[FoRK] Re: Anything to be learned from religion?
Stephen D. Williams
Thu Aug 11 23:46:59 PDT 2005
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.
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.
>J. Andrew Rogers
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