Carl,
After reading your last post I think we are in complete agreement. I'm not sure what was meant by the word "supposition." I took it to mean that there were assumptions present in the statement without which it would not be true.
Some feedback on your post:
<<Glad you liked the party, I keep wondering if I have walked into one
:-))>>
I liked that. I felt a human connection.
<<Again, I started with an example from logics, and that seemed to go right
past those who responded. When I replied, I guessed than an example would be
helpful. I could have chosen a more subtle example, but I still focused on
the initial assertion and simply providing an example where it did not
apply. So I figured, the simpler my proposition the better. Knowing the love
for pilpul on this list, I tried to choose an example which was in and of
itself unassailable. I carefully noted some potential arguments in the hope
that this would serve as a indicator that I too, could go down this road.
Yes, I agree that we can construct exceptions, but that could be dealt with
by extending the model (making it more complex). So I chose a simple
definitional proposition in the hope of keeping the topic focused on the
simple point I was attempting to make. Perhaps I should have used something
like 4/2He = At Wt 4.00260 (Although, this applies from an engineering
perspective. If I analyze it as a chemist or physicist, I could present some
conflicting discussion on that too :-( ). Instead I took a word, blue which
is defined in English as a color with a certain spectral content (without
any of the qualifiers that we all could think up) and provided a "true
statement" based on the definition of English and a fundamental physical
quality. Yes, I know it is reductionist. But the point I was trying very
hard to make, and think I succeeded in making, is that, when dealing with
fundamental absolutes, that even if you remove the frame of reference, they
either remain absolutes or become meaningless or acquire some new meaning.
They do not become "suppositions". Unless something is being redefined
unnecessarily.>>
I judged the above paragraph as defensive. It was also very long, which led me to have difficulty reading it. I don't think I got much out of it.
<<I think you agreed with me when you said "No statement is wholly true"
:-).
Did you construct that paradox with intent? I assume so. That "true
statement" placed in any other environment (frame of reference) will remain
paradoxical, may or may not be meaningless, but cannot be said to be a
supposition.>>
Again, I'm not sure there is agreement on the word "supposition."
<<Notations by their nature are reductionist. The only notation that is not
reductionist is the thing itself. At the root, this can be demonstrated by
recourse to Heisenberg.>>
The thing itself is not really a "notation," is it? That kind of goes against the main point that there is no completely accurate map of reality. Notations are maps at best, meaningless or misleading at worst.
<< But the key to making notations work (including the
concept of "equality") it to accept (through reason) that a notation is
adequate for the problem to which it is applied. If it is not, the model
needs to be extended to make it adequate, or the theory needs to be modified
or extended in order to deal with the observation, or some other theory
applied to the problem. Having decided that a notation presents an
"adequate" model, the next question has to be "Is it useful?">>
Complete agreement.
<<Set theory has an application field where it is useful. That of
categorization. There are of course many instances - you give two good
ones - where it is not directly applicable, or perhaps not useful. Yet even
your examples fail because in some instances either example can be mapped to
sets and useful work performed by using set theory to analyze their
characteristics. For example, programs belong to the set of {problems
amenable to categorization using set theory} e.g. linear, non-linear,
computable, incomputable and personal relationships can and have been
effectively modeled using set theory - for example, in South Africa I
developed a system which analyzed intelligence data of the class of "a was
seen talking to b then c did something" to create graphic maps of peoples'
relationships and positions within hierarchies, and this system is now being
used by many police forces to analyze the structure of crime syndicates
based on partial information. Please note that I didn't claim that set
theory would be helpful in all instances. Just that all things can be
documented and analyzed using set theory.>>
The examples fail if they fail to illustrate my point to you. Since you got my point, I don't think they failed. Since the main point is that no theory, notation, or statement applies to every context, your reply that my examples do not work in some contexts is hardly a surprise, is it?
<<I would argue (while in a set theory reference frame) that any thing has
attributes. And it is those attributes that allow us to categorize things.
For now, set theory seems to be a good and useful model, which has been
given the title of a theory because it has stood up well to attack. So we
use it. And if you claim it is invalid to use it, you need to provide a
reason why. Or provide a better system. If you can't, it remains the best
classification system we have. And provides the ability to handle fuzzy
values as a subset without upsetting its effective use. You asked about
leadership potential, if somebody wanted to do a study of the attributes
contributing to leadership potential, I would suggest that after defining
leadership, that the classification of events, capacities and results would
play a key role in the analysis. While statistical and topological analysis
would play a key role in massaging the raw data from such a research project
(and possibly Fourier or wavelet analysis as well), it is set theory that
would offer the simplest way of reducing the resultant data into useful
information. Note, I have not claimed it would be the only way of dealing
with it, just that IMO it would be the easiest way. We have very good
computer based tools for this kind of data set reduction.>>
Complete agreement.
<<I am not stupid enough to believe that "reality can be mapped exactly".
Again, Heisenberg precludes that. I do believe that reality can be mapped
adequately, and when the model fails to be adequate, that we can adjust it,
or build a new model, which serves us better... until the next time. I don't
even have a problem with maintaining multiple simultaneous models - anyone
who works with EM radiation lives with the use of wave and particle duality
on a daily basis.>>
Complete agreement.
<<And yes, I do cherish the "belieph" that while the scientific method is
not
perfect, and by definition, never will be, that it is the best, nay only,
method that we have which provides us with the capability to evaluate the
models we build of reality. So far, I have not seen anything that even
begins to approach a viable alternative.>>
I am in complete agreement again. However, evaluating and selecting good models of reality is only a tool used for living life. There are far better tools for living life that immersion in the scientific method except for the rare individual who has made that her life purpose.
Thanks for this, Carl -- I feel I know you better now and I am glad.
Richard Brodie richard@brodietech.com
Author, "Getting Past OK: A Straightforward Guide to Having a Fantastic
Life"
http://www.brodietech.com/rbrodie/gpok.htm