The assertion that an experiment by Afshar et al. demonstrates violation of Bohr’s Principle of Complementarity is based on the faulty assumption that which-way information in a double-slit interference experiment can be retroactively determined from a future measurement.

Epiphenomenalist dualists hold that certain physical states give rise to non-physical conscious experiences, but that these non-physical experiences are themselves causally inefficacious. Among the most pressing challenges facing epiphenomenalists is the so-called “paradox of phenomenal judgment”, which challenges epiphenomenalism’s ability to account for our knowledge of our own conscious experiences. According to this objection, we lack knowledge of the very thing that epiphenomenalists take physicalists to be unable to explain. By developing an epiphenomenalist theory of subjects and mental states, (...) this paper argues that there is nothing paradoxical or problematic about the epiphenomenalist’s understanding of phenomenal judgments or phenomenal self-knowledge. The appearance of paradox emerges from inconsistently combining (epiphenomenalist) dualism about qualia with a physicalistic conception of subjects of experience. The lesson we should take from this is not that there is anything wrong with epiphenomenalism, but that epiphenomenalist dualists should be “dualists all the way down”—embracing a picture of mind that gives phenomenology a central place, in its understanding of both subjects and their knowledge of their own minds. Epiphenomenalist-friendly accounts of reference and memory are also developed, showing that neither of these issues creates a paradox for the epiphenomenalist. (shrink)

To resolve the lottery paradox, the “no-justification account” proposes that one is not justified in believing that one's lottery ticket is a loser. The no-justification account commits to what I call “the Harman-style skepticism”. In reply, proponents of the no-justification account typically downplay the Harman-style skepticism. In this paper, I argue that the no-justification reply to the Harman-style skepticism is untenable. Moreover, I argue that the no-justification account is epistemically ad hoc. My arguments are based on a rather surprising (...) finding that the no-justification account implies that people living in Taiwan typically suffer from the Harman-style skepticism. (shrink)

The paradox of pain refers to the idea that the folk concept of pain is paradoxical, treating pains as simultaneously mental states and bodily states. By taking a close look at our pain terms, this paper argues that there is no paradox of pain. The air of paradox dissolves once we recognize that pain terms are polysemous and that there are two separate but related concepts of pain rather than one.

Benardete paradoxes involve a beginningless set each member of which satisfies some predicate just in case no earlier member satisfies it. Such paradoxes have been wielded on behalf of arguments for the impossibility of an infinite past. These arguments often deploy patchwork principles in support of their key linking premise. Here I argue that patchwork principles fail to justify this key premise.

We examine two competing solutions to Benardete paradoxes: causal finitism, according to which nothing can have infinitely many causes, and the unsatisfiable pair diagnosis (UPD), according to which such paradoxes are logically impossible and no metaphysical thesis need be adopted to avoid them. We argue that the UPD enjoys notable theoretical advantages over causal finitism. Causal finitists, however, have levelled two main objections to the UPD. First, they urge that the UPD requires positing a ‘mysterious force’ that prevents paradoxes from (...) arising. Since such a force is implausible, the UPD is in trouble. Second, they employ recombination or patchwork principles to argue that paradoxical situations would be possible if causal finitism were false. Since such situations are not possible, causal finitism is true, and so a substantive metaphysical thesis is needed to avoid the paradoxes. We argue that the UPD proponent can successfully respond to these objections. (shrink)

We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. _Reckless_ theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; _timid_ theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; _non-transitive_ theories deny the principle that, if A is better than B and B is better than C, then A must be better than (...) C. Having set up this trilemma, we study its horns. Non-transitivity has been much discussed; we focus on drawing out the costs and benefits of recklessness and timidity when it comes to axiology, decision theory, and normative uncertainty. (shrink)

What José Luis Bermúdez calls the paradox of self-consciousness is essentially the conflict between two claims: (1) The capacity to use first-personal referential devices like “I” must be explained in terms of the capacity to think first-person thoughts. (2) The only way to explain the capacity for having a certain kind of thought is by explaining the capacity for the canonical linguistic expression of thoughts of that kind. (Bermúdez calls this the “Thought-Language Principle”.) The conflict between (1) and (2) (...) is obvious enough. However, if a paradox is an unacceptable conclusion drawn from apparently valid reasoning from apparently true premises, then Bermúdez’s conflict is no paradox. It is rather a conflict between the view that thought must be explained in terms of language, and the view that first person linguistic reference must be explained in terms of first-person thought. Neither view is immediately obvious, and nor is it obvious that the arguments for either are equally compelling. What we have here is a difference of philosophical opinion, not a paradox. (shrink)

There is no shortage of pedagogical theories from the tradition formal methods of instruction to the free-play methods of unschooling. A sharp shift in education and instruction models took place with the introduction of critical pedagogy. The focus was no longer on the authority of the teacher and the submissive, passive approach taken by the learner, but rather on the engagement between the two. Still, even when critical pedagogy is utilized in a formal model of education something is missing from (...) the system—experiential learning. Although the unschooling method has been criticized it does provide the benefit of experiential learning. This paper explores the nature of education and evaluates models and theories of pedagogy with the conclusion that a paradoxical approach in which there is a merger between the formal guidelines set by traditional educational models and the experiential learning methods of unschooling approach best prepares learners for the world and to be engaged citizens. Although what, precisely, this paradoxical system would entail is not discussed in this paper, it opens the door for further discussion on the topic and for consideration of the theories which have attempted to do exactly this and improve upon them going forward. (shrink)

How can we think or say what is not? If we equate what-is-not with nothing, then a thought of nothing is no thought at all; if we don’t, we are condemned to admit that what-is-not is, seemingly incurring in self-refutation. In this paper, I address this paradox through the lenses of Parmenides, Plato, Russell, and the early Wittgenstein.

Sometimes a fact can play a role in a grounding explanation, but the particular content of that fact make no difference to the explanation—any fact would do in its place. I call these facts vacuous grounds. I show that applying the distinction between-vacuous grounds allows us to give a principled solution to Kit Fine and Stephen Kramer’s paradox of ground. This paradox shows that on minimal assumptions about grounding and minimal assumptions about logic, we can show that grounding (...) is reflexive, contra the intuitive character of grounds. I argue that we should never have accepted that grounding is irreflexive in the first place; the intuitions that support the irreflexive intuition plausibly only require that grounding be non-vacuously irreflexive. Fine and Kramer’s paradox relies, essentially, on a case of vacuous grounding and is thus no problem for this account. (shrink)

Any theory of truth must find a way around Curry’s paradox, and there are well-known ways to do so. This paper concerns an apparently analogous paradox, about validity rather than truth, which JC Beall and Julien Murzi call the v-Curry. They argue that there are reasons to want a common solution to it and the standard Curry paradox, and that this rules out the solutions to the latter offered by most “naive truth theorists.” To this end they (...) recommend a radical solution to both paradoxes, involving a substructural logic, in particular, one without structural contraction. In this paper I argue that substructuralism is unnecessary. Diagnosing the “v-Curry” is complicated because of a multiplicity of readings of the principles it relies on. But these principles are not analogous to the principles of naive truth, and taken together, there is no reading of them that should have much appeal to anyone who has absorbed the morals of both the ordinary Curry paradox and the second incompleteness theorem. (shrink)

In Vagueness and Contradiction (2001), Roy Sorensen defends and extends his epistemic account of vagueness. In the process, he appeals to connections between vagueness and semantic paradox. These appeals come mainly in Chapter 11, where Sorensen offers a solution to what he calls the no-no paradox—a “neglected cousin” of the more famous liar—and attempts to use this solution as a precedent for an epistemic account of the sorites paradox. This strategy is problematic for Sorensen’s project, however, since, (...) as we establish, he fails to resolve the semantic pathology of the no-no paradox. (shrink)

I use the principle of truth-maker maximalism to provide a new solution to the semantic paradoxes. According to the solution, AUS, its undecidable whether paradoxical sentences are grounded or ungrounded. From this it follows that their alethic status is undecidable. We cannot assert, in principle, whether paradoxical sentences are true, false, either true or false, neither true nor false, both true and false, and so on. AUS involves no ad hoc modification of logic, denial of the T-schema's validity, or obvious (...) revenge. (shrink)

Given any proposition, is it possible to have rationally acceptable attitudes towards it? Absent reasons to the contrary, one would probably think that this should be possible. In this paper I provide a reason to the contrary. There is a proposition such that, if one has any opinions about it at all, one will have a rationally unacceptable set of propositional attitudes—or if one doesn’t, one will end up being cognitively imperfect in some other manner. The proposition I am concerned (...) with is a self-referential propositional attitude ascription involving the propositional attitude of rejection. Given a basic assumption about what constitutes irrationality, and a few assumptions about the nature of cognitively ideal agents, a paradox results. This paradox is superficially like the Liar, but it is importantly different in that no alethic notions are involved at all. As such, it stands independent of the Liar and is not a ‘revenge’ version of it. After setting out the paradox I discuss possible responses. After considering several I argue that one is best off simply accepting that the paradox shows us something surprising and interesting about rationality: that some cognitive shortfall is unavoidable even for ideal agents. I argue that nothing disastrous follows from accepting this conclusion. (shrink)

Attempts to reproduce animateness using appliances generates a paradox that provides a new view to life and death, that differs from both religious and atheistic visions.

The discrepancy between individual women and the stereotypes attributed to the group as a ‎whole has become progressively greater and more explicit over the course of history. The stereotypes remain the same age-old ‎allegations whilst the ‎developments in the occupations of women and the traits they have opportunity to express have increased the distance between women and those ascribed traits. Stereotypes’ abstention from revision in light of contrary evidence constitutes an epistemic paradox for it entails conflict between the stereotypical (...) knowledge and empirical evidence, as well as between the stereotypical knowledge and other empirical knowledges. This paradox of stubbornness also raises the question as to the epistemic source of stereotypes. For, people at young ages encounter evidence which should have formed a more complex knowledge regarding women rather than the pervasive stereotypical knowledge. It is this extremity of absurdness of stereotypes regarding women that is utile to understanding stereotypes as a whole. The epistemic paradox that is engrained in all stereotypes is exposed uncompromisingly by this group. The paradox cannot be dismissed with excuses of having a small basis of evidence, such as may be said regarding other social groups with which one may have had minimal or no contact. Thus, stereotypes of women provide a limit case to understanding the epistemology of this paradoxical form of knowledge. The traits and epistemic phenomena which render stereotypes epistemically puzzling and intriguing is the relationship between knowledges. Stereotypical knowledge regarding women as a group conflict with one’s experience-founded knowledges of particular women, deeming the corporate body of knowledge incoherent. Quine’s theory of knowledge, with its holistic empirical approach endorsing conceptual schemes, provides fertile ground for this analysis. The novelty in his account is his establishment of the criteria of coherency, which shifts the focal point of epistemic inquiry away from the adequacy of individual knowledges with empirical evidence to the intra-knowledge relationships themselves. In his empiricism, Quine rather examines the interactions between knowledges and the overarching coherence of the body of knowledge as a holistic unit. Quine creates place in his account for mechanism which provide for the epistemic incongruences of stubbornness and conflict found between stereotypical knowledges and empirical evidence. These very mechanisms are what this paper requests to examine. Quine, ultimately, formulates knowledge as a collectively held fabric consisting of relations and of posits – socially constructed mechanisms which are empirically-irreducible and implemented pragmatically for the organisation of empirical evidence. According to Quine, the fabric formation is a conceptual scheme sourced in social heritage. People are bestowed with an eclectic framework of ‎knowledge to pragmatically merge between an inherited, collective conceptual scheme and the personally experienced empirical evidence. This paper will delve into Quine’s fabric of knowledge, its relations, and inner-mechanisms. The finding of stereotypes to be an age-old posit entrenched pragmatically – thus stubbornly – in the collective conceptual scheme, will explain the epistemic paradoxes they entail and offer insight to their revision in light of empiric reality and its women. (shrink)

Thomas Kroedel argues that the lottery paradox can be solved by identifying epistemic justification with epistemic permissibility rather than epistemic obligation. According to his permissibility solution, we are permitted to believe of each lottery ticket that it will lose, but since permissions do not agglomerate, it does not follow that we are permitted to have all of these beliefs together, and therefore it also does not follow that we are permitted to believe that all tickets will lose. I present (...) two objections to this solution. First, even if justification itself amounts to no more than epistemic permissibility, the lottery paradox recurs at the level of doxastic obligations unless one adopts an extremely permissive view about suspension of belief that is in tension with our practice of doxastic criticism. Second, even if there are no obligations to believe lottery propositions, the permissibility solution fails because epistemic permissions typically agglomerate, and the lottery case provides no exception to this rule. (shrink)

A semantic solution to the liar paradox (“This statement is not true”) is presented in this article. Since the liar paradox seems to evince a contradiction, the principle of non-contradiction is preliminarily discussed, in order to determine whether dismissing this principle may be reason enough to stop considering the liar paradox a problem. No conclusive outcome with respect to the value of this principle is aspired to here, so that the inquiry is not concluded at this point (...) and the option to explore an alternative, semantic, solution remains open. This proposed solution is focused on what the liar paradox expresses and what it fails to express. (shrink)

The paper proposes to grasp handwritten signature as a metaphysical invention of the so-called “Western” civilization, where the signature is supposed to make possible juridical identification of the person who wrote it. However, despite this expectation of reliability, the Western handwritten signature is an aporetic sign, which is considered to be authentic (unrepeatable) and conventional (repeatable) at the same time. Because the signature is a sign of juridical identification and its authenticity can always be forged, Jacques Derrida tries to deconstruct (...) the contradictory functioning of Western metaphysics, which leads to confusion in our expectations of authenticity and identity in our uses of signatures. By proposing a new reading of Derridean texts concerning writing, the paper focuses on the pragmatical paradox that grounds our contradictory legal politics of signing: because the exact manual reproduction of a line is impossible, no one can satisfy the legislative obligation to sign conformably to the model signature. That’s the aporia of trace’s recognition, which establishes the signature as a sign: on the one hand, the signature is supposed to represent the juridical identity of the person who traced it; on the other hand, the signature, which constantly changes its graphical form, makes every certain identification impossible. In order to question the juridical identity traditionally guaranteed by the signature, this paper invites to grasp the legal practice of signing as a subversive performativity, which is produced during the passage between recognition of juridical identity requested by the law and its simultaneous and inevitable transgression. Finally, the paper proposes a new approach to the signature as a visual performance of the self, based on a reevaluation of the altercation between Jacques Derrida and John Searle concerning the iterative character of traces and performatives. (shrink)

In this essay I defend a solution to a skeptical paradox. The paradox I focus on concerns epistemic justification (rather than knowledge), and skeptical scenarios that entail that most of our ordinary beliefs about the external world are false. This familiar skeptical paradox hinges on a “closure” principle. The solution is to restrict closure, despite its first appearing as a fully general principle, so that it can no longer give rise to the paradox. This has some (...) extra advantages. First, it suggests a general strategy that provides solutions to other versions of the paradox, not just those that depend on closure. Second, it clarifies the relation between the paradox and other kinds of skeptical problem. (shrink)

Smith argues that, unlike other forms of evidence, naked statistical evidence fails to satisfy normic support. This is his solution to the puzzles of statistical evidence in legal proof. This paper focuses on Smith’s claim that DNA evidence in cold-hit cases does not satisfy normic support. I argue that if this claim is correct, virtually no other form of evidence used at trial can satisfy normic support. This is troublesome. I discuss a few ways in which Smith can respond.

Tullmann et Buckwalter (2014) ont récemment soutenu que le paradoxe de la fiction tenait plus de l’illusion que de la réalité. D’après eux, les théories contemporaines des émotions ne fourniraient aucune raison d’adopter une interprétation du terme « existence » qui rende les prémisses du paradoxe incompatibles entre elles. Notre discussion a pour but de contester cette manière de dissoudre le paradoxe de la fiction en montrant qu’il ne prend pas sa source dans les théories contemporaines des émotions. Bien plutôt, (...) son origine se situe dans ce que Radford (1975) décrit comme une incohérence dans nos réactions émotionnelles aux évènements fictionnels et non fictionnels. Malgré ce désaccord, nous concédons à Tullmann et Buckwalter qu’une solution satisfaisante au paradoxe de la fiction doit s’appuyer sur les théories des émotions. Ainsi, en guise de conclusion, nous expliquons comment il convient de comprendre l’incohérence en question et comment les théories des émotions pourraient contribuer à la résolution du paradoxe de la fiction. (shrink)

Most theories of suspense implicitly or explicitly have as a background assumption what I call suspense realism, i.e., that suspense is itself a genuine, distinct emotion. I claim that for a theory of suspense to entail suspense realism is for that theory to entail a contradiction, and so, we ought instead assume a background of suspense eliminativism, i.e., that there is no such genuine, distinct emotion that is the emotion of suspense. More precisely, I argue that i) any suspense realist (...) (...) theory must resolve the paradox of suspense, ii) if suspense is itself a genuine, distinct emotion, then in order to resolve the paradox of suspense it must be a radically sui generis genuine, distinct emotion, iii) according to any minimally adequate theory of the emotions, there can be no radically sui generis emotion, and so iv) there can be no genuine, distinct emotion that is the emotion of suspense. Quite simply, if a theory of suspense must entail suspense realism, then we ought to be eliminativists about suspense. This I call the Paradox of Suspense Realism, which I take to constitute a productive viability condition for any theory of suspense, i.e., any viable theory of suspense must be mutatis mutandis compatible with suspense eliminativism. (shrink)

Zeno’s paradoxes of motion, allegedly denying motion, have been conceived to reinforce the Parmenidean vision of an immutable world. The aim of this article is to demonstrate that these famous logical paradoxes should be seen instead as paradoxes of immobility. From this new point of view, motion is therefore no longer logically problematic, while immobility is. This is convenient since it is easy to conceive that immobility can actually conceal motion, and thus the proposition “immobility is mere illusion of the (...) senses” is much more credible than the reverse thesis supported by Parmenides. Moreover, this proposition is also supported by modern depiction of material bodies: the existence of a ceaseless random motion of atoms—the ‘thermal agitation’—in the scope of contemporary atomic theory, can offer a rational explanation of this ‘illusion of immobility’. Our new approach to Zeno’s paradoxes therefore leads to presenting the novel concept of ‘impermobility’, which we think is a more adequate description of physical reality. (shrink)

Illusionism is the view that conscious experience is some sort of introspective illusion. According to illusionism, there is no conscious experience, but it merely seems like there is conscious experience. This would suggest that much phenomenological enquiry, including work on phenomenological psychopathology, rests on a mistake. Some philosophers have argued that illusionism is obviously false, because seeming is itself an experiential state, and so necessarily presupposes the reality of conscious experience. In response, the illusionist could suggest that the relevant sort (...) of seeming here is not an experiential state, but is a cognitive state, such as a judgement or a belief, which is fully amenable to a physical or functionalist analysis. Herein, I argue that this response is unsuccessful and fails to undermine the reality of conscious experience. Nonetheless, the response does raise the problem of how a judgement or belief about the character of a conscious experience, even if it is true, can be justified if the conscious experience has no causal role in the formation of the judgement or belief. This is not a new problem, but is a reiteration of an old problem that is known in the philosophy of mind literature as the paradox of phenomenal judgement. I consider how the paradox of phenomenal judgement can be resolved and how the judgement or belief about conscious experience can be justified with appeal to the notion of acquaintance. (shrink)

According to the “paradox of knowability”, the moderate thesis that all truths are knowable – ... – implies the seemingly preposterous claim that all truths are actually known – ... –, i.e. that we are omniscient. If Fitch’s argument were successful, it would amount to a knockdown rebuttal of anti-realism by reductio. In the paper I defend the nowadays rather neglected strategy of intuitionistic revisionism. Employing only intuitionistically acceptable rules of inference, the conclusion of the argument is, firstly, not (...) ..., but .... Secondly, even if there were an intuitionistically acceptable proof of ..., i.e. an argument based on a different set of premises, the conclusion would have to be interpreted in accordance with Heyting semantics, and read in this way, the apparently preposterous conclusion would be true on conceptual grounds and acceptable even from a realist point of view. Fitch’s argument, understood as an immanent critique of verificationism, fails because in a debate dealing with the justification of deduction there can be no interpreted formal language on which realists and anti-realists could agree. Thus, the underlying problem is that a satisfactory solution to the “problem of shared content” is not available. I conclude with some remarks on the proposals by J. Salerno and N. Tennant to reconstruct certain arguments in the debate on anti-realism by establishing aporias. (shrink)

There are three questions associated with Simpson’s paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP? and (iii) How to proceed when confronted with SP? An adequate analysis of the paradox starts by distinguishing these three questions. Then, by developing a formal account of SP, and substantiating it with a counterexample to causal accounts, we argue that there are no causal factors at play in answering questions (i) and (ii). Causality enters only in connection with (...) action. (shrink)

Since it was presented in 1963, Chisholm’s paradox has attracted constant attention in the deontic logic literature, but without the emergence of any definitive solution. We claim this is due to its having no single solution. The paradox actually presents many challenges to the formalization of deontic statements, including (1) context sensitivity of unconditional oughts, (2) formalizing conditional oughts, and (3) distinguishing generic from nongeneric oughts. Using the practical interpretation of ‘ought’ as a guideline, we propose a linguistically (...) motivated logical solution to each of these problems, and explain the relation of the solution to the problem of contrary-to-duty obligations. (shrink)

An important suggestion of objective Bayesians is that the maximum entropy principle can replace a principle which is known to get into paradoxical difficulties: the principle of indifference. No one has previously determined whether the maximum entropy principle is better able to solve Bertrand’s chord paradox than the principle of indifference. In this paper I show that it is not. Additionally, the course of the analysis brings to light a new paradox, a revenge paradox of the chords, (...) that is unique to the maximum entropy principle. (shrink)

Many ecological economists have argued that some natural capital should be preserved for posterity. Yet, among environmental philosophers, the preservation paradox entails that preserving parts of nature, including those denoted by natural capital, is impossible. The paradox claims that nature is a realm of phenomena independent of intentional human agency, that preserving and restoring nature require intentional human agency, and, therefore, no one can preserve or restore nature (without making it artificial). While this article argues that the preservation (...) paradox is more difficult to resolve than ordinarily recognized, it also concludes by sketching a positive way to understand what it means to preserve natural capital during the Anthropocene. (shrink)

Interesting as they are by themselves in philosophy and mathematics, paradoxes can be made even more fascinating when turned into proofs and theorems. For example, Russell’s paradox, which overthrew Frege’s logical edifice, is now a classical theorem in set theory, to the effect that no set contains all sets. Paradoxes can be used in proofs of some other theorems—thus Liar’s paradox has been used in the classical proof of Tarski’s theorem on the undefinability of truth in sufficiently rich (...) languages. This paradox (as well as Richard’s paradox) appears implicitly in Gödel’s proof of his celebrated first incompleteness theorem. In this paper, we study Yablo’s paradox from the viewpoint of first- and second-order logics. We prove that a formalization of Yablo’s paradox (which is second order in nature) is non-first-orderizable in the sense of George Boolos (1984). (shrink)

Harman’s lottery paradox, generalized by Vogel to a number of other cases, involves a curious pattern of intuitive knowledge ascriptions: certain propositions seem easier to know than various higher-probability propositions that are recognized to follow from them. For example, it seems easier to judge that someone knows his car is now on Avenue A, where he parked it an hour ago, than to judge that he knows that it is not the case that his car has been stolen and (...) driven away in the last hour. Contextualists have taken this pattern of intuitions as evidence that ‘knows’ does not always denote the same relationship; subject-sensitive invariantists have taken this pattern of intuitions as evidence that non-traditional factors such as practical interests figure in knowledge; still others have argued that the Harman Vogel pattern gives us a reason to abandon the principle that knowledge is closed under known entailment. This paper argues that there is a psychological explanation of the strange pattern of intuitions, grounded in the manner in which we shift between an automatic or heuristic mode of judgment and a controlled or systematic mode. Understanding the psychology behind the pattern of intuitions enables us to see that the pattern gives us no reason to abandon traditional intellectualist invariantism. The psychological account of the paradox also yields new resources for clarifying and defending the single premise closure principle for knowledge ascriptions. (shrink)

There has been much discussion on the two-envelope paradox. Clark and Shackel (2000) have proposed a solution to the paradox, which has been refuted by Meacham and Weisberg (2003). Surprisingly, however, the literature still contains no axiomatic justification for the claim that one should be indifferent between the two envelopes before opening one of them. According to Meacham and Weisberg, "decision theory does not rank swapping against sticking [before opening any envelope]" (p. 686). To fill this gap in (...) the literature, we present a simple axiomatic justification for indifference, avoiding any expectation reasoning, which is often considered problematic in infinite cases. Although the two-envelope paradox assumes an expectation-maximizing agent, we show that analogous paradoxes arise for agents using different decision principles such as maximin and maximax, and that our justification for indifference before opening applies here too. (shrink)

I explore options for a plenitudinarian solution to the Paradox of Flexible Origin Essentialism, taking as my unlikely starting point the views of Sarah-Jane Leslie, who holds that if plenitudinarianism is true, then there is in fact no paradox to be solved, only the illusion of one. The first three sections are expository: Sect. 1 on plenitudinarianism, Sect. 2 on the paradox, and Sect. 3 on Leslie’s views about how plenitudinarianism bears on the paradox. In Sect. (...) 4, I reject the contention that there is no paradox and critically explore three options for a plenitudinarian solution. In Sect. 5, I argue that the plenitudinarian ought to endorse a fourth option. In Sect. 6, I consider an objection. I endorse neither plenitudinarianism nor its denial; the main aim of the paper is to argue that for one who does endorse plenitudinarianism, the best solution to the Paradox of Flexible Origin Essentialism is clear. (shrink)

In this paper I consider two paradoxes that arise in connection with the concept of demonstrability, or absolute provability. I assume—for the sake of the argument—that there is an intuitive notion of demonstrability, which should not be conflated with the concept of formal deducibility in a (formal) system or the relativized concept of provability from certain axioms. Demonstrability is an epistemic concept: the rough idea is that a sentence is demonstrable if it is provable from knowable basic (“self-evident”) premises by (...) means of simple logical steps. A statement that is demonstrable is also knowable and a statement that is actually demonstrated is known to be true. By casting doubt upon apparently central principles governing the concept of demonstrability, the paradoxes of demonstrability presented here tend to undermine the concept itself—or at least our understanding of it. As long as we cannot find a diagnosis and a cure for the paradoxes, it seems that the coherence of the concepts of demonstrability and demonstrable knowledge are put in question. There are of course ways of putting the paradoxes in quarantine, for example by imposing a hierarchy of languages a` la Tarski, or a ramified hierarchy of propositions and propositional functions a` la Russell. These measures, however, helpful as they may be in avoiding contradictions, do not seem to solve the underlying conceptual problems. Although structurally similar to the semantic paradoxes, the paradoxes discussed in this paper involve epistemic notions: “demonstrability”, “knowability”, “knowledge”... These notions are “factive” (e.g., if A is demonstrable, then A is true), but similar paradoxes arise in connection with “nonfactive” notions like “believes”, “says”, “asserts”.3 There is no consensus in the literature concerning the analysis of the notions involved—often referred to as “propositional attitudes”—or concerning the treatment of the paradoxes they give rise to. (shrink)

For each of the many goals of an agent it is true that the agent wants its realization. Given further very plausible assumptions, one can show that there is no good reason for an agent not to want the realization of all of his goals. However, it seems also true that reaching all of one’s goals would be extremely boring; most human beings would consider such a life not worth living. In this respect, leading a life is like playing some (...) game: A game loses its point if one always easily wins. Human agents not only pursue goals but they also have the second-order desire to lead the life of a goal-pursuer. More precisely, they want to be goal-pursuers such that many but not all of their goals are being realized. I argue here that they have a good reason not to want the realization of all of their goals. Now, all this constitutes an antinomy: Apparently, there are very plausible arguments both for affirming as well as denying that an agent has good reasons not to want the realization of his goals. This antinomy is similar to the preface-paradox about beliefs which has a convincing solution (due to Frank Ramsey). I argue, however, that there is no such solution in the case of goals. This leaves us with the question what a solution could look like. (shrink)

In this paper, I start by describing and examining the main results about the option of formalizing the Yablo Paradox in arithmetic. As it is known, although it is natural to assume that there is a right representation of that paradox in first order arithmetic, there are some technical results that give rise to doubts about this possibility. Then, I present some arguments that have challenged that Yablo’s construction is non-circular. Just like that, Priest (1997) has argued that (...) such formalization shows that Yablo’s Paradox involves implicit circularity. In the same direction, Beall (2001) has introduced epistemic factors in this discussion. Even more, Priest has also argued that the introduction of infinitary reasoning would be of little help. Finally, one could reject definitions of circularity in term of fixed-point adopting non-well-founded set theory. Then, one could hold that the Yablo paradox and the Liar paradox share the same non-well-founded structure. So, if the latter is circular, the first is too. In all such cases, I survey Cook’s approach (2006, forthcoming) on those arguments for the charge of circularity. In the end, I present my position and summarize the discussion involved in this volume. En este artículo, describo y examino los principales resultados vinculados a la formalización de la paradoja de Yablo en la aritmética. Aunque es natural suponer que hay una representación correcta de la paradoja en la aritmética de primer orden, hay algunos resultados técnicos que hacen surgir dudas acerca de esta posibilidad. Más aún, presento algunos argumentos que han cuestionado que la construcción de Yablo no sea circular. Así, Priest (1997) ha argumentado que la formalización de la paradoja de Yablo en la aritmética de primer orden muestra que la misma involucra implícitamente circularidad. En la misma dirección, Beall (2001) ha introducido factores epistémicos en esta discusión. Más aún, Priest ha también argumentado que la introducción de razonamiento infinitario como complemento de la formalización en la aritmética sería de poca ayuda. Finalmente, se podría rechazar todo intento de dar definiciones de circularidad en términos de puntos fijos adoptando teoría de conjuntos infundados. Entonces, se podría sostener que la paradoja de Yablo y la del mentiroso comparten la misma estructura infundada. Por eso, si la última es circular, también lo es la primera. En todos los casos, presento el enfoque de Roy Cook (2006, en prensa) sobre estos argumentos que atribuyen circularidad a la construcción de Yablo. En el final, presento mi posición y un breve resumen de la discusión involucrada en este volumen. (shrink)

Most work on the semantic paradoxes within classical logic has centered around what this essay calls “linguistic” accounts of the paradoxes: they attribute to sentences or utterances of sentences some property that is supposed to explain their paradoxical or nonparadoxical status. “No proposition” views are paradigm examples of linguistic theories, although practically all accounts of the paradoxes subscribe to some kind of linguistic theory. This essay shows that linguistic accounts of the paradoxes endorsing classical logic are subject to a particularly (...) acute form of the revenge paradox: that there is no exhaustive classification of sentences into “good” and “bad” such that the T-schema holds when restricted to the “good” sentences unless it is also possible to prove some “bad” sentences. The foundations for an alternative classical nonlinguistic approach is outlined that is not subject to the same kinds of problems. Although revenge paradoxes of different strengths can be formulated, they are found to be indeterminate at higher orders and not inconsistent. (shrink)

Phenomenal conservatives claim that seemings are sui generis mental states and can thus provide foundational non-doxastic justification for beliefs. Many of their critics deny this, claiming, instead, that seemings can be reductively analyzed in terms of other mental states—either beliefs, inclinations to believe, or beliefs about one’s evidence—that cannot provide foundational non-doxastic justification. In this paper, I argue that no tenable semantic reduction of ‘seems’ can be formulated in terms of the three reductive analyses that have been proposed by critics (...) of phenomenal conservatism. This is because Moore-paradoxical statements are generated when each of the reductive analyses is substituted for ‘seems’ in statements like ‘The stick is straight, but it does not seem to me that it’s straight.’ Since the latter statement is not Moore-paradoxical, the three proposed reductive analyses of ‘seems’ are unsuccessful. Absent a successful semantic reduction, however, there is no good reason to think a successful metaphysical reduction of seemings is forthcoming. Thus, there is an additional reason, unnoticed in the existing literature, to think that seemings are sui generis mental states. (shrink)

John McDowell articulated a radical criticism of normative inferentialism against Robert Brandom’s expressivist account of conceptual contents. One of his main concerns consists in vindicating a notion of intentionality that could not be reduced to the deontic relations that are established by discursive practitioners. Noticeably, large part of this discussion is focused on empirical knowledge and observational judgments. McDowell argues that there is no role for inference in the application of observational concepts, except the paradoxical one of justifying the content (...) of an observational judgment in terms of itself. This paper examines the semantical consequences of the analysis of the content of empirical judgments in terms of their inferential role. These, it is suggested, are distinct from the epistemological paradoxes that McDowell charges the inferentialist approach with. (shrink)

Events between which we have no epistemic reason to discriminate have equal epistemic probabilities. Bertrand’s chord paradox, however, appears to show this to be false, and thereby poses a general threat to probabilities for continuum sized state spaces. Articulating the nature of such spaces involves some deep mathematics and that is perhaps why the recent literature on Bertrand’s Paradox has been almost entirely from mathematicians and physicists, who have often deployed elegant mathematics of considerable sophistication. At the same (...) time, the philosophy of probability has been left out. In particular, left out entirely are the philosophical ground of the principle of indifference, the nature of the principle itself, the stringent constraint this places on the mathematical representation of the principle needed for its application to continuum sized event spaces, and what these entail for rigour in developing the paradox itself. This book puts the philosophy and its entailments back in and in so doing casts a new light on the paradox, giving original analyses of the paradox, its possible solutions, the source of the paradox, the philosophical errors we make in attempting to solve it and what the paradox proves for the philosophy of probability. The book finishes with the author’s proposed solution—a solution in the spirit of Bertrand’s, indeed—in which an epistemic principle more general than the principle of indifference offers a principled restriction of the domain of the principle of indifference. (shrink)

According to Aristotle if a universal proposition (for example: “All men are white”) is true, its contrary proposition (“All men are not white”) must be false; and, according to Aristotle, if a universal proposition (for example: “All men are white”) is true, its contradictory proposition (“Not all men are white”) must be false. I agree with what Aristotle wrote about universal propositions, but there are universal propositions which have no contrary proposition and have no contradictory proposition. The proposition X “All (...) the propositions that contradict this proposition are true” does not have the contrary proposition and does not have the contradictory proposition. In fact: FEX “All the propositions that contradict this proposition are not true” has a different subject: the subject of the proposition X is constituted by all the propositions that contradict the proposition X; by contrast, the subject of the proposition FEX is constituted by all the propositions that contradict the proposition FEX. And FOX “Not all the propositions that contradict this proposition are true” has a different subject: the subject of the proposition X is constituted by the propositions that contradict the proposition X; by contrast, the subject of the proposition FOX is constituted by the propositions that contradict the proposition FOX. According to Aristotle, a singular proposition (in his example: "Socrates is white") which is true must have its negative proposition ("Socrates is not white") which is false. I agree with Aristotle, but there are singular propositions which do not have the corresponding negative proposition. The proposition (or, rather, the pseudo-proposition) L “This same statement is not true” does not have the negative proposition because the proposition FNL “This same statement is true” has a different subject from the subject of the proposition L: the subject of the proposition L is the proposition L; by contrast, the subject of the proposition FNL is the proposition FNL. L and FNL cannot have the same subject. By contrast, the proposition M “This mount is entirely in Swiss territory” and the proposition NM “This mount is not entirely in Swiss territory” can have the same subject (for example, the Mount Eiger): in case the subject of the proposition M and the subject of the proposition NM is the same, M and NM are opposite propositions, NM is the negative proposition of M. By contrast, the proposition (or, rather, the pseudo-proposition) L "This same statement is not true" cannot have the corresponding negative proposition because FNL "This same statement is true" has a different subject: the subject of L is L ; by contrast, the subject of FNL is FNL. Then the paper continues by analyzing some variants of the liar’s paradox: L1 “The statement L1 is not true”; the so-called liar cycle; and the so-called Yablo’s paradox. (shrink)

It is now the majority view amongst philosophers and theologians that any world could have been better. This places the choice of which world to create into an especially challenging class of decision problems: those that are discontinuous in the limit. I argue that combining some weak, plausible norms governing this type of problem with a creator who has the attributes of the god of classical theism results in a paradox: no world is possible. After exploring some ways out (...) of the paradox, I conclude that the classical theist should accept Marilyn Adams’s view that no norms apply to gods. (shrink)

The Russell's paradox concerns the foundations of naive set theory. This short short paper is about how it can be interpreted in other contexts and has significance in the world of commands. Understanding the paper assumes that the reader is broadly familiar with the foundations of set theory and its history. The text contains many formulas and therefore the reader should be comfortable in the world of logical formulas. My example is somewhat similar to the barber paradox. There, (...) too, we are puzzled by the feasibility of a task. In the case of the barber paradox there is a solution: the barber is a woman, in my example there is no such escape. (shrink)

The principle of indifference is supposed to suffice for the rational assignation of probabilities to possibilities. Bertrand advances a probability problem, now known as his paradox, to which the principle is supposed to apply; yet, just because the problem is ill‐posed in a technical sense, applying it leads to a contradiction. Examining an ambiguity in the notion of an ill‐posed problem shows that there are precisely two strategies for resolving the paradox: the distinction strategy and the well‐posing strategy. (...) The main contenders for resolving the paradox, Marinoff and Jaynes, offer solutions which exemplify these two strategies. I show that Marinoff’s attempt at the distinction strategy fails, and I offer a general refutation of this strategy. The situation for the well‐posing strategy is more complex. Careful formulation of the paradox within measure theory shows that one of Bertrand’s original three options can be ruled out but also shows that piecemeal attempts at the well‐posing strategy will not succeed. What is required is an appeal to general principle. I show that Jaynes’s use of such a principle, the symmetry requirement, fails to resolve the paradox; that a notion of metaindifference also fails; and that, while the well‐posing strategy may not be conclusively refutable, there is no reason to think that it can succeed. So the current situation is this. The failure of Marinoff’s and Jaynes’s solutions means that the paradox remains unresolved, and of the only two strategies for resolution, one is refuted and we have no reason to think the other will succeed. Consequently, Bertrand’s paradox continues to stand in refutation of the principle of indifference. (shrink)

A standard liberal claim is that freedom of choice is not only instrumentally valuable but also intrinsically valuable, that is, valuable for its own sake. I argue that each one of five conditions is plausible if freedom of choice is intrinsically valuable. Yet there exists a counter-example to the conjunction of these conditions. Hence freedom of choice is not intrinsically valuable.

The extensions of Goodman’s ‘grue’ predicate and Kripke’s ‘quus’ are constructed from the extensions of more familiar terms via a reinterpretation that permutes assignments of reference. Since this manoeuvre is at the heart of Putnam’s model-theoretic and permutation arguments against metaphysical realism (‘Putnam’s Paradox’), both Goodman’s New Riddle of Induction and the paradox about meaning that Kripke attributes to Wittgenstein are instances of Putnam’s. Evidence cannot selectively confirm the green-hypothesis and disconfirm the grue-hypothesis, because the theory of which (...) the green-hypothesis is a part has an unintended model in which the grue-hypothesis is equally confirmed; and there are no meaning-facts that determine reference, because the objects referred to by the referring terms of any language or set of intentional mental states are permutable in a way that is consistent with the truth-values of all other sentences in that language or beliefs in that set. The upshot is that the three paradoxes need to be solved in a unified way. (shrink)

The present paper investigates whether strictly classical inferences contribute to the formalization of (genuine) paradoxes within natural deduction. Tennant's criterion for paradoxicality relies on the generation of an infinite reduction sequence, which distinguishes genuine paradoxes from mere inconsistencies. His methodological conjecture posits that genuine paradoxes are never strictly classical and can be derived without classical inferences such as the Law of Excluded Middle, Dilemma, Classical Reductio, and Double Negation Elimination. -/- It appears that there were two reasons for Tennant's proposal (...) of the methodological conjecture. The one is that strictly classical inferences hinder the generation of an infinite reduction sequence and the other is that strictly classical inferences have no role in the formalization of genuine paradoxes. -/- This paper raises questions about these two reasons. Focusing on the liar paradox, it will be argued that strictly classical inferences do not interfere with the generation of an infinite reduction sequence and that the liar sentence may implicitly entail strictly classical inferences. Should this analysis hold, it would call into question not only Tennant’s motivation for advancing the methodological conjecture, but also challenge his contention that genuine paradoxes—exemplified by the liar paradox—are never constructed with reliance on strictly classical inferences. (shrink)

Non-classical solutions to semantic paradox can be associated with conceptions of paradoxicality understood in terms of entailment facts. In a K3-based theory of truth, for example, it is prima facie natural to say that a sentence φ is paradoxical iff φ ∨ ¬φ entails an absurdity. In a recent paper, Julien Murzi and Lorenzo Rossi exploit this idea to introduce revenge paradoxes for a number of non-classical approaches, including K3. In this paper, I show that on no understanding of (...) ‘is paradoxical’ (for K3) should both rules needed for their paradox be expected to hold unrestrictedly. Just which rule fails, however, depends on various factors, including whether the derivability relation of a target system of reasoning is arithmetically definable. (shrink)