Re: lattice of ontology
Azmat,
Just two points:
> ... we choose either semiotic or ontological interpretations
> along the general way: The Real World < Ontology <
> Mathematics < Logic < Theoretical Science <
> Empirical Science < Engineering and Technology < Applications.
All those (and undoubtedly many more) are involved, but I
would not put them in a linear order. I wouldn't even put
them in a lattice. There are very complex relationships
among them, and different people may approach them from
different directions.
> you are looking for some sort of an open-ended reference
> frame for theories...
I wouldn't claim that it's the only reference frame.
To use the analogy with latitude and longitude, people were
able to find their way around for centuries before those
coordinates were invented. The major stimulus was the beginning
of ocean-going explorations, where there are no landmarks.
The Spanish and Portuguese managed quite well for a long time
before the British (who designated the Greenwich longitude as 0).
And the Polynesian islanders navigated the open ocean for many
centuries with very different, but highly successful methods.
(And some kinds of birds have done so for millennia.)
Similarly, there are many ways to relate theories. But a
general coordinate system is useful. That's all I claim:
useful for a number of different purposes, which I outlined
in that theory.com paper. That does not preclude the use
of other methods of organization for other purposes.
John