Russell’s Argument Against Meaning

There is an obscure passage in Russell’s famous paper “On Denoting” that requires some interpretation. In this post, I’ll provide one reading of the passage as an argument against Frege’s notion of “sense”. In essence, Russell doesn’t think it’s possible to denote what he calls the “meaning” of a sentence or proposition (“meaning” means roughly the same thing as “sense” in Frege’s writings). I won’t go into a textual breakdown, but instead I’m just providing the basic argument and how Frege could respond:

DC = Denoting Concept

<X, Y> = proposition composed of X and Y

The argument:

“The guy with superpowers flies”

DCs=“the guy with superpowers”

<DCs, the property of flying>

The denoting concept expressed by “the guy with superpowers” is a denoting concept:

DCDCs

<DCDCs, is a denoting concept>

has the same truth value as

<DCs, is a denoting concept>

has the same truth value as

<superman, is a denoting concept>

No matter how many iterations you spell out, it ultimately breaks down to its original denoting, and therefore there is no way to denote the sentence’s “meaning”, just its denotation.

The key to the Fregean response is recognizing the tacit principle at play in this argument:

Tacit Principle: If a denoting concept DCo denotes O, then the truth value of the proposition formed from <DCo , P> is the same as the proposition formed from <O, P>.

Fregeans can make a move to avoid this result, though. Frege has no reason to accept that the substitution of denoting concepts preserves the truth value of propositions wherein those concepts appear, and therefore he can say they are not co-referring. One example to illustrate this is:

DCs = “the guy with superpowers”

“The sense expressed by “the guy with superpowers” is not subjective.” – True

Now try the substitution:

“Superman is not subjective” – Either false or no truth value.

There isn’t truth preservation across substitutions, so the two are not co-referring. So Russell hasn’t shown that it isn’t possible to denote the denotation (pick out the sense of a phrase). In other words, Russell has not demonstrated the implausibility of denoting or picking out the sense of a phrase.

So, on Russell’s tacit principle, it still does not follow that one cannot denote the sense of a phrase, since the substitution above does not preserve truth, and thus does not co-refer, and thus does not have the same truth value as the proposition formed from <S, is not purely subjective>. Therefore, <DCs, is not purely subjective> does not equal <S, is not purely subjective>.