Semantics Unlimited

Abstract

Most of these writers [on epistemic, doxastic and assertoric logics] lay it down that if p logically implies q, and it is thought or asserted that p then it must be thought or asserted that q. †But nothing, unfortunately, is more common than for people to fail to draw the consequences of what they think or say. These writers are consequently driven to admit that what they are presenting is not really a logic of belief or assertion, but a logic of consistent or rational belief or assertion. And this is comparatively uninteresting; for what we would like to see is a logical and consistent handling even of man’s illogicalities (Prior 71 p.79).

The bulk of this essay was produced in 1973-6 (hence the authorship). It does several things still needing doing (though sometimes less than satisfactorily, so it now appears). Like many an older structure, the essay has been adjusted and added to at later periods, whence again occasional less than felicitous additions detract from the grand structure. However not all recognised improved have been included. For example, recent significant improvements in semantical rules for certain types of functors have not been incorporated; they would further complicate an already sufficiently complicated structure, and as the improvements amount to special, more informative cases of the rules used, they will merge into the comprehensive framework offered.