The year 1897 saw the publication of the first of the modern logical paradoxes. It was published by Cesare Burali-Forti, the Italian mathematician whose name it has come to bear. Burali-Forti's own formulation of the paradox was not altogether satisfactory, as he had confused well-ordered sets as defined by Cantor with what he himself called “perfectly ordered sets”. However, he soon realized his mistake, and published a note admitting the error and making the correction. He concluded (...) the note with the observation that his result could be established on the basis of the correct definition of well-ordered set as easily as for the “perfectly ordered sets” for which it had first been obtained. We shall reproduce his results in their corrected form. (shrink)

Russell’s paradox is purely logical in the following sense: a contradiction can be formally deduced from the proposition that there is a set of all non-self-membered sets, in pure first-order logic—the first-order logical form of this proposition is inconsistent. This explains why Russell’s paradox is portable—why versions of the paradox arise in contexts unrelated to set theory, from propositions with the same logical form as the claim that there is a set of all non-self-membered sets. Burali-Forti’s (...) paradox, like Russell’s paradox, is portable. I offer the following explanation for this fact: Burali-Forti’s paradox, like Russell’s, is purely logical. Concretely, I show that if we enrich the language \ of first-order logic with a well-foundedness quantifier W and adopt certain minimal inference rules for this quantifier, then a contradiction can be formally deduced from the proposition that there is a greatest ordinal. Moreover, a proposition with the same logical form as the claim that there is a greatest ordinal can be found at the heart of several other paradoxes that resemble Burali-Forti’s. The reductio of Burali-Forti can be repeated verbatim to establish the inconsistency of these other propositions. Hence, the portability of the Burali-Forti’s paradox is explained in the same way as the portability of Russell’s: both paradoxes involve an inconsistent logical form—Russell’s involves an inconsistent form expressible in \ and Burali-Forti’s involves an inconsistent form expressible in \. (shrink)

Philip Jourdain put this question to Frege in a letter of 28 January 1909. Frege had, indeed, next to nothing to say about ordinals, and in this respect Bob Hale has followed the master. As I hope this chapter will show, though, the topic is worth addressing. The natural abstraction principle for ordinals combines with full, impredicative second-order logic to engender a contradiction, the so-called Burali-Forti Paradox. I shall contend that the best solution involves a retreat to a (...) predicative logic. Such a retreat has implications for other neo-Fregean theories, including the cardinal arithmetic on which Hale has focused. The discussion will touch on a topic which has been at the centre of Hale’s more recent work—namely, the interpretation of plural and higher-order quantifiers. (shrink)

The paradox that appears under Burali-Forti’s name in many textbooks of set theory is a clever piece of reasoning leading to an unproblematic theorem. The theorem asserts that the ordinals do not form a set. For such a set would be—absurdly—an ordinal greater than any ordinal in the set of all ordinals. In this article, we argue that the paradox of Burali-Forti is first and foremost a problem about concept formation by abstraction, not about sets. We (...) contend, furthermore, that some hundred years after its discovery the paradox is still without any fully satisfactory resolution. A survey of the current literature reveals one key assumption of the paradox that has gone unquestioned, namely the assumption that ordinals are objects. Taking the lead from Russell’s no class theory, we interpret talk of ordinals as an efficient way of conveying higher-order logical truths. The resulting theory of ordinals is formally adequate to standard intuitions about ordinals, expresses a conception of ordinal number capable of resolving Burali-Forti’s paradox, and offers a novel contribution to the longstanding program of reducing mathematics to higher-order logic. (shrink)

After briefly reviewing the standard set-theoretic resolutions of the Burali-Forti paradox, we examine how the paradox arises in set theory formalized with plural quantifiers. A significant choice emerges between the desirable unrestricted availability of ordinals to represent well-orderings and the sensibility of attempting to refer to ‘absolutely all ordinals’ or ‘absolutely all well-orderings’. This choice is obscured by standard set theories, which rely on type distinctions which are obliterated in the setting with plurals. Zermelo's attempt ( 1930 (...) ) to secure ordinal representability of arbitrary well-orderings through relativization of quantification to set-theoretic models is reviewed and found wanting. The natural modal-structural recasting provides, it is claimed, a good repair. (shrink)

Graham Priest (1994) has argued that the following paradoxes all have the same structure: Russell’s Paradox, Burali-Forti’s Paradox, Mirimanoff’s Paradox, König’s Paradox, Berry’s Paradox, Richard’s Paradox, the Liar and Liar Chain Paradoxes, the Knower and Knower Chain Paradoxes, and the Heterological Paradox. Their common structure is given by Russell’s Schema: there is a property φ and function δ such that..

We are familiar with various set-theoretical paradoxes such as Cantor's paradox, Burali-Forti's paradox, Russell's paradox, Russell-Myhill paradox and Kaplan's paradox. In fact, there is another new possible set-theoretical paradox hiding itself in Wittgenstein’s Tractatus. From the Tractatus’s Picture theory of language we can strictly infer the two contradictory propositions simultaneously: the world and the language are equinumerous; the world and the language are not equinumerous. I call this antinomy the world-language paradox. (...) Based on a rigorous analysis of the Tractatus, with the help of the technical resources of Cantor’s naive set theory and Zermelo-Fraenkel set theory with the axiom of choice, I outline the world-language paradox and assess the unique possible solution plan, i.e., the mathematical plan utilizing ‘infinity’. I conclude that Wittgenstein cannot solve the hidden set-theoretical paradox of the Tractatus successfully unless he gives up his finitism. (shrink)

In studying the early history of mathematical logic and set theory one typically reads that Georg Cantor discovered the so-called Burali-Forti (BF) paradox sometime in 1895, and that he offered his solution to it in his famous 1899 letter to Dedekind. This account, however, leaves it something of a mystery why Cantor never discussed the paradox in his writings. Far from regarding the foundations of set theory to be shaken, he showed no apparent concern over the (...) class='Hi'>paradox and its implications whatever. Against this account, I will argue here that in fact Cantor never saw any paradox at all, but that his conception of set at that time, and already as far back as 1883, was one in which the paradoxes cannot arise. (shrink)

I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible. -/- It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit quantification, but (...) on the logical conception of set which motivates naive set theory. The accepted solution is to replace this with the iterative conception of set. -/- I show that this picture is doubly mistaken. After a close examination of the paradoxes in chapters 2--3, I argue in chapters 4 and 5 that it is possible to rescue naive set theory by restricting quantification over sets and that the resulting restrictivist set theory is expressible. In chapters 6 and 7, I argue that it is the iterative conception of set and the thesis of absolutism that should be rejected. (shrink)

The starting point of this work is the existence of historical paradoxes in the set theory. These are: Russell's paradox, applied to the set W, Cantor's, for the set U, and Burali-Forti's, of the set Omega. A systematic analysis aimed at the simplification and the refining of such paradoxes showed that: there exist at least eight contradictory expressions instead of three; another contradictory set is suggested by an extension of Burali-Forti's paradox; almost all of (...) the contradictions apply to more than one paradoxical set. (shrink)

Georg Cantor's absolute infinity, the paradoxical Burali-Forti class Ω of all ordinals, is a monstrous non-entity for which being called a "class" is an undeserved dignity. This must be the ultimate vexation for mathematical philosophers who hold on to some residual sense of realism in set theory. By careful use of Ω, we can rescue Georg Cantor's 1899 "proof" sketch of the Well-Ordering Theorem––being generous, considering his declining health. We take the contrapositive of Cantor's suggestion and add Zermelo's choice (...) function. This results in a concise and uncomplicated proof of the Well-Ordering Theorem. (shrink)

Such contradictions arise “at the limits of thought” in the following sense: we have reason to set boundaries to certain conceptual processes, which, however, turn out to actually cross those boundaries. The boundaries cannot be crossed, yet they can, for they are crossed. For example, Kant regarded noumena as beyond the limit of the conceivable, yet he made judgments about them, so he did conceive of them. For another example, Russell’s theory of types cannot be expressed, yet he does express (...) it. And so on, from Aristotle’s notion of prime matter to Derrida’s différance. The boundaries that cannot be but are crossed may concern iteration, expression, cognition, or conception. In most cases, a single argument pattern is operative, according to Priest. He calls it the Inclosure Schema [=IS]. It is a contradiction-generating mechanism that works as follows: suppose we define a set Ω, on the basis of a condition φ ); suppose that Ω exists and that it has property ψ. Next, suppose we can define a function δ such that, for any subset x of Ω that has property ψ, we have both δ ∉ x and δ ∈ Ω. As Ω is a subset of itself and it has ψ by hypothesis, a contradiction follows: both δ ∈ Ω and δ ∉ Ω. The two sides of the contradiction—or perhaps the operations by which they are established—are called Closure and Transcendence. ). For example, take Burali Forti’s paradox that is greater than all members of On, and therefore not an ordinal). Here Ω = On, and δ is the function that assigns to x the least ordinal greater than all members of x is both an ordinal—δ ∈ Ω, “Closure”—and not a member of x ). The condition φ is just the property of being an ordinal. (shrink)

The principle _determinatio est negatio_—that determination is achieved through negation—has philosophical roots extending back to Plato and Aristotle, and it later influenced early modern thinkers such as Francisco Suárez and Spinoza. This paper has two aims. The first demonstrates how the principle of negation functions as a tool for conceptual determination across various philosophical frameworks, and the second demonstrates that the principle plays a key role in the analysis and resolution of the Burali-Forti paradox within the context of (...) the naïve and axiomatic set theories. In the first section, the analysis focuses on the evolution of the principle from ancient philosophy to early modern metaphysics, examining Plato’s dialectics, Aristotle’s metaphysical distinctions, Suárez’s scholastic theories, and Spinoza’s monist metaphysics. The second section shifts to mathematics, where _determinatio est negatio_ plays a key role in resolving set-theoretical paradoxes, particularly the Burali-Forti paradox. By exploring Cantor’s solution and its reliance on the distinction between consistent and inconsistent sets, this study demonstrates how this principle is essential for avoiding self-referential inconsistencies. The contributions of Zermelo and von Neumann, who developed axiomatic frameworks to address these paradoxes, further elaborate the philosophical foundations of set theory. Ultimately, the study reveals a deep connection between metaphysical principles and the mathematical treatment of paradoxes, emphasizing the ongoing relevance of _determinatio est negatio_ in both domains. (shrink)

The starting point of this work is the existence of historical paradoxes in the set theory. These are: Russell's paradox, applied to the set W, Cantor's, for the set U, and Burali-Forti's, of the set Omega. A systematic analysis aimed at the simplification and the refining of such paradoxes showed that: (i) there exist at least eight contradictory expressions instead of three; (ii) another contradictory set is suggested by an extension of Burali-Forti's paradox; (iii) (...) almost all of the contradictions apply to more than one paradoxical set. (shrink)

We present a semi-formal foundational theory of sorts, akin to sets, named librationism because of its way of dealing with paradoxes. Its semantics is related to Herzberger’s semi inductive approach, it is negation complete and free variables (noemata) name sorts. Librationism deals with paradoxes in a novel way related to paraconsistent dialetheic approaches, but we think of it as bialethic and parasistent. Classical logical theorems are retained, and none contradicted. Novel inferential principles make recourse to theoremhood and failure of theoremhood. (...) Identity is introduced à la Leibniz-Russell, and librationism is highly non-extensional. Π 1 1 -comprehension with ordinary Bar-Induction is accounted for (to be lifted). Power sorts are generally paradoxical, and Cantor’s Theorem is blocked as a camouflaged premise is naturally discarded. (shrink)

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)

A possible world is a junky world if and only if each thing in it is a proper part. The possibility of junky worlds contradicts the principle of general fusion. Bohn (2009) argues for the possibility of junky worlds, Watson (2010) suggests that Bohn‘s arguments are flawed. This paper shows that the arguments of both authors leave much to be desired. First, relying on the classical results of Cantor, Zermelo, Fraenkel, and von Neumann, this paper proves the possibility of junky (...) worlds for certain weak set theories. Second, the paradox of Burali-Forti shows that according to the Zermelo-Fraenkel set theory ZF, junky worlds are possible. Finally, it is shown that set theories are not the only sources for designing plausible models of junky worlds: Topology (and possibly other "algebraic" mathematical theories) may be used to construct models of junky worlds. In sum, junkyness is a relatively widespread feature among possible worlds. (shrink)

L'historiographie des paradoxes ensemblistes attribue classiquement la "découverte" du paradoxe du plus grand ordinal au mathématicien italien Burali-Forti. Un examen attentif de ses démonstration et revirement révèle qu'il n'en est rien. Nous tenterons de dégager l'impact de la publication des Principles de Russell sur la constitution de cette version historiographique officielle, avant d'aborder la question de la définition des paradoxes et ce qui peut en motiver une conception restrictive.

Tento článek se zabývá dvěma aritmetickými systémy - konkrétně systémem, který představil R. Dedekind a systémem, který vytvořil G. Frege - a paradoxy, které se zde vyskytují - tedy Burali-Fortiho paradoxem (což je vůbec první fomrulace moderního paradoxu), Cantorovým paradoxem a Russellovým paradoxem. Hlavním cílem je ukázat, co mají tyto paradoxy společného a zdůvodnit, že ačkoli se tyto paradoxy vyskytují v různých systémech, mají společné znaky. Na základě studia uvedených systémů, paradoxů i různých řešení těchto paradoxů, autorka dospívá k (...) tvrzení, že zkoumané paradoxy vznikají na stejném základě, a to na základě problému nehierarchizovanosti.V dodatku tohoto článku navíc čtenář nalezne dva zajímavé historické exkurzy. První z nich předkládá v historicky autentické podobě odvození Burali-Fortiho paradoxu Druhý exkurz je věnován Russellovu paradoxu a představuje jej nejen v podobě, jak jej vyjádřil B. Russell, ale také ve formulaci G. Frega. (shrink)

This work is, in large part, a series of refutations; it is also the author's Ph.D. thesis. First to be refuted is Russell's vicious circle principle as a general remedy for the solution of the paradoxes. The author rejects the classification of paradoxes into syntactic and semantic, since in his view there are no purely syntactic paradoxes. The distinction in logic between the uninterpreted syntactical aspect of a system and the system when given a determinate interpretation is held to be (...) untenable. Tarski's distinction between object-language and meta-language and his concept of semantically closed language are considered irrelevant for the solution of the Liar paradox. The author claims that the usual versions of the Liar paradox have the same structure as the Barber paradox, viz., [S ↔ ~S]. The author solves the Liar paradox by pointing out that it does not have a proper reference. Cantor's diagonal argument for the indenumerability [[sic]] of the real numbers is labeled as unsatisfactory. Since the diagonal number is dependent upon the real numbers in the constructed list, the author claims that this makes the diagonal number to be of a different nature and status than the real numbers in the list; thus we have what the author calls the dependence fallacy. The author also refuses to accept Cantor's nested interval proof of the indenumerability [[sic]] of the real numbers. Within the proof, two infinite sequences are constructed, each of which converges to a limit. Because the proof does not give a "definite rule of convergence," the author is not satisfied that the infinite sequences converge. Also rejected is Cantor's theorem. Other paradoxes analyzed are the Berry, Richard, heterological, "Richardian", Russell, Cantor, and Burali-Forti paradoxes.--T. G. N. (shrink)

The injective version of Cantor’s theorem appears in full second-order logic as the inconsistency of the abstraction principle, Frege’s Basic Law V (BLV), an inconsistency easily shown using Russell’s paradox. This incompatibility is akin to others—most notably that of a (Dedekind) infinite universe with the Nuisance Principle (NP) discussed by neo-Fregean philosophers of mathematics. This paper uses the Burali–Forti paradox to demonstrate this incompatibility, and another closely related, without appeal to principles related to the axiom of choice—a (...) result hitherto unestablished. It discusses both the general interest of this result, its interest to neo-Fregean philosophy of mathematics, and the potential significance of the Burali–Fortian method of proof. (shrink)

A number of authors have recently weighed in on the issue of whether it is coherent to have bound variables that range over absolutely everything. Prima facie, it is difficult, and perhaps impossible, to coherently state the “relativist” position without violating it. For example, the relativist might say, or try to say, that for any quantifier used in a proposition of English, there is something outside of its range. What is the range of this quantifier? Or suppose we ask the (...) relativist if there are some things that cannot appear in the range of any bound variable. The likely response would be along these lines: “No. For each object o, it possible to include o in the range of quantifiers, but one cannot quantify over everything at once.” This sentence contains unrestricted quantifiers, or so it seems, pending some clever move from a relativist. On the other hand, in the context of set theory, the reasoning behind the Burali-Forti paradox strongly suggests that there are well-orderings strictly longer than the collection of all ordinals. And set theorists regularly do transfinite recursions and transfinite reductions along such well-orderings. The relativist simply points out that one can always define new ordinals, and thus expand the range of one’s bound variables. The purpose of this paper is to explore the iterative framework, proposed in Zermelo’s 1930 paper, “Über Grenzzahlen und Mengenbereiche” (“On boundary numbers and domains of sets”), in order to shed light on these issues, and see what is involved in resolving them. (shrink)

As it is well known, in the forties of the past century, Curry proved that in any logic S closed under Modus Ponens, uniform substitution of propositional variables and the Contraction Law, the naïve Comprehension axiom trivializes S in the sense that all propositions are derivable in S plus CA. Not less known is the fact that, ever since Curry published his proof, theses and rules weaker than W have been shown to cause the same effect as W causes. Among (...) these, the Contraction rule or the Modus Ponens axiom, for example, are to be noted. But, moreover, as Brady has proved, even the Generalized Modus Ponens axiom or the Generalized Contraction rule give rise to “Curry’s Paradox” under the same circumstances as W does. In some previous work by us, “weak relevant model structures” are defined on “weak relevant matrices” by generalizing Brady’s model structure MCL built upon Meyer’s Crystal matrix CL. We have proved that wr-ms only verify logics with the “depth relevance condition”. The aim of this paper is to show how to falsify gMPa and gRW in certain wr-ms. In particular, it will be shown that gMPa is falisfied in any wr-ms and gRW in any wr-ms verifying Routley and Meyer’s basic positive logic B+. (shrink)

Of Zeno’s book of forty paradoxes, it was the first that attracted Socrates’ attention. This is the paradox of the like and the unlike. On contemporary assessments, this paradox is largely considered to be Zeno’s weakest surviving paradox. All of these assessments, however, rely heavily on reconstructions of the paradox. It is only relative to these reconstructions that there is nothing paradoxical involved, or that there is some rather obvious mistake being made. This paper puts forward (...) and defends a novel interpretation of this paradox, according to which the concept of a unit plays a central role. There is every reason to think the paradox turns on the concept of a unit: after the presentation of the paradox the text of the Parmenides immediately turns to a discussion of units, and the concept of a unit is also central to the Greek conception of a plurality. If this interpretation is correct then the paradox that Zeno presented was the same as one discussed and solved in Frege’s Grundlagen. (shrink)

We present an order-theoretic analysis of set-theoretic paradoxes. This analysis will show that a large variety of purely set-theoretic paradoxes (including the various Russell paradoxes as well as all the familiar implementations of the paradoxes of Mirimanoff and Burali-Forti) are all instances of a single limitative phenomenon.

This study of Western philosophic systems, their types, history, relations, and projected future in the next half century, stems from Robert S. Brumbaugh’s forty-year fascination with the paradox of the many consistent overarching systems of ideas that are nevertheless mutually exclusive. Brumbaugh argues that when we isolate these systems’s patterns and look at them more abstractly, they consistently fall into four main types, and the interaction of these four types of explanation and order is a dominant theme in the (...) history of Western philosophy. In Brumbaugh’s view these four philosophic systems are not, as some critical historians and thinkers have claimed, so different that they are mutually unintelligible, forcing us to make a choice among them that is entirely arbitrary. But neither are they, as a majority of past thinkers and historians have hoped, simply parts of some single "right" or "orthodox" scheme. Their mutual understanding requires a method of transformation that interprets one to another without destroying their diversity. The history of Western philosophy from the fifth century A.D. to the present shows a pattern of alternating revolutions in systematic method and direction of explanation. Brumbaugh feels that the pattern is continuing in a change toward a revised Platonism, just beginning with the twenty-first century. He anticipates that it will be a Platonism of a new texture, one that has matured and learned a great deal in the course of the adventures of its ideas through space and time. (shrink)

Reasonning in naive set theory (with unlimited comprehension), we derive a paradox (a formal contradiction) which can be seen as a variant of the Burali-Forti paradox.

Jean Baudrillard, the misfit. Jean Baudrillard, who told us that the Gulf Warnever happened, who drew our attention to the perils of a civilization thatchoses to lead a virtual existence in an arena of images and simulacra - this isthe Baudrillard we are mostly familiar with. But Jean Baudrillard, thechampion of appearances? Baudrillard, more-feminist-than-the-feminists?This Baudrillard remains buried in the stacks of a prolific career spanningover forty years and involving some of the most radical systematicdeconstructions of Western culture, society and politics. (...) Baudrillard hasprimarily been heralded as an enemy of the world of images, the surfacesuperficiality of consumer culture; it stands as no surprise, then, that in mosttheoretical assessments of his work there is little mention of Seduction , a text aimed at restoring a great amount of value to the surface ofthings.1While apostles of Baudrillard such as Norman K. Denzin tend tooffer brief and, in this writer’s opinion, erroneous summaries of seduction’s‘potential of unmasking the order of appearances’ , Seduction hasyet to be understood as a praise for the world of appearances, play, andreversibility, as encouragement for the resistance of the orders of law certainty, and production. 2 In the following pages, I hope to introduce readers to a fascinating but often overlooked text of Baudrillard’s and, in doing so, to demonstrate that Baudrillard’s text offers a unique and yet unexplored insight into the dichotomous and contradictory nature of cinema - this medium which as an instrument of popular culture acts according to the modern logic of production, but as a form owes more to the transformative and playful semiology of the pre-modern. (shrink)

Despite the fact that the sociological notion ‘individualization’ contains the most heterogeneous phenomena, the article develops an interpretation of the fate of individualization in Western capitalism today. After having differentiated three different meanings of that notion with the help of Georg Simmel, the position is defended that the claims to individual self-realization, which have rapidly multiplied in the Western societies of thirty or forty years ago, have become so much a feature of the institutionalized expectations inherent in social reproduction that (...) the particular goals of such claims are lost and they are transmuted into a support of the system’s legitimacy. The result of this paradoxical reversal, where the processes which once promised an increase of qualitative freedom are henceforth altered into an ideology of de-institutionalization, is the emergence in individuals of a number of symptoms of inner emptiness, of feeling oneself to be superfluous, and of absence of purpose. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Julia Annas ACTION AND CHARACTER IN DOSTOYEVSKY'S NOTES FROM UNDERGROUND Notes from Underground was written with a specific purpose in mind: to answer Chernyshevsky's novel What Is to Be Done?1 And many features of Dostoyevsky's work can only be understood when we bear in mind its specifically Russian setting. The narrator is a romantic idealist of the forties transformed into something rather different by 1864, and no doubt we (...) lose much if we do not bear in mind that Dostoyevsky is looking back across the gulf of imprisonment and suffering at his own idealistic youth.2 But the intense and radically peculiar nature of Dostoyevsky's writing takes us to a level of the work which is accessible to those without knowledge of the local conditions of the work's production. As Mochulsky says, "the author steadily emerges beyond the confines of the Russian intellectual... the underground man's paradoxes are not the whims of some half-mad eccentric, but a new revelation of man about man." The book is "the philosophical preface to the cycle of the great novels" (p. 245). Even though Dostoyevsky's passionate and extreme temperament made him quite incapable of constructing a piece of precise philosophical argument, there is much of genuine philosophical interest in part I. It is not just a particular moral and political theory, like Chernyshevsky's, which is to be discredited, but something deeper, the presuppositions of a whole type of moral theory. In this article I shall examine the implications of what Dostoyevsky says for the philosophy of action and thence for ethics. I shall argue that he challenges a very basic model of human action, which is both intuitively plausible and basic to many moral theories. I shall also argue that as the work stands, there is a lack of continuity between parts I and II on the philosophical as well as on the literary level. In concentrating on the consequences for moral theory, I shall be ignoring the social and political aspects of the work. It may well be urged that such a division of the moral from the political is unrealistic in treating 257 258Philosophy and Literature a Russian writer. In defense I can only say that this narrowing of focus brings out in a sharper and more tractable way the philosophical issue which is my main concern. I Tell me, who was it who first declared, proclaiming it to the whole world, that a man does evil only because he does not know his real interests, and if he is enlightened and has his eyes opened to his own best and normal interests, man will cease to do evil and at once become virtuous and noble, because when he is enlightened and understands what will really benefit him he will see his own best interest in virtue, and since it is well known that no man can knowingly act against his best interests, consequently he will inevitably, so to speak, begin to do good. Oh, what a baby! Oh, what a pure innocent child! (part I section 7; all quotations are from the translation by Jessie Coulson [London: Penguin, 1972]). What exactly is the target here of the Underground Man?3 Every moral theory presupposes some theory of human action, although this may not be explicit; since moral philosophy is concerned with human actions, it must presuppose some account of what it is for a human action to be performed. One very influential tradition thinks of the paradigm of action as essentially aimed at some good: "Every art and every inquiry, and similarly every action and pursuit, is thought to aim at some good" is the opening sentence of Aristotle's Ethics.4 What is it for every action to aim at some good? We have the assumption here that every action is purposive and rational; purposive in that there is some goal which the agent sees as a good and rational in that performing the action is believed by the agent to be an appropriate means or way of bringing about the desired goal. This model of action is developed very fully in Aristotle, but it is not conceptually linked to... (shrink)

Hempel's paradox of the ravens has to do with the question of what constitutes confirmation from a logical point of view; Wason 's selection task has been used extensively to investigate how people go about attempting to confirm or disconfirm conditional claims. This paper presents an argument that the paradox is resolved, and that people's typical performance in the selection task can be explained, by consideration of what constitutes an effective strategy for seeking evidence of the tenability of (...) universal or conditional claims in everyday life. (shrink)

The aim of this paper is to distinguish between, and examine, three issues surrounding Humphreys's paradox and interpretation of conditional propensities. The first issue involves the controversy over the interpretation of inverse conditional propensities — conditional propensities in which the conditioned event occurs before the conditioning event. The second issue is the consistency of the dispositional nature of the propensity interpretation and the inversion theorems of the probability calculus, where an inversion theorem is any theorem of probability that makes (...) explicit (or implicit) appeal to a conditional probability and its corresponding inverse conditional probability. The third issue concerns the relationship between the notion of stochastic independence which is supported by the propensity interpretation, and various notions of causal independence. In examining each of these issues, it is argued that the dispositional character of the propensity interpretation provides a consistent and useful interpretation of the probability calculus. (shrink)

The purpose of this paper is to defend and justify the hypothesis that Perelman’s New Rhetoric can enable the French school of Discourse Analysis to readjust its theoretical positions concerning the ethics of discourse. While it is no longer necessary, in the wake of linguists such as Benveniste and Kerbrat-Orecchioni, to point out the founding role of the inscription of subjectivity in language, it is, paradoxically, still necessary to justify the legitimacy of choosing the axiological dimension of discourse and its (...) ethical issues as a scientific object. Indeed, very few linguists view Perelman’s New Rhetoric as a logic and a “pragmatics” of values; most of them prefer to view it as a technical reservoir of types of arguments (Cf. concerning the critical enumeration and classification of references to the NR, raised in approximately forty linguistic works, Koren 2002: 197–228). So far, the notions of “guarantee” and “commitment” are integrated in pragmatic linguistic theories; but these notions have mostly to do with a “commitment” vis-à-vis a referential truth. Truth is still considered as the ultimate value, as the normative reference to every questioning on discursive rectitude. We are thus left with an epistemological lacuna, namely the integration of the responsibility for value judgments in linguistic theories, that could be partially answered for by the New Rhetoric. An editorial from Le Monde will be analyzed to illustrate this point of view. (shrink)

Moore’s paradox is the fact that assertions or beliefs such asBangkok is the capital of Thailand but I do not believe that Bangkok is the capital of Thailand or Bangkok is the capital of Thailand but I believe that Bangkok is not the capital of Thailand are ‘absurd’ yet possibly true. The current orthodoxy is that an explanation of the absurdity should first start with belief, on the assumption that once the absurdity in belief has been explained then this (...) will translate into an explanation of the absurdity in assertion. This assumption gives explanatory priority to belief over assertion. I show that the translation involved is much trickier than might at first appear. It is simplistic to think that Moorean absurdity in assertion is always a subsidiary product of the absurdity in belief, even when the absurdity is conceived as irrationality. Instead we should aim for explanations of Moorean absurdity in assertion and in belief that are independent even if related, while bearing in mind that some forms of irrationality may be forms of absurdity even if not conversely. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Contemporary IlluminationsReading Donne's "A Nocturnall upon S. Lucies Day through Three Twenty-First-Century PoemsTheresa M. DipasqualeIn his contribution to the 2017 volume John Donne and Contemporary Poetry, edited by Judith Scherer Herz, Jonathan F. S. Post explores "a nearly endless landscape of comparisons and contrasts" that unfolds between Stephen Edgar's 2008 poem "Nocturnal" and Donne's "A nocturnall upon S. Lucies day, Being the shortest day."1 Post's essay illuminates what Calvin (...) Bedient, in the same volume, calls the "great glacier-gloom" of Donne's "Nocturnall," its devastated "solemnity."2 In doing so, Post renders largely moot many questions that have preoccupied critics of Donne's poem: whether or how this poem reflects Donne's experience; whether the woman lamented by the speaker is a fiction or a historical person lamented by the poet; and if the latter, whether the poem mourns the 1617 death of John Donne's wife, Anne More Donne; the 1627 death of Donne's patroness Lucy, Countess of Bedford; or the Countess' near-fatal illness in 1612–13.3 These biographical and historical questions are not without value, but they draw the critic's attention away from more compelling questions regarding the "I" of the poem—a persona who claims not to be a person at all, but an inscription, a grave, "A quintessence" derived or "expresse[d]/... even from nothingnesse."4In this article, I widen and intensify the pool of light cast on Donne's "Nocturnall" by Post's presentist and intertextual analysis of Edgar's poem, examining three of the many other twenty-first-century poems that tap into Donne's poem, allude to it, quote it, adopt its structure, or respond to the anguish it expresses.5 Each of the three I discuss is [End Page 1] luminous in its own right but also a potent critical response to Donne's five-stanza poem. Each teaches something different about Donne's lyric. The poets whose work I consider—Liz Lochhead, Jay Wright, and Meena Alexander—all address twenty-first-century concerns; they grapple with questions and sorrows beyond the scope of Donne's conscious imagining yet latent in his poem. Each picks up where critics leave off when they "assume," as Alison R. Rieke notes, "that the speaker... is a husband or lover, possibly Donne, who experiences grief upon his wife's or mistress' death."6 Each takes up the challenge that Donne's persona issues when it denies that it is either "a man" (30) or any other living thing.In the first stanza of "A Nocturnall upon S. Lucies Day," this anti-persona observes that "all" other things around it are "Dead and enterr'd" and "yet" that "all these seeme to laugh, / Compar'd with mee, who am their Epitaph" (8–9). If it is an incised text rather than a human being, the poem's "mee" can no more speak than laugh; it is as silent as the grave it marks or as the dead flesh interred there. Indeed, it goes on to claim that it is "every dead thing" and that love's alchemical "art" has "expresse[d] / A quintessence even from" this mass of nonliving objects, this "nothingnesse" (12, 14–15). Struggling to define its anti-essential essence, it declares itself a mass burial site: "I, by loves limbecke, am the grave / Of all, that's nothing" (21–22). An epitaph, dead things, nothingness, a grave: all these are silent. And yet, in Donne's poem, they strenuously assert their nonbeing; they pulse with a paradoxically audible sense of self. After "Compar'd with mee" in the final line of the opening stanza, the reader encounters sixteen additional instances of the first-person singular in the poem's forty-five lines: "my" appears once, "mee" five times, and "I" eleven times. And the "I" issues a directive to readers: commanding, in the opening line of stanza 2, "Study me then, you who shall lovers bee" (10). But those who obey this order, making themselves students of the poem's inscribed nothingness, find themselves dismissed in the poem's final stanza. Having insisted that its "Sunne" will never "renew... (shrink)

My aim in this paper is to suggest a new outlook concerning the nature of Zeno’s paradoxes. The attention is directed towards the three famous paradoxes known as “Dichotomy,” “Achilles and the Tortoise,” and “The Arrow.” An analysis of the paradigmatic proposals for a solution shows that an adequate solution has not yet been reached. An answer is provided instead to the question “How Zeno’s paradoxes emerge in their quality of aporiae?,” that is to say in their quality of impasses, (...) of problem situations without an exit, what is the original meaning of the Greek word “aporia.” It is my claim that this is the correct rational approach for solving these conceptual puzzles. In other words, I am not proposing formal solutions by criticizing and/or altering their premises assuming the continuous or discrete nature of space and time, but I try to draw the philosophical attention to the way we possess the phenomenon of motion as a result of the perception of space-time in human experience. (shrink)

There are three questions associated with Simpson’s Paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP?, and (iii) What should be done about SP? By developing a logic-based account of SP, it is argued that (i) and (ii) must be divorced from (iii). This account shows that (i) and (ii) have nothing to do with causality, which plays a role only in addressing (iii). A counterexample is also presented against the causal account. Finally, the causal and (...) logic-based approaches are compared by means of an experiment to show that SP is not basically causal. (shrink)

G. E. Moore observed that to assert, 'I went to the pictures last Tuesday but I don't believe that I did' would be 'absurd'. Over half a century later, such sayings continue to perplex philosophers. In the definitive treatment of the famous paradox, Green and Williams explain its history and relevance and present new essays by leading thinkers in the area.

According to Emma Borg, minimalism is (roughly) the view that natural language sentences have truth conditions, and that these truth conditions are fully determined by syntactic structure and lexical content. A principal motivation for her brand of minimalism is that it coheres well with the popular view that semantic competence is underpinned by the cognition of a minimal semantic theory. In this paper, I argue that the liar paradox presents a serious problem for this principal motivation. Two lines of (...) response to the problem are discussed, and difficulties facing those responses are raised. I close by issuing a challenge: to construe the principal motivation for BM in such a way so as to avoid the problem of paradox. (shrink)

G. E. Moore famously observed that to assert ‘I went to the pictures last Tuesday but I do not believe that I did’ would be ‘absurd’. Moore calls it a ‘paradox’ that this absurdity persists despite the fact that what I say about myself might be true. Krista Lawlor and John Perry have proposed an explanation of the absurdity that confines itself to semantic notions while eschewing pragmatic ones. We argue that this explanation faces four objections. We give a (...) better explanation of the absurdity both in assertion and in belief that avoids our four objections. (shrink)

G.E. Moore noticed the oddity of statements like: “It's raining, but I don't believe it.” This oddity is often seen as analogous to the oddity of believing akratically, or believing what one believes one should not believe, and has been appealed to in denying the possibility of akratic belief. I describe a Belief Akratic's Paradox, analogous to Moore's paradox and centered on sentences such as: “I believe it's raining, but I shouldn't believe it.” I then defend the possibility (...) of akratic belief against appeals to this analogy, arguing both that akratic belief does not require belief-akratic-paradoxical belief, and that the latter is importantly different from Moorean belief. I conclude by considering the implications of these arguments for an understanding of both Moorean and akratic belief. (shrink)