It is fairly common for pure maths to change from ideas generated in practical physics. Georges' scheme lays out such possibilities without direct reference to examples. The use of Yang-Mills-type theories (maths explanations of interactions between sub-atomic particles) in developing unexpected properties in 4-dimensional manifolds (Simon Donaldson) that had defied resolution for decades is an example. No one is giving up scientific method to get to such intuitions and no one I know gives up on the underlying thought that the axioms in use may not, at some point, turn out not to be axiomatic. Of course, there is a wider 'dictionary' of terms in use we can access to try and understand what people are on about, and the possibility of radical translation that is courteous towards human beliefs without giving up on reason (another Donaldson). Not everyone is much good at expressing what is axiomatic to them.
On 9 Sep, 04:35, "Sam Carana" <[EMAIL PROTECTED]> wrote: > Nice post, Georges. > Personally, I like to avoid the term 'axiom' for the simple reason > that so many people do not seem able/willing to understand/stick to > the meaning of the word to start with. > > 4. Axiom of Sam Carana > Given the nature of human beings, > it's impossible for them to draw a line that even briefly remains in > parallel with another line. > > Feel free to add my addition to your site, Georges. > > Cheers! > Sam Carana > > On Mon, Sep 8, 2008 at 11:07 PM, Georges Metanomski <[EMAIL PROTECTED]> wrote: > > > --- 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 -~----------~----~----~----~------~----~------~--~---
