Critical Notice: Paul Russell's The Riddle of Hume's Treatise: Skepticism,Naturalism, and Irreligion (OUP 2008)

In The Riddle of Hume's Treatise: Skepticism, Naturalism, and Irreligion (2008), Paul Russell makes a strong case for the claim that “The primary aim of Hume's series of skeptical arguments, as developed and distributed throughout the Treatise, is to discredit the doctrines and dogmas of Christian philosophy and theology with a view toward redirecting our philosophical investigations to areas of ‘common life,’ with the particular aim of advancing ‘the science of man’” (2008, 290). Understanding Hume in this way, according to Russell, sheds light on the “ultimate riddle” of the Treatise: “is it possible to reconcile Hume's (extreme) skeptical principles and conclusions with his aim to advance the ‘science of man’” (2008, 3)? Or does Hume's skepticism undermine his “secular, scientific account of the foundations of moral life in human nature” (290)? Russell's controversial thesis is that “the irreligious nature of Hume's fundamental intentions in the Treatise” is essential to solving the riddle (11). Russell makes a compelling case for Hume's irreligion as well as his atheism. Contrary to this interpretation I argue that Hume is an irreligious theist and not an atheist.     

Discriminatory Capacities,Russell's Principle,and the Importance of Losing Sight of Objects

What capacities for discrimination must a subject possess in order to entertain singular thoughts? Evans has suggested that a subject must be able to discriminate his referent from all other entities in order to be able to do so; what he calls Russell's Principle. Evans' view has few followers, and he has been repeatedly accused of presenting no argument in its favour. In this paper I present what I take to be Evans' argument. I suggest that he has been misinterpreted as introducing Russell's Principle for the purpose of fixing reference. Rather, he introduces it in order to ensure that our conceptual capacities have the functional complexity to allow for objective thought. I suggest that the logical types of our thought are constituted by their inferential potential and argue that, even though singular thought may be possible without the satisfaction of Russell's Principle, singular thought that forms part of an objective world view is not.     

Russell's Schema,Not Priest's Inclosure

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.      

The truth and nothing but the truth,yet never the whole truth: Frege,Russell and the analysis of unities

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.     

Beltrami's model and the independence of the parallel postulate

In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell's Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege's extant logical system, if Frege's system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege's logical system, even without its naive class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therin. therein.     

Sense data and logical relations: Karin Costelloe-Stephen and Russell’s critique of Bergson

ABSTRACT

Though scholarship has explored Karin Costelloe-Stephen’s contributions to the history of psychoanalysis, as well as her relations to the Bloomsbury Group, her philosophical work has been almost completely ignored. This paper will examine her debate with Bertrand Russell over his criticism of Bergson. Costelloe-Stephen had employed the terminology of early analytic philosophy in presenting a number of arguments in defence of Bergson’s views. Costelloe-Stephen would object, among other things, to Russell’s use of an experiment which, as she points out, was first conducted by Carl Stumpf. Russell appeals to Stumpf's experiment in his attempt to prove that sense data are terms in logical relations, a thesis presupposed by the project of logical analysis outlined in Our Knowledge of the External World. A reformulated version of Costelloe-Stephen's argument put forth by this paper shows that Russell's argument fails to provide adequate proof for his thesis. Further modifications of the argument can also address a reconstruction (based on contemporary reports) of Russell's reply to Costelloe-Stephen. In his reply, Russell would use, already in 1914, the term ‘analytic philosophy’ in contrasting his and Moore’s approach to a continental one, exemplified by Bergson and Costelloe-Stephen.     

Platonism and metaphor in the texts of mathematics: Gödel and Frege on mathematical knowledge

In this paper, I challenge those interpretations of Frege that reinforce the view that his talk of grasping thoughts about abstract objects is consistent with Russell's notion of acquaintance with universals and with Gödel's contention that we possess a faculty of mathematical perception capable of perceiving the objects of set theory. Here I argue the case that Frege is not an epistemological Platonist in the sense in which Gödel is one. The contention advanced is that Gödel bases his Platonism on a literal comparison between mathematical intuition and physical perception. He concludes that since we accept sense perception as a source of empirical knowledge, then we similarly should posit a faculty of mathematical intuition to serve as the source of mathematical knowledge. Unlike Gödel, Frege does not posit a faculty of mathematical intuition. Frege talks instead about grasping thoughts about abstract objects. However, despite his hostility to metaphor, he uses the notion of ‘grasping’ as a strategic metaphor to model his notion of thinking, i.e., to underscore that it is only by logically manipulating the cognitive content of mathematical propositions that we can obtain mathematical knowledge. Thus, he construes ‘grasping’ more as theoretical activity than as a kind of inner mental ‘seeing’.

     

Fiction,Pleasurable Tragedy,and the HOT Theory of Consciousness

Abstract

The ‘feeling fiction problem’ asks: is it rational to be moved by what happens to fictional characters? The so-called ‘paradox of tragedy’ is embodied in the question: Why or how is it that we take pleasure in artworks which are clearly designed to cause in us such feelings as sadness and fear? My focus in this paper is to examine these problems from the point of view of the so-called ‘higher-order thought theory of consciousness’ (HOT theory) which says that the best explanation for what makes a mental state conscious is that it is accompanied by a thought that one is in that state. I examine the feeling fiction problem in light of the HOT theory and through a critique of Colin Radford's view. For example, I argue that Radford equivocates in his use of the term ‘aware’ in his response to some of the proposed solutions to the feeling fiction problem. Finally, I show how Susan Feagin's approach to the paradox of tragedy can be analysed and supported by the HOT theory.     

The completeness of the pragmatic solution to Moore’s paradox in belief: a reply to Chan

Moore’s paradox in belief is the fact that beliefs of the form ‘p and I do not believe that p’ are ‘absurd’ yet possibly true. Writers on the paradox have nearly all taken the absurdity to be a form of irrationality. These include those who give what Timothy Chan calls the ‘pragmatic solution’ to the paradox. This solution turns on the fact that having the Moorean belief falsifies its content. Chan, who also takes the absurdity to be a form of irrationality, objects to this solution by arguing that it is circular and thus incomplete. This is because it must explain why Moorean beliefs are irrational yet, according to Chan, their grammatical third-person transpositions are not, even though the same proposition is believed. But the solution can only explain this asymmetry by relying on a formulation of the ground of the irrationality of Moorean beliefs that presupposes precisely such asymmetry. I reply that it is neither necessary nor sufficient for the irrationality that the contents of Moorean beliefs be restricted to the grammatical first-person. What has to be explained is rather that such grammatical non-first-person transpositions sometimes, but not always, result in the disappearance of irrationality. Describing this phenomenon requires the grammatical first-person/non-first person distinction. The pragmatic solution explains the phenomenon once it is formulated in de se terms. But the grammatical first-person/non-first-person distinction is independent of, and a fortiori, different from, the de se/non-de se distinction presupposed by pragmatic solution, although both involve the first person broadly construed. Therefore the pragmatic solution is not circular. Building on the work of Green and Williams I also distinguish between the irrationality of Moorean beliefs and their absurdity. I argue that while all irrational Moorean beliefs are absurd, some Moorean beliefs are absurd but not irrational. I explain this absurdity in a way that is not circular either.     

Indefinite Divisibility

Some hold that the lesson of Russell’s paradox and its relatives is that mathematical reality does not form a ‘definite totality’ but rather is ‘indefinitely extensible’. There can always be more sets than there ever are. I argue that certain contact puzzles are analogous to Russell’s paradox this way: they similarly motivate a vision of physical reality as iteratively generated. In this picture, the divisions of the continuum into smaller parts are ‘potential’ rather than ‘actual’. Besides the intrinsic interest of this metaphysical picture, it has important consequences for the debate over absolute generality. It is often thought that ‘indefinite extensibility’ arguments at best make trouble for mathematical platonists; but the contact arguments show that nominalists face the same kind of difficulty, if they recognize even the metaphysical possibility of the picture I sketch.     

The Versatility of Universality in Principia Mathematica

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.     

Knowing failably and Moorean assertions

Knowledge-fallibilism is a species of a genus that I call knowledge-failabilism. Each is a theory of knowledge's nature. One apparent challenge to knowledge-failabilism's truth is the prima facie absurdity of Moorean assertions like ‘It's raining but I do not believe that it is.’ Does each such assertion convey an implicit and unfortunate contrast, even a contradiction? I argue that this Untenable Contrast analysis fails: no such contrast is present within the speaker's perspective at the pertinent time.     

SENSATION,INTENTIONALITY, AND ANIMAL CONSCIOUSNESS: MALEBRANCHE'S THEORY OF THE MIND

In general, seventeenth-century philosophers seem to have assumed that intentionality is an essential characteristic of our mental life. Malebranche is perhaps the only philosopher in the period who stands out clearly against the prevailing orthodoxy; he is committed to the thesis that there is a large class of mental items - sensations - which have no representational content. In this paper I argue that due attention to this fact makes it possible to mount at least a partial defence of his notorious doctrine of ‘the rainbow-coloured soul’; Malebranche's doctrine is a striking anticipation of modern adverbial theories of sensation. I then argue that failure to appreciate the non-intentional character of sensations for Malebranche vitiates one recent attempt to explain why he accepted the Cartesian doctrine of the beastmachine; in contrast to the Radners, I suggest that Malebranche has the philosophical resources to offer an interesting theory of animal consciousness, and that his failure to develop such a theory rests largely on his acceptance of certain theological arguments. The paper ends by speculating about how Malebranche's theological commitments may have encouraged him to adopt the philosophically important thesis that intentionality is not the mark of the mental.     

ALSTON ON BELIEF AND ACCEPTANCE IN RELIGIOUS FAITH1

In this paper, I shall examine William Alston's influential view that the cognitive element in religious faith should be identified with ‘acceptance’ rather than ‘belief’. Although I am sympathetic to Alston's reluctance to regard belief as essential to faith, I shall argue that one can redescribe the cases that Alston invokes in support of his claim in terms of the standard notion of degrees‐of‐belief without loss. It will be further argued that, given Alston's constraints, his notion of acceptance, if not identical to belief, is at least a species of belief.     

Gödel on Concepts

This article is an attempt to present Gödel's discussion on concepts, from 1944 to the late 1970s, in particular relation to the thought of Frege and Russell. The discussion takes its point of departure from Gödel's claim in notes on Bernay's review of ‘Russell's mathematical logic’. It then retraces the historical background of the notion of intension which both Russell and Gödel use, and offers some grounds for claiming that Gödel consistently considered logic as a free-type theory of concepts, called intensions, considered as the denotations of predicate names.     

I. Some criticisms of the katzian metatheory of semantics

C. Fred Alford contends that the manner in which I objected to Feyerabend's democratic relativism is vulnerable to Feyerabend's rhetorical strategy, and that a better strategy would be to show that Feyerabend fails to demonstrate that democratic relativism is desirable. I reply in defense of the ‘plausibility’ issue on the grounds that Feyerabend's theory lends itself to uses (and abuses) beyond Utopian critique (in Alford's sense). I argue that it is the fact that critics ‐ myself included ‐ have assumed the burden of demonstrating the impossibility of Feyerabend's political theory that has led to the stalemate Alford describes, and that we may retain the ‘plausibility’ question while avoiding the stalemate by placing the burden of argument on Feyerabend to show that his theory is plausible.     

Impossible objects∗

This paper deals with the Meinong‐Russell controversy on nonsubsistent objects. The first part notes the similarity of certain contemporary semantical developments to Meinonj;'s theory of nonsubsistent objects. Then it lays out the major features of Meinong's famous theory, considers Russell's objections to same and Meinong's counter‐objections to Russell, and argues that Russell's well‐known argument fails. However, it is possible to augment Russell's argument against Meinong with sound Russellian principles in such a way that it presents at least a strong inclining reason against Meinong's theory of impossible objects.