This remarkable collection explores the legacy of Wittgenstein's work in contemporary American philosophy. The contributors (including several celebrated philosophers) take a variety of approaches to Wittgenstein; they discuss such topics as rule-following, realism about mathematics, the method of the Tractatus, the relation between style and content in Wittgenstein, and his distinction between sense and nonsense. Wittgenstein also is discussed in relation to subsequent philosophers such as Quine and Kripke.

Let us sum up. We began with the question, “What is the interest of a model-theoretic definition of validity?” Model theoretic validity consists in truth under all reinterpretations of non-logical constants. In this paper, we have described for each necessity concept a corresponding modal invariance property. Exemplification of that property by the logical constants of a language leads to an explanation of the necessity, in the corresponding sense, of its valid sentences. I have fixed upon the epistemic modalities in characterizing (...) the logical constants: to be a logical constant in the language of a population is to be invariant over a modality describing complete possible epistemic states of that population (or an idealized analogue thereof). The grounds for this characterization are these: (1) It leads, I believe, to an extensionally reasonable demarcation of the logical constants, including clear cases and excluding clear non-cases. It gives a principled criterion for deciding unclear cases. (2) It provides an analysis of the topic-neutrality of logic. (3) It leads to an explanation of the epistemic necessity of the logical truths in terms of the topic-neutrality of the logical constants.All the same, it is reasonable to ask, even if the suggested demarcation of logic is extensionally correct, whether it can reasonably be expected to be fundamental. The epistemic invariance of an expression is a rather striking property, one which we should want to explain. What is missing, then, is an explanation of the distinguishing epistemic properties of the constants in terms of more fundamental properties involving their understanding and use. It would be these that properly define the nature, not just the extent, of logic. (shrink)

I discuss a general limitative consequence of the unrestricted mereological composition thesis. The unrestricted composition thesis, which is roughly the assertion that every plurality of objects possesses a fusion or sum, is shown to be in conflict with general existence-conditions for certain categories of mereologically non-composite objects. The conclusion is that the unrestricted composition thesis, which is a maximizing principle about what aggregates exist, places sharp limits on what unaggregated items can exist.

McCarthy develops a theory of radical interpretation--the project of characterizing from scratch the language and attitudes of an agent or population--and applies it to the problems of indeterminacy of interpretation first described by Quine. The major theme in McCarthy's study is that a relatively modest set of interpretive principles, properly applied, can serve to resolve the major indeterminacies of interpretation.

A persistent complaint about modal forms of the ontological argument is that the characteristic modalized existence assumptions of these arguments are simply too close to the conclusion to be of much probative value in establish­ing it. I present an abstract form of the ontological argument in which the properties imputed to the divine nature by these assumptions are replaced by any of a wide class of properties of a sort I call “actualizing.” These include basic theistic attributes such as authorship, (...) sovereignty and omniscience. The import of these arguments is to show that the metaphysical coherence of some of the most familiar conceptions of the divine nature ensures their actual realization. (shrink)

In a note appended to the translation of “On consistency and completeness” (), Gödel reexamined the problem of the unprovability of consistency. Gödel here focuses on an alternative means of expressing the consistency of a formal system, in terms of what would now be called a ‘reflection principle’, roughly, the assertion that a formula of a certain class is provable in the system only if it is true. Gödel suggests that it is this alternative means of expressing consistency that we (...) should be interested in from a foundational point of view, and he gives a result that shows certain reflection principles to be underivable in extensions of elementary number theory under conditions significantly weaker than the Hilbert-Bernays derivability conditions. In this paper I shall discuss the background to Gödel's result and the foundational significance he claims for it. Along the way, I shall present a new proof of the result which places it in an even more general context than the one considered by Gödel in the 1960s. (shrink)