Much contemporary ontological inquiry takes place within the so-called ‘Quinean tradition’ but, given that some aspects of Quine’s project have been widely abandoned even by those who consider themselves Quineans, it is unclear what this amounts to. Fortunately recent work in metaontology has produced two relevant results here: a clearer characterisation of the metaontology uniting the aforementioned Quineans, most notably undertaken by Peter van Inwagen, and a raft of criticisms of that metaontology. In this paper I critique van Inwagen’s Quinean (...) metaontology, finding that certain challenges, supplemented by pressure to reflect more closely Quine’s work, should drive Quineans to adopt a stronger metaontology incorporating more of Quine’s radical views. I conclude that while van Inwagen’s Quineanism is problematic there are prospects for a viable, more wholeheartedly Quinean, metaontology. (shrink)

This paper investigates the conditions under which diagonal sentences can be taken to constitute paradigmatic cases of self-reference. We put forward well-motivated constraints on the diagonal operator and the coding apparatus which separate paradigmatic self-referential sentences, for instance obtained via Gödel’s diagonalization method, from accidental diagonal sentences. In particular, we show that these constraints successfully exclude refutable Henkin sentences, as constructed by Kreisel.

The first Ukrainian translation of the most famous Quine’s article (1951), which became one of the classic texts of Analytical Philosophy.

We are pleased to release this edition of Ralph Johnson’s The Rise of Informal Logic as Volume 2 in the series Windsor Studies in Argumentation. This edition is a reprint of the previous Vale Press edition with some typographical errors and other minor mistakes corrected. The prime motive for gathering Ralph H. Johnson’s essays under one cover is their clear articulation of the goals, concerns and problems of the discipline of informal logic. To my knowledge all of the published articles, (...) even of the 1980s, are still in print. But some are obtainable only by special request of a journal back issue. Their availability, even their existence, is not nearly widely enough known, and this volume is dedicated to remedying that disservice to those currently working in the field of informal logic, critical thinking, argumentation, and practical reasoning. Three of these sixteen pieces appear here in print for the first time. The previously published pieces have appeared from 1980 to 1992 as chapters in collective works or as articles in journals, and these in turn published in Canada, USA, The Netherlands and Belgium. It is hoped that gathering this hitherto scattered material under one cover will contribute to a greater understanding of what informal logic is, and to an enhanced sense of the impact of Johnson’s ideas. A discipline of informal logic might exist today without the writings of Johnson and his frequent co-author, J. Anthony Blair. But it would almost certainly be quite different from what it actually is. (shrink)

Natural deduction is the type of logic most familiar to current philosophers, and indeed is all that many modern philosophers know about logic. Yet natural deduction is a fairly recent innovation in logic, dating from Gentzen and Jaśkowski in 1934. This article traces the development of natural deduction from the view that these founders embraced to the widespread acceptance of the method in the 1960s. I focus especially on the different choices made by writers of elementary textbooks—the standard conduits of (...) the method to a generation of philosophers—with an eye to determining what the ‘essential characteristics’ of natural deduction are. (shrink)

One way to determine the quality and pace of change in a science as it undergoes a major transition is to follow some feature of it which remains relatively stable throughout the process. Following the chosen item as it goes through reinterpretation permits conclusions to be drawn about the nature and scope of the broader change in question. In what follows, this device is applied to the change which took place in logic in the mid-nineteenth century. The feature chosen as (...) the focal point is the categorical syllogism. (shrink)

The main purpose of this paper is to present a formal systemPin which we enjoy a smooth-running technique and which countenances a universe of classes which is symmetrical as between large and small. More exactly,Pis a system which differs from the inconsistent system of [1] only in the introduction of a rather natural new restrictive condition on the defining formulas of the elements. It will be proved that if the weaker system of [2] is consistent, thenPis also consistent.After the discovery (...) of paradoxes, it may be recalled, Russell and Zermelo in the same year proposed two different ways of safeguarding logic against contradictions. Since then various simplifications and refinements of these systems have been made. However, in the resulting systems of Zermelo set theory, generation of classes still tends to be laborious and uncertain; and in the systems of Russell's theory of types, complications in the matter of reduplication of classes and meaningfulness of formulas remain. In [2], Quine introduced a system which seems to be free from all these complications. But later it was found out that in it there appears to be an unavoidable difficulty connected with mathematical induction. Indeed, we encounter the curious situation that although we can prove in it the existence of a class V of all classes, and we can also prove particular existence theorems for each of infinitely many classes, nobody has so far contrived to prove in it that V is an infinite class or that there exists an infinite class at all. (shrink)

In this article, we study the prehistory of type theory up to 1910 and its development between Russell and Whitehead's Principia Mathematica ([71], 1910-1912) and Church's simply typed λ-calculus of 1940. We first argue that the concept of types has always been present in mathematics, though nobody was incorporating them explicitly as such, before the end of the 19th century. Then we proceed by describing how the logical paradoxes entered the formal systems of Frege, Cantor and Peano concentrating on Frege's (...) Grundgesetze der Arithmetik for which Russell applied his famous paradox and this led him to introduce the first theory of types, the Ramified Type Theory (RTT). We present RTT formally using the modern notation for type theory and we discuss how Ramsey, Hilbert and Ackermann removed the orders from RTT leading to the simple theory of types STT. We present STT and Church's own simply typed λ-calculus (λ → C) and we finish by comparing RTT, STT and λ → C. (shrink)

The unification argument, usually regarded as the main argument for predicativism about proper names, has recently been attacked by Robin Jeshion. According to Jeshion, the unification argument is based on the assumption of the literality of predicative uses of proper names in statements such as “There is one Alfred in Princeton.” In such a use, a proper name ‘N’ is used predicatively to denote those, and only those, objects called N. As Jeshion argues, however, there are many other examples in (...) which a proper name ‘N’ is used predicatively to denote objects which are not called N. Based on such cases, Jeshion challenges the predicativist to provide a justification for assuming that the original predicative use of proper names, to which the predicativist appeals in the unification argument, is literal. My aim in this paper is to defend predicativism by arguing that the predicativist’s assumption is well motivated. To this end, I first present the unification argument for predicativism and Jeshion’s challenge to it. Then, I argue that the answer provided by Delia Graff Fara to Jeshion’s challenge is unsatisfactory. Finally, I meet Jeshion’s challenge by extending the phenomena highlighted in Jeshion’s examples to the referential uses of proper names. (shrink)

Ce bel ouvrage, clair, aéré et spacieux, se caractérise à la fois par sa volonté de simplicité d’accès, et son ambition, puisqu’on y trouve notamment une démonstration de la complétude d’un certain système déductif S1 pour la logique classique des prédicats, ainsi qu’une version synoptique du théorème de Gödel, selon lequel toute théorie du premier ordre complète axiomatisable est décidable, d’où il s’ensuit que l’arithmétique, c’est-à-dire l’ensemble des énoncés du premier ordre vrais dans, n’est pas axiomatisable; ce qu’on exprime souvent (...) en disant que tout système formel pour l’arithmétique est incomplet, au sens où il y a des énoncés vrais qui ne sont pas des théorèmes du système. (shrink)

Magidor argued that category mistakes are infelicitous due to presupposition failure. The case for this position is strengthened by the consideration of a previously unnoted category of data, namely multi-sentence discourses in which category mistake phenomenology arises at the end of the last sentence, but arguably due to content contained in a previous sentence. This phenomenon is analysed in terms of the previous sentence giving rise to a presupposition that is shown to be false only in the last sentence.

Ciertas interpretaciones de la obra de Kuhn subrayan su contribución inconsciente al positivismo lógico, lo que es consecuencia de un conocimiento y una crítica superficiales de dicha corriente por su parte. En este artículo critico dicha tesis a partir de un texto inédito de Kuhn: The Quest for Physical Theory (1951), sus conferencias en el Instituto Lowell de Boston y una primera presentación del punto de vista de The Structure of Scientific Revolutions.

Set theory, it has been contended, developed from its beginnings through a progression ofmathematicalmoves, despite being intertwined with pronounced metaphysical attitudes and exaggerated foundational claims that have been held on its behalf. In this paper, the seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject. The motif is foreshadowed in Cantor's diagonal proof, and emerges in the interstices of the inclusion vs. membership (...) distinction, a distinction only clarified at the turn of this century, remarkable though this may seem. Russell runs with this distinction, but is quickly caught on the horns of his well-known paradox, an early expression of our motif. The motif becomes fully manifest through the study of functionsof the power set of a set into the set in the fundamental work of Zermelo on set theory. His first proof in 1904 of his Well-Ordering Theoremis a central articulation containing much of what would become familiar in the subsequent development of set theory. Afterwards, the motif is cast by Kuratowski as a fixed point theorem, one subsequently abstracted to partial orders by Bourbaki in connection with Zorn's Lemma. Migrating beyond set theory, that generalization becomes cited as the strongest of fixed point theorems useful in computer science.Section 1 describes the emergence of our guiding motif as a line of development from Cantor's diagonal proof to Russell's Paradox, fueled by the clarification of the inclusion vs. membership distinction. Section 2 engages the motif as fully participating in Zermelo's work on the Well-Ordering Theorem and as newly informing on Cantor's basic result that there is no bijection. Then Section 3 describes in connection with Zorn's Lemma the transformation of the motif into an abstract fixed point theorem, one accorded significance in computer science. (shrink)

Drawing on recently published correspondence as well as on a survey of Polish and international philosophical activity published in 1937 and details concerning the publisher and bookseller Aleksander Mazzucato, I provide evidence that, contrary to some recent assertions (but in line with older bibliographical entries), Tarski's ‘Der Wahrheitsbegriff in den formalisierten Sprachen’ was not published in journal form until 1936, although preprints, lacking two corrections and a small addendum, were likely available in the late months of 1935.

What formulas are tense-logically valid depends on the structure of time, for example on whether it has a beginning. Logicians have investigated what formulas correspond to what physical hypotheses about time. Analogously, we can investigate what formulas of modal logic correspond to what metaphysical hypotheses about necessity. It is widely held that physical hypotheses about time may be contingent. If so, tense-logical validity may be contingent. In contrast, validity in modal logic is typically taken to be non-contingent, as reflected by (...) the general acceptance of the so-called “rule of necessitation.” But as has been argued by various authors in recent years, metaphysical hypotheses may likewise be contingent. If, in particular, hypotheses about the extent of possibility are contingent, we should expect modal-logical validity to be contingent too. Let “contingentism” be the view that everything that is not ruled out by logic is possible. I shall investigate what the right system of modal logic is, if contingentism is true. Given plausible assumptions, the system contains the McKinsey principle, and is thus not even contained in S5. It also contains simple and elegant iteration principles for the contingency operator: something is contingent if and only if it is contingently contingent. (shrink)

Ce bel ouvrage, clair, aéré et spacieux, se caractérise à la fois par sa volonté de simplicité d’accès, et son ambition, puisqu’on y trouve notamment une démonstration de la complétude d’un certain système déductif S1 pour la logique classique des prédicats, ainsi qu’une version synoptique du théorème de Gödel, selon lequel toute théorie du premier ordre complète axiomatisable est décidable, d’où il s’ensuit que l’arithmétique, c’est-à-dire l’ensemble des énoncés du premier ordre vrais dans, n’est pas axiomatisable; ce qu’on exprime souvent (...) en disant que tout système formel pour l’arithmétique est incomplet, au sens où il y a des énoncés vrais qui ne sont pas des théorèmes du système. (shrink)

On the surface, bi- and multilingualism would seem to be an ideal context for exploring questions of typological proximity. The obvious intuition is that the more closely related two languages are, the easier it should be to implement the two languages in one mind. This is the starting point adopted here, but we immediately run into the difficulty that the overwhelming majority of cognitive, computational, and linguistic research on bi- and multilingualism exhibits a monolingual bias (i.e., where monolingual grammars are (...) used as the standard of comparison for outputs from bilingual grammars). The primary questions so far have focused on how bilinguals balance and switch between their two languages, but our perspective on typology leads us to consider the nature of bi- and multi-lingual systems as a whole. Following an initial proposal from Hsin ( 2014 ), we conjecture that bilingual grammars are neither isolated, nor (completely) conjoined with one another in the bilingual mind, but rather exist as integrated source grammars that are further mitigated by a common, combined grammar (Cook, 2016 ; Goldrick et al., 2016a, b ; Putnam and Klosinski, 2017 ). Here we conceive such a combined grammar in a parallel, distributed, and gradient architecture implemented in a shared vector-space model that employs compression through routinization and dimensionality reduction. We discuss the emergence of such representations and their function in the minds of bilinguals. This architecture aims to be consistent with empirical results on bilingual cognition and memory representations in computational cognitive architectures. (shrink)

This is the introductory essay to a collection commemorating the 100th anniversary of the publication in Mind of Bertrand Russell’s paper ‘On Denoting’.

Concept originalism, recently introduced and defended by Sainsbury and Tye, Tye, and Sainsbury, holds that “atomic concepts are to be individuated by their historical origins, as opposed to their semantic or epistemic properties”. The view is immune to Gareth Evans’s “Madagascar” objection to the Causal Theory of Reference since it allows a concept to change its reference over time without losing its identity. The possibility of reference-shift, however, raises the problem of misleading belief reports. S&T try to tackle the problem (...) by strengthening the sufficient condition for a truthful belief report. We will argue that, first, their solution fails, second, and more importantly, their diagnosis of the root of the problem is misguided, third, two initially appealing ways out of the problem fail, and fourth, the prospect of finding a solution to the problem within CO is dim. The view opens the Pandora’s box of reference-shift, in a wide range of cases, without providing the necessary semantic means to take care of them. (shrink)

This paper is about the mode of being of names. The paper begins by explaining why the joke is on commentators who see Lewis Carroll's White Knight as applying the use/mention distinction. Then it argues that the real problem with the distinction is that the idea that names are used to mention what they name depends on mistakenly conceiving of language as existing autonomously; and that philosophers have this conception because they fail to appreciate what they are doing when they (...) philosophise about language. This failure also explains why philosophers mistakenly think of any manifestation of a name as a (physical) token. (shrink)

In 1942, before his duties began in the USA Navy, W.V. Quine lectured at the Free School of Sociology and Politics of São Paulo. He wrote up the lectures in Por.

In 1942, before his duties began in the USA Navy, W.V. Quine lectured at the Free School of Sociology and Politics of São Paulo. He wrote up the lectures in Por.

The second printing of Principia Mathematica in 1925 offered Russell an occasion to assess some criticisms of the Principia and make some suggestions for possible improvements. In Appendix A, Russell offered *8 as a new quantification theory to replace *9 of the original text. As Russell explained in the new introduction to the second edition, the system of *8 sets out quantification theory without free variables. Unfortunately, the system has not been well understood. This paper shows that Russell successfully antedates (...) Quine's system of quantification theory without free variables. It is shown as well, that as with Quine's system, a slight modification yields a quantification theory inclusive of the empty domain. (shrink)

It is widely assumed that Russell's problems with the unity of the proposition were recurring and insoluble within the framework of the logical theory of his Principles of Mathematics. By contrast, Frege's functional analysis of thoughts (grounded in a type-theoretic distinction between concepts and objects) is commonly assumed to provide a solution to the problem or, at least, a means of avoiding the difficulty altogether. The Fregean solution is unavailable to Russell because of his commitment to the thesis that there (...) is only one ultimate ontological category. This, combined with Russell's reification of propositions, ensures that he must hold concepts and objects to be of the same logical and ontological type. In this paper I argue that, while Frege's treatment of the unity of the proposition has immediate advantages over Russell's, a deeper consideration of the philosophical underpinnings and metaphysical consequences of the two approaches reveals that Frege's supposed solution is, in fact, far from satisfactory. Russell's repudiation of the Fregean position in the Principles is, I contend, convincing and Russell's own position, despite its problems, conforms to a greater extent than Frege's with common sense and, furthermore, with certain ideas which are central to our understanding of the origins of the analytical tradition. (shrink)