--- On Mon, 9/8/08, ornamentalmind <[EMAIL PROTECTED]> wrote:
> Perhaps 'facts' = axioms???
=============
Or, perhaps not.
Again pops up the axiom-drivel which we have clarified
at least 12 times.
Let's go for the 13'th.
I give you a sporting 1 to 100 that your post will trigger
parrots quoting idiotic dictionaries defining Axiom as a
truth (whatever it may mean) assumed to be self-evident.
Follows the 13th repetition of the clarifying message:
Here is the second most discussed axiom in history
after the Euclidean of Parallels:
<If t is a disjointed set which does not contain
the null-set, the Cartesian product Pt is
different from the null-set.>
Self-evident like goddam hell.
Here come other 3 self-evidences:
1.Axiom of Euclides:
<Given a line and a point not on the line, it is
possible to draw through the point exactly one line
parallel to the line>
2.Axiom of Riemann:
<Given a line and a point not on the line, it is
impossible to draw through the point any line
parallel to the line>
3.Axiom of Lobaczevski:
<Given a line and a point not on the line, it is
possible to draw through the point any number
greater than 1 of lines parallel to the line>
One wonders which of the above self-evidences is
self-evidenter than the others and how can
self-evidences contradict one another.
Leaving the drivel we pass to the definition of Axiom
such as it appears in contemporary scientific Models,
which are ALL axiomatic:
Since rational science is born, scientific theories
have the structure of inferencing networks.
Middle nodes or "Theorems" are deduced from upper
neighbors (premises) and induced from lower nodes
(conclusions).
Top nodes or "Axioms" having no premises cannot be
deduced, thus are set arbitrarily by intuition and
taken as granted as long as they are not inductively
refuted by their conclusions.
Bottom nodes or "Facts" having no conclusions cannot
be induced and their logical value (certainty) is
set empirically.
All rational theories are by definition falsifiable,
i.e. structured in a way to support bottom-up
induction from Facts via Theorems to Axioms, which may
eventually refute Axioms and thus the theory.
Georges.
=============
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups
"Epistemology" group.
To post to this group, send email to [email protected]
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at
http://groups.google.com/group/epistemology?hl=en
-~----------~----~----~----~------~----~------~--~---
