

For example below are the non logical axioms of Peano Arithmetic.

Does it makes intuitive sense ?

I suggest you try to find the logical axioms and the inference rules in

Podnieks page. This will define a precise exemple of loebian machine,

exactly those I will interview about the geometry of their

maximal consistent extensions (their comp histories) to see if it looks

like quantum logic as comp predict.

AxP(x) should be read: For any (natural number) x we have P(x), for

example: Ax((x = 0) or not (x = 0)) is a intuitively true proposition.

==============

The specific (non-logical) axioms of the first order arithmetic:

x=x,

x=y -> y=x,

x=y -> (y=z -> x=z),

x=y -> x+1=y+1,

~(0=x+1),

x=y -> x+1=y+1,

x+0=x,

x+(y+1)=(x+y)+1,

x*0=0,

x*(y+1)=(x*y)+x,

+ the following infinite set of formula:

B(0) & Ax(B(x)->B(x+1)) -> AxB(x), where B is any formula.

Any comments ?

Bruno

PS I have finished my french paper, and I will write the paper for

Amsterdam. The goal is always the same: how to be clear, short and

understandable .... (given the apparent "enormity" of the result!)

http://iridia.ulb.ac.be/~marchal/

Received on Sat Jun 26 2004 - 11:33:02 PDT

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