Ravi, (01)
I mostly agree with your remarks. Some comments: (02)
RS> I have a feeling that the two mechanisms for science (e.g.
> physics) and ontology (math) may not be all that different?? (03)
I believe that the underlying mechanisms of human thinking that
support both have a great deal in common. They are formed by
abstractions from our mental models, which are based on our
perceptions and actions. (04)
RS> Great clarity on Math Vs Science! However, in Physics (probably
> less exactly in other sciences?) we have phenomenological explanations
> like the ones you describe. These are parametric. And then there are
> theories that are based on some math (axioms) formalism such as
> equations of type ... etc. (05)
Thank you for the note of support. But the point I emphasize is
that all of our axioms are abstractions from reality. And as
Whitehead emphasized many times, every abstraction omits an enormous
amount of detail. For some problems, that detail may be irrelevant,
but for others, those details may be the central concern. (06)
As abstractions, axioms never come at the *beginning* of any
empirical study. Copernicus, Galileo, and Kepler were essential
to Newton's synthesis. (07)
In electromagnetic theory, Faraday's intuitive insights and careful
experiments were a prerequisite for Maxwell. Faraday had very
little training in mathematics, but he had an outstanding ability
to visualize and imagine the fields of force. Maxwell worked
with Faraday for a long time before he could "see" those lines of
force clearly enough to represent them in mathematics. Finally,
Maxwell wrote his four famous equations, which he had to work
and rework for some time before he got them right. (08)
Fundamental principles about axioms in any empirical study: (09)
1. Axioms are always abstractions that omit details that may
become extremely important for other studies. (010)
2. Axioms always come at the *end* of the study, never at the
beginning. (011)
3. Engineers may use axioms as a starting point, but they are
building on the insights of many years, decades, or even
centuries of science. (012)
4. Even when engineers start with axioms, they inevitably make
modifications and approximations to simplify the computation
and accommodate the annoying details that were omitted from
the original formulation. (013)
John (014)
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