Suppose that in the course of an argument I say both 'p' and 'not-p'. You protest that I have contradicted myself; that I am inconsistent.
Now further suppose that I am a pragmatist. My position, my theory of truth, is that truth is purely a matter of practical utility, of what works satisfactorily if accepted. A proposition or belief is true if and only if it has practical utility or (on the other version) works satisfactorily.
This is a loose charactersation but I am not persuaded that Capaldi has anything more precise in mind. Pragmatism doesn't rule out - deny the possibility of - contradiction, of inconsistency. It simply doesn't worry about it if it serves practical utility.
In light of this, it does not follow that, in the example, I (the pragmatist for a moment) am not inconsistent, since pragmatism recognises inconsistency. I am inconsistent; the point is rather that inconsistency doesn't matter if it has practical utility.
That's one point dealt with - the 'it does not follow' point to which fallacy is relevant.
What of the other ? 'Appeal to a higher truth' ? The idea appears to be that while you and I have a mundane or standard theory of truth on which a statement and its direct denial ('not both p and not-p) cannot be true together, the pragmatist has a different and preferable - a 'superior' - theory of truth on which inconsistency is no necessary problem since an inconsistency can have practical utility.