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?
I am looking at the following for more information about this:
- Bolander, Thomas, "Self-Reference", The Stanford Encyclopedia of Philosophy (Fall 2017 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/fall2017/entries/self-reference/.
- Beall, Jc, Glanzberg, Michael and Ripley, David, "Liar Paradox", The Stanford Encyclopedia of Philosophy (Fall 2017 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/fall2017/entries/liar-paradox/.
- Priest, G. (1979). The logic of paradox. Journal of Philosophical logic, 8(1), 219-241.
- Shramko, Y., & Wansing, H. (2011). Truth and falsehood: An inquiry into generalized logical values (Vol. 36). Springer Science & Business Media.
- Shaw, J. R. (2014). What is a truth-value gap?. Linguistics and philosophy, 37(6), 503-534.