[FoRK] Anything to be learned from religion?

Albert S. albert.scherbinsky
Fri Aug 12 07:27:11 PDT 2005


I think Andrew is correct on this point. Mathematical
axioms are pure creation. In the early days of
Mathematics axioms were chosen to correspond to
experiential analogs. However, in the last century
vast new vistas of Mathematics were opened by chosing
axioms essentially arbitrarily to see what would
happen. Amazing things happened, sometimes even useful
things.

Cheers,
Albert

--- "Stephen D. Williams" <sdw at lig.net> wrote:

> I look at mathematical axioms as equivalent to
> theories in science (real 
> theories, the ones backed up by facts, not
> conjectures and myth called 
> theories).  Is not a mathematical axiom a model of a
> system that is 
> testable in the real world (or imaginary world that
> is, indirectly, a 
> model of the real world)?  True if the best
> explanation for something 
> observable and not proven false.
> 
> Many of you have the benefit (or curse) of far more
> formal math training 
> than I, but I fail to see how math is less firm of a
> science than 
> science in general.  Sure, there's plenty of mental
> masturbation about 
> meta recursive models or stress-testing symbolic
> models by applying them 
> to new, non-reality systems (or those that might or
> might not be a 
> useful model).  That doesn't detract from the core
> goal of predictive 
> explanation of observable truth.
> 
> sdw
> 
> J. Andrew Rogers wrote:
> 
> >On 8/11/05 10:28 PM, "Stephen D. Williams"
> <sdw at lig.net> wrote:
> >  
> >
> >>I think your argument is deep into semantic
> absolutism.  If math and
> >>science isn't "truth", what would be an example of
> "truth"?
> >>    
> >>
> >
> >
> >The difference between math and science is that
> science has no axioms
> >(except maybe math?).  That this difference exists
> is the result of explicit
> >choices.  The closest things to axioms we have in
> science, like
> >thermodynamics, falls out of the math anyway.
> >
> >The problem with axiomatic systems is that they
> assert 'truth' when no such
> >assertion can be legitimately made by humans.  I do
> not have a problem
> >working from some given set of assumptions as I do
> it all the time, but what
> >I do have a problem with is when people do not
> recognize that those
> >assumptions should not be treated as true axioms in
> the abstract.  The vast,
> >vast majority of the time it is perfectly safe to
> treat the small number of
> >de facto axioms as absolute truths, but it is also
> useful to keep in mind
> >that those axioms are nonetheless arbitrary.
> >
> >My argument is not philosophical, at least as I see
> it.  It is more about
> >knowing precisely what you have, to the extent
> possible, and not fabricating
> >any convenient 'truths' or additional information
> to round out the
> >collection.  There is nothing wrong with assuming a
> set of axioms if one is
> >aware that this is what they are doing.
> >
> >
> >Cheers,
> >
> >J. Andrew Rogers
> >
> >
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