on whether a certain sentence is both true and not true.

Consider the putative claim¹:

(1)   This phrase fails to say something about the world.

Is (1) true? It seems that (1) is true, for (1) seems to say something true about the world, namely:

(1’)   The phrase ‘this phrase’ fails to say something about the world.

It seems that (1’) is true, for the simple reason that the phrase ‘this phrase’ fails to say something about the world.

Is (1) not true? It seems that (1) is not true, for (1) seems to say something not true about the world, namely:

(1’’)    (1) fails to say something about the world.

But (1’’) is not true, for, as we have seen, (1’) is true.

Therefore, (1) is true and (1) is not true.

On the contrary, I answer that (1) is ambiguous between (1’) and (1’’). If (1) is read as (1’), then (1) is true.  If (1) is read as (1’’), then (1) is not true. However, (1’) and (1’’) do not express the same proposition, and therefore (1) is not both true and not true.

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¹ I mean to say that what follows seems to be a claim, not that what follows is both a claim and is true. However, supposing that it is a claim, it would presumably be true or not true. My point is that I wish to highlight the apparent claimhood of what follows, not its truth value, whatever it may be.