Abstract

The subtitle of this text intended for philosophy students’ 2nd course in logic is in no way misleading. It is a lucid introduction to the philosophic activities of uncovering metaphysical presuppositions of logical techniques and altering logical techniques, and hence assessments of deductive validity, to conform to metaphysical presuppositions. They do not, though, assume that techniques for assessing deductive validity are or should be wholly dependent upon metaphysical presuppositions. They write on p. 213 in their section on intensional discourse: "And logic wherever possible ought not to wait upon philosophy, for logic wherever possible ought to be neutral between different philosophical analyses." In their investigations of metaphysical presuppositions and logical techniques, they consider primarily the consequences of existential presuppositions about the use of singular terms, viz., individual variables, individual names, and definite descriptions. They favor freeing use of singular terms from existential presuppositions. The consideration of allowing non-referring names and definite descriptions makes their text one of the first, if not the first, for teaching Free Logic. The gist of Free Logic is not to allow existential generalization of Fb to unless there is an auxiliary premise asserting the existence of b, because use of the name b has been freed from the presupposition that it names something. It is suitable that these authors have a text on Free Logic since Lambert is the major figure in its origin while van Fraassen has established some of the most significant results about Free Logic systems. They go on to consider alternative logical rules to those of Russell for dealing with nonreferring definite descriptions. These alternatives to standard logic are philosophically motivated. They are not simply dumped upon students as rules for symbol manipulation. For instance, on pp. 152-157 they give a succinct analysis of the Russell-Meinong debate when they agree with Meinong that one can talk of the thing that is such and such without accepting that there is such a thing. The treatment of singular terms leads them to discussions of topics such as: What is it for a logic to be extensional and is Free Logic extensional?, the substitution interpretation of quantifiers, and the notion of presupposition.