I defend the historical definition of "function" originally given in my Language, Thought and Other Biological Categories (1984a). The definition was not offered in the spirit of conceptual analysis but is more akin to a theoretical definition of "function". A major theme is that nonhistorical analyses of "function" fail to deal adequately with items that are not capable of performing their functions.

Undergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text by one of the centuries greatest authorities on the subject. Part I offers an elementary but thorough overview of mathematical logic of first order. The treatment does not stop with a single method of formulating logic; students receive instruction in a variety of techniques, first learning model theory (truth tables), then Hilbert-type proof theory, and proof theory handled through derived rules. Part II supplements (...) the material covered in Part I and introduces some of the newer ideas and the more profound results of logical research in the twentieth century. Subsequent chapters introduce the study of formal number theory, with surveys of the famous incompleteness and undecidability results of Godel, Church, Turing, and others. The emphasis in the final chapter reverts to logic, with examinations of Godel's completeness theorem, Gentzen's theorem, Skolem's paradox and nonstandard models of arithmetic, and other theorems. Unabridged republication of the edition published by John Wiley & Sons, Inc. New York, 1967. Preface. Bibliography. Theorem and Lemma Numbers: Pages. List of Postulates. Symbols and Notations. Index. (shrink)

There are two likely paths for philosophers to follow in their encounters with Artificial Life: they can see it as a new way of doing philosophy, or simply as a new object worthy of philosophical attention using traditional methods. Is Artificial Life best seen as a new philosophical method or a new phenomenon? There is a case to be made for each alternative, but I urge philosophers to take the leap and consider the first to be the more important and (...) promising. (shrink)

When they abandoned the analytic-synthetic distinction, analytic philosophers substituted for it uncritical appeals to thought experiments or conceivability arguments. Although the history of philosophy is replete with thought experiments, medieval and early modern philosophers developed sophisticated theories concerning what governs what happens in thought experiments. By contrast, contemporary philosophers subscribe to the thesis of facile conception according to which casual allegations of conceivability or inconceivability are taken as good evidence of possibility or impossibility. Philosophers need to adopt standards of thought (...) experimentation like those found in science and to ground them in a general theory of conceivability. (shrink)