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.

Explaining the notion of legal luck and exploring its justification. Focusing on how legal luck relates to moral luck, legal causation and negligence, and to civil and criminal liability.

Some modern critics of Kant, like Bernard Williams, argue that his ideal of morality is a form of action which lies beyond any empirical determination. The aim of this article is to show that Kant was not only fully aware of the role of contingent elements in moral action, but that his fundamental conception of practical rationality is itself partly constituted by contingent factors. Practical rationality cannot be separated from its exercise and hence from the necessary empirical conditions of human (...) psychology and historical circumstances. Without a maxim there can be no manifestation of practical reason. Without a human character there is no room for moral virtue. Without achievement no moral action can be complete . Thus, human agency extends beyond the realm of pure motive. These themes reflecting Kant's recognition of the importance of contingency in his general theory of rational action are discussed primarily in the light of the Metaphysics of Morals, which in its structure and program explicitly sets out to tie together the a priori and contingent elements in a unified theory. Legality without morality is blind; morality without legality is vacuous. Einige moderne Kritiker Kants wie Bernard Williams behaupten, Kants Sittlichkeitsideal weise auf eine Handlungsform, die außerhalb alles empirisch Feststellbaren liege. Ziel dieses Beitrags ist es zu zeigen, daß Kant sich der Rolle kontingenter Elemente im moralischen Handeln nicht nur voll bewußt war, sondern daß sein grundlegender Entwurf praktischer Vernunft selbst teilweise auf kontingente Faktoren gegründet ist. Praktische Vernunft kann nicht von ihrer Anwendung getrennt werden und also auch nicht von den notwendig empirischen Bedingungen menschlicher Psychologie und von den historischen Umständen des Handelns. Ohne eine Maxime gibt es keine praktische Vernunft. Ohne einen menschlichen Charakter gibt es keine moralische Tugend. Ohne ein erreichtes Ziel kann keine moralische Handlung vollständig sein. Menschliches Handeln überschreitet die Grenzen des Bereichs bloßer Motive.Die Themen zeigen, daß Kant in seiner allgemeinen Theorie vernünftigen Handelns die Kontingenz ernst nimmt. Sie werden hauptsächlich im Lichte der Metaphysik der Sitten diskutiert, die sich in ihrem Programm und in ihrer Struktur explizit vornimmt, apriorische und kontingente Elemente in einer einheitlichen Theorie zu verbinden. Legalität ohne Moralität ist blind; Moralität ohne Legalität ist leer. (shrink)

The article aims to introduce the issue of legal luck and set the direction for further research on this topic. It contains an answer to the question about the relationship between moral luck and legal luck. Three positions are analyzed. The first one, represented by Arthur Ripstein, says that moral luck and legal luck are autonomous issues. The second one, represented by David Enoch, states that legal luck is the result (...) of applying moral luck to law. The third one, on the contrary, refers to the concept of moral luck as a result of applying legal luck to morality. The author discusses diverse conceptions, indicating their strong and weak points, and finally opts for one of them, which leads to a certain view of further research on legal luck. (shrink)

This thesis examines some of the legal philosophical issues that are implicated in the problem of outcome luck. In the context of criminal law, the problem asks whether we should hold agents criminally liable for the consequences of their actions given that those consequences are never wholly within anyone’s control. I conclude that outcomes should matter to an agent’s liability and punishment, and I make this argument indirectly by examining some of the foundational questions in legal theory. (...) The thesis begins by considering a current trend in some areas of philosophy. This trend involves attempts to address philosophical problems surrounding luck by doing conceptual analyses on the nature of luck. Chapter 1 critically examines modal theories, which conceptualize luck, as well as the related concept of risk, in terms of close possible worlds rather than probabilistic likelihood. I argue that not only are modal theories uninformative, but conceptual analyses on luck are unhelpful in addressing philosophical questions surrounding luck. Chapter 2 then returns to the traditional notion of luck as lack of control, and focuses on the relationship between luck, risk, and culpability. Some theorists argue that culpability, for any offence, is in part a function of the degree of risk the agent imposes on others. In the context of criminal law, degrees of luck and risk can both be understood in terms of degrees of control, so the suggestion that culpability is a function of the level of risk imposed (and thus of the degree of control an agent exercises) is attractive for insulating culpability judgments from luck. However, I argue that this view is mistaken because culpability is only sensitive to risk in reckless actions, but not in purposeful actions. The problem of outcome luck may raise different questions for reckless actions and purposeful actions. Chapter 3 looks at the mens rea element of criminal attempts, which is crucial for understanding the problem of luck in the context of purposeful actions. I discuss a variation of what are sometimes referred to as impossible attempts, which have helped shape current English law. I argue that the current doctrine is largely correct, and that perhaps with the exception of few paradigm sexual offences, the mens rea element for attempts should require a direct intention as to the consequence element of an offence, and knowledge or belief as to the circumstance element of that offence. Chapters 4 and 5 then look at normative justifications of criminal punishment. In order to understand whether outcomes should matter for punishment, we must first understand whether and why punishment is an appropriate response to criminal offending. Here, I defend a communicative theory, where punishment is a communicative process between the offender, the political community, and the victim. What punishment communicates is the appropriate degree of censure that is warranted in response to the offender’s wrongdoing. And in doing this, it publicly recognizes the wrong that has been committed by the offender. Chapter 4 offers a detailed explanation of this account, and argues that the political community’s recognition of wrongdoing is a valuable aim of communication. Chapter 5 then takes up a crucial challenge against communicative theories of punishment, which is that such theories fail to take crime prevention seriously. Against this criticism, I will show that general prevention can in fact be an essential part of communicative punishment. And I will show that it is specifically the political community’s recognition of wrongdoing that entails punishment’s preventive aims. (shrink)

© The Author 2018. Published by Oxford University Press on behalf of The Analysis Trust. All rights reserved. For Permissions, please email: [email protected] article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model...Philosophy of law was until recently dominated by abstract investigation into the nature of law, a pursuit known as ‘general jurisprudence’. In this way, it resembled a branch of metaphysics or mid-twentieth century philosophy of mind, seeking to uncover the essential properties (...) of a general and multiply realizable phenomenon. Today, philosophers study law with a sharper focus, and with a more specialized lens – that of ethicists, for example, or epistemologists, or philosophers of action.That is not to say there has been a drop in groundbreaking work in general jurisprudence (see, for... (shrink)

Is there a difference in moral blameworthiness between a murderer and an attempted murderer? Should there be a legal difference between them? These questions are particular instances of the question of moral luck and legal luck (respectively). In this paper, I survey and explain the main argumentative moves within the general philosophical discussion of moral luck. I then discuss legal luck, and the different ways in which this discussion may be related to that (...) of moral luck. (shrink)

In this Article, I elaborate on and defend the following argument: There is no moral luck. If there is no moral luck, there should be no legal luck. Therefore, there should be no legal luck and ). If there is no normatively significant difference between the law doing and allowing, or intending and foreseeing, then there is no normatively significant difference between legal luck and just plain luck that has legal (...) implications. There is no normatively significant difference between the law doing and allowing, or intending and foreseeing. Therefore, there is no normatively significant difference between legal luck and just plain luck that has legal implications and ). Therefore, plain luck should have no legal implications and ). (shrink)

A case of Moral Luck occurs whenever we normatively assess agents for things that depend on factors beyond their control. The paper takes a comparative approach and examines how morality and law deal with such cases. The comparative perspective allows us to explain the problem of Moral Luck as a tension inherent in normative orders: While normative orders are based on a strong connection between responsibility and voluntariness, this idealist assumption is at least partly at odds with their (...) functional requirements as social orders. The paper examines how law and morality converge and differ in resolving this tension in cases of Moral Luck. Finally, the paper concludes with a brief discussion of some more general features of the normative orders of morality and the law that follow from this “bottom-up” analysis of Moral Luck. (shrink)

In a series of ten preregistered experiments (N=2043), we investigate the effect of outcome valence on judgments of probability, negligence, and culpability – a phenomenon sometimes labelled moral (and legal) luck. We found that harmful outcomes, when contrasted with neutral outcomes, lead to increased perceived probability of harm ex post, and consequently to increased attribution of negligence and culpability. Rather than simply postulating a hindsight bias (as is common), we employ a variety of empirical means to demonstrate that (...) the outcome-driven asymmetry across perceived probabilities constitutes a systematic cognitive distortion. We then explore three distinct strategies to alleviate the hindsight bias and its downstream effects on mens rea and culpability ascriptions. Not all are successful, but at least some prove promising. They should, we argue, be taken into consideration in criminal jurisprudence, where distortions due to the hindsight bias are likely considerable and deeply disconcerting. (shrink)

In the criminal law, the law of attempts is of comparatively recent vintage. It is part of an important contemporary legal trend towards early intervention in the criminal process. There are now a substantial number of crimes on the books that, like the crime of attempt, only require that the perpetrator start down the road to carrying out his criminal intentions and do not require him actually to have harmed his victim. Besides the law of attempts, these new crimes (...) include conspiracy and solicitation, forgery and counterfeiting, the possession offences, even corruption of youth. In all these cases, the law is stepping in to forestall harm, rather than waiting until a harm has already happened. (shrink)

In a series of ten preregistered experiments (N=2043), we investigate the effect of outcome valence on judgments of probability, negligence, and culpability – a phenomenon sometimes labelled moral (and legal) luck. We found that harmful outcomes, when contrasted with neutral outcomes, lead to increased perceived probability of harm ex post, and consequently to increased attribution of negligence and culpability. Rather than simply postulating a hindsight bias (as is common), we employ a variety of empirical means to demonstrate that (...) the outcome-driven asymmetry across perceived probabilities constitutes a systematic cognitive distortion. We then explore three distinct strategies to alleviate the hindsight bias and its downstream effects on mens rea and culpability ascriptions. Not all are successful, but at least some prove promising. They should, we argue, be taken into consideration in criminal jurisprudence, where distortions due to the hindsight bias are likely considerable and deeply disconcerting. (shrink)

John Donne's song was hardly written in the tradition of political philosophy, but it has a good deal to say about the theme of luck, both good and bad, which I want to address. There is no doubt but that bad luck has bad consequences for the persons who suffer from it. If there were a costless way in which the consequences of bad luck could be spread across everyone in society at large, without increasing the risk (...) of its occurrence, then most of us would pronounce ourselves better off for the change. In this sense it can be said, for example, that there is a utilitarian grounding for a moral obligation to care and provide for those persons who suffer the fortunes of bad luck. For the sake of argument I do not wish to contest this particular starting point, although there are many who would. Instead, I want to ask the question of whether this moral obligation should be converted into a legal obligation, backed by public force. The dominant answer to that question today is yes. Even those who think that markets should determine decisions on production find that the state has a proper role to reduce the adverse consequences of bad luck. My cast of mind is more skeptical. In life, or, in this instance, politics, “come bad chance, and we do join to it our strength.” In general the effort to use coercion to counter the adverse effects of luck tends only to make matters worse. (shrink)

John Donne's song was hardly written in the tradition of political philosophy, but it has a good deal to say about the theme of luck, both good and bad, which I want to address. There is no doubt but that bad luck has bad consequences for the persons who suffer from it. If there were a costless way in which the consequences of bad luck could be spread across everyone in society at large, without increasing the risk (...) of its occurrence, then most of us would pronounce ourselves better off for the change. In this sense it can be said, for example, that there is a utilitarian grounding for a moral obligation to care and provide for those persons who suffer the fortunes of bad luck. For the sake of argument I do not wish to contest this particular starting point, although there are many who would. Instead, I want to ask the question of whether this moral obligation should be converted into a legal obligation, backed by public force. The dominant answer to that question today is yes. Even those who think that markets should determine decisions on production find that the state has a proper role to reduce the adverse consequences of bad luck. My cast of mind is more skeptical. In life, or, in this instance, politics, “come bad chance, and we do join to it our strength.” In general the effort to use coercion to counter the adverse effects of luck tends only to make matters worse. (shrink)

The notion of individualised evidence holds the key to solve the puzzle of statistical evidence, but there’s still no consensus on how exactly to define it. To make progress on the problem, epistemologists have proposed various accounts of individualised evidence in terms of causal or modal anti-luck conditions on knowledge like appropriate causation, sensitivity and safety. In this paper, I show that each of these fails as satisfactory anti-luck condition, and that such failure lends abductive support to the (...) following conclusion: once the familiar anti-luck intuition on knowledge is extended to individualised evidence, no single causal or modal anti-luck condition on knowledge can succeed as the right anti-luck condition on individualised evidence. This conclusion casts serious doubts on the fruitfulness of the move from anti-luck conditions on knowledge to anti-luck conditions on individualised evidence. I expand on these doubts and point out further aspects where epistemology and the law come apart: epistemic anti- luck conditions on knowledge do not adequately characterise the legal notion of individualised evidence. (shrink)

In the penultimate scene of the Ecclesiazusae, the young man who has come to see his lover is accosted in succession by three old women, each insisting that the new legal code requires him to sleep with her first. In lines 999–1000, the first of these old women, faced with his refusal to cooperate sexually, swears by Aphrodite.

The essence of the moral luck question is whether the responsibility of persons is determined only in light of actions that are within their control or also in light of factors, such as the consequences of their actions, which are beyond their control. Most people seem to have contrasting intuitions regarding this question. On the one hand, there is a common intuition that the responsibility of persons should be judged only in light of what is within their control. On (...) the other hand, there is a strong intuition that the consequences of actions sometimes affect the responsibility of agents even when these consequences depend on factors that are beyond their control. A parallel dilemma is present in the law. Legal rules, particularly criminal law rules and tort rules, often differentiate between agents in light of factors that are beyond their control, and in this sense involve legal luck. Of course, factors beyond the control of persons, including the consequences of their actions, can be significant, with respect to the evaluation of the responsibility of persons for instrumental or epistemic reasons. The question is thus only with respect to the independent significance of factors beyond the control of agents, and particularly the consequences of actions, to the evaluation of the (extent of the) responsibility of agents. Benjamin Zipursky offers an interesting argument in order to support the intuition in favor of moral and legal luck, particularly with regard to consequences, especially the rule according to which the punishment of completed offences is more severe than the punishment of attempts and the rule that tort liability applies only to actions that have caused harm. The aim of this Comment is to evaluate this argument. I will try to consider to what extent Zipursky's explanation merely reiterates the familiar intuition that the normative evaluation of the conduct of persons should be influenced by consequential luck, and to what extent it provides new insights that might appeal also to those who are more forcefully drawn to the contrasting intuition that we should judge people only in light of factors that are within their control. I argue that while Zipursky's suggestions might appeal to those who already share the intuition in favor of (consequential) moral and legal luck, they would not convince those who have doubts regarding moral and legal luck. (shrink)

Brain-computer interfaces (BCIs) are devices primarily intended to allow agents to use prosthetic body parts, wheelchairs, and other mechanisms by forming intentions or performing certain mental actions. In this paper I illustrate how the use of BCIs leads to two unique and unrecognized problems of moral luck. In short, it seems that agents who depend upon BCIs for bodily movement or the use of other mechanisms (henceforth “BCI-agents”) may end up deserving of blame and legal punishment more so (...) than standard counterparts simply due to factors beyond their control. My aim is to explore whether we can avoid the implication that BCI-agents are subject to these unique sources of moral luck. In doing so I offer a number of possible solutions and then defend one of these solutions as the best. As it turns out, the solution I defend addresses both problems of moral luck at once and has broader implications for theorizing about moral luck as well as the epistemic condition on moral responsibility. (shrink)

The problem of legal luck asks why defendants who cause harm should receive more punishment than analogous actors who, simply due to luck, don’t cause harm. Here I consider one type of justification that assumes luckily harmless actors are just as culpable as their harmful counterparts. Specifically, I focus on the legislature’s reasons to ratchet down punishments for harmless wrongdoers beneath what is permitted on culpability grounds. After critiquing several such arguments, I develop a more promising version (...) based on the idea that the legislature has a duty not to be cruel. The legislature would violate this duty if it always passed laws imposing the maximum punishments permitted on culpability grounds. Withholding some punishment otherwise due harmless wrongdoers thanks to their culpability is a particularly appropriate way for the legislature to eschew cruelty. This provides a promising new justification for punishing luckily harmless misconduct less harshly. (shrink)

Crime and Culpability, by Larry Alexander, Kimberly Kessler Ferzan (with Stephen Morse) is a visionary work of moral and legal philosophy. Nonetheless, it is fundamentally morally misguided. In seeking to free criminal law from what the authors take to be the distorting influence of outcome luck, they arrive at a position that is overly exculpatory. It fails to hold actors liable for the harms they cause when they have taken less care they should. -/- I argue, first, that (...) the authors’ attempt to strip criminal law of outcome luck is incoherent in its own terms, and that any attempt to follow through on their program would require a much more severe loss of accountability than the authors acknowledge. I then argue that outcome luck is pervasive in our moral lives, and that, given the choice of (a) not being able to hold agents accountable for much, or (b) holding them accountable for the results of their choices, including outcomes that result in part from moral luck, the right choice is (b). I wrap up with a concluding observation about the implausible moral psychology that underlies the authors’ view of culpable action. (shrink)

Christopher New recently argued for the seemingly paradoxical idea that there is no moral reason not to punish someone before she commits her crime (‘prepunishment’), provided that we can be sure that she will, in fact, commit the crime in the future. I argue that the air of paradox dissolves if we understand the possibility of prepunishment as relying on an anti‐moral‐luck position. However, New does not draw the full conclusions from such a position, which would allow prepunishment even (...) prior to the formation of a wrongful intention, on the basis of the idea that bad character is enough to entail blameworthiness. I conclude by examining a legal system which seems to use the idea of prepunishment, i.e. the Talmudic idea that we might punish a child who has not yet sinned in order to save him from sinning in the future. (shrink)

I offer in this paper an argument in support of the orthodox view that resultant luck should not affect judgments of blameworthiness—and so, for example, that we should not blame the successful assassin more than the attempted assassin who equally tries but fails. This view, though widely held among moral philosophers and legal scholars, has been severely challenged as implying either the implausible rejection of moral luck or an equally implausible theory of wrongness according to which actual (...) consequences may play no wrong-making role. The argument I offer, however, assumes both challenges to be true and shows that the orthodox view is consistent with holding them. Indeed, I argue that all other things being equal, successful offenders are no more to blame than their unsuccessful counterparts, even though agents are responsible for what they actually do , and successful offenders do more wrong than their unsuccessful counterparts do . The reason is that the difference in the amount of wrong done by one and the other offender, I show, is counterbalanced by a difference in the degree to which the successful offense and the unsuccessful one are attributable to their respective agents—blameworthiness being a function of both amount of wrong done and degree of attributability. (shrink)

When Hegel first addresses moral responsibility in the Philosophy of Right, he presupposes that agents are only responsible for what they intended to do, but appears to offer little, if any, justification for this assumption. In this essay, I claim that the first part of the Philosophy of Right, “Abstract Right”, contains an implicit argument that legal or external responsibility (blame for what we have done) is conceptually dependent on moral responsibility proper (blame for what we have intended). This (...) overlooked argument satisfies the first half of a thesis Hegel applies to action in the Encyclopaedia Logic, namely, that the outer must be inner, and thus provides a necessary complement for his more explicit treatment of the second half of that thesis, that the inner must be outer. The claim that agents are only responsible for what they intended to do might appear, at first, to risk conflating legal and moral responsibility and to lack the necessary means to deal with the phenomenon of moral luck, but I argue that if it is properly situated within the whole of Hegel's philosophy of action it can be saved from both of these consequences and so take its place as an essential component of Hegel's full theory of moral responsibility. (shrink)

Starting from the intuition, shared by many women, that the legal right to an abortion must be defended but that they themselves could never undergo one, I offer an account of why pregnancy is morally valuable and why, nevertheless, it is often permissible to end one. Developing the idea that human pregnancy centrally involves the activity of calling a fetus into personhood, I argue that the permissibility of stopping this activity hinges on the goodness or badness of one's moral (...) luck. (shrink)

Notwithstanding the demands of retributive desert, strict criminal liability is sometimes defensible when the strict liability pertains, not to whether conduct is to be criminalized at all, but to the seriousness of the actor’s crime. Suppose an actor commits an intentional assault or rape, and accidentally brings about a death. Punishing the actor more seriously because the death resulted is sometimes justifiable, even absent proof of his independent culpability as to the death. But what punishment is proportionate for such an (...) actor? Should he be punished as harshly as an intentional or knowing killer? This article offers a framework for analysing these difficult questions. After rejecting a broad forfeiture justification for strict liability in grading, it articulates a more promising set of arguments, premised on the actor’s ‘change of normative position’ by choosing to commit a crime. Three principles of culpability sometimes justify strict liability in grading: holistic culpability, attention to the degree of unjustifiability of the risk, and rough comparability in culpability. Strict liability in grading can be appropriate when the risk of committing the more serious crime (i) is a risk intrinsic to the less serious crime or (ii) is minimally foreseeable. The article also addresses the relevance of moral luck, ie the principle that the fortuitous occurrence of a result or circumstance increases the actor’s just deserts. Even if moral luck is recognized, it cannot fully justify strict liability in grading. (shrink)

Starting from the intuition, shared by many women, that the legal right to an abortion must be defended but that they themselves could never undergo one, I offer an account of why pregnancy is morally valuable and why, nevertheless, it is often permissible to end one. Developing the idea that human pregnancy centrally involves the activity of calling a fetus into personhood, I argue that the permissibility of stopping this activity hinges on the goodness or badness of one's moral (...) luck. (shrink)

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)

There is a gap between, on the one hand, the tragic character of human action and, on the other hand, our moral and legal conceptions of responsibility that focus on individual agency and absolute guilt. Drawing on Kierkegaard’s understanding of tragic action and engaging with contemporary discourse on moral luck, poetic justice, and relational responsibility, this paper argues for a reform of our legal practices based on a less ‘harsh’ (Kierkegaard) conception of moral and legal responsibility (...) and directed more at empathic understanding based on the emotional and imaginative appreciation of personal narratives. This may help our societies and communities to better cope with unacceptable deeds by individuals who are neither criminals nor patients, to make room for praise as well as blame and punishment, and to set up practices and institutions that do not rely on a conception of responsibility that is hard to bear for all of us. (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)

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)