Tuesday, November 27, 2007

6.123 It is clear: The logical laws must not themselves be subject to further logical laws.

(There is not, as Russell thought, a unique law of contradiction for each “type”, rather one is enough, since it is not to be applied to itself.)

Black (p. 326) quotes Russell’s Principia vol. 1, p. 127 “Negation and disjunction and their derivatives must have a different meaning when applied to elementary propositions from that which they have when applied to such propositions as (x).φx or (Ex).φx” and Logic and Knowledge p. 63 “The first difficulty that confronts us [after adopting the “vicious circle principle”] is as to the fundamental principles of logic known under the quaint name of “laws of thought”. “All propositions are either true or false”, for example, has become meaningless. If it were significant, it would be a proposition, and would come under its own scope.”

On Wittgenstein’s view, apparently, there is only logic, rules for the combination of propositions into tautologies, contradictions, and other propositions. There is no logic of logic, rules for the application of the rules.

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