Rigid general terms and essential predicates

What does it mean for a general term to be rigid? It is argued by some that if we take general terms to designate their extensions, then almost no empirical general term will turn out to be rigid; and if we take them to designate some abstract entity, such as a kind, then it turns out that almost all general terms will be rigid. Various authors who pursue this line of reasoning have attempted to capture Kripke’s intent by defining a rigid general term as one that applies to the objects in its extension essentially. I argue that this account is significantly mistaken for various reasons: it conflates a metaphysical notion (essentialism) with a semantic one (rigidity); it fails to countenance the fact that any term can be introduced into a language by stipulating that it be a rigid designator; it limits the extension of rigid terms so much that terms such as ‘meter’, ‘rectangle’, ‘truth’, etc. do not turn out to be rigid, when they obviously are; and it wrongly concentrates on the predicative use of a general term in applying a certain test offered by Kripke to determine whether a term is rigid.     

A pragmatic defense of Millianism

A new kind of defense of the Millian theory of names is given, which explains intuitive counter-examples as depending on pragmatic effects of the relevant sentences, by direct application of Grice’s and Sperber and Wilson’s Relevance Theory and uncontroversial assumptions. I begin by arguing that synonyms are always intersubstitutable, despite Mates’ considerations, and then apply the method to names. Then, a fairly large sample of cases concerning names are dealt with in related ways. It is argued that the method, as applied to the various cases, satisfies the criterion of success: that for every sentence in context, it is a counter-example to Millianism to the extent that it has pragmatic effects (matching speakers’ intuitions).     

Three-Valued Temporal Logic <Emphasis Type="Italic">Q</Emphasis><Subscript><Emphasis Type="Italic">t</Emphasis></Subscript> and Future Contingents

Prior’s three-valued modal logic Q was developed as a philosophically interesting modal logic. Thus, we should be able to modify Q as a temporal logic. Although a temporal version of Q was suggested by Prior, the subject has not been fully explored in the literature. In this paper, we develop a three-valued temporal logic Q _t and give its axiomatization and semantics. We also argue that Q _t provides a smooth solution to the problem of future contingents. Presented by Daniele Mundici     

Logics of public communications

Multi-modal versions of propositional logics S5 or S4—commonly accepted as logics of knowledge—are capable of describing static states of knowledge but they do not reflect how the knowledge changes after communications among agents. In the present paper (part of broader research on logics of knowledge and communications) we define extensions of the logic S5 which can deal with public communications. The logics have natural semantics. We prove some completeness, decidability and interpretability results and formulate a general method that solves certain kind of problems involving public communications—among them well known puzzles of Muddy Children and Mr. Sum & Mr. Product. As the paper gives a formal logical treatment of the operation of restriction of the universe of a Kripke model, it contributes also to investigations of semantics for modal logics. This paper was originally published as Plaza, J. A. (1989). Logics of public communications. In M. L. Emrich, M. S. Pfeifer, M. Hadzikadic, & Z.W. Ras (Eds.), Proceedings of the fourth international symposium on methodologies for intelligent systems: Poster session program (pp. 201–216). Publisher: Oak Ridge National Laboratory, ORNL/DSRD-24. Research partly supported by NSF Grant CCR-8702307 and PSC-CUNY Grant 668283.     

What we know now that we didn’t know then: reply to critics of <Emphasis Type="Italic">The Age of Meaning</Emphasis>

Author’s response to critical essays by Brian Weatherson, Alex Byrne, and Stephen Yablo on Philosophical Analysis in the Twentieth Century, Volume 2 The Age of Meaning     

Validity and Necessity

In this paper I argue against the commonly received view that Kripke’s formal Possible World Semantics (PWS) reflects the adoption of a metaphysical interpretation of the modal operators. I consider in detail Kripke’s three main innovations vis-à-vis Carnap’s PWS: a new view of the worlds, variable domains of quantification, and the adoption of a notion of universal validity. I argue that all these changes are driven by the natural technical development of the model theory and its related notion of validity: they are dictated by merely formal considerations, not interpretive concerns. I conclude that Kripke’s model theoretic semantics does not induce a metaphysical reading of necessity, and is formally adequate independently of the specific interpretation of the modal operators.     

On the Predicate Logic of Linear Kripke Frames and some of its Extensions

We propose a new, rather simple and short proof of Kripke-completeness for the predicate variant of Dummett's logic. Also a family of Kripke-incomplete extensions of this logic that are complete w.r.t. Kripke frames with equality (or equivalently, w.r.t. Kripke sheaves [8]), is described.     

Critical Notices

Abstract

I argue that a practice can only be taken to be one of apparent rule following if it contains a practice of policing moves within the practice. So the existence of an apparently rule‐governed practice entails the existence of, what I call, a policing practice. I then argue that this entailment cannot be reconciled with a non‐factualist construal of the policing practice. Thus non‐factualism about the policing practice is false. Factualism about the policing practice entails realism about rules. So I conclude that we ought to be realists about rules. Finally I distinguish a position which I call ultra‐realism about rules and note that this too is a casualty of the view developed here.     

Foundationalism,Coherentism and Rule-Following Scepticism

Semantic holists view what one's terms mean as function of all of one's beliefs and applications. Holists will thus be coherentists about how one's usage is justified: showing that one's usage of a term is justified involves showing how it coheres with the rest of one's beliefs and applications. Semantic reductionists, on the other hand, will understand such justification in a classically foundationalist fashion. Now Saul Kripke has, on Wittgenstein's behalf, famously argued for a type of scepticism about meaning and the possibility of demonstrating the correctness of one's usage. However, Kripke's argument has bite only if one understands justification in classically foundationalist terms. Consequently, Kripke's arguments, if good, lead not to a type of scepticism about meaning, but rather to the conclusion that one should be a coherentist about the justification of our usage, and thus a holist about semantic facts.     

Rule Following,Error Theory and Eliminativism

Abstract

In this paper, I argue for three main claims. First, that there are two broad sorts of error theory about a particular region of thought and talk, eliminativist error theories and non-eliminativist error theories. Second, that an error theory about rule following can only be an eliminativist view of rule following, and therefore an eliminativist view of meaning and content on a par with Paul Churchland’s prima facie implausible eliminativism about the propositional attitudes. Third, that despite some superficial appearances to the contrary, non-eliminativist error theory does not provide a plausible vehicle for understanding the ‘sceptical solution’ to the sceptical paradox about rule-following developed in Saul Kripke’s Wittgenstein on Rules and Private Language.