JAMES CARGILE, Russell’s Formal Logic


Russell’s formal logic has been criticized by some formal logicians as not having fully precise syntax (form). However, he is guided by the principle of formal logic, (Form) that proof depends entirely on form, independently of content. This is a profoundly questionable view of proof. It conflicts with recognizing that (i) “The set of dogs is a non-self-member” and (ii) “The set of cats is a non-self-member” are attributing different properties in spite of having the same predicate. The predicate form Rx: “x is a non-self-member” is common to (i) and (ii) but the content of the predicate, the property attributed, is different. This is the key to resolving Russell’s paradox and is unavailable to Russell due to his commitment to (Form). His “Vicious Circle Principle” is not well stated and its concern with content conflicts with (Form). But a proper understanding of the principle does provide an answer to the “Truthteller Paradox”. That allows me to close on a note of agreement with Russell.

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