Paradoxes 2: Curry's Paradox

Wikipedia says of Curry’s paradox: ‘The resolution of Curry's paradox is a contentious issue because resolutions (apart from trivial ones ...) are difficult and not intuitive.’ The paradox itself:

Claims of the form "if A, then B" are called conditional claims. It is not necessary to believe the conclusion (B) to accept the conditional claim (if A, then B) as true. For instance, consider the following sentence:

If a man with flying reindeer has delivered presents to all the good children in the world in one night, then Santa Claus exists.

Imagine that a man with flying reindeer has, in fact, done this. Does Santa Claus exist, in that case? It would seem so. Therefore, without believing that Santa Claus exists, or that this scenario is even possible, it seems that we should agree that if a man with flying reindeer has delivered presents to all the good children in the world in one night, then Santa Claus exists, and so the above sentence is true.
Now consider this other sentence:

If this sentence is true, then Santa Claus exists.

As before, imagine that the antecedent is true - in this case, "this sentence is true". Does Santa Claus exist, in that case? Well, if the sentence is true, then what it says is true: namely that if the sentence is true, then Santa Claus exists. Therefore, without necessarily believing that Santa Claus exists, or that the sentence is true, it seems we should agree that if the sentence is true, then Santa Claus exists.

But then this means the sentence is true. So Santa Claus does exist. Furthermore we could substitute any claim at all for "Santa Claus exists". This is Curry's paradox.

But the first sentence, here, isn’t stated in a very precise way. It would be better to say: “If a man with flying reindeer has delivered presents to all the good children in the world in one night, then we might as well call him Santa Claus.”

This exposes the problem with attempting to hook a conditional claim after Curry's manner: “If this sentence is true, then we might as well call him Santa Claus.”

Obviously this doesn’t make sense; a sentence isn’t a him. In other words what Curry’s paradox actually pinpoints is that any paradox that relies on the selfreflexive gambit of ‘this sentence is true’ cannot be moved from the pure to the applied maths magisterium. ‘All Cretans are liars’ can’t generate any paradoxes, even if the Cretan uttering it is a liar, because all Cretans aren’t liars. (If somebody speaks a falsehood it does not mean they are necessarily a liar--they might be mistaken or misinformed--and that somebody is 'a liar' does not mean that they lie every time all the time).

It does not follow that ‘we could substitute any claim at all for "Santa Claus exists”’; but even those terms that can be inserted (let's say: ‘if it is possible to evenly divide every single positive integer, then nine is an even number’) needs to properly formulated, initially (better: ‘if it is possible to evenly divide every single positive integer, then we could call nine an even number’), such that the subsequent conditional state no more than it may: ‘if this sentence is true, then we could call nine an even number’. Could is crucially (logically) different to is. Like many supposed paradoxes, Curry's depends upon a sleight of hand [I originally wrote 'sleigh of hand'--ha!] that deliberately elides the indicative and the subjunctive mode.