I would like to know what would be the best way to overcome the criticism of Frege laid out by Russell in "On denoting", especially in regard to the third "paradox" presented. This paradox states something along the lines that Frege's theory couldn't explain the fact that a sentence like "the difference between A and B does not subsist" is true, assuming A is equal to B, because the description "the difference between A and B" would lack a reference, and therefore the whole sentence would not be capable of referring to a truth value. I believe that a possible solution could involve distinction between first order predicates and second order predicates when a context like this arises (Frege does something similar for sentences that include other sentences inside them) but I don't know much about that and can't work it out on my own. Any help would be greatly appreciated!

  • In a nutshell, R's critique is based on the rejection of Frege's theory about Sinn und Bedeutung: this theory, when applied to sentences, says that every sentence has a sense (meaning) and a reference (denotation). If A does not differes from B, the denoting phrase "the difference between..." has no reference and thus, according to Frege compositional semantics we cannot use it in complex expressions (contrary to our intutition and practice, says Russell). – Mauro ALLEGRANZA Nov 20 '18 at 7:48
  • See Pelletier and Linsky, Russell vs. Frege on Definite Descriptions as Singular Terms. – Mauro ALLEGRANZA Nov 20 '18 at 7:50

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