Solutions to Russell’s paradox of propositions and to Kaplan’s paradox are proposed based on an extension of von Neumann’s method of avoiding paradox. It is shown that Russell’s ‘anti-Cantorian’ mappings can be preserved using this method, but Kaplan’s mapping cannot. In addition, several versions of the Epimenides paradox are discussed in light of von Neumann’s method.
One of the logical problems with which Arthur Prior struggled is the problem of finding, in Prior’s own phrase, a “logic for contingent beings.” The difficulty is that from minimal modal principles and classical quantification theory, it appears to follow immediately that every possible object is a necessary existent. The historical development of quantified modal logic (QML) can be viewed as a series of attempts---due variously to Kripke, Prior, Montague, and the fee-logicians---to solve this problem. In this paper, I review (...) the extant solutions, finding them all wanting. Then I suggest a new solution inspired by Kripke’s theory of rigid designation and Kaplan’s logic of demonstratives, the latter in particular. It turns out that the basic mechanism of Kaplan’s logic can be exploited to yield a version of QML that will serve as a viable logic for contingent beings. This result, as I show, sheds new light on the problems of singular negative existential propositions, the question of actualism, the question of the existence of the contingent a priori, the relation between logical truth and necessity, and various modal problems and paradoxes going back to Chrysippus, Ramsey, and Moore. (shrink)
The subsystem S of Parry's AI [10] (obtained by omitting modus ponens for the material conditional) is axiomatized and shown to be strongly complete for a class of three valued Kripke style models. It is proved that S is weakly complete for the class of consistent models, and therefore that Ackermann's rule is admissible in S. It also happens that S is decidable and contains the Lewis system S4 on translation — though these results are not presented here. S is (...) arguably the most relevant relevant logic known at this time to be decidable. (shrink)
Stacie Friend (2012) dismisses the traditional view that it is an author's imaginative activity of ‘making the story up’ rather than the reader's make-believe, that is of the essence of fiction. She claims that this view is ‘neither plausible nor popular’. I argue that her claim is false and that her arguments are unconvincing. I argue further in defence of the traditional view that it is quite easy to find or to simply construct counterexamples to the standard view that fiction (...) necessarily involves an invitation to the reader or audience to engage in make-believe. The counterexamples are the direct result of the fact that composing fiction need not involve any invitation to engage in make-believe. (shrink)
One of the logical problems with which Arthur Prior struggled is the problem of finding, in Prior’s own phrase, a “logic for contingent beings.” The difficulty is that from minimal modal principles and classical quantification theory, it appears to follow immediately that every possible object is a necessary existent. The historical development of quantified modal logic can be viewed as a series of attempts---due variously to Kripke, Prior, Montague, and the fee-logicians---to solve this problem. In this paper, I review the (...) extant solutions, finding them all wanting. Then I suggest a new solution inspired by Kripke’s theory of rigid designation and Kaplan’s logic of demonstratives, the latter in particular. It turns out that the basic mechanism of Kaplan’s logic can be exploited to yield a version of QML that will serve as a viable logic for contingent beings. This result, as I show, sheds new light on the problems of singular negative existential propositions, the question of actualism, the question of the existence of the contingent a priori, the relation between logical truth and necessity, and various modal problems and paradoxes going back to Chrysippus, Ramsey, and Moore. (shrink)
According to the well-known Kripke-Putnam view developed in Naming and Necessity and ‘The Meaning of Meaning’, proper names and ‘natural kind terms’ - words for natural substances, species, and phenomena - are non-descriptional and rigid. A singular term is rigid if it has the same referent in every possible world, and is non-descriptional if, roughly speaking, its referent is not secured by purely descriptive conditions analytically tied to the term. Thus, ‘the inventor of bifocals’ is nonrigid and descriptional, while ‘the (...) unique even and prime integer’ is rigid and descriptional, and ‘Noam Chomsky’ is rigid and non-descriptional. (shrink)
Alonzo Church (1903–1995) was a renowned mathematical logician, philosophical logician, philosopher, teacher and editor. He was one of the founders of the discipline of mathematical logic as it developed after Cantor, Frege and Russell. He was also one of the principal founders of the Association for Symbolic Logic and the Journal of Symbolic Logic. The list of his students, mathematical and philosophical, is striking as it contains the names of renowned logicians and philosophers. In this article, we focus primarily on (...) Church’s philosophical contributions. (For an account of his life and academic history see the Introduction to The Collected Works of Alonzo Church (2019).) However, we also discuss his mathematical results when it is desirable to do so in order to pursue a philosophical issue. (shrink)
This paper develops a model theoretic semantics for so called “natural kind terms” that reflects the viewpoint of (Kripke, 1980) and (Putnam, 1975). The semantics generates a formal counterpart of the “K-mechanism” investigated in (Salmon, 1981) and in unpublished work by Keith Donnellan.
We argue that the epistemic theory of vagueness cannot adequately justify its key tenet-that vague predicates have precisely bounded extensions, of which we are necessarily ignorant. Nor can the theory adequately account for our ignorance of the truth values of borderline cases. Furthermore, we argue that Williamson’s promising attempt to explicate our understanding of vague language on the model of a certain sort of “inexact knowledge” is at best incomplete, since certain forms of vagueness do not fit Williamson’s model, and (...) in fact fit an alternative model. Finally, we point out that a certain kind of irremediable inexactitude postulated by physics need not be-and is not commonly-interpreted as epistemic. Thus, there are aspects of contemporary science that do not accord well with the epistemicist outlook. (shrink)
