Can Frege overcome Russell's criticism in “On denoting”?

EmaFort November 20, 2018 at 00:11 2450 views 2 comments

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!

Comments (2)

Mentalusion November 20, 2018 at 23:06 #229748 0 likes

1) Doesn't the description for Frege just unpack into the referents? That's the whole point of the "morning star" example, isn't it? So in the case of

Quoting EmaFort

"the difference between A and B does not subsist"

references the fact that A=B is true. In other words, it's essentially just the negation of the claim that ~(A=B), i.e. ~~(A=B).

2) If you use structured predicates the way Russell did to "resolve" the liar paradox, then you have to contend with incompleteness issues a la Godel...although Russell would have agreed you can solve it that way.

Nicholas Ferreira May 03, 2019 at 02:21 #285071 0 likes

Quoting Mentalusion

"the difference between A and B does not subsist"
— EmaFort

references the fact that A=B is true. In other words, it's essentially just the negation of the claim that ~(A=B), i.e. ~~(A=B).

Yeah, you're right, this is true. But, for Frege, the statement "the difference between A and B does not subsist" wouldn't be neither true nor false, simply because "the difference between A and B" does not have any reference. It has meaning, but doesn't points to anything. That is what his theory tells us.