In this paper I describe the birth of Russell’s notion of a propositional function on 3 May 1902 and its immediate context and implications. In particular, I consider its significance in relation to the development of his views on analysis.

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.

Many people think that truth somehow depends upon the way things are. Yet, it has proven difficult to precisely explain the nature of this dependence. The most common view is that truth depends upon the way things are by corresponding to things. But this account relocates the difficulty: one now wonders what correspondence is. It is worth emphasizing that the question of how truth relates to reality is not only a question for correspondence theorists; theorists of all stripes may wonder (...) how truth and reality connect. There are many reasons one might care to have an analysis of how truth relates to reality. Here are two. First, an analysis would help philosophers better understand how truth could depend upon the way things are. Why is it that when Joe shoves his cat off his pillow, the proposition that Joe's cat is on his pillow switches from true to false? It may seem puzzling that an abstract thing, such as a proposition, should be affected by physical changes to concrete particulars. How does that happen? The difficulty of seeing just how true propositions are able to systematically relate to reality will be called "the Problem of Matching." A thorough analysis of the relationship between truth and reality would effectively solve the Problem of Matching. (shrink)

In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics, meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content. Winner of The Bertrand Russell Society Book Award 2013.

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...

The paper argues that philosophers commonly misidentify the substitutivity principle involved in Russell’s puzzle about substitutivity in “On Denoting”. This matters because when that principle is properly identified the puzzle becomes considerably sharper and more interesting than it is often taken to be. This article describes both the puzzle itself and Russell's solution to it, which involves resources beyond the theory of descriptions. It then explores the epistemological and metaphysical consequences of that solution. One such consequence, it argues, is that (...) Russell must abandon his commitment to propositions. (shrink)

The paper critically scrutinizes the widespread idea that Russell subscribes to a "Universalist Conception of Logic." Various glosses on this somewhat under-explained slogan are considered, and their fit with Russell's texts and logical practice examined. The results of this investigation are, for the most part, unfavorable to the Universalist interpretation.

This paper concerns the debate on the nature of Rudolf Carnap'sproject in his 1928 book The Logical Structure of the Worldor Aufbau. Michael Friedman and Alan Richardson haveinitiated much of this debate. They claim that the Aufbauis best understood as a work that is firmly grounded inneo-Kantian philosophy. They have made these claims in oppositionto Quine and Goodman's ``received view'' of the Aufbau. Thereceived view sees the Aufbau as an attempt to carry out indetail Russell's external world program. I argue (...) that both sidesof this debate have made errors in their interpretation ofRussell. These errors have led these interpreters to misunderstandthe connection between Russell's project and Carnap's project.Russell in fact exerted a crucial influence on Carnap in the1920s. This influence is complicated, however, due to the factthat Russell and Carnap disagreed on many philosophical issues. Iconclude that interpretations of the Aufbau that ignoreRussell's influence are incomplete. (shrink)

Alex Oliver; XI*—A Few More Remarks on Logical Form, Proceedings of the Aristotelian Society, Volume 99, Issue 1, 1 June 1999, Pages 247–272, https://doi.org/10.

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

Idealist Heresies in Philosophy of Science: Cassirer, Carnap, and Kuhn. As common wisdom has it, philosophy of science in the analytic tradition and idealist philosophy are incompatible. Usually, not much effort is spent for explaining what is to be understood by idealism. Rather, it is taken for granted that idealism is an obsolete and unscientific philosophical account. In this paper it is argued that this thesis needs some qualification. Taking Carnap and Kuhn as paradigmatic examples of positivist and postpositivist philosophies (...) of science it is shown that these accounts share important features with Cassirer's idealist philosophy of science developed in the first half of this century. As it turns out, often Cassirer is more modern than those classical philosophers of (post)posivitist philosophy of science. For instance, Quine's criticism against Carnap's empiricist philosophy of science launched in Two Dogmas of Empiricism is anticipated by Cassirer for several decades. (shrink)

The transition from the traditional to the representational theory of measurement around the turn of the century was accompanied by little sustained criticism of the former. The most forceful critique was Bertrand Russell''s 1897 Mind paper, On the relations of number and quantity. The traditional theory has it that real numbers unfold from the concept of continuous quantity. Russell''s critique identified two serious problems for this theory: (1) can magnitudes of a continuous quantity be defined without infinite regress; and (2) (...) can additive relations between such magnitudes exist if magnitudes are not divisible? The present paper shows how the traditional theory answers these questions and compares the traditional and representational theories as contributions to our understanding of the logic of application. (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)

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.

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...

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)

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 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)

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)

This is the introductory essay to the collection of essays: 'Acquaintance: New Essays' (eds. Knowles & Raleigh, forthcoming, OUP). In this essay I provide some historical background to the concept of acquaintance. I examine various Russellian theses about acquaintance that contemporary acquaintance theorists may wish to reject. I consider a number of questions that acquaintance theorists face. I provide a survey of current debates in philosophy where acquaintance has recently been invoked. And I also provide brief summaries of the other (...) essays in this volume. (shrink)

In this paper, I develop a new defense of logicism: one that combines logicism and nominalism. First, I defend the logicist approach from recent criticisms; in particular from the charge that a cruciai principie in the logicist reconstruction of arithmetic, Hume's Principle, is not analytic. In order to do that, I argue, it is crucial to understand the overall logicist approach as a nominalist view. I then indicate a way of extending the nominalist logicist approach beyond arithmetic. Finally, I argue (...) that a nominalist can use the resulting approach to provide a nominalization strategy for mathematics. In this way, mathematical structures can be introduced without ontological costs. And so, if this proposal is correct, we can say that ultimately all the nominalist needs is logic (and, rather loosely, ali the logicist needs is nominalism). (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)

It is commonly held that Bradley’s regress has a solution within a trope ontology. This seems to happen when a bundle is understood as constituted by non-transferable tropes. It also seems to happen when a bundle is understood as constituted by transferable tropes related by a relational trope of compresence whose existence specifically depends on those relata. In this article I demonstrate that these proposals fail in addressing the essential question that underlies the regress, incurring in a question-begging response already (...) anticipated by Bradley. (shrink)

Skinner has been criticized for advancing essentialist interpretations of meaning in which meaning is treated as the property of a word or a grammatical form. Such a practice is consistent with a "words and things" view that sought to advance an ideal language as well as with S-R views that presented meaning as the property of a word form. These views imply an essentialist theory of meaning that would be consistent with Skinner's early S-R behaviorism. However, Skinner's more developed account (...) of meaning is based on his later selectionist behaviorism, and this account of meaning is aligned in many respects with the views of Darwin, Peirce, F. C. S. Schiller, Dewey, and Wittgenstein. After adopting a selectionist theory of meaning, it was inconsistent for Skinner to maintain essentialist practices although Skinner did so in response to influences that had little to do with his selectionist theory. Skinner's particular contribution to this pragmatic-selectionist tradition of meaning is the integration of meaning within his three-term contingency for operant behavior. In this account, meaning lies in the probabilistic functional relations of verbal behavior rather than in its form. (shrink)

This thesis is concerned with the challenge truth-value gaps pose to the principle of bivalence. The central question addressed is: are truth-value gaps counterexamples to bivalence and is the supposition of counterexamples coherent? My aim is to examine putative cases of truth-value gaps against an argument by Timothy Williamson, which shows that the supposition of counterexamples to bivalence is contradictory. The upshot of his argument is that either problematic utterances say nothing, or they cannot be neither true nor false. I (...) start by identifying truth-bearers: an utterance, for instance, is a truth-bearer if it says that something is the case. Truth-bearers are evaluable items, with truth- and falsity-conditions statable in corresponding instances of schemas for truth and falsehood. A genuine case of a truth-value gap should be an utterance that is neither true nor false but says something to be the case. But it is inconsistent to accept the schemas for truth and falsehood and the existence of genuine cases of truth-value gaps. Secondly, I expound Williamson’s argument, which explores this inconsistency, and I identify two kinds of strategy to disarm his argument: those that preserve the schemas for truth and falsehood, and those that do not. Neither strategy is found to be persuasive. Thirdly, I argue that cases of reference failure causing truth-value gaps illustrate the upshot of Williamson’s argument. Fourthly, I examine Scott Soames’s account of liar sentences as counterexamples to bivalence. Soames adopts a strategy of the first kind to avoid contradictions. I argue that his solution allows some contradictions to be true, and that he fails to show that liar sentences are truth-bearers. Finally, I examine Charles Travis’s case for isostheneia: an equal balancing of reasons to evaluate a statement as true or as false, in which case a statement is neither. Travis avoids contradictions by adopting a strategy of the second kind. I argue that the schemas for truth and falsehood are immune to Travis’s objections, and that isostheneia fails to identify evaluable items. The cases examined confirm that utterances that are neither true nor false say nothing. My claim is thus that truth-value gaps are not counterexamples to bivalence. (shrink)

Many of our ordinary beliefs about the world around us are a result of inference from more fundamental beliefs. Foundationalists in epistemology have thought that, if these ordinary beliefs are to be rationally justified, the chain of inferential justification must terminate in a belief that is justified noninferentially. Foundationalists, of the internalist variety, have thought that the most plausible candidates for ending the regress of empirical justification are experiential states, the justifying features of which the believing subject is aware. The (...) Sellarsian dilemma, taking its name from philosopher Wilfrid Sellars, has been a persistent argument against foundationalist theories of epistemic justification. There have been various formulations of the dilemma over the years, but in its most general form it says that for any construal of an experiential state where the experiential state provides justification, the experiential state will need further justification. Sellars thought that an experience, all by itself, cannot provide justification unless we apply concepts to the experience. However, the application of concepts is judgmental and conceptual judgments, like beliefs, require further justification. So, the experiential state construed this way would perpetuate the regress it was designed to terminate. On the other hand, if the experiential state is construed such that it is not in need of justification, then it cannot itself provide justification. Both options are devastating to a foundationalist epistemology. My thesis is that a solution to all forms of the Sellarsian dilemma is to require for foundational justification direct awareness of the fit between one's conceptual judgment and the justifying experiential state. I concede that one must conceptualize one's experiential states for these states to play an epistemic role. However, I argue that conceptual judgments of this sort are the foundations. The importance of this solution is that it not only terminates the regress of justification but it also captures the primary intuitions that motivate internalism and foundationalism. This is to say that although I have framed my account as a response to the Sellarsian dilemma, it is not merely an ad hoc patch that avoids what stood as a serious problem. Instead, it is a return to what has motivated and what I take to be most persuasive about internalist foundationalism. (shrink)

Je m’oppose ici à la théorie « structurale » de la sensation développée par Kurt Koffka dans les années 1920, et reprise notamment par Merleau-Ponty, qui en fait le centre théorique des analyses de la psychologie de la forme. Je commence donc par examiner cette théorie et les faits sur lesquels elle repose, en montrant notamment, à l’aide de la méréologie husserlienne, qu’ils ne peuvent paraître corroborer une théorie structurale de la sensation que si l’on confond « abstraire » et (...) « séparer réellement » une qualité de son contexte. Il s’agit par là plus largement de montrer l’impossibilité, en fait comme en droit, de toute philosophie de la perception qui chercherait à réduire les sensations ou « qualia » à des prédicats relationnels. Je convoque alors William James à l’appui de ces conclusions, en rappelant qu’il avait déjà montré contre les théories néo-hégéliennes de son époque l’illégitimité de leur prétention à se réclamer de faits psychologiques similaires, et qu’il avait soutenu contre eux une théorie de la connaissance par accointance et de l’absoluité ontologique des qualités sensorielles que je cherche à reprendre à mon compte. (shrink)

The goal of this paper is to discuss Russell’s Theory of Denoting Concepts, mainly to see clearly why he adopted it and, especially, why he abandoned it. With regard to TDC, I detect three kinds of problems: ontological (the denotation of empty denoting concepts), logical (the infinite regress of meaning in the case of denoting concepts) and epistemological (the relation between denoting concepts and acquaintance). I will not consider here the first point, but only the last two. The chapter will (...) be thus divided into two main parts: in the first part I will present the inner logical difficulty of TDC, whereas in the second part I will discuss the connection of denoting concepts with the Principle of Acquaintance. (shrink)