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Some Brief Thoughts on Schlick and Hilbert

By tdberg

Moritz Schlick, inspired by David Hilbert’s work, took the concept of separating epistemology from its intuitive content much further. Schlick asserts, “it seemed intolerable that the ultimate principals- the axioms of geometry, which underlie all proofs and therefore are not themselves provable-should still owe their validity to intuition alone.” (The Nature of Knowledge, pg. 32) As such, he praised Hilbert for the introduction of concepts whose validity could be defined solely by their axiomatic satisfaction. Moreover, it can be argued that Hilbert’s principles opened the door for Schlick’s further exploration of implicit definition– a notion that, in my opinion, began to exclude any relationship to semantic reality.

Even so, as a consequent, we could now allow formal symbolization to represent chairs, women, or logarithms, since “the introduction of any ambiguous symbol initiated a separation of content from the purely logical form.” (The Nature of Knowledge, pg. 36) In other words, for the argument x(Px ->Qx), x(Rx -> Px) :: x(Rx -> Qx), it would not matter what the symbols represented, only that their relations were specified and satisfied by the axioms, since the logical relationship would hold regardless.

Although Schlick’s support of Hilbert may be ultimately warranted, as the latter’s contribution to formal logic is both immense and undisputedly pioneering, he fails to prove that the use of a priori justification is superfluous. So, the question remains, is the total disuse of intuition either plausible or advisable. Or, more importantly, does an appeal to analytic a priori knowledge have no place in our formal structures? Although Schlick would respond with a resounding no, both Frege and Hilbert viewed intuition as a necessary condition for the selection of axioms. It seems that certain relations, concepts, and spatial definitions require the use of empirical justification, and that to completely remove analytic thought from them is questionable. For this reason, Hilbert, by finding a balance between Frege’s lack of conceptuality and Schlick’s total disdain for intuitive thought, seems the most coherent.

1 Response to Some Brief Thoughts on Schlick and Hilbert

  1. Elmira

    You are so awesome.

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