Azamat, (01)
You should join our President George W. Bush, since you both
believe in faith and hope based systems instead of reality. (02)
To clarify the issues, I suggest that every occurrence of the
word 'axiom' be replaced with the word 'assumption'. In mathematics,
everybody is free to make any assumptions (axioms) they please.
But in physics, the assumptions made at the beginning are usually
proven false by experiment and observation of reality. In a textbook,
physicists often present the thoroughly tested assumptions at the
beginning and call them "laws". But that is a pedagogical method,
which does not show the years, decades, and even centuries of very
hard work to discover and test them. (03)
AA> Ontologism is the theory that all of scientific and mathematical
> principles can be derived from a universal ontology, its fundamental
> classes, rules, axioms or constraints. (04)
As Leibniz said, finite human reason in mathematics can be precise
because many important mathematical systems have only a finite number
of axioms and many finite proofs. But in physical reality, everything
has some influence, however small, on everything else, and only an
infinite mind, such as God, could comprehend it all. (05)
For that reason, only God is able to construct and comprehend the
field you call "ontologism". No mere mortal ever can or ever will
comprehend everything by starting from axioms (assumptions). On
the contrary, human is eminently fallible, and all knowledge is
acquired by observation, a posteriori. And that knowledge is
always limited and fallible. (06)
AA> Everybody in this world knows that the propositions and axioms
> of mathematics do not need experimental verification, unlike the
> natural sciences. (07)
I am delighted to hear you say that. If we can all agree with
Leibniz and Newton that the methodologies of math and physics are
180 degrees opposite from each other, then we can begin to talk
rationally about these subjects. (08)
AA>>> All great scientific minds followed Euclid' axiomatic approach
>>> trying to establish a single foundation in their field of knowledge. (09)
JFS>> That is absolutely *false*. (010)
AA> Too strong negation. That might be false or might be right. (011)
I apologize. I missed the word 'trying'. It is true that the ultimate
goal of science is to find the ultimate laws that govern the world.
Therefore, science is *trying* to find a unified set of laws of
everything. Unfortunately, that goal is *always* in the far, far
distant future. It has never been and probably can never be achieved. (012)
> See Newton's Philosophiae naturalis principia mathematica
> See Principia Mathematica
> See Hilbert's Foundations of Geometry
> See Theoretical Physics of Landau and Lifshitz
> See all classical ontological works since Aristotle. (013)
Those are five very good books. But they don't belong in the same
group. #1 and #4 are textbooks about physics. #2 and #3 are
foundational studies in mathematics. And #4 is Aristotle's
metaphysics (and I don't know what other classical ontological
works you have in mind, perhaps Kant, but that is not important). (014)
As I pointed out, the assumptions in the beginning of #1 and #4
were gained by a much more difficult test than those in #2 and #3. (015)
As for metaphysics, the usual word for it is "speculation".
Although I have a very high regard for Aristotle and Kant, many
people dismiss metaphysics. I consider their ideas important,
but they are, like most of us, merely human. (016)
John (017)
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