At 16:44 04/07/04 -0400, John M wrote:

I think we got into a semantic quagmire. I feel a different meaning in my (5th language English) "TRUTH" from what I read as the (4th language French) 'verité'. I use 'truth' as the OPINION one accepts as being not false.

Yes but then you will misunderstand the Theaetetus definition of knowledge (as true opinion). I think it is just a question of vocabulary. See below...

What you imply sounds to me as 'constructing a reality". Truth has nothing to do with decisionmaking. "Decision" comes into the picture only in the 1st person thinking to "decide" whether the item is not false. If I agree, it is (my) truth as well.

?

> JM:

> >the fact

> >that anything we may "know" (believe or find), is interpreted by the ways

> >how our 'human' mind works -

>

> BM: SURE! (but it is invalid to infer from that that truth itself depends on

our beliefs and findings).

>

JM: Sorry, Bruno, you sound in the parethetized remark as a person who believes

in some eternal 'truth' chisled in the (nonexistent) stone of (nonexistent)

supernatural 'law', - or rather: takes something like 'truth' as the

installations (facts??)of the world. There is no such thing as "THE TRUTH -

ITSELF" at least not among people who think... Maybe some religious fanatic

fundamentalists know "the truth", the only ONE, worthwhile killing (-dying)

for.

`Nobody in this list pretend to know the truth. A theory is always a`

(hopefully consistent) set of beliefs, mainly.

But we can privately hope our beliefs are true. The point is: do you find

comp inconsistent? Do you find QM inconsistent? Do you find PA inconsistent?

(and then do you find that plausible, etc.)

Also, can you conceive that QM could be "true", independently of us knowing

it, except in the thaetetus sense of just believing it, and that by chance it *is* true.

Also, "truth" is an object of study by logicians. In classical propositional logic

truth is just a function from the propositional variable {p, q, r, ...} into {O, 1}, in

the company of rules to extend those "truth values" to compound propositions,

like saying that "p&q" is true in case p is true and q is true, which for the logician

means only the function above send p and q on 1. But logicians considers

many, many, many other sort of "truth valuation" (abstractly they are sub-object

classifier, truth being the object itself, so in classical logic truth can be represented

by a set, in intuitionistic logic truth can be represented by a topological space,

in quantum logic truth can be represented by a Hilbert space, but that's for much latter ...).

(hopefully consistent) set of beliefs, mainly.

But we can privately hope our beliefs are true. The point is: do you find

comp inconsistent? Do you find QM inconsistent? Do you find PA inconsistent?

(and then do you find that plausible, etc.)

Also, can you conceive that QM could be "true", independently of us knowing

it, except in the thaetetus sense of just believing it, and that by chance it *is* true.

Also, "truth" is an object of study by logicians. In classical propositional logic

truth is just a function from the propositional variable {p, q, r, ...} into {O, 1}, in

the company of rules to extend those "truth values" to compound propositions,

like saying that "p&q" is true in case p is true and q is true, which for the logician

means only the function above send p and q on 1. But logicians considers

many, many, many other sort of "truth valuation" (abstractly they are sub-object

classifier, truth being the object itself, so in classical logic truth can be represented

by a set, in intuitionistic logic truth can be represented by a topological space,

in quantum logic truth can be represented by a Hilbert space, but that's for much latter ...).

Even the "facts" are explanations for observations - and we saw lately discussions on observers. The flat Earth: a fact (Ptolemaios), hell: a fact (A. Dante), the atoms in the molecules I synthesized: facts, then all these things turned into fiction. Props of some belief system.

I doubt very much Ptolemaios maked flat earth a fact. For Dante I don't know

but I would have believe he wrote a fiction (?)

Anyway, we are interested in ALL belief systems. I should have give you a better

answer last day when you asked:

"With the ideas about 'quite' different universes why are we

closed to the idea of 'quite' different mathematical thinking?"

I should have told you that this is exactly what the Universal Dovetailer

Argument (UDA) *forces* us to do: if comp is true we have to explain

the physical appearances by a sort of mean on all consistent belief

systems. And giving the fact that the tool exists to study the basic shape

of that means (the interview of the universal machine), we can do it, and

compare with the "empirical physics".

I doubt very much Ptolemaios maked flat earth a fact. For Dante I don't know

but I would have believe he wrote a fiction (?)

Anyway, we are interested in ALL belief systems. I should have give you a better

answer last day when you asked:

"With the ideas about 'quite' different universes why are we

closed to the idea of 'quite' different mathematical thinking?"

I should have told you that this is exactly what the Universal Dovetailer

Argument (UDA) *forces* us to do: if comp is true we have to explain

the physical appearances by a sort of mean on all consistent belief

systems. And giving the fact that the tool exists to study the basic shape

of that means (the interview of the universal machine), we can do it, and

compare with the "empirical physics".

Now let me take a deep breath and if I am still 'on' this list, later I will come back to 'math'. (I don't know Wilfried Hodge, will not read him for this purpose.)

`You know John to tell you the truth I would like to confess you that I am`

a believer indeed in the sense that I really feel bad (like lying to myself)

when I try to put into doubt the laws of the excluded middle concerning arbitrary

arithmetical sentences. I believe the 667nth fortran program running on the data

766 will either stop or ... not stop.

This does not prevent me to appreciate many other logics. (and classical logic

is the simplest to talk

It is "Wilfrid Hodges, I put a "e" because it is a common Flemish name here,

I probably mess up with the "s" as I always do.

Apology to Wilfrid Hodges.

I recommend it much for the non mathematically minded people who

want a first rate introduction to (classical) logic. Hodges defines logic as the study

of the consistent set of beliefs, and show quickly and simply the relation

with the more common definition of logic as science of the valid argumentation.

He wrote also good (but more technical) books in model theory.

Hodges' "Logic" book is a nice cheap companion to Smullyan's "Forever Undecided".

Shortcuts to G. (The key mathematical tool to transform the reversal between the

"physical universes"/"psychological universes" forced in the UDA.

a believer indeed in the sense that I really feel bad (like lying to myself)

when I try to put into doubt the laws of the excluded middle concerning arbitrary

arithmetical sentences. I believe the 667nth fortran program running on the data

766 will either stop or ... not stop.

This does not prevent me to appreciate many other logics. (and classical logic

is the simplest to talk

It is "Wilfrid Hodges, I put a "e" because it is a common Flemish name here,

I probably mess up with the "s" as I always do.

Apology to Wilfrid Hodges.

I recommend it much for the non mathematically minded people who

want a first rate introduction to (classical) logic. Hodges defines logic as the study

of the consistent set of beliefs, and show quickly and simply the relation

with the more common definition of logic as science of the valid argumentation.

He wrote also good (but more technical) books in model theory.

Hodges' "Logic" book is a nice cheap companion to Smullyan's "Forever Undecided".

Shortcuts to G. (The key mathematical tool to transform the reversal between the

"physical universes"/"psychological universes" forced in the UDA.

Till then, I celebrate July 4th

... so I will drink a coffee,

:-)

Bruno

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