Nathan Salmón

Metaphysics, Mathematics, and Meaning brings together Nathan Salmon's influential papers on topics in the metaphysics of existence, non-existence, and fiction; modality and its logic; strict identity, including personal identity; numbers and numerical quantifiers; the philosophical significance of Godel's Incompleteness theorems; and semantic content and designation. Including a previously unpublished essay and a helpful new introduction to orient the reader, the volume offers rich and varied sustenance for philosophers and logicians.

Alonzo Church provided three criteria for “strict synonymy”, i.e., sameness of semantic content: Alternatives (0), (1), and (2)--in order of increasing course-grainedness of content. On (2) expressions are strictly synonymous iff they are logically equivalent. (1) is a significant improvement over (2). On (1) expressions are synonymous iff they are lambda-convertible. Even on (1), assuming the Millian account of proper names, ‘Tully admires Cicero’ is deemed synonymous with ‘Cicero is self-admiring’. On (0) expressions are strictly synonymous iff they are “synonymously isomorphic” in Church’s sense. A fourth alternative, here called ‘(3)’, has been maintained by several philosophers. On (3) expressions are strictly synonymous iff they are co-intensional. In particular, sentences are strictly synonymous iff they are true with resect to the same possible worlds. This criterion’s notion of content is even more course grained than that of (2). Several objections to (3) are considered.

The topic is time travel of the sort depicted in H. G. Wells’ classic novel, The Time Machine—Wellsian time travel. The range of proper applicability of the concept of Wellsian time travel is investigated. The results of this investigation are applied to provide a new argument against the metaphysical possibility of time travel in absolute time. Alternatively, the argument is against the possibility of Wellsian time travel relative to a single temporal frame of reference. The argument leaves open the prospect that an object nontrivially moves relative to one temporal reference frame from one time to another relative to another temporal reference frame. The argument does not turn on closed timelike curves or “causal loops” of any kind. It does however invoke the prospect of backward causation—a consequence of backward time travel in conjunction with common sense—but it invokes this possibility only in the weak sense of mere logical consistency.

The concept of a proposition is important in several areas of philosophy and central to the philosophy of language. This collection of readings investigates many different philosophical issues concerning the nature of propositions and the ways they have been regarded through the years. Reflecting both the history of the topic and the range of contemporary views, the book includes articles from Bertrand Russell, Gottlob Frege, the Russell-Frege Correspondence, Alonzo Church, David Kaplan, John Perry, Saul Kripke, Hilary Putnam, Mark Richard, Scott Soames, and Nathan Salmon.