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)

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)

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.

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)

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 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)

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)

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)

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)

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 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)

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)

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 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)

Our evidence can be about different subject matters. In fact, necessarily equivalent pieces of evidence can be about different subject matters. Does the hyperintensionality of ‘aboutness’ engender any hyperintensionality at the level of rational credence? In this paper, I present a case which seems to suggest that the answer is ‘yes’. In particular, I argue that our intuitive notions of independent evidence and inadmissible evidence are sensitive to aboutness in a hyperintensional way. We are thus left with a paradox. While (...) there is strong reason to think that rational credence cannot make such hyperintensional distinctions, our intuitive judgements about certain cases seem to demand that it does. (shrink)

The paradox of hedonism is the idea that making pleasure the only thing that we desire for its own sake can be self-defeating. Why would this be true? In this paper, I survey two prominent explanations, then develop a third possible explanation, inspired by Joseph Butler's classic discussion of the paradox. The existing accounts claim that the paradox arises because we are systematically incompetent at predicting what will make us happy, or because the greatest pleasures for human beings are found (...) in certain special goods which hedonists cannot enjoy. On the account that I develop, the paradox is a consequence of a theory about the nature of pleasure, together with a view about the requirements of rational belief. Which of these explanations is correct, I argue, bears on central questions about how to understand the nature and extent of the paradox. (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.

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)

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)

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)

The coordinated attack scenario and the electronic mail game are two paradoxes of common knowledge. In simple mathematical models of these scenarios, the agents represented by the models can coordinate only if they have common knowledge that they will. As a result, the models predict that the agents will not coordinate in situations where it would be rational to coordinate. I argue that we should resolve this conflict between the models and facts about what it would be rational to (...) do by rejecting common knowledge assumptions implicit in the models. I focus on the assumption that the agents have common knowledge that they are rational, and provide models to show that denying this assumption suffices for a resolution of the paradoxes. I describe how my resolution of the paradoxes fits into a general story about the relationship between rationality in situations involving a single agent and rationality in situations involving many agents. (shrink)

Solutions to ninety paradoxes, some old, some new.

. 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)

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)

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.

This paper uses a paradox inherent in any solution to the Hard Problem of Consciousness to argue for God’s existence. The paper assumes we are “thought machines”, reading the state of a relevant physical medium and then outputting corresponding thoughts. However, the existence of such a thought machine is impossible, since it needs an infinite number of point-representing sensors to map the physical world to conscious thought. This paper shows that these sensors cannot exist, and thus thought cannot come solely (...) from our physical world. The only possible explanation is something outside, argued to be God. (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)

The current debates in social sciences show that the paradox of observing—the embeddedness of observer in the process of observing—is at the heart of the controversy about their cognitive status and future. Although the problem of observing has been addressed in numerous theoretical perspectives—some of which (Habermas, Leydesdorff, Maturana, and Luhmann) are examined in this article—the prospects for resolving this paradox remain problematic. Locating a point that allows reflection on the process of autopoiesis in general, not just the operation of (...) a particular autopoietic system, may be one condition for resolving this paradox. Such point will offer reflection on all autopoietic systems, including the observer. The dynamic balance between equilibrium and disequilibrium is the mechanism which regulates the process of autopoiesis. Since the function of regulation is essentially a reflective function, this equilibrium between equilibrium and disequilibrium, which can be identified with the concept of homeorhesis introduced by Conrad Waddington, may offer a possibility to reflect on the process of observing. (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)

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)

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)

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)

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 (...) class='Hi'>paradoxes in our reasoning and logic. (shrink)

If feeling a genuine emotion requires believing that its object actually exists, and if this is a belief we are unlikely to have about fictional entities, then how could we feel genuine emotions towards these entities? This question lies at the core of the paradox of fiction. Since its original formulation, this paradox has generated a substantial literature. Until recently, the dominant strategy had consisted in trying to solve it. Yet, it is more and more frequent for scholars to try (...) to dismiss it using data and theories coming from psychology. In opposition to this trend, the present paper argues that the paradox of fiction cannot be dissolved in the ways recommended by the recent literature. We start by showing how contemporary attempts at dissolving the paradox assume that it emerges from theoretical commitments regarding the nature of emotions. Next, we argue that the paradox of fiction rather emerges from everyday observations, the validity of which is independent from any such commitment. This is why we then go on to claim that a mere appeal to psychology in order to discredit these theoretical commitments cannot dissolve the paradox. We bring our discussion to a close on a more positive note, by exploring how the paradox could in fact be solved by an adequate theory of the emotions. (shrink)

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

In the emerging literature on judgment aggregation over logically connected proposi- tions, expert rights or liberal rights have not been investigated yet. A group making collective judgments may assign individual members or subgroups with expert know- ledge on, or particularly affected by, certain propositions the right to determine the collective judgment on those propositions. We identify a problem that generalizes Sen's 'liberal paradox'. Under plausible conditions, the assignment of rights to two or more individuals or subgroups is inconsistent with the (...) unanimity principle, whereby unanimously accepted propositions are collectively accepted. The inconsistency can be avoided if individual judgments or rights satisfy special conditions. (shrink)

According to the principle of Conjunction Closure, if one has justification for believing each of a set of propositions, one has justification for believing their conjunction. The lottery and preface paradoxes can both be seen as posing challenges for Closure, but leave open familiar strategies for preserving the principle. While this is all relatively well-trodden ground, a new Closure-challenging paradox has recently emerged, in two somewhat different forms, due to Backes :3773–3787, 2019a) and Praolini :715–726, 2019). This paradox synthesises (...) elements of the lottery and the preface and is designed to close off the familiar Closure-preserving strategies. By appealing to a normic theory of justification, I will defend Closure in the face of this new paradox. Along the way I will draw more general conclusions about justification, normalcy and defeat, which bear upon what Backes :2877–2895, 2019b) has dubbed the ‘easy defeat’ problem for the normic theory. (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)

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)

I present a new argument for the repugnant conclusion. The core of the argument is a risky, intrapersonal analogue of the mere addition paradox. The argument is important for three reasons. First, some solutions to Parfit’s original puzzle do not obviously generalize to the intrapersonal puzzle in a plausible way. Second, it raises independently important questions about how to make decisions under uncertainty for the sake of people whose existence might depend on what we do. And, third, it suggests various (...) difficulties for leading views about the value of a person’s life compared to her nonexistence. (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.

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)

Saying that x is ineffable seems to be paradoxical – either I cannot say anything about x, not even that it is ineffable – or I can say that it is ineffable, but then I can say something and it is not ineffable. In this article, I discuss Alston’s version of the paradox and a solution proposed by Hick which employs the concept of formal and substantial predicates. I reject Hick’s proposal and develop a different account based on some passages (...) from Pseudo-Dionysius’ Mystica Theologia. ‘God is ineffable’ is a metalinguistic statement concerning propositions about God: not all propositions about God are expressible in a human language. (shrink)

Why can testimony alone be enough for findings of liability? Why statistical evidence alone can’t? These questions underpin the “Proof Paradox” (Redmayne 2008, Enoch et al. 2012). Many epistemologists have attempted to explain this paradox from a purely epistemic perspective. I call it the “Epistemic Project”. In this paper, I take a step back from this recent trend. Stemming from considerations about the nature and role of standards of proof, I define three requirements that any successful account in line with (...) the Epistemic Project should meet. I then consider three recent epistemic accounts on which the standard is met when the evidence rules out modal risk (Pritchard 2018), normic risk (Ebert et al. 2020), or relevant alternatives (Gardiner 2019 2020). I argue that none of these accounts meets all the requirements. Finally, I offer reasons to be pessimistic about the prospects of having a successful epistemic explanation of the paradox. I suggest the discussion on the proof paradox would benefit from undergoing a ‘value-turn’. (shrink)

Russell claims in his autobiography and elsewhere that he discovered his 1905 theory of descriptions while attempting to solve the logical and semantic paradoxes plaguing his work on the foundations of mathematics. In this paper, I hope to make the connection between his work on the paradoxes and the theory of descriptions and his theory of incomplete symbols generally clearer. In particular, I argue that the theory of descriptions arose from the realization that not only can a class (...) not be thought of as a single thing, neither can the meaning/intension of any expression capable of singling out one collection (class) of things as opposed to another. If this is right, it shows that Russell’s method of solving the logical paradoxes is wholly incompatible with anything like a Fregean dualism between sense and reference or meaning and denotation. I also discuss how this realization lead to modifications in his understanding of propositions and propositional functions, and suggest that Russell’s confrontation with these issues may be instructive for ongoing research. (shrink)

Chinese Chan or Zen Buddhism is renowned for its improvisational, atypical, and perplexing use of words. In particular, the tradition’s encounter dialogues, which took place between Chan masters and their interlocutors, abound in puzzling, astonishing, and paradoxical ways of speaking. In this chapter, we are concerned with Chan’s use of paradoxical language. In philosophical parlance, a linguistic paradox comprises the confluence of opposite or incongruent concepts in a way that runs counter to our common sense and ordinary rational thinking. One (...) naturally wonders about Chan masters’ rationales for their use of paradox. There are also concerns about whether the use violates the logical principle of noncontradiction to the effect that nothing can be both P and not-P all over in the same way at the same time. Chan became a viable Chinese Buddhist tradition during the Tang dynasty (618−907) and continued to develop for several centuries. The tradition had produced a huge literature; consequently, our investigation of its use of paradox cannot but be limited and selective. In the second section, I first sketch key ideas of Chan that are pertinent to our investigation and then examine the use of paradox in the sermons associated with certain Tang masters of the southern Chan. In the third section, I analyze the presence of paradoxical language in post-Tang encounter dialogues. The fourth section concludes. (shrink)

Philosophical Issues, Volume 31, Issue 1, Page 355-373, October 2021.