How did Fitch’s opposition to the Russell-Whitehead theory of types turn out since the 1950’s?

In a footnote to Appendix C of Frederic Fitch’s Symbolic Logic (page 217), Fitch writes about his article, “Self-Reference in Philosophy”:

It is reprinted here in order to indicate more fully my motives for rejecting the Russell-Whitehead theory of types and in order to emphasize the philosophical importance of self-referential propositions and a need for a logic, such as the present one, which can handle such propositions.

In this book, Fitch divides propositions between definite propositions for which the law of the excluded middle applies and indefinite propositions for which it doesn’t. He writes,

An example of an indefinite proposition is the proposition expressed by the sentence, “This proposition itself is false”.

His book was published in 1952. How did Fitch’s opposition to the Russell-Whitehead theory of types turn out since then?

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