Glad you liked the party, I keep wondering if I have walked into one :-))
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 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.
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. 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?"
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.
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.
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.
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.
TheHermit <Trying to figure out the similarity between ravens and writing desks>
> -----Original Message-----
> From: owner-virus@lucifer.com
> [mailto:owner-virus@lucifer.com]On Behalf
> Of Richard Brodie
> Sent: Tuesday, May 11, 1999 2:03 PM
> To: virus@lucifer.com
> Subject: RE: virus: maxims and ground rules
>
>
> Carl,
>
> Your tea-party example had me rolling on the floor.
>
> In your example, as with any symbolic statement, the validity of the
> statement presupposes a number of things. Chief among them are the
> definitions of the symbols and the correspondence between the
> symbols and
> reality.
>
> <<Suppose we say:
> Physics:Optics:Properties of Light:(The wavelength of blue
> light) = (475
> nm)>>
>
> This particular statement is perhaps a poor example because
> it is a simple
> statement of definition. Blue light is defined as having that
> wavelength. It
> was defined that way by humans, and the only reason we care
> about it is that
> we have sensors in our eyes that notice that wavelength of
> light. There is
> no intrinsic meaning to that number.
>
> <<Why does a "true statement" supposedly become a
> "supposition" when removed from its "frame of reference"?
> Unless some of the
> other words in that sentence no longer carry the generally
> accepted English
> meaning. I have provided a "true statement". I have changed
> its reference.
> It does not seem to me to be a supposition.>>
>
> I don't think the assertion was that you couldn't change
> ANYTHING about the
> frame of reference without the statement becoming a
> supposition, but rather
> that there was a PARTICULAR frame of reference (perhaps with
> variables such
> as the time and location of the observer being flexible)
> which was necessary
> for the statement to be true.
>
> Just to throw out some examples: if by "blue light" we
> instead mean "any
> light that looks blue to the average human eye," then the
> wavelength of blue
> light might be 474 or 476 nm (I'm just making that up). If by
> "blue light"
> we mean "any light that looks blue to my friend who is blue-green
> colorblind," then the wavelength of blue light might be something else
> again. Is that clear?
>
> <<P.S. Set theory tells us that all things are things, and
> all real things
> have attributes. Would you call an attribute a name? Or a
> boundary? We also
> know that there are big differences between "real things"
> with attributes
> (boundaries?) and "imaginary things" (like sets of things)
> which need not
> have boundaries. Please say more to this issue.>>
>
> Set theory is not true. It is a model and only valid within a
> particular
> frame of reference. For one thing, it is reductionist. It
> does nothing to
> explain phenomena that do not consist of nested components,
> for instance the
> execution of computer programs or interpersonal relationships.
>
> It is not True that things have attributes. That is simply a
> convenient
> model we use that sometimes is more useful than other times.
> For instance,
> what attributes of a human being correspond to his or her
> potential for
> leadership? It's fuzzy.
>
> <<PPS Finally, re symbolic logic. If you cannot write a "true
> statement" in
> the format of a valid symbolic logic equation then it is not a valid
> proposition. The reverse is of course not necessarily true.
> But to rephrase
> your "may give us insight into operating in reality", the act
> of putting a
> statement into symbolic form often brings out the falsities
> of a position in
> ways that simple argument does not. It is a fact that any
> statement, true or
> false, can be encoded that allows us to simplify and test the
> structure of a
> statement. Where I disagree with your conclusion that
> "ultimately do not
> yield any truth about reality" is that, it should be evident
> that, if you
> discover an error of logic, or if you discover that the
> equation does not
> equate, then you have discovered that the statement cannot be
> true. And if
> the statement purported to be a statement about reality, that
> symbolic logic
> proves that your "reality" was flawed.>>
>
> No statement is wholly true. If you find a logical
> contradiction, all it
> means is that you have a wrong assumption. Since no
> assumption about the
> physical world is ever true in all cases, you have only
> proved something
> probabilistically, which in most cases is good enough.
>
> You seem to cherish the belief that reality can be mapped
> exactly. I don't
> think that is the case.
>
> Richard Brodie richard@brodietech.com
> Author, "Virus of the Mind: The New Science of the Meme"
> Free newsletter! http://www.brodietech.com/rbrodie/meme.htm
>
>