People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which we call (...) *Countable Independence*. In violating these principles, they display foibles like those of people who deviate from standard expected utility theory in more mundane cases: they choose dominated strategies, pay to avoid information, and reject expert advice. We precisely characterize the preference relations that satisfy Countable Independence in several equivalent ways: a structural constraint on preferences, a representation theorem, and the principle we began with, that every prospect has a value that some outcome could have. (shrink)

In his paper “St. Anselm’s ontological argument succumbs to Russell’s paradox” Christopher Viger presents a critique of Anselm’s Argument from the second chapter of Proslogion. Viger claims there that he manages to show that the greater than relation that Anselm used in his proof leads to inconsistency. I argue firstly, that Viger does not show what he maintains to show, secondly, that the flaw is not in the nature of Anselm’s reasoning but in Viger’s (mis)understanding of Anselm as (...) well as in Viger’s (mis)application of some set-theoretical notions. I also describe some features of Anselmian greater than relation, which indeed plays a crucial role in his Ontological Argument. Last but not least, I present the Argument itself. (shrink)

We prove a representation theorem for preference relations over countably infinite lotteries that satisfy a generalized form of the Independence axiom, without assuming Continuity. The representing space consists of lexicographically ordered transfinite sequences of bounded real numbers. This result is generalized to preference orders on abstract superconvex spaces.

In this short note we respond to the claim made by Christopher Viger in [4] that Anselm’s so-called ontological argument falls prey to Russell’s paradox. We show that Viger’s argument is based on a flawed premise and hence does not in fact demonstrate what he claims it demonstrates.

In the Proslogion, St. Anselm presents a philosophical argument for the existence of God. Anselm's proof, known since the time of Kant as the ontological argument for the existence of God, has played an important role in the history of philosophy and has been incorporated in various forms into the systems of Descartes, Leibniz, Hegel, and others. Included in this edition of the Proslogion are Gaunilo's "A Reply on Behalf of the Fool" and St. Anselm's "The Author's Reply to Gaunilo." (...) All three works are in the original Latin with English translation on facing pages. Professor Charlesworth's introduction provides a helpful discussion of the context of the Proslogion in the theological tradition and in Anselm's own thought and writing. (shrink)

'These propositions may seem mild, yet, if accepted, they would absolutely revolutionize human life.' With these words Bertrand Russell introduces what is indeed a revolutionary book. Taking as his starting-point the irrationality of the world, he offers by contrast something 'wildly paradoxical and subversive' Sceptical Essays has never been out of print since its first publication in 1928. Today, besieged as we are by the numbing onslaught of twenty-first-century capitalism, Russell's defense of scepticism and independence of mind is as timely (...) as ever. In clear, engaging prose, he guides us through the key philosophical issues that affect our daily life. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Technology and Our Relationship with GodAnselm Ramelow O.P.God's Original Plan and the FallTechnology may appear to be a very secular thing, but to assume that technology can be understood without God would be a mistake. Technology is deeply involved in our relationship with God. This involvement is, moreover, profoundly ambivalent.1To begin with the positive side of this ambivalence: the growing awareness of the dangers of technology should not lead (...) Christians to think that technology is necessarily a bad thing. It is, in fact, not even merely a "necessary evil." Rather, we can find in the use of technology an unfolding of our God-given rational nature. If we believe that God "made us in his image and likeness," then this quite directly implies two things: (1) God is a maker (he made us), and (2) since he made us in his image and likeness, we are makers as well. The making of technology thus reflects our dignity as made in the image and likeness of God.2 Accordingly, the Church has been more positive towards the development of technology than one might expect, and some of our technologies (e.g., agricultural, architectural, and time-keeping technologies) have their roots in medieval monasteries.3 [End Page 159]We should therefore expect that Adam and Eve, had they not fallen, nevertheless would have become makers of technology in some form or other. They would have exhibited inventiveness and tool use, though perhaps not a tool use focused on warding off evil (which did not exist in Eden), but concerned with promoting positive forms life, such as tools of art and communication. Art and communication technologies are, like all tools, means to an end; but these in particular contain their ends in themselves. In Aristotelian terms, their making (poiesis) concerns a praxis (such as "making conversation"). That is why we sometimes forget to list such technologies among our typical examples of technologies. We forget, for example, that, among the technologies of communication, language as a physical tool (sounds or written marks) is an obvious example. And it is a prelapsarian feature: the book of Genesis has Adam naming things before the Fall. In doing so, Adam echoes God's own creative "technique" of speaking or calling things into being.4 Even in its oral form, language is a matter of human making and a technology of communication. In paradise, communication would not have been merely instrumental, not merely a means, but an intrinsic good, embodying knowledge and intersubjective communion.Other forms of prelapsarian technology, however, are a matter of speculation. And whether or not one agrees with Jacques Ellul's thesis that there was no such prelapsarian technology,5 the ambivalence of technology is clear from the very beginning as well. This is at least what we see in the book of Genesis. For, as a matter of biblical record, it was Cain and his descendants who founded cities and developed technology (e.g., Tubal-Cain as the "forger of all instruments of bronze and iron" in Gen 4:22). And the history [End Page 160] of these urban civilizations does not display the best part of human behavior. But if, as we have said, technology is not necessarily a bad thing, then this must be a corruption of technology. What might this corruption consist in?I want to suggest that it consists precisely in the corruption of our relationship with God, from which technology can never abstract and in which it is, for better or for worse, embedded. Unsurprisingly, therefore, as technology progresses, this relationship becomes more and more explicit, and it does so in a paradoxical way: initially, it is an attempt to put humanity in charge and control, to replace our need for reliance on God by allowing us to play God ourselves. But in our current situation, particularly with the emergence of artificial intelligence (AI) and machine learning, the roles appear reversed: rather than putting humanity in charge, technology in turn is increasingly in control—to the point of becoming itself a god or idol that rules human life. As a result, we only end up having replaced one God with another... (shrink)

Could space consist entirely of extended regions, without any regions shaped like points, lines, or surfaces? Peter Forrest and Frank Arntzenius have independently raised a paradox of size for space like this, drawing on a construction of Cantor’s. I present a new version of this argument and explore possible lines of response.

This paper investigates the relationship between James’ radical empiricism and Deleuze’s study of the genesis of sense without a transcendental subject as necessary condition. It shows that James’ concept of pure experience changes the form of relation between mind and world. Considering how to conceptualize experience without a fixed metaphysical or transcendental subject destabilizes ontological identity, leads to a founding conceptual divergence from traditional phenomenology, and motivates Deleuze’s efforts towards transcendental empiricism. The paper reads Deleuze’s work on the genesis of (...) sense in this context, arguing that one important result is an ontological pluralism. Such pluralism is crucial in considering how meaning can be made between and across differences and is in keeping with radical empiricism’s openness to life’s complexity. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Scientific Method in PhilosophyAuthor's note: Thanks to Gregory Landini for helpful clarifications.Gregory Landini. Repairing Bertrand Russell's 1913 Theory of Knowledge. (History of Analytic Philosophy.) London: Palgrave Macmillan, 2022. Pp. x, 397. isbn: 978-3-030-66355-1, us$139 (hb); 978-3-030-66356-8, us$109 (ebook).The title of this book might suggest a rather narrow study of a problem with Russell's Theory of Knowledge and a proposed solution. But as with Landini's first book, Russell's Hidden Substitutional (...) Theory, the title does not capture the full scope of the work. That work did not just point out the lingering substitution theory in Principia, but gave a sweeping view of Russell's overall development from Principles to Principia and one of the most detailed accounts of the formal system in Principia in any work. This work gives a sweeping overview of Russell's philosophy up to 1918, including not just Russell's multiple-relation theory of judgment, but the whole project of what Russell called scientific method in philosophy, which was the subtitle to his 1914 Our Knowledge of the ExternalWorld. Landini thinks this is the height of Russell's philosophy and proposes a fix to the problems which led Russell to abandon the project.Landini does not just present Russell's views during this period, but vigorously defends them, and not just the multiple-relation theory of judgment mostly associated with Theory of Knowledge, but also the views that logic should be understood as synthetic a priori, Russell's doctrine of acquaintance, including the acquaintance with universals as the grounding of synthetic a priori knowledge, and Russell's view that logic is the essence of philosophy. The book contains a wide range of discussions, including issues in philosophy of mind, theories of representation, theories of universals, evolution in philosophy, and the metaphysics of time and space.The book opens with an overview of some main themes, including Landini's view of the three main phases of Russell's post-idealist philosophy and his discussion of what he calls the revolutions in logic and mathematics. The three phases Landini has in mind are the Principles phase, the Principia phase [End Page 81] (which includes The Problems of Philosophy and Theory of Knowledge) and the neutral monist phase, which Landini sees as a mistake Russell made when he didn't see how to repair his 1913 work. According to Landini, the Principles era ends with the failure of the substitution theory from the po /ao paradox, the Principia era ends by 1918 with the abandonment of the attempt to finish the project of the 1913 Theory of Knowledge, and the neutral monist era begins in 1919 and continues through 1948. Landini wants to concentrate on repairing the view in the Principia era. Any remarks of Russell's from later rejecting, for example, his view of the subject, of acquaintance, of neutral monism, and remarks concerning logic as consisting of tautologies are to be rejected. Landini firmly believes that after abandoning the 1913 project, Russell took a wrong turn. Landini's discussion of the multiple-relation theory of judgment is therefore quite different from the other discussion in the literature, in that most commentators have thought Russell was correct in abandoning the theory and most think there is something to Wittgenstein's criticism. Landini thinks Wittgenstein's criticism was based on his new vision of logic, and that Russell should have rejected it and proceeded with the project of Theory of Knowledge.Given the controversies involved in these claims, I think the best way forward is an explication of Landini's new emphasis on the revolutions in logic and mathematics and some of the key claims Landini makes concerning the Principia era. Then we can look at the details of Landini's repairing of the project.the two revolutionsWhat is striking about Landini's more recent work is his emphasis on these two revolutions. One is the revolution within logic, which originates with Frege; the other a revolution in mathematics which originates with Weierstrass, von Staudt, Pieri and Cantor. While most historians of this period are aware of the important shifts... (shrink)

The paradox of mass voting is not, generally speaking, matched by a paradoxical mass attempt to be politically well informed. As Converse underscored, most people are grossly politically ignorant—just as they would be if, as rational‐ignorance theory holds, they realized that their votes don't matter. Yet many millions of them contradict the theory by voting. This contradiction, and the illogical reasons people offer for voting, suggest that the logic of collective action does not come naturally to people. To equate (...) public ignorance with “rational ignorance,” then, attributes too much theoretical self‐consciousness to people. Even if their ignorance is not based on a grasp of the collective‐action problem, however, people's political ignorance is “rational”: but it is less a matter of calculating the low benefit likely to flow from one vote in a sea of millions, than of encountering the much higher cost of being well informed as compared to voting. As the high cost of becoming well informed appears likely to grow, it may be advisable to move off of the political agenda issues that have no clear continuum toward which a mostly ignorant median voter may gravitate. (shrink)

While it has perhaps always accompanied philosophical thought – one immediately thinks of Plato’s Dialogues – the problem of the communication of that thought, and therefore of its capacity to be taught, has acquired a new insistence in the work of post-Kantian thinkers. As evidence of this one could cite Fichte’s repeated efforts to formulate a definitive version of his Wissenschaftslehre, the model of the Bildungsroman that Hegel adopts for his Phenomenology of Spirit, Kierkegaard’s pseudonymous works, Nietzsche’s Thus Spoke Zarathustra, (...) and Heidegger’s uncompleted Being and Time. Certainly each of these thinkers, as well as their projects, are quite distinct from the others, but their works are also signposts. It is not a question here of reducing the puzzles and difficulties of these works to some single element, some trace of a philosophical zeitgeist. Rather, it is enough to indicate this preoccupation with the problem of the communicability of thinking in order to raise the question of the modality of such a communication. How has thinking come to be so fundamentally troubled by its own expression? That Kant’s Critical philosophy has precipitated this preoccupation ought to come as no surprise, for it was Kant, most famously in the Critique of Pure Reason, who sought to definitively set the limits of philosophical thinking. In doing so, however, Kant is unable to remain utterly silent about what he himself sets outside the bounds of meaningful thought and speech: things-in-themselves. The mere fact that this meaningless element is an essential component of Kant’s philosophical exposition is an indication of the paradoxical logic of the limit: to postulate a limit is simultaneously to set out its obverse side. In Kant’s case, then, the demarcation of what can be thought carries with it the implicit thinking of what is ruled out of bounds for thought. Beginning with Fichte, the philosophical project of Kant’s successors and inheritors is then largely determined by an effort to incorporate or at least accommodate this alien element within thinking. The initial phase of this effort is marked by a tragic motif, a conjoining of thought with the experience of loss and suffering that is characteristic of Romanticism, that culminates in the dialectic of Hegel’s Absolute Knowing. In Absolute Knowing, thought has not vanquished its limitations, it has instead discovered the resources with which it can perpetually surmount them. This first phase is followed by a reaction or response to this seeming completion and overcoming of the Kantian limitation. Now, the tragic movement of thought comes to be understood as itself limited, and necessarily so according to the logic of the limit that imposes itself upon every gesture of closure. Tragedy thereby gives way to comedy insofar as the limitation that is incorporated as an obstacle to be overcome by tragic thought is shown to be the external condition of that very thought. Finally, if the comic is the fate of the limitations of tragedy, the thought of comedy itself demands a third mode of thinking, one capable of something more than the mere reiteration of the limit between comedy and tragedy that troubles them both. This third form of expression is parody, an expression appropriate to a thinking that repeats and completes the threefold movement of tragic thought while, in this very repetition, creating a limitless domain of thoughtful expression. (shrink)

The objective of this paper is to show that Russell's paradox cannot be solved just by defining a class as what is classified, as Balzer thinks. It can be solved not by defining a class, as he does, but by rejecting the assumption on which the validity of argument is based, that is, not conceding the truth of the disjunctive premise that a class is either an instance of itself or not an instance of itself.

Deleuze’s “transcendental empiricism” and the “empirical side” of Whitehead’s metaphysics are paradoxical unless placed in the context of their unorthodox readings of empiricism. I explore this context focusing on their engagements with Hume. Both subvert presumptions of a categorical gap between external nature and internal human experience and open possibilities for a speculative empiricism that is non-reductive while still affirming experience as source for philosophical thinking. Deleuze and Whitehead follow Hume in beginning with events of sensation as primary but do (...) not presume the logic of (human) subjects and objects (of nature) as necessary structuring polarities for their interpretation. This challenges a basic distinction (between inner and outer or between self and world) that seems inherent in the ordinary concept of experience, thus earning the moniker speculative. The speculative empiricist studies how these abstractions arise from events of experience prior to their consolidation in representation. This includes a critical component: to what extent do unexamined assumptions about conceptual abstraction hinder, block, or prefigure experiential attention? This critical component has existential implications for how we attend to the affective, intuitive, and preconceptual. (shrink)

The first aim of this paper is to try and determine what St. Anselm meant in his original argument in the Proslogion. This needs to be done because not only are the writers who expound his demonstration divided in their interpretations of it, and these interpretations quite different, but, very strangely, one does not find that they mention that there is any ambiguity and that other writers construe Anselm's words differently from themselves. Since there are in fact two arguments in (...) the classical formulation of his proof, I want to try and disentangle them, decide which of them Anselm intendedand what is its connection with the demonstration in the third chapter of the Proslogion, and thus to offer an opinion on what exactly the ontological argument of St. Anselm is. Then on the basis of the clarification, I hope to show what it was that Gaunilo and St. Thomas attacked, to touch briefly on the relation of the 17th century ontological argument to Anselm's, and in general to indicate the curious round-aboutness of the historical criticism of Anselm. Anselm argued and Gaunilo and Thomas refuted something, though not, I think, precisely what Anselm meant, or, at any rate, not all that he meant. Actually it was Descartes that Thomas refuted by refuting half of Anselm. Kant refuted the other half of Anselm in an irrelevant criticism of Descartes. So that it could properly be said that Anselm's proof has been broken by philosophers who were either only partly aware of what he was maintaining, or who never had him in mind at all. Finally, because the important thing about the ontological argument, in my opinion, is not whether it is a demonstration of God's existence, but whether its refutation is a demonstration of the impossibility of God's existence, and because this question seems to arise most sharply in connexion with Anselm's position, I want to say something about that. (shrink)

Edmund Husserl’s engagement with Bertrand Russell’s paradox stands in a continuum of reciprocal reception and discussions about impossible objects in the School of Brentano. Against this broader context, we will focus on Husserl’s discussion of Russell’s paradox in his manuscript A I 35α from 1912. This highly interesting and revealing manuscript has unfortunately remained unpublished, which probably explains the scant attention it has received. I will examine Husserl’s approach in A I 35α by relating it to (...) earlier discussions of relevant topics in his manuscripts and the broader historical context of the School of Brentano and early phenomenology. (shrink)

This book is an introduction, entirely by example, to the possibilities of using computer models as tools in phosophical research in general and in philosophical logic in particular. Topics include chaos, fractals, and the semantics of paradox; epistemic dynamics; fractal images of formal systems; the evolution of generosity; real-valued game theory; and computation and undecidability in the spatialized Prisoner's Dilemma.

Relativized Metaphysical Modality (RMM: Murray and Wilson, 'Relativized metaphysical modality', Oxford Studies in Metaphysics, 2012; Murray, Perspectives on Modal Metaphysics, 2017) exploits 'two-dimensionalist' resources to metaphysical, rather than epistemological, ends: the second dimension offers perspective-dependence without contingency, diverting attacks on 'Classical' analyses of modals (in effect, analyses validating S5 and the Barcan Formulae). Here, we extend the RMM program in two directions. First, we harvest resources for RMM from Lewis's 1980 'Context--Index' (CI) framework: (a) the ban in CI on binding (...) into context-arguments (akin to Kaplan's 'monstrosity' ban) projects a bright line between perspective-dependence and contingency; and (b) CI-postulated connections among meaning, content, truth, argument-structure, context, and modality collectively generate a 'Generalized Humphrey Problem' for any non-Classical analysis (examples covered include appeals to accessibility, contingent domains, and counterpart relations). Second, we sharpen the tools of RMM-based metaphysical analysis, and extend their domain of coverage across familiar anomalies for Classical modals: we revisit earlier RMM-based bulwarks for S5 (against 'Chisholm's Paradox' for moderate flexibility of essence, and nomological necessitarianism); and we now similarly shore up the Barcan Formulae (against the apparent contingency of existence and nonexistence). (shrink)

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. (shrink)

Zeno's paradoxes of motion and the semantic paradoxes of the Liar have long been thought to have metaphorical affinities. There are, in fact, isomorphisms between variations of Zeno's paradoxes and variations of the Liar paradox in infinite-valued logic. Representing these paradoxes in dynamical systems theory reveals fractal images and provides other geometric ways of visualizing and conceptualizing the paradoxes.

In this review of Milan Ćirković’s The Great Silence: Science and Philosophy of Fermi’s Paradox, we attempt to reconstruct the logic of Fermi’s paradox as understood by the author, and we critically examine the reasoning that leads to the paradox. We show that there is no plausible solution to Fermi’s paradox that can satisfy all of Ćirković’s proposed desiderata, which in turn suggests that the author’s standards for hypothesis adjudication need to be revised.

F. Russell Sullivan analyzes the relationship between faith and reason in Kierkegaard's philosophy. Kierkegaard is widely considered to be an irrationalist. Sullivan argues that he views faith as reasonable in a distinct way that must be uncovered. In some of his pseudonymous works, Kierkegaard speaks of the movement of faith as paradoxical and absurd. There is evidence from his non-pseudonymous works that Kierkegaard does not consider faith irrational. He denigrates reason only in that he wishes to impress upon nominal Christians (...) (who look upon faith only as a body of doctrine) that more and more understanding of the tenets of faith can never yield logical certainty.The doctrines of faith can be argued pro and contra. For Kierkgaard, faith in this context is illogical, but not irrational. (shrink)

I attempt to rescue Frege's naive conception of a set according to which there is a set for every property by redefining the technical concept of degree of an open sentence. Instead of making degree a function of the number of free variables, I make it a function of free variable occurrences. What Russell proved, then, is that there is not a relation-in-extension for every relation-in-intension. In a brief paper it is not possible to discuss how redefining the function-argument correlation (...) affects Frege's system. (shrink)

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 therein. (shrink)

I present the traditional debate about the so called explanation of Russell’s paradox and propose a new way to solve the contradiction that arises in Frege’s system. I briefly examine two alternative explanatory proposals—the Predicativist explanation and the Cantorian one—presupposed by almost all the proposed solutions of Russell’s Paradox. From the discussion about these proposals a controversial conclusion emerges. Then, I examine some particular zig zag solutions and I propose a third explanation, presupposed by them, in (...) which I emphasise the role of an implicit premise in the derivation of the paradox. In conclusion, I propose a different zig zag solution obtained by the adoption of a negative free logic. (shrink)

Most of the material in this book is based upon a series of four lectures delivered at a Carnegie Summer Institute at the University of Notre Dame. McInerny states in the Preface that the purpose of the book is not to offer an "original" interpretation of the subject, but rather is "written for those who would like a swift survey of moral philosophy as seen through the eyes of Thomas Aquinas." While the purpose is to give a succinct yet faithful (...) account of St. Thomas's positions, McInerny's book does provide a rather fresh discussion of the main themes. It is not a manual-style exposition; and although the author stays close to St. Thomas's own thought, he frequently addresses some of the more recent interpretations of particular issues in Thomistic ethics. (shrink)

I present the traditional debate about the so called explanation of Russell’s paradox and propose a new way to solve the contradiction that arises in Frege’s system. I briefly examine two alternative explanatory proposals—the Predicativist explanation and the Cantorian one—presupposed by almost all the proposed solutions of Russell’s Paradox. From the discussion about these proposals a controversial conclusion emerges. Then, I examine some particular zig zag solutions and I propose a third explanation, presupposed by them, in (...) which I emphasise the role of an implicit premise in the derivation of the paradox. In conclusion, I propose a different zig zag solution obtained by the adoption of a negative free logic. (shrink)

Though the phrase 'x is true of x' is well formed grammatically, it does not express any predicate in the logical sense, because it does not satisfy the principle of reduction for statements containing 'x is true of'. recognition of this allows for solution of russell's paradox without his restrictive theory of types.

Russell's "new contradiction" about "the totality of propositions" has been connected with a number of modal paradoxes. M. Oksanen has recently shown how these modal paradoxes are resolved in the set theory NFU. Russell's paradox of the totality of propositions was left unexplained, however. We reconstruct Russell's argument and explain how it is resolved in two intensional logics that are equiconsistent with NFU. We also show how different notions of possible worlds are represented in these intensional logics.

_'These propositions may seem mild, yet, if accepted, they would absolutely revolutionize human life.'_ With these words Bertrand Russell introduces what is indeed a revolutionary book. Taking as his starting-point the irrationality of the world, he offers by contrast something 'wildly paradoxical and subversive' - a belief that reason should determine human actions. Today, besieged as we are by the numbing onslaught of twenty-first-century capitalism, Russell's defence of scepticism and independence of mind is as timely as ever. In clear, engaging (...) prose, he guides us through the key philosophical issues that affect our daily lives - freedom, happiness, emotions, ethics and beliefs - and offers no-nonsense advice. (shrink)

Throughout this paper my objective will be to establish and clarify Hume's original intentions in his discussion of causation in Book I of the Treatise. I will show that Hume's views on ontology, presented in Part IV of that book, shed light on his views on causation as presented in Part III. Further, I will argue that Hume's views on ontology account for the original motivation behind his two definitions of 2 cause. This relationship between Hume's ontology and his account (...) of causation explains something which has baffled Hume scholars for some time,- namely, why does Hume's discussion of causation in I, iii, 14 have such a paradoxical air about it? I will show that Hume's views on causation have a paradoxical air about them because they rest on an ontology of "double existence" - an ontology which Hume describes as the monstrous offspring of two principles, which are contrary to each other, which are both at once embrac'd by the mind, and which are unable mutually to destroy each other (T 215) My interpretation will centre on the following two claims: (i) When Hume wrote Section 14, Of the idea of necessary connexion, he was primarily concerned to attack the view that the origin of our idea of necessity was to be discovered in the operations of matter or bodies. Of the suggested sources from which our idea of necessity could be thought to originate this is the source which, initially, interested Hume the most. It is, therefore, of great importance that we interpret Hume's remarks in light of this fact. (ii) Hume offers the first definition of cause as an account of causation as it exists in the material world independent of our thought and reasoning.He offers the second definition as an account of causation as we find it in our perceptions. It will also be argued, in this context, that necessity constitutes "an essential part" of both of Hume's two definitions of cause. (shrink)

Russell's paradox represents either of two interrelated logical antinomies. The most commonly discussed form is a contradiction arising in the logic of sets or classes. Some classes (or sets) seem to be members of themselves, while some do not. The class of all classes is itself a class, and so it seems to be in itself. The null or empty class, however, must not be a member of itself. However, suppose that we can form a class of all classes (...) (or sets) that, like the null class, are not included in themselves. The paradox arises from asking the question of whether this class is in itself. It is if and only if it is not. The other form is a contradiction involving properties. Some properties seem to apply to themselves, while others do not. The property of being a property is itself a property, while the property of being a cat is not itself a cat. Consider the property that something has just in case it is a property (like that of being a cat ) that does not apply to itself. Does this property apply to itself? Once again, from either assumption, the opposite follows. The paradox was named after Bertrand Russell, who discovered it in 1901. (shrink)

The surviving pictorial hagiographical cycles of St Panteleimon were executed in the period between the 10th and 15th centuries. The most elaborate one is on a vita icon, consisting of sixteen scenes, at the monastery of St Catherine, Mt. Sinai and is at the centre of this research. The painter used the Passion of St Panteleimon by Symeon Metaphrastes as a main textual source for its creation. In addition, we may presume that the iconography of the images was influenced by (...) other existing pictorial cycles of the life of the saint. Also, the selection of the images, included in the saint's cycle, reflects the devotional needs and wishes of the unknown donor. (shrink)

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)

_'These propositions may seem mild, yet, if accepted, they would absolutely revolutionize human life.'_ With these words Bertrand Russell introduces what is indeed a revolutionary book. Taking as his starting-point the irrationality of the world, he offers by contrast something 'wildly paradoxical and subversive' - a belief that reason should determine human actions. Today, besieged as we are by the numbing onslaught of twenty-first-century capitalism, Russell's defence of scepticism and independence of mind is as timely as ever. In clear, engaging (...) prose, he guides us through the key philosophical issues that affect our daily lives - freedom, happiness, emotions, ethics and beliefs - and offers no-nonsense advice. (shrink)

This volume shows Bertrand Russell in transition from a neo-Kantian and neo-Hegelian philosopher to an analytic philosopher of the highest rank. During this period, his research centered on writing The Principles of Mathematics. The volume draws together previously unpublished drafts which shed light on Russell's struggle to accept Cantor's notion of continuum as well as Russell's infinite ordinal and cardinal numbers. It also includes the first version of Russell's Paradox.

Bertrand Russell offered an influential paradox of propositions in Appendix B of The Principles of Mathematics, but there is little agreement as to what to conclude from it. We suggest that Russell's paradox is best regarded as a limitative result on propositional granularity. Some propositions are, on pain of contradiction, unable to discriminate between classes with different members: whatever they predicate of one, they predicate of the other. When accepted, this remarkable fact should cast some doubt upon some (...) of the uses to which modern descendente of Russell's paradox of propositions have been put in recent literature. (shrink)