Re: OOP/OOD Philosophy

On 15 Jul 2005 01:35:15 -0700, "Mark Nicholls"
<Nicholls.Mark@xxxxxxxxx> wrote:

>
>
>Stefan Ram wrote:
>> "Mark Nicholls" <Nicholls.Mark@xxxxxxxxx> writes:
>> >Careful mathematics is a belief system based (usually) on the
>> >axioms of ZFC.
>>
>> It suffices to just specify the axioms as an assertion A and
>> then investigate the consequences of A. It is not neccessary
>> to "belief" that A is actually true.
>
>OK, I agree, but if we are to believe that we can apply the model to
>the universe around us, we must believe that the axioms apply to that
>universe

Not quite. We use the logical system of math to describe empirical
observations. If the descriptions fail to match those observations,
then we choose new axioms.

>So I should really say science and applied maths are belief systems.

They are. But they are belief systems of a fundamentally different
kind than religion. Math is a belief that conclusions can be derived
from initial axioms through logic. Science is a belief that the laws
of the universe can be derived from observations and described by
math. Religion is a belief based on faith.

>If you believe F=MA applies, you must believe that time is absolute for
>all observers,

We observe F=MA to apply in many contexts, and have observed that it
does not apply in others. In those contexts where we have observed
F=MA to apply, it applies for every observation and does not deviate.
Based upon this we conclude (believe) that within the contexts where
we have observed F=MA to apply, it will continue to apply in the
future.

>if you believe relativity, you can scrub this belief,

We have observed the laws of relativity to correctly describe a vast
number of events and processes. And we have also observed situations
that appear to deviate from it.

>but there are a whole lot more including and the existence of the empty
>set, and the axiom of choice (or its negation), ZFC (or equivalent) etc
>etc

Those axioms seem to generate a system of logic that has the
expressive power to describe most events in the world. So far we
haven't found a lot of contradictions. It took quite awhile, and a
lot of trial and error, to come up with a set of axioms that generated
a system that was so expressive.

>and a set of existential beliefs about existence, and that the
>universe itself is deterministic in the same manner that maths
>is.......thats a lot of belief, thankfully it seems to work.

There is belief involved, certainly.



-----
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"The aim of science is not to open the door to infinite wisdom,
but to set a limit to infinite error."
-- Bertolt Brecht, Life of Galileo
.

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