Dear Günther,

Le 12-sept.-07, à 16:49, Günther Greindl a écrit :

> The problem is: in math what follows from the axioms is true per
> definition (that is what following from the axioms mean).

Not at all. If you were true, no inconsistent theory in math would 
appear. "Axioms" are just provisory statements on which we agree. For 
simple filed like number theory, it happens that nobody doubts them, 
and in that case I am willing to say I do believe them true, but I am a 
few bit less sure for ZF set theory, and quite skeptical for a theory 
like NF (Quine's new foundation).
All the first theories extending the lambda calculus or the combinators 
were inconsistent.

> How would you be able to "refute" comp? There is no way to do that, one
> can only call the axioms into question (and that is what John is 
> doing).

Not at all. Well, you can doubt the axioms indeed, but this could lead 
to long and useless debate. It is better, imo, to try to make the 
postulate (axioms) sufficiently precise so that we can infer some 
absurdity (internal or empirical). Many years ago I thought comp was 
easy to refute because it makes the indirect evidence of "many world" 
necessary, but then QM did confirm this.
You can read the UD Argument; it shows comp is refutable because it put 
very strong constraints on the possible physics. Comp and its 
consequences would have been discovered at Newton time, it would have 
been considered as refuted by many philosophers. Probably not by Newton 
himself, because Newton has seen quickly that "classical mechanics" 
could not really been the end of the history in physics.

>>> because the Flat Earth did not prove true later, either.
>> We have no proof that the earth is round, only solid evidence that the
>> roundity of earth is a solid *local* truth.
> In which models would the Earth not be round? (I am speaking here of
> models which have the property "roundness" in them and which other
> objects similar to Earth are also round - I guess that is as close to
> what we can call as something being true.) In this sense I would call
> the Earth as being round true.

In the model were I wake up and realize that the earth is flat, in all 
serious appearances. My point was trivial here: I'm not arguing against 
the round aspect of earth, I am just arguing that we cannot pretend to 
have a proof. There are just no proof about reality. It is a simple 
triviality I am recalling. Proofs occur only through theories, and 
theories or just "world views" are only inferred.

>> No serious scientist will ever try to convince others (except for the
>> mundane purpose of getting some funds). As I said a scientist, not 
>> only
>> does not want to convince others, he want others to show him wrong
>> instead. You confuse scientists, and mediatico-pseudo-scientists, 
>> which
>> can exist still today due to 1500 years of abandon of the fundamental
>> question to political pseudo-religious authorities. Of course they 
>> have
>> had no choice, because it is best to do pseudo-science than to burn
>> alive ... (I don't judge them here).
> I agree strongly with you Bruno that science is about doubt and 
> modesty.
> But I do not think that a scientist has to be so agnostic as to never
> want to convince anybody else of some positions (which is what teaching
> essentially is);

I don't think so. Teaching in science, for adult,  is (I mean  ideal 
teaching *should* be) an invitation to deduction in hypothetical 
context, inductive inference and then the art of observation and 

> I am adopting a critical rationalist position here: a scientist can 
> look
> at the models and assign different plausibilities to them; he can say
> that the evidence speaks more for A than for B. But he sometimes can
> also say that C is strictly ruled out

I agree with this. You can rule out a theory when it leads to a 
contradiction, but only *once* you get that contradiction. (A theory 
can be contradictory without you ever knowing that fact).

> (of course, this is often said too
> soon in practice, but if one is careful one can nevertheless say this,
> of inconsistent theories for instance).

... of some of them. You can have an inconsistent theory in which the 
shorter proof of the falsity is *very* long.



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