It is argued that the finitist interpretation of wittgenstein fails to take seriously his claim that philosophy is a descriptive activity. Wittgenstein's concentration on relatively simple mathematical examples is not to be explained in terms of finitism, But rather in terms of the fact that with them the central philosophical task of a clear 'ubersicht' of its subject matter is more tractable than with more complex mathematics. Other aspects of wittgenstein's philosophy of mathematics are touched on: his view that mathematical (...) propositions are 'grammatical propositions' (and so, Strictly speaking, Not genuine propositions at all) and his view that in mathematics 'everything is algorithm, Nothing meaning'. His views on consistency and his anti-Foundationalism are linked with this central thesis. (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 is to resort to unpublished manuscripts, which show the publications of these years to be the extremities of one same iceberg.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)

This paper defends a reference-based approach to concept individuation against the objection that such an approach is unable to make sense of concepts that fail to refer. The main line of thought pursued involves clarifying how the referentialist should construe the relationship between a concept's (referential) content and its role in mental processes. While the central goal of the paper is to defend a view aptly titled Concept Referentialism , broader morals are drawn regarding reference-based approaches in general. The paper (...) closes by calling for a shift in the current debate between referentialists and their opponents. (shrink)

Sequel to Part I. In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions and equivalence classes of coextensional properties. Part II addresses Russell’s own various attempts to solve these paradoxes, (...) including strategies that he considered and rejected (limitation of size, the zigzag theory, etc.), as well as his own final views whereupon many purported entities that, if reified, lead to these contradictions, must not be genuine entities, but ‘logical fictions’ or ‘logical constructions’ instead. (shrink)

Certain commentators on Russell's “no class” theory, in which apparent reference to classes or sets is eliminated using higher-order quantification, including W. V. Quine and (recently) Scott Soames, have doubted its success, noting the obscurity of Russell’s understanding of so-called “propositional functions”. These critics allege that realist readings of propositional functions fail to avoid commitment to classes or sets (or something equally problematic), and that nominalist readings fail to meet the demands placed on classes by mathematics. I show that Russell (...) did thoroughly explore these issues, and had good reasons for rejecting accounts of propositional functions as extra-linguistic entities. I argue in favor of a reading taking propositional functions to be nothing over and above open formulas which addresses many such worries, and in particular, does not interpret Russell as reducing classes to language. (shrink)

§§3-4 of the Begriffsschrift present Frege’s objections to a dominant if murky nineteenth-century semantic picture. I sketch a minimalist variant of the pre-Fregean picture which escapes Frege’s criticisms by positing a thin notion of semantic content which then interacts with a multiplicity of kinds of truth to account for phenomena such as modality. After exploring several ways in which we can understand the existence of multiple truth properties, I discuss the roles of pointwise and setwise truth properties in modal logic. (...) I argue that thinking of supertruth and determinate truth as setwise truth properties allows an understanding of supervaluationist approaches to vagueness which escapes both Williamson’s objections to and a needless metalinguistic orientation of traditional supervaluationism. (shrink)

The positions of Frege, Russell and Wittgenstein on the priority of complexes over (propositional) functions are sketched, challenging those who take the "judgment centered" aspects of the Tractatus to be inherited from Frege not Russell. Frege's views on the priority of judgments are problematic, and unlike Wittgenstein's. Russell's views on these matters, and their development, are discussed in detail, and shown to be more sophisticated than usually supposed. Certain misreadings of Russell, including those regarding the relationship between propositional functions and (...) universals, are exposed. Wittgenstein's and Russell's views on logical grammar are shown to be very similar. Russell's type theory does not countenance types of genuine entities nor metaphysical truths that cannot be put into words, contrary to conventional wisdom. I relate this to the debate over "inexpressible truths" in the Tractatus. I lastly comment on the changes to Russell's views brought about by Wittgenstein's influence. (shrink)

In the language of second-order logic, first- and second-order variables are distinguished syntactically and cannot be grammatically substituted. According to a prominent argument for the deployment of these languages, these substitution failures are necessary to block the derivation of paradoxes that result from attempts to generalize over predicate interpretations. I first examine previous approaches which interpret second-order sentences using expressions of natural language and argue that these approaches undermine these syntactic restrictions. I then examine Williamson’s primitivist approach according to which (...) second-order sentences are not offered readings in a previously understood language. I argue that the syntactic restrictions alone do not block the derivation of the paradox, unless they are backed by a principled reason that the language cannot be expanded to allow the grammatical substitution of first- and second- order variables. I argue that there is neither a syntactic nor a semantic principle that prohibits such an expansion. (shrink)

I characterize and argue against the standard interpretation of logical atomism. The argument against this reading is historical: the standard interpretation of logical atomism (1) fails to explain how the view is inspired by nineteenth-century developments in mathematics, (2) fails to explain how logic is central to logical atomism, and (3) fails to explain how logical atomism is a revolutionary and new "scientific philosophy." In short, the standard interpretation is a bad history of logical atomism. A novel interpretation of the (...) view that repairs these difficulties is sketched in the concluding section. (shrink)

Arguments against the Russellian theory of definite descriptions based on cases that involve failures of uniqueness are a recurrent theme in the relevant literature. In this paper, I discuss a number of such arguments, from Strawson (1950), Ramachandran (1993) and Szabo (2005). I argue that the Russellian has resources to account for these data by deploying a variety of mechanisms of quantifier domain restrictions. Finally, I present a case that is more problematic for the Russellian. While the previous cases all (...) involve referential uses of descriptions (or some variations of such uses), the most effective objection to the uniqueness condition draws on genuine attributive uses. (shrink)

Todd (2016) proposes an analysis of future-directed sentences, in particular sentences of the form 'will(φ)', that is based on the classic Russellian analysis of definite descriptions. Todd's analysis is supposed to vindicate the claim that the future is metaphysically open while retaining a simple Ockhamist semantics of future contingents and the principles of classical logic, i.e. bivalence and the law of excluded middle. Consequently, an open futurist can straightforwardly retain classical logic without appeal to supervaluations, determinacy operators, or any further (...) controversial semantical or metaphysical complication. In this paper, we will show that this quasi-Russellian analysis of 'will' both lacks linguistic motivation and faces a variety of significant problems. In particular, we show that the standard arguments for Russell's treatment of definite descriptions fail to apply to statements of the form 'will(φ)'. (shrink)

The most common account of attitude reports is the relational analysis according towhich an attitude verb taking that-clause complements expresses a two-placerelation between agents and propositions and the that-clause acts as an expressionwhose function is to provide the propositional argument. I will argue that a closerexamination of a broader range of linguistic facts raises serious problems for thisanalysis and instead favours a Russellian `multiple relations analysis' (which hasgenerally been discarded because of its apparent obvious linguistic implausibility).The resulting account can be (...) given independent philosophical motivations within anintentionalist view of truth and predication. (shrink)

First, language and axioms of Church's paper 'Comparison of Russell's Resolution of the Semantical Antinomies with that of Tarski' are slightly modified and a version of the Liar paradox tentatively reconstructed. An obvious natural solution of the paradox leads to a hierarchy of truth predicates which is of a different kind from the one defined by Church: it depends on the enlargement of the semantical vocabulary and its levels do not differ in the ramified-type-theoretical sense. Second, two attempts are made (...) in order to justify the Russellian, and perhaps Churchian, idea that language should not be fragmented beyond what is required by type distinctions. After all, because of reducibility, which seems to allow a semantics without propositions, this comes out to be possible only at the cost of resorting to two disputable theses. (shrink)

Abductivists claim that explanatory considerations (e.g., simplicity, parsimony, explanatory breadth, etc.) favor belief in the external world over skeptical hypotheses involving evil demons and brains in vats. After showing how most versions of abductivism succumb fairly easily to obvious and fatal objections, I explain how rationalist versions of abductivism can avoid these difficulties. I then discuss the most pressing challenges facing abductivist appeals to the a priori and offer suggestions on how to overcome them.

In his influential paper 'Speaker's Reference and Semantic Reference', Kripke defends Russell's theory of descriptions against the charge that the existence of referential and attributive uses of descriptions reflects a semantic ambiguity. He presents a purely defensive argument to show that Russell's theory is not refuted by the referential usage and a number of methodological considerations which apparently tell in favour of Russell's unitary theory over an ambiguity theory. In this paper, I put forward a case for the ambiguity theory (...) that thwarts Kripke's defensive strategy and argue that it is not undermined by any of his methodological points. (shrink)

In his book Language in Context, Jason Stanley provides a novel solution to certain interpretational puzzles (Stanley, 2007). The aphonic approach, as we call it, hangs upon a substantial syntactic thesis. Here, we provide theoretical and empirical arguments against this particular syntactic thesis. Moreover, we demonstrate that the interpretational puzzles under question admit of a better solution under the explicit approach.

Is linguistic understanding a form of knowledge? I clarify the question and then consider two natural forms a positive answer might take. I argue that, although some recent arguments fail to decide the issue, neither positive answer should be accepted. The aim is not yet to foreclose on the view that linguistic understanding is a form of knowledge, but to develop desiderata on a satisfactory successor to the two natural views rejected here.

I argue that three main interpretations of the aim of Russell’s early logicism in The Principles of Mathematics (1903) are mistaken, and propose a new interpretation. According to this new interpretation, the aim of Russell’s logicism is to show, in opposition to Kant, that mathematical propositions have a certain sort of complete generality which entails that their truth is independent of space and time. I argue that on this interpretation two often-heard objections to Russell’s logicism, deriving from Gödel’s incompleteness theorem (...) and from the non-logical character of some of the axioms of Principia Mathematica respectively, can be seen to be inconclusive. I then proceed to identify two challenges that Russell’s logicism, as presently construed, faces, but argue that these challenges do not appear unanswerable. (shrink)

In Appendix B of Russell's The Principles of Mathematics occurs a paradox, the paradox of propositions, which a simple theory of types is unable to resolve. This fact is frequently taken to be one of the principal reasons for calling ramification onto the Russellian stage. The paper presents a detaiFled exposition of the paradox and its discussion in the correspondence between Frege and Russell. It is argued that Russell finally adopted a very simple solution to the paradox. This solution had (...) nothing to do with ramified types but marked an important shift in his theory of propositions. (shrink)

Viebahn (2018) has recently argued that several tests for ambiguity, such as the conjunction-reduction test, are not reliable as tests for polysemy, but only as tests for homonymy. I look at the more fine-grained distinction between regular and irregular polysemy and I argue for a more nuanced conclusion: the tests under discussion provide systematic evidence for homonymy and irregular polysemy but need to be used with more care to test for regular polysemy. I put this conclusion at work in the (...) context of the debate over the alleged referential-attributive ambiguity of the definite article. In reply to various criticisms, defenders of the ambiguity view argue that this is a case of polysemy. But opponents object that the dual use of the definite article fails tests for ambiguity. The debate seems to have come to stalemate, unless the relevance of the tests is determined for cases of alleged polysemy. I conclude that the balance of considerations incline towards rejecting the ambiguity thesis. (shrink)

In "the principles of mathematics" russell accepts (a) that word meaning (e.G., That 'fido' means fido) is irrelevant to logic and (b) that such sentences as 'all men are mortal' do not express quantified propositions but are about things (in this case, The class of men). If we note these confusions, And also that (b), Though not (a) has been abandoned by 'on denoting', We see what denoting is and how russell relates to frege on sinn and bedautung.

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

Se analizan algunas consecuencias del escepticismo humeano concernientes a laexistencia de un Yo substancial y permanente anterior a la experiencia y coordinadorde ella. Se presentan dos propuestas: la teoría de los agregadosautoorganizativos favorecida por Francisco Varela y la tesis de las ideascognoscentes de William James. Luego se examinan tres problemas que suscitanposturas a-yoicas del tipo James-Varela: el problema de la identidad, el de latemporalidad y el de la intencionalidad como propósito. Se plantean algunassoluciones y se sugiere que la consideración de (...) un paradigma a-yoico está todavíasujeta a una filosofía especulativa.We analyze some implications of Humean scepticism regarding the existence of apermanent and substantial Self that would precede and coordinate experience.Two proposals are presented: Francisco Varela’s theory of selforganizingaggregates and William James’ thesis about ideas that know. We then examinethree problems raised by “no-self” stances of the James-Varela kind, viz., theproblems of identity, of temporality and of intentionality . We sketchsome solutions and we suggest that the consideration of a “no-self” paradigm isstill a matter of speculative philosophy. (shrink)

The widely held assumption about what motivated On Denoting is irreconcilable with Russell's position shortly beforehand; but discarding it leaves one with a carefully worked out solution whose problem is missing. The real motivation is to be found in a notoriously obscure passage in OD, in which Russell exposes a decisive (though easily overlooked) flaw in his former theory of denoting; a flaw which also cripples Frege's theory of sense and reference. A comprehensive account of this passage is the chief (...) concern of the present paper. Recognizing the critical role of this argument of Russell's leads to a more credible account of his argumentation in that essay. It also suggests that the fundamental standpoint underlyingThe Principles of Mathematics remains intact. In this light, the appropriation of OD to the philosophy of language may be misguided. (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)

According to one creation myth, analytic philosophy emerged in Cambridge when Moore and Russell abandoned idealism in favour of naive realism: every word stood for something; it was only after “the Fall,” Russell's discovery of his theory of descriptions, that they realized some complex phrases (“the present King of France”) didn't stand for anything. It has become a commonplace of recent scholarship to object that even before the Fall, Russell acknowledged that such phrases may fail to denote. But we need (...) to go further: even before the Fall, Russell had taken an altogether more discerning approach to the ontology of logic and relations than is usually recognized. (shrink)

This thesis explores the development of Bertrand Russell‘s theory of definite descriptions. It aims at demonstrating the connection between Russell‘s views on the subject of denoting and his attempt, in the period 1903-05, to develop a solution to 'the Contradiction'. The thesis argues that the discovery of the theory of descriptions, and the way in which it works, are best understood against the backdrop of Russell‘s work on the paradoxes. A new understanding of Russell‘s seminal paper 'On Denoting' is presented, (...) including a novel interpretation of the notorious 'Gray‘s Elegy Argument', in which Russell argues against his earlier theory of denoting. That Russell‘s work on denoting is connected to his work on the paradoxes is reasonably well-known: the nature of the connection has not, however, been adequately brought out in the literature. This is addressed through demonstrating the relationship between Russell‘s work on denoting and his development of the 'substitutional theory' of classes and relations. This theory eliminates classes and propositional functions in favour of matrices and substitutions. The role of the theory of descriptions in the development of the substitutional theory is commonly supposed to be merely that the theory of descriptions facilitates the ontological elimination of classes. But this elimination was equally possible on Russell‘s earlier theory of denoting. In the thesis it is suggested that the theory of descriptions brings with it a new conception of analysis, and that it is through the introduction of this new form of analysis—rather than through the elimination of classes—that the theory of descriptions facilitates the substitutional approach. (shrink)