(If figure 1 is distorted, please refer to one of my earlier posts.)
Howard wrote:
"The mathematical concepts are rule-governed (110914-1)
symbols and the physical universe is law-governed
matter. The relation between symbolic rules and
natural laws is both "occult and mysterious" (Peirce)
and "unreasonably effective" (Wigner)."
I wonder if the basic idea of (110914-1) can be represented
diagrammatically thus:
f g
Reality --------- > Phenomenon ------- > Theories
| ^
| |
|__________________________________________|
h
f = law governed-matter
g = rule-governed symbols
h = unreasonable effectiveness
or mind-body identity (?)
Or reality, phenomenon and theories may form an irreducible triad, or a
mathematical category so that these cannot be discussed as dual opposites
without falling into contradictions (?)
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
> At 11:04 PM 11/8/2014, Jon Awbrey wrote:
>
>>It is necessary to distinguish the mathematical concepts of
>>continuity and infinity from the question of their physical
>>realization. The mathematical concepts retain their practical
>>utility for modeling empirical phenomena quite independently of the
>>(meta-)physical question of whether these continua and cardinalities
>>are literally realized in the physical universe.
>
> HP: Yes! To reduce confusion this necessity should always be kept in
> mind. Consequently, so should the
> <https://www.google.com/?gws_rd=ssl#q=%22symbol-matter+problem%22>symbol-matter
> problem it must entail. The mathematical concepts are rule-governed
> symbols and the physical universe is law-governed matter. The
> relation between symbolic rules and natural laws is both "occult and
> mysterious" (Peirce) and "unreasonably effective" (Wigner).
>
> Peirce: "What is a law, then? It is a formula to which real events
> truly conform. By ' conform,' I mean that, taking the formula as a
> general principle, if experience shows that the formula applies to a
> given event, then the result will be confirmed by experience. But
> that such a general formula is a symbol, and more particularly, an
> asserted symbolical proposition, is evident." (cf. Hertz)
>
> Max Planck: "It is not therefore the case, as is sometimes stated,
> that the physical world image [in brains] can or should contain only
> directly observable magnitudes. The contrary is the fact. The world
> image contains no observable magnitudes at all; all that it contains
> is symbols." The Philosophy of Physics. New York: W. W. Norton, 1936,
> p.55.
>
> Herman Weyl: However, the only decisive feature of all measurements
> is, it seems, symbolic representation." Philosophy of Mathematics and
> Natural Science, Princeton Univ. Press, 1949, p.144.
>
> Max Born: "All knowledge is subjective, without exception." . . .
> "Symbols are the carriers of communication between individuals and
> thus decisive for the possibility of objective knowledge." (Symbol
> and Reality)
>
> In my opinion the need for additional epistemological models
> (realist, nominalist, idealist, constructivist, etc.) is motivated
> by our desire to reduce the mystery and unreasonableness of the
> symbol-matter relation. But no epistemology can alter this basic
> necessity of symbolic representation. I think there is evidence that
> most epistemologies reflect largely unconscious psychological,
> cultural, aesthetic and religious influences, because they have
> proven historically to be logically and empirically undecidable.
>
> Howard
>
>
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