This essay takes up two questions. First, what does it mean to say that someone creates her own luck? At least colloquially speaking, luck is conceived as something out of an agent's control. So how could an agent increase or decrease the likelihood that she'll be lucky? Building on some recent work on the metaphysics of luck, the essay argues that there is a sense in which agents can create their own luck because people with more (...) skill tend to have more opportunities to benefit from luck. Second, what implications does this conception of luck have for related topics such as how we evaluate performances (like shooting an arrow), including coming to know something? The ubiquitous presence of luck in our actions is often underappreciated. The essay argues that when we combine an expected outcomes view of luck with a counterfactual view of causation, the distinction between environmental and intervening veritic luck seems to disappear. We need a more nuanced view of how luck sometimes undermines credit for success in agents' actions. The upshot of this view is that while luck may undermine the creditworthiness of an agent's success, it only partially undermines creditworthiness. (shrink)

Epistemic luck has been the focus of much discussion recently. Perhaps the most general knowledge-precluding type is veritic luck, where a belief is true but might easily have been false. Veritic luck has two sources, and so eliminating it requires two distinct conditions for a theory of knowledge. I argue that, when one sets out those conditions properly, a solution to the generality problem for reliabilism emerges.

Epistemic luck is a generic notion used to describe any of a number of ways in which it can be accidental, coincidental, or fortuitous that a person has a true belief. For example, one can form a true belief as a result of a lucky guess, as when one believes through guesswork that “C” is the right answer to a multiple-choice question and one’s belief just happens to be correct. One can form a true belief via wishful thinking; for (...) example, an optimist’s belief that it will not rain may luckily turn out to be correct, despite forecasts for heavy rain all day. One can reason from false premises to a belief that coincidentally happens to be true. One can accidentally arrive at a true belief through invalid or fallacious reasoning. And one can fortuitously arrive at a true belief from testimony that was intended to mislead but unwittingly reported the truth. In all of these cases, it is just a matter of luck that the person has a true belief. -/- Until the twenty-first century, there was nearly universal agreement among epistemologists that epistemic luck is incompatible with knowledge. Call this view “the incompatibility thesis.” In light of the incompatibility thesis, epistemic luck presents epistemologists with three distinct but related challenges. The first is that of providing an accurate analysis of knowledge (in terms of individually necessary and jointly sufficient conditions for “S knows that p,” where ‘S’ represents the knower and ‘p’ represents the proposition known). An adequate analysis of knowledge must succeed in specifying conditions that rule out all instances of knowledge-destroying epistemic luck. The second challenge is to resolve the skeptical paradox that the ubiquity of epistemic luck generates: As will become clear in section 2c, epistemic luck is an all-pervasive phenomenon. Coupling this fact with the incompatibility thesis entails that we have no propositional knowledge. The non-skeptical epistemologist must somehow reconcile the strong intuition that epistemic luck is not compatible with knowledge with the equally evident observation that it must be. The third challenge concerns the special skeptical threat that epistemic luck seems to pose for more reflective forms of knowledge, such as knowing that one knows. Each of these challenges will be explored in the present article. (shrink)

Among epistemologists, it is not uncommon to relate various forms of epistemic luck to the vexed debate between internalists and externalists. But there are many internalism/externalism debates in epistemology, and it is not always clear how these debates relate to each other. In the present paper I investigate the relation between epistemic luck and prominent internalist and externalist accounts of epistemic justification. I argue that the dichotomy between internalist and externalist concepts of justification can be characterized in terms (...) of epistemic luck. Whereas externalist theories of justification are incompatible with veritic luck but not with reflective luck, the converse is true for internalist theories of justification. These results are found to explain and cohere with some recent findings from elsewhere in epistemology, and support a surprising picture of justification, on which internalism and externalism are complementary rather than contradictory positions. (shrink)

This essay takes up two questions. First, what does it mean to say that someone creates her own luck? At least colloquially speaking, luck is conceived as something out of an agent's control. So how could an agent increase or decrease the likelihood that she'll be lucky? Building on some recent work on the metaphysics of luck, the essay argues that there is a sense in which agents can create their own luck because people with more (...) skill tend to have more opportunities to benefit from luck. Second, what implications does this conception of luck have for related topics such as how we evaluate performances (like shooting an arrow), including coming to know something? The ubiquitous presence of luck in our actions is often underappreciated. The essay argues that when we combine an expected outcomes view of luck with a counterfactual view of causation, the distinction between environmental and intervening veritic luck seems to disappear. We need a more nuanced view of how luck sometimes undermines credit for success in agents' actions. The upshot of this view is that while luck may undermine the creditworthiness of an agent's success, it only partially undermines creditworthiness. (shrink)

The problem of epistemic luck arises when a person has a true belief that is only true by luck. Before Gettier, it was believed that the element of justification would be sufficient for knowledge; but he showed that it is possible to have a justified true belief that is not an example of knowledge because of the intrusion of luck. Duncan Pritchard has examined epistemic luck in an extensive and detailed manner. He offers a modal account (...) of luck based on two elements: a possible-worlds analysis of counterfactual conditions and a significance condition for the factors that make the truth of the belief lucky. Pritchard argues for the superiority of this account to those that focus on whether the truth of the belief is “accidental” and on whether the believer has sufficient control over the belief. Epistemic luck may be “reflective” or “veritic”. Both undermine knowledge claims, although Pritchard gives the central role to veritic luck in his anti-luck epistemology, which is based on two elements: a safety principle and a condition to ensure that the cognitive faculties of the agent are not impaired. In this article, we will describe, analyze, and subsequently, evaluate the viewpoint of Pritchard. In addition to the critiques offered by others, ambiguities in his counterfactual account of luck and other components of his theory detract from his theory. (shrink)

Among epistemologists, it is not uncommon to relate various forms of epistemic luck to the vexed debate between internalists and externalists. But there are many internalism/externalism debates in epistemology, and it is not always clear how these debates relate to each other. In the present paper I investigate the relation between epistemic luck and prominent internalist and externalist accounts of epistemic justification. I argue that the dichotomy between internalist and externalist concepts of justification can be characterized in terms (...) of epistemic luck. Whereas externalist theories of justification are incompatible with veritic luck but not with reflective luck, the converse is true for internalist theories of justification. These results are found to explain and cohere with some recent findings from elsewhere in epistemology, and support a surprising picture of justification, on which internalism and externalism are complementary rather than contradictory positions. (shrink)

Although there has been little written to date that speaks directly to problems of religious luck, described in other terms these problems have a long history. Contemporary contributors to the literature have referred to “soteriological luck” (Anderson 2011) “salvific luck” (Davidson 1999) and “religious luck” (Zagzebski 1994). Using “religious” as the unifying term, Part I of this monograph begins with the need a more comprehensive taxonomy. Serious philosophic interest in moral and epistemic luck took hold (...) only after comprehensive taxonomies for those kinds of luck were introduced, but this has not yet been done for religious luck. Even if incomplete, the more comprehensive taxonomy, as introduced in Chapter One enables better diagnostic questions to be raised for researchers. Emerging questions about potentially ‘luck leaning’ attributions of good/bad religious luck, and of the possibility and desirability of “luck free theologies,” are questions which I hope to motivate as of central interest to researchers in philosophy of religion, both secular and religious. The taxonomy highlights why we should take two concerns — with the concept of religious luck and with asymmetric or sharply differential ascriptions of religious value — to be inextricably connected. The connection between attributing good/bad luck and violating inductive norms is easy to see upon reflection. One related distinction common in recent work on epistemic luck is that between benign evidential luck (‘benign’ because consistent with justified belief and knowledge), and malign (positive epistemic status undercutting) veritic luck. How, philosophically, this distinction should be understood is an especially acute problem when it comes to testimonial trust, and to intellectually virtuous or vicious ways of assessing testimonial claims, and sources of claims. So the chapter concludes with development of the case of Tess, as an example of testimonial environmental veritic luck. The Tess case is constructed to be formally analogous to the environmental veritic luck operating in fake barn cases (where visual perception rather than reception of testimony is the source of the agent’s belief). There does seem to be an intrinsic connection between epistemic assessment of the agent’s beliefs and the inductive context in which their own and their religious community’s inquiry takes place. This will allow for some potentially powerful thought experiments in successive chapters, about luck, risk, and questions of epistemic in/justice as they pertain to religious faith ventures. (shrink)

Does ‘remembering that p’ entail ‘knowing that p’? The widely-accepted epistemic theory of memory answers affirmatively. This paper purports to reveal the tension between ETM and the prevailing anti-luck epistemology. Central to my argument is the fact that we often ‘vaguely remember’ a fact, of which one plausible interpretation is that our true memory-based beliefs formed in this way could easily have been false. Drawing on prominent theories of misremembering in philosophy of psychology, I will construct cases where the (...) subject vaguely remembers that p while fails to meet the safety condition, which imply either that ETM is false or that safety is unnecessary for knowledge. The conclusion reached in this paper will be a conditional: if veritic epistemic luck is incompatible with knowledge, then ‘remembering that p’ does not entail ‘knowing that p’. (shrink)

Duncan Pritchard’s book (Epistemic Luck, Oxford University Press, 2005) concerns the interplay between two disturbing kinds of epistemic luck, termed “reflective” and “veritic,” and two types of arguments for skepticism, one based on a closure principle for knowledge and the other on an underdetermination thesis about the quality of our evidence for the everyday propositions we believe. Pritchard defends the view that a safety-based account of knowledge can answer the closure argument and provide an account of how (...) veritic epistemic luck is eliminated. He also argues that reflective epistemic luck cannot be eliminated, and that even though it is the sort of luck with which the underdetermination argument is concerned, the fact that this type of luck cannot be eliminated doesn’t undermine knowledge. Instead, it undermines the assertibility of our knowledge, at least in skeptical contexts. So when the skeptic challenges the idea that we know using the underdetermination principle, we have no legitimate response to offer, and it is this fundamental fact of epistemic life that Pritchard terms our inevitable epistemic angst. (shrink)

One of the most widely recognised intuitions about knowledge is that knowing precludes believing truly as a matter of luck. On Pritchard’s highly influential modal account of epistemic luck, luckily true beliefs are, roughly, those for which there are many close possible worlds in which the same belief formed in the same way is false. My aim is to introduce a new challenge to this account. Starting from the observation—as documented by a number of recent EEG studies—that our (...) capacity to detect visual stimuli fluctuates with the phase of our neural oscillations, I argue that there can be very close possible worlds in which an actual-world detectable stimulus is undetectable. However, this doesn’t diminish our willingness to attribute knowledge in the case that the stimulus is detectable, even when undetectability would result in the same belief formed in the same way being false. As I will argue at length, the modal account appears unable to accommodate this result. (shrink)

In this article, I develop and defend a version of reliabilism – internal reasons reliabilism – that resolves the paradox of epistemic luck, solves the Gettier problem by ruling out veritic luck, is immune to the generality problem, resolves the internalism/externalism controversy, and preserves epistemic closure.

The recent movement towards virtue–theoretic treatments of epistemological concepts can be understood in terms of the desire to eliminate epistemic luck. Significantly, however, it is argued that the two main varieties of virtue epistemology are responding to different types of epistemic luck. In particular, whilst proponents of reliabilism–based virtue theories have been focusing on the problem of what I call “veritic” epistemic luck, non–reliabilism–based virtue theories have instead been concerned with a very different type of epistemic (...) luck, what I call “reflective” epistemic luck. It is argued that, prima facie at least, both forms of epistemic luck need to be responded to by any adequate epistemological theory. The problem, however, is that one can best eliminate veritic epistemic luck by adducing a so–called safety–based epistemological theory that need not be allied to a virtue–based account, and there is no fully adequate way of eliminating reflective epistemic luck. I thus conclude that this raises a fundamental difficulty for virtue–based epistemological theories, on either construal. [ABSTRACT FROM AUTHOR]. (shrink)

Clare, the titular character of The Time Traveller's Wife, reflects that "Everything seems simple until you think about it." This might well be a mantra for the whole of philosophy, but a fair few terms tend to stick out. "Knowledge", "goodness" and "happiness" for example, are all pervasive everyday terms that undergo significant philosophical analysis. "Luck", I think, is another one of these terms. Wishing someone good luck in their projects, and cursing our bad luck when success (...) seems so close to our reach or failure could have so easily been otherwise, happens so often that we rarely stop to reflect on what we really mean. Philosophical reflection on the nature of luck has a rich tradition, that is by no stretch confined to the Western philosophical canon. However, it has only very recently become one of the goals of philosophy to provide a clear account of what luck actually amounts to. This, in part, is the goal of this thesis. The thesis has two primary motivations. The first is to offer and defend a general account of luck that overcomes the problems faced by the current accounts of luck that are available in the current philosophical literature. The second is to apply this general account of luck to the areas of metaethics and epistemology where luck has been a pervasive and problematic concept, and demonstrate how this account of luck may resolve or further illuminate some of the problems that the notion has generated. The thesis is roughly split into two parts. The first half of the thesis focuses on the former objective of offering an account of luck. Chapter 1 offers a selected history of the philosophy of luck that spans from the Ancient Greeks to the present day, so that we might properly situate the current work on luck as part of the broader historical importance of the concept. Chapter 2 will set out the major rival to the theory of luck that I will offer - the lack of control account of luck. LCAL has various iterations across the literature, but is most clearly articulated by Wayne Riggs and E.J. Coffman. Both Coffman and Riggs add and adapt their own conditions to LCAL specifically so that the account may overcome several problems that have been levied against it. These further conditions are not incompatible so, to provide the strongest lack of control account possible, I have combined them to form a lack of control account I have called Combined LCAL - LCAL. The latter part of the chapter pits LCAL against some of the problems that have been raised against LCAL. However, despite the efforts of both Riggs and Coffman, even LCAL fails to counter some of these objections. For these reasons I have rejected LCAL has a viable candidate for an account of luck. Chapter 3 sets out a modal account of luck, as argued for by Pritchard, where an event is lucky only if it occurs in the actual world, but not in a relevant set of nearby possible worlds. Here I further elaborate on how we should understand the modal distances using Lewisian possible world semantics, and what worlds should be taken into consideration when fixing the relevant set of nearby possible worlds. I argue that these relevant sets of worlds should be fixed according to the domain of inquiry of which the luck is being applied - this I call the type of luck. Examples of this is the current literature are resultant luck - the type of luck concerned with the results of our actions, and veritic luck - the type of luck concerned with the modal safety of our belief formation. Due to the multitude of types of luck across disciplinary areas, a general modal account of luck requires flexibility in what factors should fix the relevant sets of possible worlds. I achieve this by providing a [TYPE] function for the general modal account of luck, which is used as a mean of inserting the relevant fixing conditions for any domain of inquiry. Chapter 3, in a similar vein to Chapter 2, pits the general modal account of luck against some of the problems that have been levied against MAL, specifically the Buried Treasure problem raised by Lackey and the agent causation problem as raised by Levy. More successfully, the modal account offered stands up against these criticisms. For these reasons, the modal condition understood with the [TYPE] function and Lewisian semantics concerning modal distances, will be adopted to make up one half of the conditions for my account of luck. Chapter 4 will look at the second condition for an account of luck - the significance condition. The chapter will set out the reasons for adopting a significance condition at all, and some of the ways in which the condition has been articulated by Rescher, Pritchard and Ballantyne. All of these current views of the significance condition will be found wanting due to their inability to make sense of certain kinds of luck in specific normative domains. For example, Ballantyne's account of significance focuses on the interests of an agent, yet for certain types of moral luck, the interests of the agent are irrelevant. Instead, I propose a relativised significance condition, where the value of the event is relative to the value of the normative domain in which the luck is being ascribed. Epistemic luck requires a focus on the epistemic significance of the event for the agent, moral luck requires a focus on the moral or ethical significance of the event for the agent, and so on. This I call the kind of luck. Similar to the [TYPE] function for the modal condition for luck, the significance condition requires a [NORMATIVE DOMAIN] function where the relevant normative domain can be inserted depending on the kind of luck. This version of the significance condition will be conjoined with the modal condition as set out in Chapter 3 to form the correct general account of luck. Chapter 5 is the first chapter of the second half of the thesis that concerns applying the account of luck set out in part 1 to more specific domains of inquiry. Chapter 5 concerns moral luck, more specifically, resultant moral luck. Moral luck has traditionally been understood in terms of lack of control. This chapter looks at how Pritchard and Driver have attempted to understand moral luck using modal conditions. However, it is argued that these attempts would be more successful if we adopted the account of luck that I have offered in previous chapters. The chapter will go on to look at two possible problems that may be faced by this modal account of luck, and how it may resolve these problems. Chapter 6, the final chapter, looks at epistemic luck, specifically how the adoption of the modal account I have offered resolves a particular problem targeted at anti-luck epistemology by Ballantyne. The problem, Ballantyne argues, is that given that luck requires a significance condition, the degree of significance affects the degree of luck and that the degree of luck involved in our belief formation affects whether we are in a position to know the target proposition, that the result is that degree of significance affects our ability to know. For at least some instances of this - such as the aesthetic significance that we assign to the target proposition - the result will be that non-epistemic factors that have no relevance at all whether an agent is in a position to know will affect that agent's position to know. The resolution to this problem can be found in a two part solution. The first part is to demonstrate that any degree of veritic epistemic luck results in the agent failing to know. The second is that through the relativisation of the significance condition, any type of value will not affect an agent's position to know, only the epistemic value. With these two considerations in mind, the latter of which that can only be held through the adoption of the modal account of luck I have offered, the problem may be resolved. (shrink)

There is a widely shared belief in contemporary epistemology that propositional knowledge is incompatible with certain kinds of luck, most of all with so called veritic luck. A subject is veritically lucky in his or her belief that p if this belief is true not due to its foundations (for example, reasons which an agent has to believe that p) but by mere accident. The acceptance of the thesis of incompatibility of knowledge with this kind of (...) class='Hi'>luck led to significant modifications of a popular modern epistemological tripartite analysis of propositional knowledge according to which subject knows that p if and only if he or she believes that p is true, p is actually true, and an agent’s belief that p is true is justified. In his famous paper “Is True Justified Belief Knowledge” E. Gettier demonstrated that true justified belief may not be knowledge. The core of the problem is that in the cases described by Gettier and the like an agent’s belief, though justified, is true by accident. This gave rise to a set of theories introducing additional conditions of knowledge which could exclude veritic luck. In this paper the author critically discusses main modifications of the tripartite concept of knowledge aimed at making it independent on veritic luck, and show that they are unable to solve this problem. He agrees with those who think that the very thesis of incompatibility of knowledge with veritic luck is wrong. But he disagrees that all kinds of veritic luck are compatible with knowledge: the author supposes that good veritic luck is compatible with knowledge only when it compensates some negative effect of antecedent bad epistemic luck. According to this view original Gettier examples are not cases of knowledge whereas broken-clocks case and fake-barns case are. This account allows treating many classic cases of dependence of knowledge on luck as cases of knowledge-acquirement, but in the same time it excludes the inclusion into the class of knowledge such intuitively irrelevant outcomes as lucky guess and wishful thinking. (shrink)

The idea that knowledge as an individual mental attitude with certain propositional content is not only true justified belief but a belief the truth of which does not result from any kind of luck, is widely spread in contemporary epistemology. This account is known as anti-luck epistemology. A very popular explanation of the inconsistency of that concept of knowledge with the luck-dependent nature of truth (so called veritic luck taking place when a subject’s belief could (...) not be true if not by mere coincidence) presumes that the status of propositional knowledge crucially depends on the qualities of actions that result in the corresponding belief, or processes backing them, which reflect the socalled intellectual virtues mainly responsible for subject’s relevant competences. This account known as Virtue Epistemology presumes that if a belief is true exclusively or mainly due to its dependence on intellectual virtues, it just cannot be true by luck, hence no place for lucky knowledge. But this thesis is hard to prove given the existence of true virtuous beliefs which could nevertheless be false if not for some lucky (for the knower) accident. This led to an appearance of virtue epistemological theories aimed specifically at an assimilation of such cases. Their authors try to represent the relevant situations as such where the contribution of luck is not crucial whereas the contribution of virtues is crucial. This article provides a critical analysis of the corresponding arguments as part of a more general study of the ability of Virtue Epistemology to provide justification for the thesis of incompatibility of propositional knowledge with veritic luck. It is shown that there are good reasons to doubt that Virtue Epistemology can do this. (shrink)

The core thesis of anti-luck epistemology is the incompatibility thesis, that is, knowledge is incompatible with veritic epistemic luck. Traditionally, anti-luck epistemologists hold that there are two distinct types of veritic epistemic luck, viz, intervening luck and environmental luck. The former occurs when something luckily intervenes between the subject’s belief and the target fact, which renders the subject’s belief luckily true. The latter can be found in cases where the subject’s belief is (...) luckily true when she is in an unfriendly epistemic environment. This paper purports to show that there is another long-neglected type of veritic epistemic luck—I name it ‘interpretative luck’. It refers to the type of luck occurring when the subject accidentally chooses the correct interpretation of evidence and thus her belief is luckily true. I will demonstrate that no proper reasons can support the incompatibility between interpretative luck and knowledge. Instead, the price for insisting this incompatibility would be unacceptably high. Therefore, the existence of interpretative luck falsifies the incompatibility thesis of anti-luck epistemology. (shrink)

Explores the embodied aspects of ownership and private property as these emerge in a range of American literary texts across the late eighteenth and early nineteenth century.

Explores the embodied aspects of ownership and private property as these emerge in a range of American literary texts across the late eighteenth and early nineteenth century.

We prove that forp-optimal fields a cell decomposition theorem follows from methods going back to Denef’s paper [7]. We derive from it the existence of definable Skolem functions and strongp-minimality. Then we turn to stronglyp-minimal fields satisfying the Extreme Value Property—a property which in particular holds in fields which are elementarily equivalent to ap-adic one. For such fieldsK, we prove that every definable subset ofK×Kdwhose fibers overKare inverse images by the valuation of subsets of the value group is semialgebraic. Combining (...) the two we get a preparation theorem for definable functions onp-optimal fields satisfying the Extreme Value Property, from which it follows that infinite sets definable over such fields are in definable bijection iff they have the same dimension. (shrink)

We study finitely generated free Heyting algebras from a topological and from a model theoretic point of view. We review Bellissima’s representation of the finitely generated free Heyting algebra; we prove that it yields an embedding in the profinite completion, which is also the completion with respect to a naturally defined metric. We give an algebraic interpretation of the Kripke model used by Bellissima as the principal ideal spectrum and show it to be first order interpretable in the Heyting algebra, (...) from which several model theoretic and algebraic properties are derived. In particular, we prove that a free finitely generated Heyting algebra has only one set of free generators, which is definable in it. As a consequence its automorphism group is the permutation group over its generators. (shrink)

In this paper a new resolution to the gamer’s dilemma is presented. The first part of the paper is devoted to strictly formulating the dilemma, and the second to establishing its resolution. The proposed resolution, the grave resolution, aims to resolve not only the gamer’s dilemma, but also a wider set of analogous paradoxes – which together make up the paradox of treating wrongdoing lightly.

Most people agree that murder is wrong. Yet, within computer games virtual murder scarcely raises an eyebrow. In one respect this is hardly surprising, as no one is actually murdered within a computer game. A virtual murder, some might argue, is no more unethical than taking a pawn in a game of chess. However, if no actual children are abused in acts of virtual paedophilia (life-like simulations of the actual practice), does that mean we should disregard these acts with the (...) same abandon we do virtual murder? In this paper I shall outline several arguments which attempt to permit virtual murder, whilst prohibiting virtual paedophilia. (shrink)

Journal of Mathematical Logic, Volume 22, Issue 02, August 2022. Motivated by results of Bagaria, Magidor and Väänänen, we study characterizations of large cardinal properties through reflection principles for classes of structures. More specifically, we aim to characterize notions from the lower end of the large cardinal hierarchy through the principle [math] introduced by Bagaria and Väänänen. Our results isolate a narrow interval in the large cardinal hierarchy that is bounded from below by total indescribability and from above by subtleness, (...) and contains all large cardinals that can be characterized through the validity of the principle [math] for all classes of structures defined by formulas in a fixed level of the Lévy hierarchy. Moreover, it turns out that no property that can be characterized through this principle can provably imply strong inaccessibility. The proofs of these results rely heavily on the notion of shrewd cardinals, introduced by Rathjen in a proof-theoretic context, and embedding characterizations of these cardinals that resembles Magidor’s classical characterization of supercompactness. In addition, we show that several important weak large cardinal properties, like weak inaccessibility, weak Mahloness or weak [math]-indescribability, can be canonically characterized through localized versions of the principle [math]. Finally, the techniques developed in the proofs of these characterizations also allow us to show that Hamkin’s weakly compact embedding property is equivalent to Lévy’s notion of weak [math]-indescribability. (shrink)

In his monumental edition of Callimachus, R. Pfeiffer has questioned the authenticity of three epigrams. More than fifty years ago U. v. Wilamowitz- Moellendorff had rejected Ep. 33 and Ep. 36 4; but Pfeiffer seems to be the first critic to exclude Ep. 63 from the collection of Callimachus' epigrams. Although he sets forth his objections in a long footnote, none of the reviewers has so far discussed this point.

In his recently published Propertiana, Mr. D. R. Shackleton Bailey has given what I believe to be the correct interpretation of the first two lines. He maintains that sacra has no direct connexion with poetry, that it may be virtually synonymous with Manes or possibly signify the rites paid to the dead, or that it can be taken in the sense of their physical relics, the ashes in the urn. He reminds us that nemus is more than a ‘poetic grove’; (...) it must be a ‘consecrated grove’. (shrink)

Let k be an infinite cardinal. A subset of $(^k k)^n $ is a $\Sigma _1^1 $ -subset if it is the projection p[T] of all cofinal branches through a subtree T of $(lt;kk)^{n + 1} $ of height k. We define $\Sigma _k^1 - ,\Pi _k^1 $ - and $\Delta _k^1$ subsets of $(^k k)^n $ as usual. Given an uncountable regular cardinal k with k = k (...) there is a shrink)

In this paper I will evaluate Ali’s dissolution of the gamer’s dilemma. To this end the dilemma will be summarized and Ali’s dissolution formulated. I conclude that Ali has not dissolved the dilemma (at least not fully).

We study the influence of the existence of large cardinals on the existence of wellorderings of power sets of infinite cardinals κ with the property that the collection of all initial segments of the wellordering is definable by a Σ1‐formula with parameter κ. A short argument shows that the existence of a measurable cardinal δ implies that such wellorderings do not exist at δ‐inaccessible cardinals of cofinality not equal to δ and their successors. In contrast, our main result shows that (...) these wellorderings exist at all other uncountable cardinals in the minimal model containing a measurable cardinal. In addition, we show that measurability is the smallest large cardinal property that imposes restrictions on the existence of such wellorderings at uncountable cardinals. Finally, we generalise the above result to the minimal model containing two measurable cardinals. (shrink)

Russell and Walker proposed different ways of constructing instants from events. For an explanation of "time as a continuum," Thomason favored Walker's construction. The present article shows that Russell's construction fares as well. To this end, a mathematical characterization problem is solved which corresponds to the characterization problem that Thomason solved with regard to Walker's construction. It is shown how to characterize those event structures (formally, interval orders) which, through Russell's construction of instants, become linear orders isomorphic to a given (...) (or, deriving, to some—nontrivial ordered) real interval. As tools, separate characterizations for each of resulting (i) Dedekind completeness, (ii) separability, (iii) plurality of elements, (iv) existence of certain endpoints are provided. Denseness is characterized to replace Russell's erroneous attempt. Somewhat minimal nonconstructive principles needed are exhibited, and some alternative approaches are surveyed. (shrink)

Let [Formula: see text] be an expansion of either an ordered field [Formula: see text], or a valued field [Formula: see text]. Given a definable set [Formula: see text] let [Formula: see text] be the ring of continuous definable functions from [Formula: see text] to [Formula: see text]. Under very mild assumptions on the geometry of [Formula: see text] and on the structure [Formula: see text], in particular when [Formula: see text] is [Formula: see text]-minimal or [Formula: see text]-minimal, or (...) an expansion of a local field, we prove that the ring of integers [Formula: see text] is interpretable in [Formula: see text]. If [Formula: see text] is [Formula: see text]-minimal and [Formula: see text] is definably connected of pure dimension [Formula: see text], then [Formula: see text] defines the subring [Formula: see text]. If [Formula: see text] is [Formula: see text]-minimal and [Formula: see text] has no isolated points, then there is a discrete ring [Formula: see text] contained in [Formula: see text] and naturally isomorphic to [Formula: see text], such that the ring of functions [Formula: see text] which take values in [Formula: see text] is definable in [Formula: see text]. (shrink)

Let p be prime number, K be a p‐adically closed field, a semi‐algebraic set defined over K and the lattice of semi‐algebraic subsets of X which are closed in X. We prove that the complete theory of eliminates quantifiers in a certain language, the ‐structure on being an extension by definition of the lattice structure. Moreover it is decidable, contrary to what happens over a real closed field for. We classify these ‐structures up to elementary equivalence, and get in particular (...) that the complete theory of only depends on m, not on K nor even on p. As an application we obtain a classification of semi‐algebraic sets over countable p‐adically closed fields up to so‐called “pre‐algebraic” homeomorphisms. (shrink)

Given an uncountable regular cardinal κ, we study the structural properties of the class of all sets of functions from κ to κ that are definable over the structure 〈H,∈〉 by a Σ1-formula with parameters. It is well known that many important statements about these classes are not decided by the axioms of ZFC together with large cardinal axioms. In this paper, we present other canonical extensions of ZFC that provide a strong structure theory for these classes. These axioms are (...) variations of the Maximality Principle introduced by Stavi and Väänänen and later rediscovered by Hamkins. (shrink)

I argue that there exists a proportional relationship between degrees of moral culpability and degrees of probability, where the more an agent believes her actions will result in certain consequences, the more morally culpable she is for these consequences. I assert that this degree of probability is necessarily diminished by the existence of active supernatural powers. Consequently, agents who believe in such powers are less morally culpable than agents who do not.

In this paper we consider whether Christopher Bartel has resolved the gamer’s dilemma. The gamer’s dilemma highlights a discrepancy in our moral judgements about the permissibility of performing certain actions in computer games. Many gamers have the intuition that virtual murder is permissible in computer games, whereas virtual paedophilia is not. Yet finding a relevant moral distinction to ground such intuitions can be difficult. Bartel suggests a relevant moral distinction may turn on the notion that virtual paedophilia harms women in (...) a way that virtual murder does not. We argue that this distinction is only in a position to provide a partial solution to the dilemma. (shrink)

Montefiore and Formosa (Ethics Inf Technol 24:31, 2022) provide a useful way of narrowing the Gamer’s Dilemma to cases where virtual murder seems morally permissible, but not virtual child molestation. They then resist the dilemma by theorising that the intuitions supporting it are not moral. In this paper, I consider this theory to determine whether the dilemma has been successfully resisted. I offer reason to think that, when considering certain variations of the dilemma, Montefiore and Formosa’s theory may not be (...) the most likely theory available to us. (shrink)