This book is in two parts. The first is a text on logic as seen through Richard Martin's eyes. It alone makes this book worth the price. In his 1941 Yale PhD, Martin discovered the theory of virtual sets and relations. The discussion of this theory in chpts. 1&2 is the best there is. (Quine discovered this theory independently while writing up his 1942 Brazil lectures, but never truly did it justice.) This is followed by an introduction to mereology, a vastly undervalued mathematical theory of the part-whole relation. Martin goes on to develop an event logic, and a theory of semantics (only Carnap himself can rival Martin as a master of formal semantics). Martin sketches out his ideas can be used to ground mathematics as well as linguistics. The result is a brilliant introduction to a number of issues in philosophical logic. There is a major omission: metatheory, the crowning glory of mathematical logic which Martin never really understood.
Part II uses the logic of part I to develop a formal theory of linguistics. Martin had been a Penn colleague of Zelig Harris. Chomsky studied under Harris and learned most of his logic from Martin. Part II is one of the few places you'll see Harris's theories discussed. The mathematical treatment of the preposition is especially intriguing. Martin believed that language and formal logic were more closely related than is generally believed, and this book makes a good case for this.
What is Martin not better known? Because he was a radical nominalist. In the church of set theory, founded by Cantor and Zermelo, Martin was an atheist. Yet Martin went ahead and wrote much on formalized semantics and pragmatics. Almost everybody who has written on those topics believes that doing so requires set theory, and a model theory grounded in set theory. Martin insisted that one could think about semantics and pragmatics using, in place of set theory, virtual sets/relations, a Boolean version of the calculus of individuals (anathema to nearly everyone writing on mereology), and an idiosyncratic event logic. Nearly everyone who encountered Martin's writings, Richard Montague in particular, threw up their hands saying "this guy simply doesn't get it." I say that they jury is still out re the fate of Martin's approach.
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