Wednesday, August 20, 2008

Formal exhaustion…

…can only be achieved by a formally adequate means, and since a material and/or imagistic means of description can always be appended, revised, or rejected, no physical account of formal truths (such as mathematical and logical operations) can be produced. This is the thrust of James F. Ross's essay, "Immaterial Aspects of Thought". This anti-physicalist claim, based on the inexhaustibility of formal operations, bears on Wittgenstein's picture-theory of meaning, in the words of Kelley L. Ross (no relation?), thus:

"…it is not by means of a "picture" (a theory carried over from the Tractatus) that anything is understood. Only the very crudest Empiricism would have it so. This gives Wittgenstein's demonstration no more force that [sic] Locke's refutation of "innate ideas" by way of his own definition of "ideas" as images. A "triangular prism" may be the projection of a cube, but then every "drawing of a cube" is a projection of a cube. In fact, nothing drawn on a flat surface can be a cube, which is a three dimensional object. We tend to identify a drawing like the one at right as a cube because we in fact see things by means of two dimensional projections, onto the retina. No such drawing or projection has anything to do with the meaning of "cube," which is not and cannot be defined by means of drawings. Wittgenstein's argument only demonstrates that meanings are not pictures."

Definition is a formal operation, not a bestowing of graphic 'definition'. Hence, truth is a formal, materially inexhaustible source of knowledge that cannot be represented, much less produced, by sheerly material means.

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