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)

There are infinitely many ways the world might be, and there may well be infinitely many people in it. These facts raise moral paradoxes. We explore a conflict between two highly attractive principles: a Pareto principle that says that what is better for everyone is better overall, and a statewise dominance principle that says that what is sure to turn out better is better on balance. We refine and generalize this paradox, showing that the problem is faced by many (...) theories of interpersonal aggregation besides utilitarianism, and by many decision theories besides expected value theory. Considering the range of consistent responses, we find all of them to be quite radical. (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.

Neil Tennant was the first to propose a proof-theoretic criterion for paradoxicality, a framework in which a paradox, formalized through natural deduction, is derived from an unacceptable conclusion that employs a certain form of id est inferences and generates an infinite reduction sequence. Tennant hypothesized that any derivation in natural deduction that formalizes a genuine paradox would meet this criterion, and he argued that while the liar paradox is genuine, Russell's paradox is not. -/- The present (...) paper delves into Tennant's conjecture for genuine paradoxes and suggests that to validate the conjecture, one of two issues must be addressed. The first issue is the need for a philosophical consensus on the identification of a genuine paradox in an informal sense. The second issue is the requirement for a uniform approach to formalize paradoxes in natural deduction. If either of these issues is addressed, the conjecture could be validated, or at the very least, it could hold philosophical importance in delineating the proof-theoretic features of paradoxicality. (shrink)

Fitch's knowability paradox shows that for each unknown truth there is also an unknowable truth, a result which has been thought both odd in itself and at odds with views which impose epistemic constraints on truth and/or meaningfulness. Here a solution is considered which has received little attention in the debate but which carries prima facie plausibility. The decidability solution is to accept that Fitch sentences are unknowably true but deny the significance of this on the grounds that Fitch (...) sentences are nevertheless decidable. The decidability solution is particularly attractive for those whose primary concern is an epistemic constraint on meaningfulness (‘verificationists’). For those whose main concern is truth (‘anti-realists’), the situation is more complex: Melia takes the solution to exonerate anti-realism completely; Williamson sees it as completely irrelevant. The truth lies between these two extremes: there is one broad anti-realist commitment to which the solution does not apply, but there is also one, the “fundamental tenet” of anti-realism according to Dummett, to which it does. (shrink)

Benardete paradoxes involve infinite collections of Grim Reapers, assassins, demons, deafening peals, or even sentences. These paradoxes have recently been used in arguments for finitist metaphysical theses such as temporal finitism, causal finitism, and discrete views of time. Here we develop a new finite Benardete-like paradox. We then use this paradox to defend a companions in guilt argument that challenges recent applications of patchwork principles on behalf of the aforementioned finitist arguments. Finally, we develop another problem for those (...) applications by examining the notion of exact duplication. (shrink)

I offer a new, limited solution to divine hiddenness based on a particular epistemic paradox: sometimes, knowing about a desired outcome or relevant features of that desired outcome would prevent the outcome in question from occurring. I call these cases epistemically self-defeating situations. This solution, in essence, says that divine hiddenness or silence is a necessary feature of at least some morally excellent or desirable states of affairs. Given the nature of the paradox, an omniscient being cannot completely (...) eliminate hiddenness, just as an omnipotent being cannot create a rock so heavy that they cannot lift it. Epistemically self-defeating situations provide an undercutting defeater for the assumption that any nonresistant nonbeliever could always, at any time, be in conscious relationship with a perfectly loving God. Thankfully, silence is a temporary feature of epistemically self-defeating situations: once the outcome is achieved, agents can know in full. (shrink)

This paper presents the Paradoxical Theorem, which states that no imperfect being can determine the truth or falsity of any statement with absolute perfection. We then apply the theorem to itself for any imperfect being, which leads to a self-referential paradox.

This paper explores the relationships between some the problems of the Fermi Paradox (FP), with its variety of possible answers; and the Problem of Induction, and thus the possibility of a Theory of Everything. We seek to improve the hierarchy of plausibility within answers to FP, given by what we call “preference criteria”, among which we particularly highlight culture-independence. We argue that, if the question of whether a Theory of Everything is possible is answered negatively, then FP becomes much (...) more serious than otherwise, and this makes many of FP’s solutions less preferable. This constitutes a further preference criterion. Armed with this tool, we try to outline a network of relative truths between FP and the Problem of Induction, in the form of a cross-answer table. Only two or three combinations of answers survive as preferable: 1) degenerate, pure solipsistic metaphysics; 2) accept Induction and the Anthropic Principle at the same time, thus saying that the human condition is a very rare one in the universe; or 3) that the Theory of Everything exists and its discovery is the Great Filter. This latter possibility is discussed with its implications for the current scientific and economic progress of our civilization. (shrink)

The liberal international legal order faces a legitimacy crisis today that becomes visible with the recent anti-internationalist turn, the rise of populism and the recent Russian invasion of Ukraine. Either its authority or legitimacy has been tested many times over the last three decades. The article argues that this anti-internationalist trend may be read as a reaction against the neoliberal form taken by international law, not least over the last three decades. In uncovering the intricacies of international law’s legitimacy crisis, (...) the article uncovers the paradox of global constitutionalism: that its need to adopt a sectoral form of integration may cause a legitimacy gap/deficit because international authorities, resting their legitimacy primarily on instrumental grounds, may face problems in compensating for the legitimacy deficit caused by the erosion of domestic sovereignty and extending their legitimacy to non-instrumental grounds. This paradox has one necessary structural and two contingent content-related implications for domestic democracies: (1) it necessarily narrows down the regulatory space of nation-states; and this may in turn (2) impair democratic stability and solidarity, and (3) provide a fertile ground for populism. Drawing on Raz’s service conception, the article focuses on the interaction between international and domestic authorities and highlights the problematic aspects of the neoliberal constitutionalization of international law. (shrink)

The black hole information loss paradox is a catch-all term for a family of puzzles related to black hole evaporation. For almost 50 years, the quest to elucidate the implications of black hole evaporation has not only sustained momentum, but has also become increasingly populated with proposals that seem to generate more questions than they purport to answer. Scholars often neglect to acknowledge ongoing discussions within black hole thermodynamics and statistical mechanics when analyzing the paradox, including the interpretation (...) of Bekenstein-Hawking entropy, which is far from settled. To remedy the dialectical gridlock, I have formulated an overarching, unified framework, which I call ``Black Hole Paradoxes'', that integrates the debates and taxonomizes the relevant `camps' or philosophical positions. -/- I demonstrate that black hole evaporation within Hawking's semi-classical framework insinuates how late-time Hawking radiation is an entangled global system, a contradiction in terms. The relevant forms of information loss are associated with a decrease in maximal Boltzmann entropy and an increase in global von Neumann entropy respectively, which engender what I've branded the ``paradox of phantom entanglement''. Prospective solutions are then tasked with demonstrating how late-time Hawking radiation is either exclusively an entangled subsystem, in which a black hole remnant lingers as an information safehouse, or exclusively an unentangled global system, in which information is evacuated to the exterior. -/- The disagreement between safehouse and evacuation solutions boils down to the statistical interpretation of thermodynamic black hole entropy, i.e., Bekenstein-Hawking entropy. Safehouse solutions attribute Bekenstein-Hawking entropy to a minority of black hole degrees of freedom, those that are associated with the horizon. Evacuation solutions, in contrast, attribute Bekenstein-Hawking entropy to all black hole degrees of freedom. I argue that the interpretation of Bekenstein-Hawking entropy is the litmus test to vet the overpopulated proposal space. So long as any proposal rejecting Hawking's original calculation independently derives black hole evaporation, globally conserves degrees of freedom and entanglement, preserves a version of semi-classical gravity at sub-Planckian scales, and describes black hole thermodynamics in statistical terms, then it counts as a genuine solution to the paradox. (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)

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 self-refutation. In this paper, I address this paradox through the lenses of Parmenides, Plato, Russell, and the early Wittgenstein.

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)

Supererogatory acts—good deeds “beyond the call of duty”—are a part of moral common sense, but conceptually puzzling. I propose a unified solution to three of the most infamous puzzles: the classic Paradox of Supererogation (if it’s so good, why isn’t it just obligatory?), Horton’s All or Nothing Problem, and Kamm’s Intransitivity Paradox. I conclude that supererogation makes sense if, and only if, the grounds of rightness are multi-dimensional and comparative.

I distinguish paradoxes and hypodoxes among the conundrums of time travel. I introduce ‘hypodoxes’ as a term for seemingly consistent conundrums that seem to be related to various paradoxes, as the Truth-teller is related to the Liar. In this article, I briefly compare paradoxes and hypodoxes of time travel with Liar paradoxes and Truth-teller hypodoxes. I also discuss Lewis’ treatment of time travel paradoxes, which I characterise as a Laissez Faire theory of time travel. Time travel paradoxes are impossible according (...) to Laissez Faire theories, while it seems hypodoxes are possible. (shrink)

Paradoxes have played an important role both in philosophy and in mathematics and paradox resolution is an important topic in both fields. Paradox resolution is deeply important because if such resolution cannot be achieved, we are threatened with the charge of debilitating irrationality. This is supposed to be the case for the following reason. Paradoxes consist of jointly contradictory sets of statements that are individually plausible or believable. These facts about paradoxes then give rise to a deeply troubling (...) epistemic problem. Specifically, if one believes all of the constitutive propositions that make up a paradox, then one is apparently committed to belief in every proposition. This is the result of the principle of classical logical known as ex contradictione (sequitur) quodlibetthat anything and everything follows from a contradiction, and the plausible idea that belief is closed under logical or material implication (i.e. the epistemic closure principle). But, it is manifestly and profoundly irrational to believe every proposition and so the presence of even one contradiction in one’s doxa appears to result in what seems to be total irrationality. This problem is the problem of paradox-induced explosion. In this paper it will be argued that in many cases this problem can plausibly be avoided in a purely epistemic manner, without having either to resort to non-classical logics for belief (e.g. paraconsistent logics) or to the denial of the standard closure principle for beliefs. The manner in which this result can be achieved depends on drawing an important distinction between the propositional attitude of belief and the weaker attitude of acceptance such that paradox constituting propositions are accepted but not believed. Paradox-induced explosion is then avoided by noting that while belief may well be closed under material implication or even under logical implication, these sorts of weaker commitments are not subject to closure principles of those sorts. So, this possibility provides us with a less radical way to deal with the existence of paradoxes and it preserves the idea that intelligent agents can actually entertain paradoxes. (shrink)

The present work outlines a logical and philosophical conception of propositions in relation to a group of puzzles that arise by quantifying over them: the Russell-Myhill paradox, the Prior-Kaplan paradox, and Prior's Theorem. I begin by motivating an interpretation of Russell-Myhill as depending on aboutness, which constrains the notion of propositional identity. I discuss two formalizations of of the paradox, showing that it does not depend on the syntax of propositional variables. I then extend to propositions a (...) modal predicative response to the paradoxes articulated by an abstraction principle for propositions. On this conception, propositions are “shadows” of the sentences that express them. Modal operators are used to uncover the implicit relation of dependence that characterizes propositions that are about propositions. The benefits of this approach are shown by application to other intensional puzzles. The resulting view is an alternative to the plenitudinous metaphysics of impredicative comprehension principles. (shrink)

Counterfactuals are somewhat tolerant. Had Socrates been at least six feet tall, he need not have been exactly six feet tall. He might have been a little taller—he might have been six one or six two. But while he might have been a little taller, there are limits to how tall he would have been. Had he been at least six feet tall, he would not have been more than a hundred feet tall, for example. Counterfactuals are not just tolerant, (...) then, but bounded. This paper presents a surprising paradox: If counterfactuals are tolerant and bounded, then we can prove a flat contradiction using natural rules of inference. Something has to go then. But what? (shrink)

This paper presents a paradox based on the following assumptions: that emotions are warranted when you are justified in thinking that the emotion is fitting, that there are warranted cases of past-directed fear, that fear is fitting in the face of its formal object: dangerousness, and that this formal object consists in a probability of damage or harm to something of value. The paper then discusses three likely solutions: (1) denying that past-directed fear can be warranted, (2) using an (...) alternative formulation of fear's formal object, and (3) giving up warrant as justified as fittingness. Finally, it provides a case for the third solution and presents a warrant-based approach to fittingness and the appropriateness of emotions in general. (shrink)

This book is devoted to the presentation of the new quantum mechanical formalism based on the probability representation of quantum states. In the 20s and 30s it became evident that some properties in quantum mechanics can be assigned only to the quantum mechanical system, but not necessarily to its constituents. This led Einstein, Podolsky and Rosen (EPR) to their remarkable 1935 paper where they concluded that quantum mechanics is not a complete theory of nature (EPR paradox). In order to (...) avoid the contradiction which arises from instantaneous action at a distance mentioned above we introduce an extension of the canonical relativity by using measure algebra of physical events in Minkowski space-time. The canonical QM formalism is extended by additional new postulate of EPRB nonlocality for continuous and discrete observables, chapter I. The postulate of EPRB nonlocality is supported by new quantum mechanical formalism based on the probability representation of quantum states. Chapter II is devoted to the new quantum mechanical formalism based on the probability representation of quantum states. Chapter III is devoted to the Einstein's 1927 gedanken experiment resolution. Chapter IV is devoted to the EPR paradox resolution. Chapter V is devoted to the EPR-B paradox resolution. Chapter VI is devoted to the Schrödinger's cat (measured spin) paradox resolution. Chapter VII is devoted to the Bell inequalities revisited. Remind that the canonical arguments which were presented by many authors, namely, that violations of Bell type inequalities signal us that the classical Kolmogorovian model of probability is inapplicable to quantum phenomena. We claimed that the canonical assumption, under which Bell type inequalities were derived, is not supported by real physical nature of the EPRB experiments. The fundamental physical nature violations of the canonical Bell type inequalities explained by Postulate of EPR-Nonlocality and Heisenberg noise-disturbance uncertainty relations. (shrink)

In this article, some classical paradoxes of infinity such as Galileo’s paradox, Hilbert’s paradox of the Grand Hotel, Thomson’s lamp paradox, and the rectangle paradox of Torricelli are considered. In addition, three paradoxes regarding divergent series and a new paradox dealing with multiplication of elements of an infinite set are also described. It is shown that the surprising counting system of an Amazonian tribe, Pirah ̃a, working with only three numerals (one, two, many) can help (...) us to change our perception of these paradoxes. A recently introduced methodology allowing one to work with finite, infinite, and infinitesimal numbers in a unique computational framework not only theoretically but also numerically is briefly described. This methodology is actively used nowadays in numerous applications in pure and applied mathematics and computer science as well as in teaching. It is shown in the article that this methodology also allows one to consider the paradoxes listed above in a new constructive light. (shrink)

I present a paradoxical combination of desires. I show why it's paradoxical, and consider ways of responding. The paradox saddles us with an unappealing trilemma: either we reject the possibility of the case by placing surprising restrictions on what we can desire, or we deny plausibly constitutive principles linking desires to the conditions under which they are satisfied, or we revise some bit of classical logic. I argue that denying the possibility of the case is unmotivated on any reasonable (...) way of thinking about mental content, and rejecting those desire-satisfaction principles leads to revenge paradoxes. So the best response is a non-classical one, according to which certain desires are neither determinately satisfied nor determinately not satisfied. Thus, theorizing about paradoxical propositional attitudes helps constrain the space of possibilities for adequate solutions to semantic paradoxes more generally. (shrink)

This article shows that there is a liar-like paradox that arises for rational credence that relies only on very weak logical and credal principles. The paradox depends on a weak rational reflection principle, logical principles governing conjunction, and principles governing the relationship between rational credence and proof. To respond to this paradox, we must either reject even very weak rational reflection principles or reject some highly plausible logical or credal principle.

This paper explores the liar paradox and its implications for logic and philosophical reasoning. It analyzes the paradox using classical logic principles and paraphrases it as "affirmation of the falsity of the very affirmation." The study draws connections between the liar paradox and Hegel's speculative sentence and suggests it functions as a "quasi-speculative sentence." Additionally, it examines parallels with the logocentric predicament and the determinist's assertion, highlighting their paradoxical nature. Through these analyses, the paper aims to illuminate (...) the fundamental paradoxes in our reasoning and logic. (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)

This paper gives a definition of self-reference on the basis of the dependence relation given by Leitgeb (2005), and the dependence digraph by Beringer & Schindler (2015). Unlike the usual discussion about self-reference of paradoxes centering around Yablo's paradox and its variants, I focus on the paradoxes of finitary characteristic, which are given again by use of Leitgeb's dependence relation. They are called 'locally finite paradoxes', satisfying that any sentence in these paradoxes can depend on finitely many sentences. I (...) prove that all locally finite paradoxes are self-referential in the sense that there is a directed cycle in their dependence digraphs. This paper also studies the 'circularity dependence' of paradoxes, which was introduced by Hsiung (2014). I prove that the locally finite paradoxes have circularity dependence in the sense that they are paradoxical only in the digraph containing a proper cycle. The proofs of the two results are based directly on König's infinity lemma. In contrast, this paper also shows that Yablo's paradox and its nested variant are non-self-referential, and neither McGee's paradox nor the omega-cycle liar paradox has circularity dependence. (shrink)

It is widely accepted that there is what has been called a non-hypocrisy norm on the appropriateness of moral blame; roughly, one has standing to blame only if one is not guilty of the very offence one seeks to criticize. Our acceptance of this norm is embodied in the common retort to criticism, “Who are you to blame me?”. But there is a paradox lurking behind this commonplace norm. If it is always inappropriate for x to blame y for (...) a wrong that x has committed, then all cases in which x blames x (i.e. cases of self-blame) are rendered inappropriate. But it seems to be ethical common-sense that we are often, sadly, in position (indeed, excellent, privileged position) to blame ourselves for our own moral failings. And thus we have a paradox: a conflict between the inappropriateness of hypocritical blame, and the appropriateness of self-blame. We consider several ways of resolving the paradox, and contend none is as defensible as a position that simply accepts it: we should never blame ourselves. In defending this startling position, we defend a crucial distinction between self-blame and guilt. (shrink)

This paper argues that the so-called ‘paradox’ of dehumanization is a mirage arising from misplaced abstraction. The alleged ‘paradox’ is taken as a challenge that arises from a skeptical stance. After reviewing the history of that skeptical stance, it is reconstructed as an argument with two premises. With the help of an epistemologically structured but pluralistic frame it is then shown how the two premises of the Skeptic’s argument can both be debunked. As part of that it emerges (...) that there are a couple of ways how dehumanization can be realized, and one such realization can be sufficient for affirming the reality of dehumanization for a specific case. (shrink)

Philosophers have long argued that duties to oneself are paradoxical, as they seem to entail an incoherent power to release oneself from obligations. I argue that self-release is possible, both as a matter of deontic logic and of metaethics.

This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning---one which takes meaning to be constituted by assertibility and deniability conditions---and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system---ST---that conservatively extends (...) classical logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered. (shrink)

A paradox about sets of properties is presented. The paradox, which invokes an impredicatively defined property, is formalized in a free third-order logic with lambda-abstraction, through a classically proof-theoretically valid deduction of a contradiction from a single premise to the effect that every property has a unit set. Something like a model is offered to establish that the premise is, although classically inconsistent, nevertheless consistent, so that the paradox discredits the logic employed. A resolution through the ramified (...) theory of types is considered. Finally, a general scheme that generates a family of analogous paradoxes and a generally applicable resolution are proposed. (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)

Most paradoxes of self-reference have a dual or ‘hypodox’. The Liar paradox (Lr = ‘Lr is false’) has the Truth-Teller (Tt = ‘Tt is true’). Russell’s paradox, which involves the set of sets that are not self-membered, has a dual involving the set of sets which are self-membered, etc. It is widely believed that these duals are not paradoxical or at least not as paradoxical as the paradoxes of which they are duals. In this paper, I argue that (...) some paradox’s duals or hypodoxes are as paradoxical as the paradoxes of which they are duals, and that they raise neglected and interestingly different problems. I first focus on Richard’s paradox (arguably the simplest case of a paradoxical dual), showing both that its dual is as paradoxical as Richard’s paradox itself, and that the classical, Richard-Poincaré solution to the latter does not generalize to the former in any obvious way. I then argue that my argument applies mutatis mutandis to other paradoxes of self-reference as well, the dual of the Liar (the Truth-Teller) proving paradoxical. (shrink)

Is it possible to provide a theory of truth that is capable of distinguishing the semantic status of paradoxical sentences from that of other ungrounded sentences without bringing meta-linguistic resources into play? We explore an account that extends Kripke's theory of truth with two primitive operators, one standing for the notion of paradoxicality and the other for the notion of hypodoxicality. Our results are mixed. While the paradoxicality operator behaves nicely, a number of restrictions need to be imposed to accommodate (...) the hypodoxicality operator. (shrink)

Paradoxes of nested modality, like Chisholm’s paradox, rely on S4 or something stronger as the propositional logic of metaphysical modality. Sarah-Jane Leslie’s objection to the resolution of Chisholm’s paradox by means of rejection of S4 modal logic is investigated. A modal notion of essence congenial to Leslie’s objection is clarified. An argument is presented in support of Leslie’s crucial but unsupported assertion that, on pain of inconsistency, an object’s essence is the same in every possible world. A fallacy (...) in the argument is exposed. Alternative interpretations of Leslie’s objection are provided and are found to involve equivocation between different notions of “essence.” A material artifact’s modal essence, as distinct from its quiddity essence, could have been different than it is. (shrink)

This paper is concerned with the paradox of decrease. Its aim is to defend the answer to this puzzle that was propounded by its originator, namely, the Stoic philosopher Chrysippus. The main trouble with this answer to the paradox is that it has the seemingly problematic implication that a material thing could perish due merely to extrinsic change. It follows that in order to defend Chrysippus’ answer to the paradox, one has to explain how it could be (...) that Theon is destroyed by the amputation without changing intrinsically. In this paper, I shall answer this challenge by appealing to the broadly Aristotelian idea that at least some of the proper parts of a material substance are ontologically dependent on that substance. I will also appeal to this idea in order to offer a new solution to the structurally similar paradox of increase. In this way, we will end up with a unified solution to two structurally similar paradoxes. (shrink)

In our research about Fuzzy Time and modeling time, "Unexpected Hanging Paradox" plays a major role. Here, we compare this paradox to the Zeno Paradox and the relations of them with our standard models of continuum and Fuzzy numbers. To do this, we review the project "Fuzzy Time and Possible Impacts of It on Science" and introduce a new way in order to approach the solutions for these paradoxes. Additionally, we have a more general discussion about paradoxes, (...) as Philosophical back ground of the subject and in this way, we introduce the concepts of General View, the first picture, BBF-General View. (shrink)

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)

The mathematical prowess of pure mathematician J. E. Littlewood (1885-1977), and of his elder cousin the mathematical educator Philippa Fawcett (1868-1948), is illustrated in the context of the Mathematical Tripos examination at Cambridge. Littlewood’s brilliant though highly condensed treatment in his splendid Miscellany (1953) of a perplexing problem from an old Tripos paper – familiar to some as “The Paradox of the Second Ace” – is then expanded with reference to Coxeter’s treatment of it in his revision of Rouse (...) Ball’s Mathematical Recreations (1939) and ultimately explained in the light of Wittgenstein’s later philosophy. The discussion touches on the nature of mathematical supposition. (shrink)

Brock and Glasgow recently introduced a new definition of paradox and argue that this conception of paradox itself leads to paradox, the so-called Paradox Paradox. I show that they beg the questions during the course of their argument, but, more importantly, do so in a philosophically interesting way: it reveals a counterexample to the equivalence between being a logical truth and having a probability of one. This has consequences regarding norms of rationality, undermining the grounds (...) for the Conjunction Fallacy. (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)

We regularly intentionally expose ourselves to fictions we take to be likely to elicit in us emotions we generally find unpleasant when prompted by actual states of affairs. This is the so-called “paradox of tragedy”. We contribute to solving the paradox of tragedy by denying that, when fiction-directed, most of these emotions are in themselves unpleasant. We first provide strong evidence that these emotions, such as fear, sadness, or pity, are often enjoyed when fiction-directed. We then advance an (...) explanation of what makes these fiction-directed emotions often not unpleasant, while their reality-directed counterparts are generally so. In the last section, we advance an explanation of what makes fiction-directed emotions often enjoyable, and argue that a complete solution to the paradox of tragedy should be pluralist. (shrink)

This essay critically discusses the rising interest in process philosophy in recent years. I argue that the appeal of process philosophy lies in its ability to circumnavigate the binary dichotomies pervasive in European philosophy and defend an interpretation of process philosophy in terms of relationality, difference, and change. After outlining the central tenets of process philosophy, Graham Harman’s critique of a relational account of process philosophy is examined, particularly his assertion that this type of philosophy cannot fully explain genuine change. (...) Despite the merits of Harman’s critique, I will show that his object-oriented ontology faces similar limitations. Turning to Graham Priest’s dialethism I suggest that philosophy, instead of striving for a consistent representation of fundamental metaphysics, must embrace paradox to some extent. This leads the philosophical discipline to understand itself as a transformative process. This essay critically discusses the rising interest in process philosophy in recent years. I argue that the appeal of process philosophy lies in its ability to circumnavigate the binary dichotomies pervasive in European philosophy and defend an interpretation of process philosophy in terms of relationality, difference, and change. After outlining the central tenets of process philosophy, Graham Harman’s critique of a relational account of process philosophy is examined, particularly his assertion that this type of philosophy cannot fully explain genuine change. Despite the merits of Harman’s critique, I will show that his object-oriented ontology faces similar limitations. Turning to Graham Priest’s dialethism I suggest that philosophy, instead of striving for a consistent representation of fundamental metaphysics, must embrace paradox to some extent. This leads the philosophical discipline to understand itself as a transformative process. (shrink)

I present a paradox concerning a person who desires to fail to achieve the goal that matters most to them. I recently encountered a similar paradox, but radical solipsism is a solution to it. This is not a solution to the paradox that I present.

This paper resolves a paradox concerning colour constancy. On the one hand, our intuitive, pre-theoretical concept holds that colour constancy involves invariance in the perceived colours of surfaces under changes in illumination. On the other, there is a robust scientific consensus that colour constancy can persist in cerebral achromatopsia, a profound impairment in the ability to perceive colours. The first stage of the solution advocates pluralism about our colour constancy capacities. The second details the close relationship between colour constancy (...) and contrast. The third argues that achromatopsics retain a basic type of colour constancy associated with invariants in contrast processing. The fourth suggests that one person-level, conscious upshot of such processing is the visual awareness of chromatic contrasts ‘at’ the edges of surfaces, implicating the ‘colour for form’ perceptual function. This primitive type of constancy sheds new light on our most basic perceptual capacities, which mark the lower borders of representational mind. (shrink)

Christopher Cowie argues that moral error theory is uniquely placed to avoid embracing any of the troubling and counter-intuitive horns of moral paradoxes. Contra Cowie, I argue that moral non-cognitivists can also avoid embracing any such troubling and counter-intuitive horns. Rather than supporting moral error theory, I argue that moral paradoxes more precisely support moral nihilism—a first-order view that is consistent with moral error theory and with moral non-cognitivism. Moreover, I argue that reconstructing the argument from moral paradoxes as an (...) argument for moral nihilism enhances its philosophical significance in two ways. First, the argument from moral paradoxes is the first unified argument in support of moral nihilism. Second, given that the logical space of moral nihilism is greater than the logical space of moral error theory, the threat that the argument from moral paradoxes poses to moral philosophy is more serious than Cowie acknowledges. (shrink)

Beginning with the paradoxes of zombie twins, we present an argument that dualism is both true and false. We show that avoiding this contradiction is impossible. Our diagnosis is that consciousness itself engenders this contradiction by producing contradictory points of view. This result has a large effect on the realism/anti-realism debate, namely, it suggests that this debate is intractable, and furthermore, it explains why this debate is intractable. We close with some comments on what our results mean for metaphysics and (...) philosophy, in general. (shrink)

Attention has turned from Hobbes the systematic thinker to his inconsistencies, as the essays in the Hobbes symposium published in the recent volume of Political Theory suggest. Deborah Baumgold, in “The Difficulties of Hobbes Interpretation,” shifted the focus to “the history of the book,” and Hobbes’s method of serial composition and peripatetic insertion, as a major source of his inconsistency. Accepting Baumgold’s method, the author argues that the manner of composition does not necessarily determine content and that fundamental paradoxes in (...) Hobbes’s work have a different provenance, for which there are also contextual answers. Hobbes was a courtier’s client, but one committed early to a materialist ontology and epistemology, and these commitments shackled him in treating the immediate political questions with which he was required to deal, leading to systemic paradoxes in his treatment of natural law, liberty, authorization, and consent. (shrink)