At 10:14 13/01/04 +0100, Georges Quenot wrote:

Some people do argue that there is no arithmetical property
independent of us because there is no thing on which they would
apply independentkly of us. What we would call their arithmetical
properties is simply a set of tautologies that do come with them
when they are considered but exist no more than them when they
are not considered.



But then what would be an undecidable proposition?


You know, about arithmetic, and about machines btw, a lot of
people defends idea which are just no more plausible since
Godel has proved its incompleteness theorems.
Arithmetical proposition are just not tautologies. This is how
Russell's and Whitehead logicism has break down. There is a ladder
of arithmetical propositions which ask for more and more
ingenuity to be proved. Actually arithmetical truth extend far beyond
the reach of any consistent machine (and consistent human with
comp). There is an infinity of surprise in there.
I guess you know that there is no natural number p and q such that
(p/q)(p/q) is equal to 2. If mathematical truth were conventionnal,
why did the pythagoreans *hide* this fact for so long?
So those propositions are neither tautologies, nor conventions.
David Deutsch, following Johnson's criteria of reality, would say
that such propositions kick back.


> Giving that I hope getting some understanding of the complex human
> from something simpler (number property) the approach of those
> people will never work, for me.


And certainly vice versa. Though it is difficult to have them saying it explicitely I have the feeling that the reason why they do not want the natural numbers to be out there and even as not possibly being considered as out there is that they do not accept that the complex human be understood from something simpler (number property). They do not even accept the idea being considered, were it as a mere conjecture or working hypothesis. Their more official argument is that such a view would prevent the foundation of human dignity.


Damned!!!  If there is one thing which could prevent the foundation
of human dignity, it is certainly that totalitarian idea following which
some ideas can not even be considered as an hypothesis or conjecture.
But that happens all the time. There has been days you could be burned even
just because you ask yourself if by chance it was not the sun but
the earth which was moving. Are you defending those guys? Are you
asking me how to reply to those guy? My suggestion: if many people
things like that around you, just leave them. Like Valery said, those who are
not willing to use logic with you (that is to argument) are in war with you.
Run or kill them! It is not enough they have good intention, if they does not
want arguments, they are dangerous for all humans. I like to insist, in Valery
spirit, that logic is not a question of truth, but of politeness.


I have not met any of them physically but I had discussion with
some of them via Internet. There might not be so many of them but
there are. You will find, at least in the US, a lot of people
considering the views of evolution and/or of the big-bang as evil.


Then what? If they disagree with dialog and argumentation, *I* will
consider them as evil. (btw I think there are much more people like that
in France and in Belgium, especially in Belgium, but that's another story).


If they finally have to abandon these positions due to the amount
of evidence in favor of it, the last line of defence for their
conception of a personal God and for a significant role for Him
could be at the level of artihmetical realism. Artihmetical
realism by itself (not from a distinct personal God) is therefore
seen as evil by them. As I mentionned, they usually do not put it
that way. Rather they argue that such a view would prevent the
foundation of human dignity and the like.


They make probably the same confusion of those who believe
that determinism is in contradiction with free will.
Actually I tend to think that Godel's and other incompleteness
result makes comp a sort of vaccine against reductionist view of
self and reality (and arithmetic).
You know "reason" works only through doubt, and through the ability
to listen to different opinions. Now with Godel we can say more,
which is that "good faith" never fears "reason" and rationality.
Sincere Faith can only extend Ratio, and is always open to dialog.

Bruno






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