Previous claims to have resolved the two-envelope paradox have been premature. The paradoxical argument has been exposed as manifestly fallacious if there is an upper limit to the amount of money that may be put in an envelope; but the paradoxical cases which can be described if this limitation is removed do not involve mathematical error, nor can they be explained away in terms of the strangeness of infinity. Only by taking account of the partial sums of (...) the infinite series of expected gains can the paradox be resolved. (shrink)

This paper discusses the finite version of the two envelope paradox. (That is, we treat the paradox against the background assumption that there is only a finite amount of money in the world.).

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)

Clark and Shackel have recently argued that previous attempts to resolve the two-envelope paradox fail, and that we must look to symmetries of the relevant expected-value calculations for a solution. Clark and Shackel also argue for a novel solution to the peeking case, a variant of the two-envelope scenario in which you are allowed to look in your envelope before deciding whether or not to swap. Whatever the merits of these solutions, they go beyond accepted decision (...) theory, even contradicting it in the peeking case. Thus if we are to take their solutions seriously, we must understand Clark and Shackel to be proposing a revision of standard decision theory. Understood as such, we will argue, their proposal is both implausible and unnecessary. (shrink)

This article concerns the psychology of the paradoxical Two Envelope Problem. The goal is to find instructive variants of the envelope switching problem that are capable of clear-cut resolution, while still retaining paradoxical features. By relocating the original problem into different contexts involving commutes and playing cards the reader is presented with a succession of resolved paradoxes that reduce the confusion arising from the parent paradox. The goal is to reduce confusion by understanding how we sometimes misread (...) mathematical statements; or, to completely avoid confusion, either by reforming language, or adopting an unambiguous notation for switching problems. This article also suggests that an illusion close in character to the figure/ground illusion hampers our understanding of switching problems in general and helps account for the intense confusion that switching problems sometimes generate. (shrink)

This paper elaborates a new solution to the lottery paradox, according to which the paradox arises only when we lump together two distinct states of being confident that p under one general label of ‘belief that p’. The two-state conjecture is defended on the basis of some recent work on gradable adjectives. The conjecture is supported by independent considerations from the impossibility of constructing the lottery paradox both for risk-tolerating states such as being afraid, hoping or hypothesizing, (...) and for risk-averse, certainty-like states. The new proposal is compared to views within the increasingly popular debate opposing dualists to reductionists with respect to the relation between belief and degrees of belief. (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)

My aim in this paper is to develop a unified solution to two paradoxes of bounded rationality. The first is the regress problem that incorporating cognitive bounds into models of rational decisionmaking generates a regress of higher-order decision problems. The second is the problem of rational irrationality: it sometimes seems rational for bounded agents to act irrationally on the basis of rational deliberation. I review two strategies which have been brought to bear on these problems: the way of weakening which (...) responds by weakening rational norms, and the way of indirection which responds by letting the rationality of behavior be determined by the rationality of the deliberative processes which produced it. Then I propose and defend a third way to confront the paradoxes: the way of level separation. (shrink)

In this paper, we axiomatize the deontic logic in Fusco 2015, which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help make explicit the (...) restrictions Fusco’s account must place on free-choice inferences. They are also of independent interest, as they raise difficult questions about how to ‘lift’ a Kripke frame for a one- dimensional modal logic into two dimensions. (shrink)

1) We will begin by offering a short introduction to Epistemic Logic and presenting Fitch’s paradox in an epistemic‑modal logic. (2) Then, we will proceed to presenting three Epistemic Temporal logical frameworks creat‑ ed by Hoshi (2009) : TPAL (Temporal Public Announcement Logic), TAPAL (Temporal Arbitrary Public Announcement Logic) and TPAL+P ! (Temporal Public Announcement Logic with Labeled Past Operators). We will show how Hoshi stated the Verificationist Thesis in the language of TAPAL and analyze his argument on why (...) this version of it is immune from paradox. (3) Edgington (1985) offered an interpretation of the Verificationist Thesis that blocks Fitch’s paradox and we will propose a way to formulate it in a TAPAL‑based lan‑ guage. The language we will use is a combination of TAPAL and TPAL+P ! with an Indefinite (Unlabeled) Past Operator (TAPAL+P !+P). Using indexed satisfi‑ ability relations (as introduced in (Wang 2010 ; 2011)) we will offer a prospec ‑ tive semantics for this language. We will investigate whether the tentative re‑ formulation of Edgington’s Verificationist Thesis in TAPAL+P !+P is free from paradox and adequate to Edgington’s ideas on how „all truths are knowable“ should be interpreted. (shrink)

The paper defends the argument that the Resemblance Paradox (RP), or the problem of the ‘under-determination of meaning’, and the Rule-Following Paradox (RFP) are two sides of the same paradox threatening meaning from opposite extremes. After presenting the case, the paradox is reconsidered anew and the supposition that the threat is a pervasive one is challenged.

Using “brute reason” I will show why there can be only one valid interpretation of probability. The valid interpretation turns out to be a further refinement of Popper’s Propensity interpretation of probability. Via some famous probability puzzles and new thought experiments I will show how all other interpretations of probability fail, in particular the Bayesian interpretations, while these puzzles do not present any difficulties for the interpretation proposed here. In addition, the new interpretation casts doubt on some concepts often taken (...) as basic and unproblematic, like rationality, utility and expectation. This in turn has implications for decision theory, economic theory and the philosophy of physics. (shrink)

I argue that trends of diagnosing anti-Muslim attitudes and activism as “Islamophobia” in European and the U.S. contexts may actually aid and abet more subtle varieties of the very stigmatization and exclusion that the “phobia” moniker aims to isolate and oppose. My comparative purpose is to draw into relief—to make explicit and subject to critical analysis— features of normative public discourse in these two sociopolitical contexts broadly perceived to be peaceful, prosperous, liberal-democratic. The features I focus on function under the (...) auspices of tolerant and nonexclusionary forms of “civic nationalism” that, in effect, fuel the conflict in question. (shrink)

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)

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.

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)

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)

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)

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)

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)

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)

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)

We outline Brentano’s theory of boundaries, for instance between two neighboring subregions within a larger region of space. Does every such pair of regions contain points in common where they meet? Or is the boundary at which they meet somehow pointless? On Brentano’s view, two such subregions do not overlap; rather, along the line where they meet there are two sets of points which are not identical but rather spatially coincident. We outline Brentano’s theory of coincidence, and show how he (...) uses it to resolve a number of Zeno-like paradoxes. (shrink)

This paper reports (in section 1 “Introduction”) some quotes from Nelson Goodman which clarify that, contrary to a common misunderstanding, Goodman always denied that “grue” requires temporal information and “green” does not require temporal information; and, more in general, that Goodman always denied that grue-like predicates require additional information compared to what green-like predicates require. One of the quotations is the following, taken from the first page of the Foreword to chapter 8 “Induction” of the Goodman’s book “Problems and Projects”: (...) “Nevertheless, we may by now confidently conclude that no general distinction between projectible and non- projectible predicates can be drawn on syntactic or even on semantic grounds. Attempts to distinguish projectible predicates as purely qualitative, or non-projectible ones as time-dependent, for example, have plainly failed”. Barker and Achinstein in their famous paper of 1960 tried to demonstrate that the grue-speaker (named Mr. Grue in their paper) needs temporal information to be able to determine whether an object is grue, but Goodman replied (in “Positionality and Pictures”, contained in his book “Problems and Projects”, chapter 8, section 6b) that they failed to prove that Mr. Grue needs temporal information to determine whether an object is grue. According to Goodman, since the predicates “blue” and “green” are interdefinable with the predicates “grue” and “bleen”, “if we can tell which objects are blue and which objects are green, we can tell which ones are grue and which ones are bleen” [pages 12-13 of “Reconceptions in Philosophy and Other Arts and Sciences”]. But this paper points out that an example of interdefinability is also that one about the predicate “gruet”, which is a predicate that applies to an object if the object either is green and examined before time t, or is non-green and not examined before time t. The three predicates “green”, “gruet”, “examined before time t” are interdefinable: and even though the predicates “green” and “examined before time t” are interdefinable, being able to tell if an object is green does not imply being able to tell if an object is examined before time t (the interdefinability among three elements is a type of interdefinability present, for example, also among the logical connectives). Thus, it is wrong the Goodman’s thesis according to which if it is possible to determine without having temporal information whether the predicate “green” has to be applied to an object, then it is also possible to determine without having temporal information whether a predicate interdefinable with “green” has to be applied to an object. Another example of interdefinability is that one about a decidable predicate PD, which is interdefinable with an undecidable predicate PU: therefore even though we can tell whether an object is PD and whether an object is non-PD, we cannot tell whether an object is PU (since PU is an undecidable predicate) and whether an object is non-PU. Although the predicates PD and PU are interdefinable, the possibility to determine whether an object is PD does not imply the possibility to determine whether an object is PU (since PU is an undecidable predicate). Similarly, although the predicates “green” and “grue” are interdefinable, the possibility to determine whether an object is “green” even in absence of temporal information does not imply the possibility to determine whether an object is “grue” even in absence of temporal information. These and other examples about “grue” and “bleen” point out that even in case two predicates are interdefinable, the possibility to apply a predicate P does not imply the possibility to apply a predicate interdefinable with P. And that the possibility to apply the predicate “green” without having temporal information does not imply the possibility to apply the predicate “grue” without having temporal information. Furthermore, knowing that an object is both green and grue implies temporal information: in fact, we know by definition that a grue object can only be: 1) either green (in case the object is examined before time t); 2) or blue (in case the object is not examined before time t). Thus, knowing that an object is both grue and green, we know that we are faced with case 1, the case of a grue object that is green and examined before time t. Then the paper points out why the Goodman-Kripke paradox is a paradox about meaning that cannot have repercussions on induction. Finally the paper points out why Hume’s problem is a problem different from Goodman’s paradox and requires a specific treatment. -/- . (shrink)

*As mentioned in Peter Coy's NYT essay "When Being Good Is Just a Matter of Being Lucky" (2023) -/- ----- -/- How is the problem of free will related to the problem of moral luck? In this essay, I answer that question and outline a new solution to the paradox of moral luck, the source-paradox solution. This solution both explains why the paradox arises and why moral luck does not exist. To make my case, I highlight a (...) few key connections between the paradox of moral luck and two related problems, namely the problem of free will and determinism and the paradox of self-creation. Piecing together intuitions, arguments, and insights from recent work on each of these three problems, I argue that the type of control necessary for moral responsibility can only be had by someone who is a genuine source of his own actions, but the relevant notion of sourcehood admits no coherent characterization. If our commonsense view of moral responsibility is incoherent, it is unsurprising that our commitment to the existence of morally responsible agents commits us to some paradoxical things—e.g. to both the existence and impossibility of moral luck. For more information about this article, please write to gmail account: kristin.mickelson.42. (shrink)

In this paper, I argue that the cause of morally self-defeating acts at the collective level is greed and, at the individual level, an unrestrained impulse for pleasure beyond Innocent Asouzu’s primordial instinct for self-preservation and ignorance. In investigating why humans act in self-defeating ways, Asouzu came up with two possible factors responsible for self-defeating acts: The primordial instinct for selfpreservation and ignorance. Besides Asouzu’s explanation, I here argue that the problem of self-defeating acts goes beyond the primordial instinct for (...) selfpreservation and ignorance to reveal a flaw characteristic of the human condition. At the collective level, the flaw responsible for self-defeating acts is greed and the unrestrained impulse for pleasure at the individual level. I employ the conversational method to interrogate the different views on self-defeating acts from Socrates to Asouzu and show why my explanation offers a better understanding of the problem. (shrink)

We shall evaluate two strategies for motivating the view that knowledge is the norm of belief. The first draws on observations concerning belief's aim and the parallels between belief and assertion. The second appeals to observations concerning Moore's Paradox. Neither of these strategies gives us good reason to accept the knowledge account. The considerations offered in support of this account motivate only the weaker account on which truth is the fundamental norm of belief.

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)

This paper brings two fresh perspectives on Lewis’s theory of time travel. First: many key aspects and theoretical desiderata of Lewis’s theory can be captured in a framework that does not commit to eternalism about time. Second: implementing aspects of Lewisian time travel in a non-eternalist framework provides theoretical resources for a better treatment of time travel to the future. While time travel to the past has been extensively analyzed, time travel to the future has been comparatively underexplored. I make (...) progress on this topic. Along the way, I discuss Lewis’s lesser-known time travel oeuvre, especially his volume of correspondence and lectures on the topic collected in Beebee and Fisher (2020) and Janssen-Lauret & MacBride (forthcoming). Lewis’s body of unpublished work on time travel yields fruitful insights into his broader thinking on the subject. (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)

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)

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)

We call something a paradox if it strikes us as peculiar in a certain way, if it strikes us as something that is not simply nonsense, and yet it poses some difficulty in seeing how it could make sense. When we examine paradoxes more closely, we find that for some the peculiarity is relieved and for others it intensifies. Some are peculiar because they jar with how we expect things to go, but the jarring is to do with imprecision (...) and misunderstandings in our thought, failures to appreciate the breadth of possibility consistent with our beliefs. Other paradoxes, however, pose deep problems. Closer examination does not explain them away. Instead, they challenge the coherence of certain conceptual resources and hence challenge the significance of beliefs which deploy those resources. I shall call the former kind weak paradoxes and the latter, strong paradoxes. Whether a particular paradox is weak or strong is sometimes a matter of controversy—sometimes it has been realised that what was thought strong is in fact weak, and vice versa,— but the distinction between the two kinds is generally thought to be worth drawing. In this Cchapter, I shall cover both weak and strong probabilistic paradoxes. (shrink)

Expressivists explain the expression relation which obtains between sincere moral assertion and the conative or affective attitude thereby expressed by appeal to the relation which obtains between sincere assertion and belief. In fact, they often explicitly take the relation between moral assertion and their favored conative or affective attitude to be exactly the same as the relation between assertion and the belief thereby expressed. If this is correct, then we can use the identity of the expression relation in the two (...) cases to test the expressivist account as a descriptive or hermeneutic account of moral discourse. I formulate one such test, drawing on a standard explanation of Moore's paradox. I show that if expressivism is correct as a descriptive account of moral discourse, then we should expect versions of Moore's paradox where we explicitly deny that we possess certain affective or conative attitudes. I then argue that the constructions that mirror Moore's paradox are not incoherent. It follows that expressivism is either incorrect as a hermeneutic account of moral discourse or that the expression relation which holds between sincere moral assertion and affective or conative attitudes is not identical to the relation which holds between sincere non-moral assertion and belief. A number of objections are canvassed and rejected. (shrink)

Philosophy of science is seen by most as a meta-discipline – one that takes science as its subject matter, and seeks to acquire knowledge and understanding about science without in any way affecting, or contributing to, science itself. Karl Popper’s approach is very different. His first love is natural philosophy or, as he would put it, cosmology. This intermingles cosmology and the rest of natural science with epistemology, methodology and metaphysics. Paradoxically, however, one of his best known contributions, his proposed (...) solution to the problem of demarcation, helps to maintain the gulf that separates science from metaphysics, thus fragmenting cosmology into falsifiable science on the one hand, untestable philosophy on the other. This has damaging repercussions for a number of issues Popper tackles, from the problem of induction to simplicity of theory and quantum theory. But his proposed solution to the demarcation problem is untenable. Metaphysical assumptions are an integral part of scientific knowledge, inherent in the persistent acceptance of unified theories against the evidence. Once this is appreciated, it becomes obvious that natural philosophy, a synthesis of science and philosophy, is both more rigorous and of greater intellectual value than the two dissociated components we have today. What Popper sought for could come to full fruition. Problems that Popper tackled, from the problem of induction, to the problem of unity of theory, problems of quantum theory, and problems concerning the scope and limits of physics, all receive more adequate resolution within the new, fully-fledged natural philosophy. (shrink)

Two semantic paradoxes, the Liar and Curry’s paradox, are analysed using a newly developed conception of procedural semantics (semantics according to which the truth of propositions is determined algorithmically), whose main characteristic is its departure from methodological realism. Rather than determining pre-existing facts, procedures are constitutive of them. Of this semantics, two versions are considered: closed (where the halting of procedures is presumed) and open (without this presumption). To this end, a procedural approach to deductive reasoning is developed, based (...) on the idea of simulation. As is shown, closed semantics supports classical logic, but cannot in any straightforward way accommodate the concept of truth. In open semantics, where paradoxical propositions naturally ‘belong’, they cease to be paradoxical; yet, it is concluded that the natural choice—for logicians and common people alike—is to stick to closed semantics, pragmatically circumventing problematic utterances. (shrink)

The Buddhist Nikāya Suttas frequently mention the concept of fear (bhaya) and related synonyms. This concept does not receive much scholarly attention by subsequent Buddhist philosophers. Recent scholars identify a ‘paradox of fear’ in several traditions of classical Indian Buddhism (Brekke 1999, Finnigan 2019, Giustarini 2012). Each scholar points out, in their respective textual contexts, that fear is evaluated in two ways; one positive and the other negative. Brekke calls this the “double role” of fear (1999: 443). Each also (...) identify fear as purposely elicited to motivate acts aimed at achieving fearlessness, where freedom from fear is characteristic of nibbāna. They all find this puzzling. Finnigan asks: “Why would one purposefully incite fear if one’s goal is its elimination?” (2019: 221). Giustarini says that fear has a “contradictory nature” (2012: 513); Brekke calls it “the paradox of fear” (1999: 442). This article introduces the ‘paradox of fear’ as it appears in the Bodhicaryāvatāra of Śāntideva and the Nikāya suttas. It then critically examines Brekke and Giustarini’s proposed solutions. It argues that they get some things right in ways that are both supported by the Nikāyas and relevant to Śāntideva but that they leave some important questions unanswered. The article contends that these questions are best answered if fear is analysed as appropriate when its objects are related to karma and rebirth. (shrink)

In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which individually, (...) but not jointly, lack the problematic feature. (shrink)

This study explored the experiences of the newly-hired faculty in the university to acquire an in-depth and profound understanding of these experiences. It involved eight purposively chosen faculty in a semi-structured interview and focus group discussion documented in voice and video recorders. Using Colaizzi’s seven step-approach to data analysis, results revealed three paradoxical themes: the joys and struggles of teaching, successes and pains of learning, and the privileges and challenges of serving. On the one hand, the joys and struggles of (...) teaching were brought about by their adjustments in instruction. On the other hand, successes and pains of learning centered on professional growth. Finally, the privileges and challenges of serving incorporated the experiences in research, production, and extension. Generally, these teachers have experienced ups and downs in their first two years of teaching at a higher education institution. On the basis of study findings, implications and recommendations are discussed. (shrink)

Judgment aggregation theory, or rather, as we conceive of it here, logical aggregation theory generalizes social choice theory by having the aggregation rule bear on judgments of all kinds instead of merely preference judgments. It derives from Kornhauser and Sager’s doctrinal paradox and List and Pettit’s discursive dilemma, two problems that we distinguish emphatically here. The current theory has developed from the discursive dilemma, rather than the doctrinal paradox, and the final objective of the paper is to give (...) the latter its own theoretical development along the line of recent work by Dietrich and Mongin. However, the paper also aims at reviewing logical aggregation theory as such, and it covers impossibility theorems by Dietrich, Dietrich and List, Dokow and Holzman, List and Pettit, Mongin, Nehring and Puppe, Pauly and van Hees, providing a uniform logical framework in which they can be compared with each other. The review goes through three historical stages: the initial paradox and dilemma, the scattered early results on the independence axiom, and the so-called canonical theorem, a collective achievement that provided the theory with its specific method of analysis. The paper goes some way towards philosophical logic, first by briefly connecting the aggregative framework of judgment with the modern philosophy of judgment, and second by thoroughly discussing and axiomatizing the ‘general logic’ built in this framework. (shrink)

This paper deals with Veronica Rodriguez-Blanco’s answer to the paradox of the normativity of law: How can autonomous self-legislating persons act, without compromising their autonomy and their will, following legal rules? Regarding Rodriguez-Blanco’s answer, I offer two main critiques. The first one is based on Rodriguez-Blanco’s comments to David Enoch’s paper in which I argue against the idea that a descriptive theoretical account of law can, and should, give an answer to general problems of normativity due to the fact (...) that a theoretical approach that engages in questions about the normativity of law cannot be purely descriptive, therefore against Rodriguez-Blanco I conclude that Enoch’s answer is the only response a descriptive account is able to offer. The second criticism focuses on Rodriguez-Blanco’s response to the paradox and argues that her solution is not, in fact, a descriptive one, but one that relies on strong normative premises, which as it turns out defend a perfectionist perspective towards the law.Resumen:Este trabajo analiza la respuesta que Veronica Rodriguez-Blanco propone para resolver la paradoja de la normatividad del derecho: ¿Cómo es posible que una persona autónoma actúe siguiendo los mandatos de normas jurídicas sin comprometer su autonomía ni su voluntad? El autor ofrece dos críticas a la respuesta de Rodriguez-Blanco. La primera de ellas está basada en los comentarios que Rodriguez-Blanco ha hecho sobre la propuesta de David Enoch. En este punto, el autor argumenta en contra de la idea según la cual una perspectiva descriptiva del derecho puede, y debe, tratar de responder a los problemas generales de la normatividad del derecho. De acuerdo con el autor, una perspectiva que pretenda dar respuesta a los problemas de la normatividad del derecho no puede ser una perspectiva puramente descriptiva. En este sentido, el autor sostiene que la respuesta que ofrece Enoch es la única respuesta que una perspectiva descriptiva del derecho puede dar. La segunda crítica está dirigida a la respuesta que Rodriguez-Blanco da sobre la paradoja de la normatividad. En este segundo punto el autor argumenta que la perspectiva de Rodriguez-Blanco no es una perspectiva descriptiva como ella presume, sino que adopta una perspectiva normativa la cual, además, está comprometida con una idea perfeccionista del derecho. (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)

Starting with a discussion of what I call Koyré’s paradox of conceptual novelty, I introduce the ideas of Damerow et al. on the establishment of classical mechanics in Galileo’s work. I then argue that although the view of Damerow et al. on the nature of Galileo’s conceptual innovation is convincing, it misses an essential element: Galileo’s use of the experiments described in the first day of the Two New Sciences. I describe these experiments and analyze their function. Central to (...) my analysis is the idea that Galileo’s pendulum experiments serve to secure the reference of his theoretical models in actually occurring cases of free fall. In this way Galileo’s experiments constitute an essential part of the meaning of the new concepts of classical mechanics. (shrink)

The importance of situational constraint for moral evaluations is widely accepted in philosophy, psychology, and the law. However, recent work suggests that this relationship is actually bidirectional: moral evaluations can also influence our judgments of situational constraint. For example, if an agent is thought to have acted immorally rather than morally, that agent is often judged to have acted with greater freedom and under less situational constraint. Moreover, when considering interpersonal situations, we judge that an agent who forces another to (...) act immorally (versus morally) uses more force. These two features can result in contradictory response patterns in which participants judge both that (1) a forcer forced a forcee to act and (2) the forcee was not forced by the forcer to act. Here, we characterize potential psychological mechanisms, in particular, “moral focus” and counterfactual reasoning that account for this paradoxical pattern of judgments. (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)

You may not know me well enough to evaluate me in terms of my moral character, but I take it you believe I can be evaluated: it sounds strange to say that I am indeterminate, neither good nor bad nor intermediate. Yet I argue that the claim that most people are indeterminate is the conclusion of a sound argument—the indeterminacy paradox—with two premises: (1) most people are fragmented (they would behave deplorably in many and admirably in many other situations); (...) (2) fragmentation entails indeterminacy. I support (1) by examining psychological experiments in which most participants behave deplorably (e.g., by maltreating “prisoners” in a simulated prison) or admirably (e.g., by intervening in a simulated theft). I support (2) by arguing that, according to certain plausible conceptions, character evaluations presuppose behavioral consistency (lack of fragmentation). Possible reactions to the paradox include: (a) denying that the experiments are relevant to character; (b) upholding conceptions according to which character evaluations do not presuppose consistency; (c) granting that most people are indeterminate and explaining why it appears otherwise. I defend (c) against (a) and (b). (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)

When two omnipotent beings are randomly and sequentially selecting positive integers, the being who selects second is almost certain to select a larger number. I then use the relativity of simultaneity to create a paradox by having omnipotent beings select positive integers in different orders for different observers.

For some reason, participants hold agents more responsible for their actions when a situation is described concretely than when the situation is described abstractly. We present examples of this phenomenon, and survey some attempts to explain it. We divide these attempts into two classes: affective theories and cognitive theories. After criticizing both types of theories we advance our novel hypothesis: that people believe that whenever a norm is violated, someone is responsible for it. This belief, along with the familiar workings (...) of cognitive dissonance theory, is enough to not only explain all of the abstract/concrete paradoxes, but also explains seemingly unrelated effects, like the anthropomorphization of malfunctioning inanimate objects. (shrink)