Curry sentences

Curry sentences are of the form:

1. If (1) is true, then p,

where I shall stipulate the "If ... then ..." to be a material conditional, and where p abbreviates something not paradoxical. If p is false (in an unparadoxical way—maybe, p is "snow is red"), (1) is paradoxical because it provides an argument for p. Now, it is clear that whatever we say about (1) we should also say about:

2. If not-p, then (2) is not true.

Now, go back to my old favorite, the contingent liar paradox. There are many versions. One of them is this. Let D be some definite description of a sentence which picks out different sentences in different worlds. Then consider:

3. The sentence satisfying D is not true.

Paradox ensues in worlds where D picks out (3). Now, consider:

4. The contingent liar (3) is unparadoxical if D picks out a first-order sentence that is unproblematically true or unproblematically false, in which case (3) has the opposite truth value to that of that sentence.

Then, consider this:

5. The following sentence is not true: "1=1" if p and (5) if not-p.

By (4), sentence (5) is unparadoxically true if p. We ought to, however, say about (5) exactly whatever we say about:

6. "1=1" is true if p, and (6) is not true if not-p.

Thus, we ought to say that (6) is unparadoxically true if p. But we observe that the first conjunct in (6) is trivially true, at least if p is not itself paradoxical. So, surely, we ought to say about (6) exactly what we say about:

7. Sentence (7) is not true if not-p.

Thus, (7) is unparadoxically true if p.

But we ought to say the same thing about (2) as we say about (7), and about (1) as about (2). So, the Curry sentence (1) is unparadoxically true if p. And if p is false, it is a liar sentence, and a contingent liar sentence if p is contingently false. All this means that the Curry paradox is not very different from the contingent liar.