It is fairly well known that Wittgenstein's criticisms of Russell's multiple‐relation theory of judgement had a devastating effect on the latter's philosophical enterprise. The exact nature of those criticisms however, and the explanation for the severity of their consequences, has been a source of confusion and disagreement amongst both Russell and Wittgenstein scholars. In this paper, I offer an interpretation of those criticisms which shows them to be consonant with Wittgenstein's general critique of Russell's conception of logic and which serves (...) to elucidate some of the notoriously enigmatic passages of the Tractatus. In particular, I seek to show the continuity of Wittgenstein's criticisms of the theory of judgement with his remarks on Russell's paradox and the theory of types. In addition, I place these issues in the context of Russell's own philosophical ambitions in order to reveal the deep divisions between the two over the nature of logical form and the analysis of propositional content. (shrink)

The Analytic Tradition in Philosophy is an excellent successor to an excellent book : It is a fine an example of the necromantic style in the history of philosophy where the object of the exercise is to resurrect the mighty dead in order to get into an argument with them, either because we think them importantly right or instructively wrong. However what was a pardonable a simplification and a reasonable omission in the earlier book has now metamorphosed into a sin (...) of omission and an oversimplification in its successor—the book lacks is an adequate discussion of the Ramified Theory of Types and Russell’s reasons for adopting it. I conclude with a brief meditation on Open Question Arguments and the threats that they pose to some of the analyses proposed by Russell and Moore themselves. (shrink)

In truth theory one aims at general formal laws governing the attribution of truth to statements. Gupta’s and Belnap’s revision-theoretic approach provides various well-motivated theories of truth, in particular T* and T#, which tame the Liar and related paradoxes without a Tarskian hierarchy of languages. In property theory, one similarly aims at general formal laws governing the predication of properties. To avoid Russell’s paradox in this area a recourse to type theory is still popular, as testified by recent work in (...) formal metaphysics by Williamson and Hale. There is a contingent Liar that has been taken to be a problem for type theory. But this is because this Liar has been presented without an explicit recourse to a truth predicate. Thus, type theory could avoid this paradox by incorporating such a predicate and accepting an appropriate theory of truth. There is however a contingent paradox of predication that more clearly undermines the viability of type theory. It is then suggested that a type-free property theory is a better option. One can pursue it, by generalizing the revision-theoretic approach to predication, as it has been done by Orilia with his system P*, based on T*. Although Gupta and Belnap do not explicitly declare a preference for T# over T*, they show that the latter has some advantages, such as the recovery of intuitively acceptable principles concerning truth and a better reconstruction of informal arguments involving this notion. A type-free system based on T# rather than T* extends these advantages to predication and thus fares better than P* in the intended applications of property theory. (shrink)

This paper embeds a theory of proper names in a general approach to singular reference based on type‐free property theory. It is proposed that a proper name “N” is a sortal common noun whose meaning is essentially tied to the linguistic type “N”. Moreover, “N” can be singularly referring insofar as it is elliptical for a definite description of the form the “N” Following Montague, the meaning of a definite description is taken to be a property of properties. The proposed (...) theory fulfils the major desiderata stemming from Kripke's works on proper names. (shrink)

In this article I try to show the philosophical continuity of Russell's ideas from his paradox of classes to Principia mathematica. With this purpose, I display the main results (descriptions, substitutions and types) as moments of the same development, whose principal goal was (as in his The principles) to look for a set of primitive ideas and propositions giving an account of all mathematics in logical terms, but now avoiding paradoxes. The sole way to reconstruct this central period in Russell (...) is to resort to unpublished manuscripts, which show the publications of these years to be the extremities of one same iceberg. Thus the logical problems (doubts about propositions, matrices and functions) are parallel to the ontological (the searching for genuine logical subjects) and methodological ones (the status of eliminative reduction). Paradoxes were the cause that the kind of (constructive) definition already applied by Russell, as an inheritance of Moorean analysis, obtained a new trait: ontological elimination, which, beginning with a ?no classes theory? and the theory of descriptions, led to a new theory of judgment (already present in manuscripts from 1906), ?incomplete symbols, and logical constructions. (shrink)

Cet article s'ajoute à la liste déjà longue de ceux qui traitent des rapports entre la théorie russellienne des descriptions définies et la théorie ramifiée des types. Seule la prétention d'aborder cette question dans une perspective nouvelle justifie ici sa présence: d'une part, la théorie des descriptions définies sera resituée dans le contexte initial et souvent méconnu de la théorie des expressions dénotantes et d'autre part, c'est à la logique intensionnelle de Russell, objet d'une méconnaissance au moins égale, que nous (...) nous intéresserons. De plus, c'est du point de vue de la théorie de la signification et non pas du point de vue ontologique, génético-historique ou logico-mathematique que nous nous proposons de traiter de ces rapports. (shrink)

In Parts of Classes (1991) and Mathematics Is Megethology (1993) David Lewis defends both the innocence of plural quantification and of mereology. However, he himself claims that the innocence of mereology is different from that of plural reference, where reference to some objects does not require the existence of a single entity picking them out as a whole. In the case of plural quantification . Instead, in the mereological case: (Lewis, 1991, p. 87). The aim of the paper is to (...) argue that one—an innocence thesis similar to that of plural reference is defensible. To give a precise account of plural reference, we use the idea of plural choice. We then propose a virtual theory of mereology in which the role of individuals is played by plural choices of atoms. (shrink)

1. For simplicity, let the domain of our first-level quantifiers, ‘∀ x’ and so on, be words, and in particular just those words which are adjectives. And let the adjective ‘heterological’ be abbreviated just to As is well known, one cannot legitimately stipulate that Why not? Well, the obvious answer is that if is supposed to be an adjective, then this alleged stipulation would imply the contradiction But contradictions cannot be true, and it is no use stipulating that they shall (...) be. Do we need to say anything more? Russell would apparently wish to add this: the stipulation is illegitimate because it attempts to define the word by a quantification over all words, and the word is itself taken to be one of the words quantified over. That is how this supposed definition would infringe his vicious-circle principle . 1 It is of course true that if our quantification is taken to range only over words of a certain kind, say first-order adjectives, and if the word is taken to be a word of a different kind, say a second-order adjective, then the contradiction is avoided. For the supposed stipulation then has no implications for whether is or is not true of any second-order words. Russell imagines the stipulation to be strengthened by adding that is to be true only of first-order words, and hence that it is not true of itself. But no contradiction now results from this. However, one must ask: did we need this explanation in terms of the VCP? It may seem helpful, because there is an initial temptation to say that the original stipulation could not be illegitimate. This is because it is thought of as introducing a new word, and explaining what it means, and one is apt to think that we …. (shrink)

Neste artigo, a partir de tópicos presentes na obra de Newton C. A. da Costa, propomos uma fundamentação rigorosa para de uma possível formulação de teorias científicas através da abordagem semântica. Seguindo da Costa, primeiramente desenvolveremos uma teoria geral das estruturas; no contexto desta teoria de estruturas mostraremos como caracterizar linguagens formais como um tipo particular de estrutura, mais especificamente, como uma álgebra livre. Em seguida, discutiremos como associar uma linguagem a uma estrutura, com a qual poderemos formular axiomas que (...) buscam captar a teoria da estrutura. Por fim, mostraremos como podemos, utilizando este aparato conceitual, fundamentar a formalização de da Costa e Chuaqui do chamado predicado de Suppes, utilizado para caracterizar teorias científicas de modo rigoroso. DOI:10.5007/1808-1711.2010v14n1p15. (shrink)

Dieser Band versammelt Beiträge zu den drei klassischen Disziplinen der Philosophie – dem Wahren, dem Guten, dem Schönen. Ihre Autoren zeichnet aus, dass sie aus dem akademischen Umfeld Michael Sukales zu seiner Zeit am Institut für Philosophie an der Carl-von-Ossietzky-Universität Oldenburg stammen. Ihm ist dieses Buch zum Abschied von seiner aktiven Lehrtätigkeit in Oldenburg gewidmet. Die thematische Vielfalt der enthaltenen Texte spiegelt die Bandbreite seines philosophischen Schaffens wider.

O presente manual tem como intenção constituir um guia para uma disciplina introdutória de filosofia da linguagem. Foi elaborado a partir da leccionação da disciplina de Filosofia da Linguagem I na Faculdade de Letras da Universidade do Porto desde 2001. A disciplina de Filosofia da Linguagem I ocupa um semestre lectivo e proporciona aos estudantes o primeiro contacto sistemático com a área da filosofia da linguagem. Pretende-se que este manual ofereça aos estudantes os instrumentos necessários não apenas para acompanhar uma (...) iniciação ao campo da filosofia da linguagem mas também para o estudo e a investigação autónomos posteriores. Para isso é percorrido um trajecto que conduz das intuições pré-teóricas acerca de linguagem, de que todos dispomos, até um conhecimento disciplinar específico, histórico e temático, da filosofia da linguagem. Em termos práticos, são considerados como precedentes da disciplina de Filosofia da Linguagem I – mesmo se, pelo existem actualmente precedências em sentido estrito – as disciplinas de Lógica I e II e de Filosofia do Conhecimento I e II. Os programas dessas disciplinas nos últimos anos estiveram presentes por trás da elaboração do manual. (shrink)

Bertrand Russell: Logic For Russell, Aristotelian syllogistic inference does not do justice to the subject of logic. This is surely not surprising. It may well be something of a surprise, however, to learn that in Russell’s view neither Boolean algebra nor modern quantification theory do justice to the subject. For Russell, logic is a synthetic … Continue reading Russell: Logic →.

The thesis examines A.N. Whitehead and B. Russell’s Ramified Theory of Types. It consists of three parts. The first part is devoted to understanding the source of impredicativity implicit in the induction principle. The question I raise here is whether second-order explicit definitions are responsible for cases when impredicativity turns pathological. The second part considers the interplay between the vicious-circle principle and the no-class theory. The main goal is to give an explanation for the predicative restrictions entailed by the vicious-circle (...) principle. The explanation is that set-existence is parasitic upon prior predicative specifications. The justification for this claim is given by employing the method of hierarchy of languages. Supposing the natural number structure and the language of Peano Arithmetic as given, I describe the construction of a set-theoretic language equipped with substitutionally interpreted quantifiers ranging over arithmetically definable sets. The third part considers the proposition-theoretic version of Russell’s antinomy. A solution to this paradox is offered on the basis of the ramified hierarchy propositions. (shrink)