Saturday, December 15, 2007

Defining 'modernity' (continued)

Spinoza could not have known that the deductive system of his great book, ETHICS, may very well be incomplete, that statements can be formulated that cannot be proved zor disproved within its system of definitions, axioms and theorems; or that the incompleteness of the ETHICS may be incorrigible. (And, I suppose, there are great falsehoods whose falsity cannot be proved either.) We owe this insight into the nature of deductive systems to the work of Kurt Godel (with an umlaut over the 'o' I think) who proved in 1931 that any axiomatic system sufficiently rich to contain the natural numbers is incomplete in this way. Bertrand Russell had made a similar discovery--much to his horror-- in his attempt to place logic, and therefore, knowledge, on an absolutely secure foundation.

(The question is: what would a modern logician make of Spinoza's logic?)

One makes what one will of such findings. They strike me as quintessentially modern, like Einstein's proof that the speed of light is an absolute limit and that things are not located in space or time but only in space-time. Or Heisenberg's uncertainty principle. Or Planck's constant which seems to define the smallest possible units of time and space.

So, when Hume showed (but of course couldn't prove) that matters of fact can never be established by reason alone,he was establishing a characteristically modern principle.

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