Bilattices and Strict Tolerant Logics (Melvin Fitting)

Strict/tolerant logic is a formally defined logic that has the same consequence relation as classical logic, though it differs from classical logic at the metaconsequence level. Specifically, it does not satisfy a cut rule. It has been recommended for use in work on theories of truth because it avoids some objectionable features arising from the use of classical logic. Here we are not interested in applications, but in the formal details themselves. We show that a wide range of logics have strict/tolerant counterparts, with the same consequence relations but differing at the metaconsequence level. Among these logics are Kleene’s K3, Priest’s LP, and first degree entailment, FDE. The primary tool we use is the bilattice. But it is more than a tool, it seems to be the natural home for this kind of investigation.

The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 in room TBD of the Graduate Center, CUNY (365 5th Avenue). The (provisional) schedule is as follows:

Feb 4. Melvin Fitting, CUNY

Feb 11. Benjamin Neeser, Geneva

Feb 18. GC CLOSED. NO MEETING

Feb 25. Achille Varzi, Columbia

Mar 4. Eric Bayruns Garcia, CUNY

Mar 11. Romina Padro, CUNY

Mar 18. Jeremy Goodman, USC

Mar 25. Kit Fine, NYU

Apr 1. Elena Ficara, Paderborn

Apr 8. Chris Scambler, NYU

Apr 15.  Jenn McDonald, CUNY

Apr 22. GC CLOSED. NO MEETING

Apr 29. Tommy Kivatinos, CUNY

May 6. Daniel Durante, Natal

May 13. Martina Botti, Columbia

May 20. Vincent Peluce, CUNY