Sung, list,
Your syllogism fails not only because of its equivocation with the word
'sign' but also its equivocation on the regard in which arbitrariness is
involved. The arbitrariness of which among various synonyms one uses to
denote an object - the arbitrariness of the Saussurian sign and the
Peircean linguistic symbol - does not involve the arbitrariness which
you are imputing to mathematics, an arbitrariness of what conception,
meaning, intension one uses to denote an object, except to the extent
that the synonyms are not quite perfectly synonymous and instead differ
in meaning or, more generally if one is to speak of icons as well as
symbols, differ in what they represent as the object's character, either
by resemblance or symbolically by imputation.
Now you've found two mathematical objects whose graphed value sets are
approximate icons of each other and, to a lesser degree, of some
positive phenomenon's set of graphed measured values. Since the two
mathematical objects do not have quite the same set of values, further
testing of the positive phenomenon may show that one of those objects
tends to be a better fit than the other to the phenomenon and, if such
isn't the result, then you have two mathematical objects neither of
which quite fits the phenomenon although both resemble it. It is hard to
see how this corroborates the idea of an unreasonable arbitrariness of
mathematics.
Your other example is of the quantum mechanics of de Broglie / Bohm
versus the Copenhagen interpretation and the like. It's hard for this
example to be of general use to philosophers and semioticians most of
whom don't have the mathematical and physical background to follow the
argument and hope to bet on the right horse. For example, one reads
physicists arguing with each other about whether de Broglie / Bohm
mechanics does or does not succeed in predicting all the phenomena that
'standard' quantum mechanics does. In other words, most of us are not in
a position to assess whether these two systems of quantum mechanics work
equally well and whether the choice between them is _/arbitrary/_, as
per your view, as far as physics is concerned, although many of us have
philosophical preferences and maybe a kind of sporting interest in the
subject. Anyway, there are always more things to say about views of
quantum mechanics, and plenty of people to say them, so I'll leave it there.
Best, Ben
On 7/3/2014 6:37 PM, Sungchul Ji wrote:
Steven, Ben, list,
I do not deny that Wigner's "Unreasonable Effectiveness of
Mathematics"(UEM) has empirical support, mainly coming from physics. All
I am saying is that the Unreaseaonable Arbitgrariness of Mathematics
(UAM) thesis is also supported by empirical results, limitted as they may
be as of now, that originate from biology. (Please try to understand the
figures that I attached to my prefvious emails, without which you may miss
the point I am trying to make with UAM.)
Please rememgber also that UAM is an empirical fact, not a theoretical
construct, although it may be theoretically derived from semiotics of
Peirce and semiolotgy of Saussure (as I have been attempting to, against
strong oppositions from some of you). If if this theoreticl attempt
happens to fail, as some of you may predict, it would not invalidate UAM,
since it is an observational fact, just as Wigner's UEM is, within its own
boundary.
On the other hand, if the syllogism I suggested as a means to derive the
UAM thesis from first principles in semiotics and linguistics happnes to
turn out to be valid, it would strongly support the theory of signs of
Peirce and the principle of the aribtraness of signs in linguistics,
since they would then be judged consistent with an empirical fact recently
discovered in biology.
With all the best.
Sung
_____________________________________________________
Sungchul Ji, Ph.D.
Associate Professor of Pharmacology and Toxicology
Department of Pharmacology and Toxicology
Ernest Mario School of Pharmacy
Rutgers University
Piscataway, N.J. 08855
732-445-4701
www.conformon.net
I have a concern in this discussion. First, this notion of Unreasonable
Arbitrariness, has absolutely nothing at all to do with Wigner's
Unreasonable Effectiveness. There is no similarity in an argument for
arbitrariness and one for effectiveness. Wigner's argument speaks to
scalability and applicability of technique, it speaks against the
arbitrary
and for a profound physical uniformity. Such that techniques that are
effective at one level may be universally applied.
Regards,
Steven
On Thursday, July 3, 2014, Sungchul Ji <[email protected]> wrote:
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