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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