Kathy, (01)
The point I was addressing, in the notes to Pat C. and Azamat,
is that there is no such thing as perfect knowledge of anything,
and all of our theories of science are, at best, approximations.
Even in physics, we must deal with a very large collection of
mutually inconsistent, ad hoc, approximations, and every other
empirical subject is in even worse shape. (02)
KBL> Hopelessness at prediction is not at all the same thing as
> lack of precision or paucity of theoretical foundations. (03)
No, but it's a symptom that there is a lot that is not
well understood. (04)
KBL> If the dynamics are highly nonlinear then prediction is
> hopeless regardless of how well-understood the system is or
> how precisely things are stated (given that initial conditions
> can never be specified with absolute precision). (05)
That's true. But it merely reinforces the point I was trying
to make: there's no such thing as perfect knowledge of anything,
not even in physics, and certainly not in any other field. (06)
Note that this is different from the point I was trying to address
in my note to Sean B: if you do have a field that is under the
control of the person who is writing the specifications, as in
mathematics and computer programming, then it is possible to specify
it in classical FOL. (07)
Kant made both of those points over 200 years ago: (08)
Since the synthesis of empirical concepts is not arbitrary but
based on experience, and as such can never be complete (for in
experience ever new characteristics of the concept can be
discovered), empirical concepts cannot be defined. (09)
Thus only arbitrarily made concepts can be defined synthetically.
Such definitions... could also be called declarations, since in
them one declares one's thoughts or renders account of what one
understands by a word. This is the case with mathematicians. (010)
They have been reiterated many times since then, notably by Peirce,
Whitehead, and Wittgenstein, among others. (011)
John (012)
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