Comments Elsewhere

Shulamite, “This sentence is false” does not attempt to ascribe falsity to the words “This sentence,” any more than “The first sentence written by Plato was false” attempts to ascribe falsity to the words “The first sentence written by Plato.” Both of them attempt to ascribe falsity to the sentence picked out by the denoting phrase.

Even setting that issue to one side, though, I don’t think your solution is even materially adequate. Among other things, it would require us to dismiss statements such as (M) for precisely the same reasons that we dismiss (L). But (M) is a perfectly ordinary bit of understood language. I think any theory that discards it is, for exactly that reason, not a good theory.

Shulamite: If “this statement is false” refers to some other statement (like “paradoxes are fun”), then the whole paradox disappears from the very beginning, and there is simply nothing to explain or even puzzle about.

This is not so. There are what are called “looped liar” paradoxes. Consider:

(P1) P2 is true.

(P2) P1 is false.

If P1 is true, then it follows that P2 is true; thus that what P2 says obtains; thus that P1 is false. But if P1 is false, then it follows that P2 is not true; thus what P2 says does not obtain; thus P1 is true. Similarly, if P2 is true then P2 is provably false, and if P2 is false then P2 is provably true. Any theory of truth that ascribes either truth or falsity to both P1 and P2 is therefore false, because internally contradictory.

There are also cases where we simply don’t know the contents of the sentence to which we are referring. For example, you might say, “the first assertive sentence Plato ever wrote was true,” or “the first assertive sentence Plato ever wrote was false.” Provided that Plato existed and did write one or more assertive sentences, one of these is true (although we will probably never know which one of them is). But allowing these kind of descriptions can be risky. For example, suppose that the first thing I say on Tuesday was, “The first thing Shulamite said today is false.” And the first thing you said on Tuesday — not knowing that I had said this — was “The first thing Rad Geek said today is true.”