I am reading Harry Gensler's Introduction to Logic (Routledge, 2002) and doing exercise 1 of 7.3b in the "Basic Modal Logic" chapter. I think I follow the steps. The answer is in the book.
My question is whether this accurately reflects a pragmatist view of truth or whether a pragmatist has a way around the argument.
The exercise contains the following three lines which need to be symbolized and then tested for validity.
If the pragmatist view of truth is right, then "A is true" entails "A is useful to believe."
"A is true but not useful to believe" is consistent.
∴ The pragmatist view of truth isn't right.
One can use the following symbolization key which seems to correspond with what is in the book's answer.
- P: The pragmatist view of truth is right.
- B: A is useful to believe.
- T: A is true.
The argument set up in this fashion can be shown to be valid even without using modal logic. I imagine a pragmatist would reject the second premise, but I don't see any obvious inconsistency.
How do pragmatists work around such an argument?
If they don't accept one or more of these premises please provide a source justifying that. If there is another modal logic that would be more appropriate for pragmatism, please provide a source for it.