Paradoxes and their Resolutions is a ‘thematic compilation’ by Avi Sion. It collects in one volume the essays that he has written in the past (over a period of some 27 years) on this subject. It comprises expositions and resolutions of many (though not all) ancient and modern paradoxes, including: the Protagoras-Euathlus paradox (Athens, 5th Cent. BCE), the Liar paradox and the Sorites paradox (both attributed to Eubulides of Miletus, 4th Cent. BCE), Russell’s paradox (UK, 1901) and its derivatives the (...) Barber paradox and the Master Catalogue paradox (also by Russell), Grelling’s paradox (Germany, 1908), Hempel's paradox of confirmation (USA, 1940s), and Goodman’s paradox of prediction (USA, 1955). This volume also presents and comments on some of the antinomic discourse found in some Buddhist texts (namely, in Nagarjuna, India, 2nd Cent. CE; and in the Diamond Sutra, date unknown, but probably in an early century CE). (shrink)

In this article the standard philosophical method involving intuition-driven conceptual analysis is challenged in a new way. This orthodox approach to philosophy takes analysanda to be the specifications of the content of concepts in the form of sets of necessary and sufficient conditions. Here it is argued that there is no adequate account of what necessary and sufficient conditions are. So, the targets of applications of the standard philosophical method so understood are not sufficiently well understood for this method to (...) be dependable. (shrink)

The preface paradox can be motivated by appealing to a plausible inference from an author’s reasonable assertion that her book is bound to contain errors to the author’s rational belief that her book contains errors. By evaluating and undermining the validity of this inference, I offer a resolution of the paradox. Discussions of the preface paradox have surprisingly failed to note that expressions of fallibility made in prefaces typically employ terms such as surely, undoubtedly, and bound to be. After considering (...) what these terms mean, I show that the motivating inference is invalid. Moreover, I argue that a closer consideration of our expressions of fallibility suggest that epistemically responsible authors would not be rational to believe that their books contain errors. I conclude by considering alternative expressions of fallibility that employ terms such as possible and probable, and discuss the role that expressions of fallibility play in conversation. (shrink)

The principle of charity is used in philosophy of language and argumentation theory as an important principle of interpretation which credits speakers with “the best” plausible interpretation of their discourse. I contend that the argumentation account, while broadly advocated, misses the basic point of a dialectical conception which approaches argumentation as discussion between two parties who disagree over the issue discussed. Therefore, paradoxically, an analyst who is charitable to one discussion party easily becomes uncharitable to the other. To overcome this (...) paradox, I suggest to significantly limit the application of the principle of charity depending on contextual factors. (shrink)

We take seriously the idea that paradoxes come in quantifiable degree by offering an exact measure of paradox. We consider three factors relevant to the degree of paradox, which are a function of the degree of belief in each of the individual propositions in the paradox set and the degree of belief in the set as a whole. We illustrate the proposal with a particular measure, and conclude the discussion with some critical remarks.

Epistemic contextualism was originally motivated and supported by the response it provides to skeptical paradox. Although there has been much discussion of the contextualist response to skeptical paradox, not much attention has been paid to the argument from skepticism for contextualism. Contextualists argue that contextualism accounts for the plausibility and apparent inconsistency of a set of paradoxical claims better than any classical invariantist theory. In this paper I focus on and carefully examine the argument from skepticism for contextualism. I argue (...) not only that the prima facie advantage of contextualism is specious, but also that contextualism is in fact at a competitive disadvantage with respect to two classical invariantist views. I also argue that contextualism takes an arbitrary and unsatisfying strategy in its response to skepticism. That contextualism is alone in taking this arbitrary strategy marks a second competitive disadvantage for it. In addition, I argue that the contextualist response to skeptical paradox regenerates a skeptical paradox which contextualism is powerless to solve. Consequently, the argument from skepticism for contextualism fails. Furthermore, this feature of the contextualist response to skeptical paradox completely undermines the motivation and support for contextualism deriving from its treatment of skeptical paradox. I conclude that the argument from skepticism for contextualism fails, and that the contextualist response to skeptical paradox fails to motivate contextualism, pending the success of another argument for the contextualist thesis. (shrink)

Assertions of statements such as ‘it’s raining, but I don’t believe it’ are standard examples of what is known as Moore’s paradox. Here I consider moral equivalents of such statements, statements wherein individuals affirm moral judgments while also expressing motivational indifference to those judgments (such as ‘hurting animals for fun is wrong, but I don’t care’). I argue for four main conclusions concerning such statements: 1. Such statements are genuinely paradoxical, even if not contradictory. 2. This paradoxicality can be traced (...) to a form of epistemic self-defeat that also explains the paradoxicality of ordinary Moore-paradoxical statements. 3. Although a simple form of internalism about moral judgment and motivation can explain the paradoxicality of these moral equivalents, a more plausible explanation can be provided that does not rely on this simple form of internalism. 4. The paradoxicality of such statements suggests a more credible understanding of the thesis that those who are not motivated by their moral judgments are irrational. (shrink)

According to Hempel's paradox, evidence (E) that an object is a nonblack nonraven confirms the hypothesis (H) that every raven is black. According to the standard Bayesian solution, E does confirm H but only to a minute degree. This solution relies on the almost never explicitly defended assumption that the probability of H should not be affected by evidence that an object is nonblack. I argue that this assumption is implausible, and I propose a way out for Bayesians. Introduction Hempel's (...) paradox, the standard Bayesian solution, and the disputed assumption Attempts to defend the disputed assumption Attempts to refute the disputed assumption A way out for Bayesians Conclusion. (shrink)

Cicero's De fato: On Hellenistic Conditionals and Free Will. The Serbo-Croatian translation of Cicero's De fato, with comments and detailed analysis of some arguments and problems of the text. -/- (s/h): Tekst Ciceronovog spisa "de fato", prevod, komentari i u dodacima, detaljnija analiza pojedinih argumenata i problema sadržanih u tekstu.

In this paper I show that one of the most fruitful ways of employing paradoxes has been as a philosophical method that forces us to reconsider basic assumptions. After a brief discussion of recent understandings of the notion of paradoxes, I show that Zeno of Elea was the inventor of paradoxes in this sense, against the background of Heraclitus’ and Parmenides’ way of argumentation: in contrast to Heraclitus, Zeno’s paradoxes do not ask us to embrace a paradoxical reality; and in (...) contrast to Parmenides, Zeno shows common assumptions to be internally problematic, not just in light of Eleatic positions. (shrink)

Der Sammelband umfasst Aufsätze zu den Grundfragen, Anwendungen und Grenzen des Unterrichts des Argumentierens, in allen Fächern und mit Fokus auf die Fächer Philosophie und Ethik. Dabei werden Fragen wie diese behandelt: Welchen Zielen dient das Argumentieren und welche verfolgt der Unterricht des Argumentierens? In welchem Verhältnis stehen diese zu anderen Zielen des Unterrichts? Welche Kenntnisse, Fähigkeiten und Tugenden des Argumentierens sollen eingeübt werden und wie? Die vorgeschlagenen Antworten sind nicht nur für Personen aus der Fachdidaktik, sondern auch aus der (...) Philosophie und der Schullehrpraxis aller Fächer interessant. Der Band trägt damit auch zur stärkeren Etablierung des Felds der Argumentationsdidaktik bei. (shrink)

Kognitive Dissonanzen und Inkonsistenzen gehören zu den zentralen Charakteristika philosophischer Probleme. Gleichzeitig wird die Philosophie zurecht dafür gepriesen, dass sie wichtige Kompetenzen und Tugenden fördert – etwa begriffliche Klarheit, treffende Problemanalyse, gute Argumentation, Kritikfähigkeit, Offenheit und konstruktives Diskutieren. Eine wichtiges Anwendungsgebiet dieser Kompetenzen und Tugenden besteht ihrerseits darin, Auswege aus kognitiven Dissonanzen finden und argumentativ begründen zu können. Inkonsistenzen sind demnach eine wichtige Gelenkstelle zwischen den Themen und Fragen der Philosophie und den zentralen Kompetenzen und Tugenden, die im Philosophieren ausgeübt (...) und geschult werden. So zumindest die Arbeitshypothese, die in diesem Beitrag verfolgt werden soll, und die zum Teil und in unterschiedlichen Hinsichten an vorliegende Ansätze anknüpft. (shrink)

The liar paradox is still an open philosophical problem. Most contemporary answers to the paradox target the logical principles underlying the reasoning from the liar sentence to the paradoxical conclusion that the liar sentence is both true and false. In contrast to these answers, Buddhist epistemology offers resources to devise a distinctively epistemological approach to the liar paradox. In this paper, I mobilise these resources and argue that the liar sentence is what Buddhist epistemologists call a contradiction with one’s own (...) words. I situate my argument in the works of Dignāga and Dharmakīrti and show how Buddhist epistemology answers the paradox. (shrink)

My thesis situates itself within the field of the Philosophy of Worldviews. Specifically, it aims to address the normative question of what the task should be of such a philosophy when faced with the problem of conflicting beliefs between religious worldviews. To answer this question, I turn to the procedure of aporetical analysis, in short, aporetics. Firstly, aporetics offers a distinct method of consistency restoration within inconsistent sets on the basis of thesis rejection and thesis modification. Secondly, aporetics leads to (...) an understanding of the availability of aporetic exits on the basis of epistemic criteria. On the one hand, this leads us to opt for an orientational monism/pluralism, which steers the middle course between the epistemic stances of exclusivism and pluralism. On the other hand, it allows us to identify epistemic criteria for worldview acquisition on the basis of three distinct superclasses. These superclasses can be derived from Jürgen Habermas' validity claims, and applied to the self-understanding of contemporary theories of religion. (shrink)

The Surprise Exam Paradox continues to perplex and torment despite the many solutions that have been offered. This paper proposes to end the intrigue once and for all by refuting one of the central pillars of the Surprise Exam Paradox, the 'No Friday Argument,' which concludes that an exam given on the last day of the testing period cannot be a surprise. This refutation consists of three arguments, all of which are borrowed from the literature: the 'Unprojectible Announcement Argument,' the (...) 'Wright & Sudbury Argument,' and the 'Epistemic Blindspot Argument.' The reason that the Surprise Exam Paradox has persisted this long is not because any of these arguments is problematic. On the contrary, each of them is correct. The reason that it has persisted so long is because each argument is only part of the solution. The correct solution requires all three of them to be combined together. Once they are, we may see exactly why the No Friday Argument fails and therefore why we have a solution to the Surprise Exam Paradox that should stick. (shrink)

In this paper we argue that our conception of and intuitions about paradoxes are themselves paradoxical. Specifically, we argue that our commitment to the existence and nature of paradoxes is inconsistent with a norm of rationality—which is a paradox.

In his Lectures on the History of Philosophy, Hegel develops a subtle analysis of Megarian paradoxes: the Liar, the Veiled Man and the Sorites. In this paper, we focus on Hegel's interpretation of...

We seek means of distinguishing logical knowledge from other kinds of knowledge, especially mathematics. The attempt is restricted to classical two-valued logic and assumes that the basic notion in logic is the proposition. First, we explain the distinction between the parts and the moments of a whole, and theories of ?sortal terms?, two theories that will feature prominently. Second, we propose that logic comprises four ?momental sectors?: the propositional and the functional calculi, the calculus of asserted propositions, and rules for (...) (in)valid deduction, inference or substitution. Third, we elaborate on two neglected features of logic: the various modes of negating some part(s) of a proposition R, not only its ?external? negation not-R; and the assertion of R in the pair of propositions ?it is (un)true that R? belonging to the neglected logic of asserted propositions, which is usually left unstated. We also address the overlooked task of testing the asserted truth-value of R. Fourth, we locate logic among other foundational studies: set theory and other theories of collections, metamathematics, axiomatisation, definitions, model theory, and abstract and operator algebras. Fifth, we test this characterisation in two important contexts: the formulation of some logical paradoxes, especially the propositional ones; and indirect proof-methods, especially that by contradiction. The outcomes differ for asserted propositions from those for unasserted ones. Finally, we reflect upon self-referring self-reference, and on the relationships between logical and mathematical knowledge. A subject index is appended. (shrink)

In philosophy and political theory, the term paradox is often used synonymously with antinomy, contradiction and aporia. This article clarifies the meaning of these terms through tracing their respective etymology. We see that antinomy denotes a deep-seated conceptual opposition, whereas contradiction and aporia represent alternative responses to antinomy. The former presents the antinomy as potentially resolvable at some future time, and the latter sees the antinomy instead as a constitutive impasse. By way of contrast, para doxa originally referred to a (...) statement that is ‘contrary to received opinion’, but this idea has generally been subsumed – both in philosophy and more common place understandings – under the notion of aporia. This conceptual recovery enables a better understanding of key traditions in social and political theory, notably post-structuralism and Habermasian critical theory, which can be demarcated through their respective responses to the emergence of ‘paradoxes’. However, the article also demonstrates the material significance of these philosophical categories through their application to contemporary democratic politics. I analyse the constitutive tension between liberalism and democracy as well as the emergence of populism and show how these conceptual tools provide new insights for understanding these most pressing political developments of our time. (shrink)

According to a standard view, paradoxes are arguments with plausible premises that entail an implausible conclusion. This is false. In many paradoxes the premises are not plausibleprecisely becausethey entail an implausible conclusion. Obvious responses to this problem—including that the premises are individually plausible and that they are plausible setting aside the fact that they entail an implausible conclusion—are shown to be inadequate. A very different view of paradox is then introduced. This is a functionalist view according to which paradoxes are (...) the kinds of things that puzzle people in characteristic ways. It is claimed that this view, too, fails and for the very same reason. The result is a new puzzle about the nature of paradoxes. (shrink)

In Paradox in Christian Theology I argued that the Christian doctrines of the Trinity and the Incarnation are paradoxical—that is, they appear to involve implicit contradictions—yet Christians can still be rational in affirming and believing those doctrines. Dale Tuggy has characterized my theory of theological paradox as a form of “positive mysterianism” and argues that the theory “faces steep epistemic problems, and is at best a temporarily reasonable but ultimately unsustainable stance.” After summarizing my proposed model for the rational affirmation (...) of theological paradox and considering whether my proposal is indeed a form of “positive mysterianism” as Tuggy defines the term, I address the two main criticisms raised in Tuggy’s paper: first, that the doctrine of divine incomprehensibility cannot bear the weight required by my defense of paradox; and second, that my proposed model is afflicted with epistemic instability. I conclude that Tuggy has failed to show that a mysterian stance with respect to paradoxical Christian doctrines is in principle unreasonable, unnatural, or unsustainable. (shrink)

Assertions of statements such as 'it's raining, but I don't believe it' are standard examples of what is known as Moore's paradox. Here I consider moral equivalents of such statements, statements wherein individuals affirm moral judgments while also expressing motivational indifference to those judgments. I argue for four main conclusions concerning such statements: 1. Such statements are genuinely paradoxical, even if not contradictory. 2. This paradoxicality can be traced to a form of epistemic self-defeat that also explains the paradoxicality of (...) ordinary Moore-paradoxical statements. 3. Although a simple form of internalism about moral judgment and motivation can explain the paradoxicality of these moral equivalents, a more plausible explanation can be provided that does not rely on this simple form of internalism. 4. The paradoxicality of such statements suggests a more credible understanding of the thesis that those who are not motivated by their moral judgments are irrational. (shrink)

‘A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science’.How many paradoxes are there? By 1920, Bertrand Russell's star student had concluded that there are few or zero paradoxes in philosophy. Most philosophical propositions ‘are not false but nonsensical’.

The concept of hypodox is dual to the concept of paradox. Whereas a paradox is incompatibly overdetermined, a hypodox is underdetermined. Indeed, many particular paradoxes have dual hypodoxes. So, naively the dual of Russell’s Paradox is whether the set of all sets that are members of themselves is self-membered. The dual of the Liar Paradox is the Truth-teller, and a hypodoxical dual of the Heterological paradox is whether ‘autological’ is autological. I provide some analysis of the duality and I search (...) for modal hypodoxes as duals to known paradoxes. I also try to continue this search further by mapping the relations between some paradoxes and hypodoxes in duality squares. This investigation increases the known extension of the concept of hypodox, and the duality relation between paradoxes and hypodoxes assists in finding some of these. (shrink)

The Russellian argument against the possibility of absolutely unrestricted quantification can be answered by the partisan of that quantification in an apparently easy way, namely, arguing that the objects used in the argument do not exist because they are defined in a viciously circular fashion. We show that taking this contention along as a premise and relying on an extremely intuitive Principle of Determinacy, it is possible to devise a reductio of the possibility of absolutely unrestricted quantification. Therefore, there are (...) intuitive reasons to believe that the counter-argument fails to support the possibility of absolutely unrestricted quantification. (shrink)

This article focuses on the construction of two types of non-logical paradoxes in news discourse: 1) inconsistencies of positions and acts; 2) conflicts between reality and expectations or common sense. I will argue that these paradoxes are constructed by various discursive devices and will demonstrate the key role played by conventional and conversational implicatures in this regard. The discussion will focus on 23 items covering disputes between ultra-Orthodox and secular Jews, broadcast on mainstream Israeli television news in 2009. I will (...) show that the journalists consistently attribute paradoxicality to Haredim, and that this corresponds with the common public bitterness towards them because they enjoy financial support from the government, while sharing little of the economic and security burden. Moreover, I will argue that the paradoxical representations of Haredim rely on the secular ‘we’ group view and serve to base its common sense and norms. (shrink)

Moore′s paradox came of age when John N. Williams gave us a simple paradoxical argument according to which the Moorean believer must hold false belief while believing contingent propositions. Simplicity was key; it was groundbreaking for the topic. On Williams′s account, given only the notions of inconsistency and self‐refutation, the thesis that belief distributes over conjunction, and a tiny bit of classical logic, we can derive a paradox from the Moorean propositional schemata. But, as argued here, it′s easy to overestimate (...) the significance of his argument to a proper understanding of the problem. His fundamental claim can be established in a way that shows how the paradox arises for any propositional attitude that distributes over conjunction, which gives us the opportunity to reconsider the problem we have been calling “Moore′s paradox”, and to conclude that all of the available analyses of the problem are, at best, incomplete. On this new approach, we lose a little formal simplicity vis‐à‐vis Williams′s approach, but make conceptual economy, as we gain a farther‐reaching problem than the one we have known. (shrink)