I see. The difference in our views comes from me being a mathematician. Curry’s Paradox is not a paradox in mathematical logic due to my objections. In mathematical logic we don’t allow statements that don’t have a well defined truth value. The premise in the start of Curry’s Paradox is a statement without a well defined truth value.
Curry’s Paradox shows the limits if naive set theory. Thus mathematically we have to be OK with the idea that not all naive set constructions produce valid sets.
In informal setttings we can argue that
If this sentence is true then Santa Claus exists
can’t be false. But then one usually assumes it must then be true. I would argue this isn’t the case. There are sentences that have no truth value. For instance,
Curry’s Paradox shows the limits if naive set theory. Thus mathematically we have to be OK with the idea that not all naive set constructions produce valid sets.
In informal setttings we can argue that
If this sentence is true then Santa Claus exists
can’t be false. But then one usually assumes it must then be true. I would argue this isn’t the case. There are sentences that have no truth value. For instance,
This sentence is false.