History and Philosophy of Logic 22 (1):13-28 (2001)
In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell’s Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege’s extant logical system, if Frege’s system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege’s logical system, even without its naive class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therein.
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References found in this work BETA
Collected Papers on Mathematics, Logic, and Philosophy.Gottlob Frege - 1991 - Wiley-Blackwell.
Citations of this work BETA
A Neglected Resolution of Russell’s Paradox of Propositions.Gabriel Uzquiano - 2015 - Review of Symbolic Logic 8 (2):328-344.
The Paradoxes and Russell's Theory of Incomplete Symbols.Kevin C. Klement - 2014 - Philosophical Studies 169 (2):183-207.
Russell, His Paradoxes, and Cantor's Theorem: Part I.Kevin C. Klement - 2010 - Philosophy Compass 5 (1):16-28.
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