Alexander George

The foundations of linguistics continue to generate philosophical debate. Jerrold Katz claims that the subject matter of linguistics consists of abstract objects and that, as a consequence, the discipline cannot be viewed as part of psychology. I respond by arguing (1) that Katz misinterprets work in the philosophy of mathematics which he believes sheds light on foundational questions in linguistics; (2) that he misunderstands aspects of Noam Chomsky's position, against whose conception of linguistics many of his claims are directed; (3) that Katz fails to dispose of a much more plausible analysis, according to which linguistics remains an empirical inquiry in spite of its abstract subject matter; and, finally, (4) that his arguments against what he calls‘generativism’, appealing to the existence of an infinitely long grammatical sentence of English, are flawed.

A rich tradition in philosophy takes truths about meaning to be wholly determined by how language is used; meanings do not guide use of language from behind the scenes, but instead are fixed by such use. Linguistic practice, on this conception, exhausts the facts to which the project of understanding another must be faithful. But how is linguistic practice to be characterized? No one has addressed this question more seriously than W. V. Quine, who sought for many years to formulate a conception of use that makes sense of certain key features of meaning. The nature, development, and adequacy of his formulations are here explored. All are found to fall short of what he wanted to achieve. Donald Davidson has introduced significant variations on Quine's project. The resulting position is also examined, but likewise found to be problematic. Finally, a neo-Quinean conception is sketched, as are some of the problems such a view would have to surmount

Those inquiring into the nature of mind have long been interested in the foundations of mathematics, and conversely this branch of knowledge is distinctive in that our access to it is purely through thought. A better understanding of mathematical thought should clarify the conceptual foundations of mathematics, and a deeper grasp of the latter should in turn illuminate the powers of mind through which mathematics is made available to us. The link between conceptions of mind and of mathematics has been a central theme running through the great competing philosophies of mathematics of the twentieth century, though each has refashioned the connection and its import in distinctive ways. The present collection will be of interest to students of both mathematics and of mind. Contents include: "Introduction" by Alexander George; "What is Mathematics About?" by Michael Dummett; "The Advantages of Honest Toil over Theft" by George Boolos; "The Law of Excluded Middle and the Axiom of Choice" by W.W. Tait; "Mechanical Procedures and Mathematical Experience" by Wilfried Sieg; "Mathematical Intuition and Objectivity" by Daniel Isaacson; "Intuition and Number" by Charles Parsons; and "Hilbert's Axiomatic Method and the Laws of Thought" by Michael Hallett.

One effect of W. V. Quine’s assault on the analytic-synthetic distinction is pressure on the boundaries between mathematics and empirical science. Assumptions about reference and knowledge that are natural in the context of the empirical sciences have been exported to the case of mathematics. Problems then arise when we ask how, given the abstractness of mathematical entities, we can refer to them or know anything about them. For if abstractness entails causal impotence, and if reference and knowledge require causal intercourse, then it seems a mystery how reference to, or knowledge of, abstract entities is at all possible.