“after all, what could be more mysterious, or could be more awe– inspiring, than to find that the structure of the physical world is intimately tied to the deep mathematical concepts, concepts which were developed out of considerations rooted only in logic and the beauty of form?”The first non sequitur is the idea, derived from the success of mathematics in science, that the “physical world is intimately tied to the deep mathematical concepts.” Why not the other way around? That

Robin J. Wilson and Jeremy Gray (eds.),Mathematical Conversations: Selections from The Mathematical Intelligencer, p. 72.

*some*deep mathematical concepts are tied to reality? And that this is an empirical and contingent fact?

After all, a considerable amount of pure mathematics has no application to the real universe, nor provides any description or model of any process or phenomenon in the real universe.

The empirical discovery that the some subset of theories in pure mathematics

*does*describe or model reality – when these models are transformed into applied mathematics – does not vindicate apriorist Rationalism. It vindicates empiricism. You cannot use armchair deduction to know with certainty that non-Euclidean geometry is the right description of the geometry of the universe. It is empiricism that has allowed us to establish this fact.

Perhaps he was only being tongue-in-cheek, but the second non sequitur is Gene Callahan’s conclusion from this quotation that modern physics is “idealist.” How does that follow? On the contrary, the assumption of an external world of matter and energy is a fundamental postulate of modern science. Our medical science in its treatment of human behavioural disorders and mental health relies on empirical evidence that the human mind is causally dependent on the healthy functioning of the brain, and so on.

Callahan doesn't understand idealism. For an idealist the mathematics is reality because there is no material world underlying the symbols.

ReplyDeleteAlso, empiricism and idealism are not in contradiction with one another. Berkeley believed that the former, properly conceived, leads to the latter.

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