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)

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)

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)

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)

(No abstract is available for this citation).

A modified filtrations argument is used to prove that the relevant logic S of [2] is decidable.

Responding to volatile criticisms frequently leveled at Leo Strauss and those he influenced, the prominent contributors to this volume demonstrate the profound influence that Strauss and his students have exerted on American liberal democracy and contemporary political thought. By stressing the enduring vitality of classic books and by articulating the theoretical and practical flaws of relativism and historicism, the contributors argue that Strauss and the Straussians have identified fundamental crises of modernity and liberal democracy.

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)

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)

Seit 1923 erscheinen in der Sammlung Tusculum maßgebende Editionen griechischer und lateinischer Werke mit deutscher Übersetzung. Die Originaltexte werden zudem eingeleitet und umfassend kommentiert; nach der neuen Konzeption bieten schließlich thematische Essays tiefere Einblicke in das Werk, seinen historischen Kontext und sein Nachleben. Die hohe wissenschaftliche Qualität der Ausgaben, gepaart mit dem leserfreundlichen Sprachstil der Einführungs- und Kommentarteile, macht jeden Tusculum-Band zu einer fundamentalen Lektüre nicht nur für Studierende, die sich zum ersten Mal einem antiken Autor nähern, und für Wissenschaftler, (...) die spezifische Aspekte eines Werkes vertiefen möchten, sondern für alle, die sich durch vertrauenswürdige Übersetzungen einen Zugang zur Antiken Welt verschaffen wollen. In der Reihe wurden bisher über 270 Titel publiziert, alle erhältlich als Buch und eBook. Dadruch werden bislang vergriffene Titel und Raritäten wieder vollständig verfügbar gemacht. Zusätzlich zu der Buchreihe erscheint bei De Gruyter zum 90-jährigen Jubiläum das eBook-PaketTusculum Online, eine digitale Sammlung aller von 1923 bis 2013 erschienenen Titel -eine gebührende Würdigung eines wichtigen Stücks deutscher Verlagsgeschichte. Mehr Informationen rund um Tusculum erhalten Sie unter: www.degruyter.com/tusculum. (shrink)

Wolfson's systematic presentation of the philosophy of Spinoza has long been a classic. It is with pride that we make it available again in a one-volume edition.

Wolfson's systematic presentation of the philosophy of Spinoza has long been a classic. It is with pride that we make it available again in a one-volume edition.

In their paper “Vagueness, Ignorance, and Margins for Error” Kenton Machina and Harry Deutsch criticize the epistemic theory of vagueness. This paper answers their objections. The main issues discussed are: the relation between meaning and use; the principle of bivalence; the ontology of vaguely specified classes; the proper form of margin for error principles; iterations of epistemic operators and semantic compositionality; the relation or lack of it between quantum mechanics and theories of vagueness.

In this long-awaited volume, on which he worked for twenty years, Mr. Wolfson describes the body of doctrine known as the Kalam.

v. 1. The philosophy of the Kabbalah.--v. 2. The philosophy of Spinoza.

In his monumental Philosophy of the Kalam the late Harry Wolfson--truly the most accomplished historian of philosophy in our century--examined the early medieval system of Islamic philosophy. He studies its repercussions in Jewish thought in this companion book--an indispensable work for all students of Jewish and Islamic traditions. Wolfson believed that ideas are contagious, but that for beliefs to catch on from one tradition to another the recipients must be predisposed, susceptible. Thus he is concerned here not so much (...) with the influence of Islamic ideas as with Jewish elaboration, adaptation, qualification, and criticism of them. To this end he examines passages reflecting Kalam views by a wide variety of Jewish thinkers, including Isaac Israeli, Judah Halevi, Abraham ibn Ezra, and Maimonides. As always in Wolfson's work, two aspects are apparent: the special dimensions of Jewish thought as well as its relation to other traditions. And as always his prose is both graceful and precise. (shrink)