Russell claims in his autobiography and elsewhere that he discovered his 1905 theory of descriptions while attempting to solve the logical and semantic paradoxes plaguing his work on the foundations of mathematics. In this paper, I hope to make the connection between his work on the paradoxes and the theory of descriptions and his theory of incomplete symbols generally clearer. In particular, I argue that the theory of descriptions arose from the realization that not only can a class not be (...) thought of as a single thing, neither can the meaning/intension of any expression capable of singling out one collection (class) of things as opposed to another. If this is right, it shows that Russell’s method of solving the logical paradoxes is wholly incompatible with anything like a Fregean dualism between sense and reference or meaning and denotation. I also discuss how this realization lead to modifications in his understanding of propositions and propositional functions, and suggest that Russell’s confrontation with these issues may be instructive for ongoing research. (shrink)

Drawing on Russell's substitutional theory, this paper examines the notion of ‘structured variable’, in order to compare Russell's and Tarski's conceptions of variables. The framework of syntactic fibrations, coming from categorical logic, is used as a common setting. The main objective of this paper is to make sense of the notion of structured variable beyond the context of Russell's theory, to question the Tarskian way of understanding what it is to be a possible value for a variable, and to bring (...) out semantically structured variables as a renewed and fruitful way of conceiving of logical structure. (shrink)

What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate on (...) Benacerraf's dilemma and the indispensability argument. Through the considerations of themes in the philosophy of language, ontology, and the philosophy of science, the book aims at offering an historically-informed introduction to the philosophy of mathematics, approached through the lenses of its most fundamental problem. (shrink)

In this article, I examine the ramified-type theory set out in the first edition of Russell and Whitehead's Principia Mathematica. My starting point is the ‘no loss of generality’ problem: Russell, in the Introduction (Russell, B. and Whitehead, A. N. 1910. Principia Mathematica, Volume I, 1st ed., Cambridge: Cambridge University Press, pp. 53–54), says that one can account for all propositional functions using predicative variables only, that is, dismissing non-predicative variables. That claim is not self-evident at all, hence a problem. (...) The purpose of this article is to clarify Russell's claim and to solve the ‘no loss of generality’ problem. I first remark that the hierarchy of propositional functions calls for a fine-grained conception of ramified types as propositional forms (‘ramif-types’). Then, comparing different important interpretations of Principia’s theory of types, I consider the question as to whether Principia allows for non-predicative propositional functions and variables thereof. I explain how the distinction between the formal system of the theory, on the one hand, and its realizations in different epistemic universes, on the other hand, makes it possible to give us a more satisfactory answer to that question than those given by previous commentators, and, as a consequence, to solve the ‘no loss of generality’ problem. The solution consists in a substitutional semantics for non-predicative variables and non-predicative complex terms, based on an epistemic understanding of the order component of ramified types. The rest of the article then develops that epistemic understanding, adding an original epistemic model theory to the formal system of types. This shows that the universality sought by Russell for logic does not preclude semantical considerations, contrary to what van Heijenoort and Hintikka have claimed. (shrink)

In 1913 Wittgenstein raised an objection to Russell’s multiple relation theory of judgment that eventually led Russell to abandon his theory. As he put it in the Tractatus, the objection was that “the correct explanation of the form of the proposition, ‘A makes the judgement p’, must show that it is impossible for a judgement to be a piece of nonsense. (Russell’s theory does not satisfy this requirement,” (5.5422). This objection has been widely interpreted to concern type restrictions on the (...) constituents of judgment. I argue that this interpretation is mistaken and that Wittgenstein’s objection is in fact a form of the problem of the unity of the proposition. (shrink)

In this thesis, I will explore the epistemological evolutionary debunking arguments in meta-ethics. I will defend these arguments by accomplishing two tasks: I will offer the best way to understand the EDA and I will also respond to two strongest objections to the EDA. Firstly, in Part I of this thesis, I will offer my account of how the EDA should be best formulated. I will start from how evolution has significantly influenced our moral beliefs. I will then explain why, (...) due to their evolutionary origin, our moral beliefs are not tracking the moral truth reliably. Furthermore, I will argue that the fact that our moral beliefs are not tracking the moral truth also provides an undercutting and a higher-order defeater for those beliefs. As a result, I will conclude that the epistemic status of our moral beliefs is undermined because of these two kinds of defeaters. Secondly, in Part II of this thesis, I will turn my attention to the two strongest objections to the EDA – the Conceptual Truth Objection and the Third Factor Objection. I will first offer two responses to the Conceptual Truth Objection and, based on these two responses, I will argue that the Conceptual Truth Objection fails as a challenge to the EDA. I will then also argue that there currently doesn’t exist an acceptable version of the Third Factor Objection and it is also unlikely that such a version could be constructed in the future. I will finally conclude that both objections are problematic and they are thus unable to give us reason to doubt the EDA. (shrink)

The notion of logical construction was used by Bertrand Russell in the early 20th century, which originally comes from A. N. Whitehead. Russell said that matter as a mind-independent thing can only be known by description. He also argued that matter is a logical construction of sense-data. However, this leads to an incoherent view of the direct or indirect connection between a mind and the external world. The problem examining is whether a collapsing house is a logical construction of the (...) sense-data of rumbling sounds and collapsing shapes. Using Russell's writings between 1911 and 1918, I will analyze how Russell characterized logical constructions. Finally, I will show Russell’s view about the relation of logical constructions to matter and sense-data. A careful interpretation of Russell's thoughts shows that the contents of the statements of the physical world are not constructions being equivalent to the contents of the sense-datum statements. (shrink)

This paper aims to shed light on an underexplored aspect of Gilbert Ryle’s interest in the notion of “knowing-how”. It is argued that in addition to his motive of discounting a certain theory of mind, his interest in the notion also stemmed (and perhaps stemmed more deeply) from two ethical interests: one concerning his own life as a philosopher and whether the philosopher has any meaningful task, and one concerning the ancient issue of whether virtue is a kind of knowledge. (...) It is argued that Ryle saw know-how as crucial in both respects and that he continued to be interested in these ethical issues throughout his career. (shrink)

Certain advocates of the so-called “neo-logicist” movement in the philosophy of mathematics identify themselves as “neo-Fregeans” (e.g., Hale and Wright), presenting an updated and revised version of Frege’s form of logicism. Russell’s form of logicism is scarcely discussed in this literature and, when it is, often dismissed as not really logicism at all (in light of its assumption of axioms of infinity, reducibility and so on). In this paper I have three aims: firstly, to identify more clearly the primary meta-ontological (...) and methodological differences between Russell’s logicism and the more recent forms; secondly, to argue that Russell’s form of logicism offers more elegant and satisfactory solutions to a variety of problems that continue to plague the neo-logicist movement (the bad company objection, the embarrassment of richness objection, worries about a bloated ontology, etc.); thirdly, to argue that neo-Russellian forms of logicism remain viable positions for current philosophers of mathematics. (shrink)

Neutral monism is the view that both ‘mind’ and ‘matter’ are grounded in a more fundamental form of reality that is intrinsically neither mental nor material. It has often been treated as an odd fringe theory deserving of at most a footnote in the broader philosophical debates. Yet such attitudes do a grave disservice to its sophistications and significance for late nineteenth and early twentieth-century philosophy of mind and psychology. This paper sheds light on this neglected view by situating it (...) within broader historical monist debates about the mind and bringing attention to one of its central internal disputes regarding ‘mental chemistry’. By taking a closer look at how Ernst Mach, William James, and Bertrand Russell address the question of whether and how our mental episodes are composed of more basic elements, it highlights deep differences among their conceptions of the fundamental ‘neutral stuff’ and its relations to ‘mind’ and ‘matter’. (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)

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 book begins with a reconstruction of Aristotle's syllogistic as viewed by some of the well-known logicians of the thirteenth and fourteenth centuries, that is, as expanded to include singular p...

Standard views of personal identity over time often hover uneasily between the subjective, first-person dimension (e. g. psychological continuity), and the objective, third-person dimension (e. g. biological continuity) of a person’s life. Since both dimensions capture something integral to personal identity, we show that neither can successfully be discarded in favor of the other. The apparent need to reconcile subjectivity and objectivity, however, presents standard views with problems both in seeking an ontological footing of, as well as epistemic evidence for, (...) personal identity. We contend that a fresh look at neutral monism offers a novel way to tackle these problems; counting on the most fundamental building blocks of reality to be ontologically neutral with regards to subjectivity and objectivity of personal identity. If the basic units of reality are, in fact, ontologically neutral – but can give rise to mental as well as physical events – these basic units of reality might account for both subjectivity and objectivity in personal identity. If this were true, it would turn out that subjectivity and objectivity are not conflictive dimensions of personal identity but rather two sides of the same coin. (shrink)

2020 update of the entry "Properties".

An account of validity that makes what is invalid conditional on how many individuals there are is what I call a conditional account of validity. Here I defend conditional accounts against a criticism derived from Etchemendy’s well-known criticism of the model-theoretic analysis of validity. The criticism is essentially that knowledge of the size of the universe is non-logical and so by making knowledge of the extension of validity depend on knowledge of how many individuals there are, conditional accounts fail to (...) reflect that the former knowledge is basic, i.e., independent of knowledge derived from other sciences. Appealing to Russell’s pre-Principia logic, I defend conditional accounts against this criticism by sketching a rationale for thinking that there are infinitely many logical objects. (shrink)

Reply to Beaney: the closing of the historical mindIn his comments, Michael Beaney sets himself up as the arbiter of what is genuine history and what isn’t. While celebrating the outpouring of specialized scholarship on Frege, he has no patience with the enterprise outlined in the Précis, which attempts to construct a large-scale picture of the richness of the analytic tradition. That enterprise is one in which great figures of our recent past are challenged by aspects of contemporary thought, and (...) our current struggles are enriched by insights of theirs that haven’t been fully absorbed. Although some work of this sort can be done piecemeal, one historical figure at a time, there is much to be learned from a more encompassing perspective. While no picture constructed by a single author can be authoritative about everything, the attempt to give informative, connected assessments of major milestones in the tradition is our best hope of understanding who we are and where we have come from. (shrink)

Bernard Linsky, The Evolution of Principia Mathematica; Bertrand Russell's Manuscripts and Notes for the Second Edition. Cambridge: Cambridge University Press. 2011. 407 pp. + two plates. $150.00/£...

On investigating a theorem that Russell used in discussing paradoxes of classes, Graham Priest distills a schema and then extends it to form an Inclosure Schema, which he argues is the common structure underlying both class-theoretical paradoxes (such as that of Russell, Cantor, Burali-Forti) and the paradoxes of ?definability? (offered by Richard, König-Dixon and Berry). This article shows that Russell's theorem is not Priest's schema and questions the application of Priest's Inclosure Schema to the paradoxes of ?definability?.1 1?Special thanks to (...) Francesco Orilia for criticisms of an early draft of this article. (shrink)

Russell’s substitutional theory conferred philosophical advantages over the simple type theory it was to emulate. However, it faced propositional paradoxes, and in a 1906 paper “On ‘Insolubilia’ and Their Solution by Symbolic Logic”, he modified the theory to block these paradoxes while preserving Cantor’s results. My aim is to draw out several quandaries for the interpretation of the role of substitution in Russell’s logic. If he was aware of the substitutional (_p_0_a_0) paradox in 1906, why did he advertise “Insolubilia” as (...) a solution to the Epimenides? If he was dissatisfied with the solution, as his correspondence suggests, why did he go on to publish it? Why did substitution reappear with orders in “Mathematical Logic as Based on the Theory of Types” if he had rejected a hierarchy of orders as intolerable? I offer the following as possible explanations: he construed the “logical Epimenides” as a version of the _p_0_a_0 paradox; his dissatisfaction with the “Insolubilia” solution was philosophical, not technical; and substitution re-emerged because he hoped for a new philosophical gloss on orders. Whether or not my explanations are correct, these issues must be addressed in accounting for Russell’s reasons for ramification. (shrink)

Temporal ontology is concerned with the ontological status of the past, the present and the future, with presentism and eternalism as main contenders since the second half of the last century. In recent years several philosophers have argued that the presentism/eternalism dispute is not substantial. They have embraced, one may say, deflationism. Denying or downplaying the meaningfulness of tenseless language and wielding the so-called triviality objection have been their main argumentative tools. Other philosophers have opposed this trend, thereby holding fast (...) to what could be named substantialism. Their leading defensive strategy has consisted in bringing to the fore tenselessness or unrestricted quantification in an attempt to resist the triviality objection. Despite this reaction, the past few years have hosted a new wave of deflationism, wherein the triviality objection and qualms about the legitimacy of tenselessness and unrestricted quantification still loom large. This paper counters this trend, by providing a new clarification of tenseless predication, unrestricted quantifiers and their role in rescuing substantialism from the triviality objection. A crucial ingredient is this: the appeal to unrestricted quantifiers and to tenseless predication are not alternative strategies, but rather two sides of the same coin, since substantialism requires quantifiers that are both tenseless and unrestricted. (shrink)

For logicians and metaphysicians curious about the evolution of Russell's logic from The Principles of Mathematics to Principia Mathematica, no volume of the Collected Papers of Bertr...