A FAMILY OF CONFORMING RELEVANT LOGICS.

摘要

Logic is easily misunderstood, especially relevant logic. Thus the philosopher Peter Geach deplores the current preoccupation with "inconsistent" logic (carefully exempting the relevant logics; for they merely permit extension (theories, worlds, models) that are non-trivial and yet inconsistent). But what use are these, anyway? And, as for entailment (logical consequence), the concept is well-developed and well-established. Why meddle with it?;In this work, we do not meddle with logical consequence. Instead, we develop a group of well-behaved logics that are conforming; i.e. that conform to the Boolean Order of Things, according to which a contradiction is the very worst, whereas a logical truth (or even a mathematical truth) is the very best. These systems are relevant, however, in that they reject modus ponens. Each admits Ackermann's rule ((gamma)).