The forces of freedom are challenged everywhere by a newly energized spirit of tyranny, whether it is Jihadist terrorism, Putin's imperialism, or the ambitions of China's dictatorship, writes Waller R. Newell in this engaging exposé of a thousand dangers. We will see why tyranny is a permanent threat by following its strange career from Homeric Bronze Age warriors, through the empires of Alexander the Great and Rome, to the medieval struggle between the City of God and the City (...) of Man, leading to the state-building despots of the Modern Age including the Tudors and 'enlightened despots' such as Peter the Great. The book explores the psychology of tyranny from Nero to Gaddafi, and how it changes with the Jacobin Terror into millenarian revolution. Stimulating and enlightening, Tyrants: Power, Injustice, and Terror will appeal to anyone interested in the danger posed by tyranny and terror in today's world. (shrink)

This is the first comprehensive exploration of ancient and modern tyranny in the history of political thought. Waller R. Newell argues that modern tyranny and statecraft differ fundamentally from the classical understanding. Newell demonstrates a historical shift in emphasis from the classical thinkers' stress on the virtuous character of rulers and the need for civic education to the modern emphasis on impersonal institutions and cold-blooded political method. By diagnosing the varieties of tyranny from erotic voluptuaries like Nero, the steely (...) determination of reforming conquerors like Alexander the Great and Julius Caesar and modernizing despots such as Napoleon and Ataturk to the collectivist revolutions of the Jacobins, Bolsheviks, Nazis and Khmer Rouge, Newell shows how tyranny is every bit as dangerous to free democratic societies today as it was in the past. (shrink)

The free-will defence holds that the value of significant free will is so great that God is justified in creating significantly free creatures even if there is a risk or certainty that these creatures will sin. A difficulty for the FWD, developed carefully by Quentin Smith, is that God is unable to do evil, and yet surely lacks no genuinely valuable kind of freedom. Smith argues that the kind of freedom that God has can be had by creatures, without a (...) risk of creatures doing evil. I shall show that Smith's argument fails – the case of God is disanalogous to the case of creatures precisely because creatures are creatures. (shrink)

Alexander R. Pruss examines a large family of paradoxes to do with infinity - ranging from deterministic supertasks to infinite lotteries and decision theory. Having identified their common structure, Pruss considers at length how these paradoxes can be resolved by embracing causal finitism.

Necessary Existence breaks ground on one of the deepest questions anyone ever asks: why is there anything? Pruss and Rasmussen present an original defence of the hypothesis that there is a necessarily existing being capable of providing an ultimate foundation for the existence of all things.

Assuming S5, the main controversial premise in modal ontological arguments is the possibility premise, such as that possibly a maximally great being exists. I shall offer a new way of arguing that the possibility premise is probably true.

Digital and analog: What do these terms mean today? The use and meaning of such terms change through time. The analog, in particular, seems to go through various phases of popularity and disuse, its appeal pegged most frequently to nostalgic longings for nontechnical or romantic modes of art and culture. The definition of the digital vacillates as well, its precise definition often eclipsed by a kind of fever-pitched industrial bonanza around the latest technologies and the latest commercial ventures. One common (...) response to the question of the digital is to make reference to things like Twitter, Playstation, or computers in general. Here one might be correct, but only coincidentally, for the basic order of digitality (the digitality of digitality) has not yet been demonstrated through mere denotation. And the second question—the question of the analog—is harder still, with responses often also consisting of mere denotations of things: sound waves, the phonograph needle, magnetic tape, a sundial. At least denotation itself is analogical. This article will aim to define the analog explicitly and argue, perhaps counterintuitively, that the golden age of analog thinking was not a few decades past, prior to the wide-spread adoption of the computer. In fact, the fields of structuralism and poststructuralism that emerged in the middle to late twentieth century, concurrent with the deployment of the digital computer, were characteristically digital, what with their focus on the symbolic order and logical economies. If anything, the golden age of analog is happening today, all around us, as evidenced by the proliferation of characteristically analog concerns: sensation, materiality, experience, affect, ethics, and aesthetics. (shrink)

Cantor proved that no set has a bijection between itself and its power set. This is widely taken to have shown that there infinitely many sizes of infinite sets. The argument depends on the princip...

Classical real-valued probabilities come at a philosophical cost: in many infinite situations, they assign the same probability value—namely, zero—to cases that are impossible as well as to cases that are possible. There are three non-classical approaches to probability that can avoid this drawback: full conditional probabilities, qualitative probabilities and hyperreal probabilities. These approaches have been criticized for failing to preserve intuitive symmetries that can be preserved by the classical probability framework, but there has not been a systematic study of the (...) conditions under which these symmetries can and cannot be preserved. This paper fills that gap by giving complete characterizations under which symmetries understood in a certain “strong” way can be preserved by these non-classical probabilities, as well as by offering some results to make it plausible that the strong notion of symmetry here is the right one. Philosophical implications are briefly discussed, but the main purpose of the paper is to offer technical results to help make further philosophical discussion more sophisticated. (shrink)

It is often loosely said that Ramsey The foundations of mathematics and other logical essays, Routledge and Kegan Paul, Abingdon, pp 156–198, 1931) and de Finetti Studies in subjective probability, Kreiger Publishing, Huntington, 1937) proved that if your credences are inconsistent, then you will be willing to accept a Dutch Book, a wager portfolio that is sure to result in a loss. Of course, their theorems are true, but the claim about acceptance of Dutch Books assumes a particular method of (...) calculating expected utilities given the inconsistent credences. I will argue that there are better ways of calculating expected utilities given a potentially inconsistent credence assignment, and that for a large class of credences—a class that includes many inconsistent examples—these ways are immune to Dutch Books and single-shot domination failures. The crucial move is to replace Finite Additivity with Monotonicity, then \\le P\)) and then calculate expected utilities for positive U via the formula \\, dy\). This shows that Dutch Book arguments for probabilism, the thesis that one’s credences should be consistent, do not establish their conclusion. Finally, I will consider a modified argument based on multi-step domination failure that does better, but nonetheless is not as compelling as the Dutch Book arguments appeared to be. (shrink)

A number of philosophers have attempted to solve the problem of null-probability possible events in Bayesian epistemology by proposing that there are infinitesimal probabilities. Hájek and Easwaran have argued that because there is no way to specify a particular hyperreal extension of the real numbers, solutions to the regularity problem involving infinitesimals, or at least hyperreal infinitesimals, involve an unsatisfactory ineffability or arbitrariness. The arguments depend on the alleged impossibility of picking out a particular hyperreal extension of the real numbers (...) and/or of a particular value within such an extension due to the use of the Axiom of Choice. However, it is false that the Axiom of Choice precludes a specification of a hyperreal extension—such an extension can indeed be specified. Moreover, for all we know, it is possible to explicitly specify particular infinitesimals within such an extension. Nonetheless, I prove that because any regular probability measure that has infinitesimal values can be replaced by one that has all the same intuitive features but other infinitesimal values, the heart of the arbitrariness objection remains. (shrink)

Scoring rules measure the deviation between a credence assignment and reality. Probabilism holds that only those credence assignments that satisfy the axioms of probability are rationally admissible. Accuracy-based arguments for probabilism observe that given certain conditions on a scoring rule, the score of any non-probability is dominated by the score of a probability. The conditions in the arguments we will consider include propriety: the claim that the expected accuracy of _p_ is not beaten by the expected accuracy of any other (...) credence _c_ by the lights of _p_ if _p_ is a probability. I argue that if we think through how a non-probabilist can respond to pragmatic arguments for probabilism, we will expect the non-probabilist to accept a condition _stronger_ than propriety for the same reasons that the probabilist gives for propriety, but this stronger condition is incompatible with the other conditions that the probabilist needs to run the accuracy argument. This makes it unlikely for the probabilist’s argument to be compelling. (shrink)

Some, notably Peter van Inwagen, in order to avoid problems with free will and omniscience, replace the condition that an omniscient being knows all true propositions with a version of the apparently weaker condition that an omniscient being knows all knowable true propositions. I shall show that the apparently weaker condition, when conjoined with uncontroversial claims and the logical closure of an omniscient being's knowledge, still yields the claim that an omniscient being knows all true propositions.

Scoring rules measure the deviation between a forecast, which assigns degrees of confidence to various events, and reality. Strictly proper scoring rules have the property that for any forecast, the mathematical expectation of the score of a forecast p by the lights of p is strictly better than the mathematical expectation of any other forecast q by the lights of p. Forecasts need not satisfy the axioms of the probability calculus, but Predd et al. [9] have shown that given a (...) finite sample space and any strictly proper additive and continuous scoring rule, the score for any forecast that does not satisfy the axioms of probability is strictly dominated by the score for some probabilistically consistent forecast. Recently, this result has been extended to non-additive continuous scoring rules. In this paper, a condition weaker than continuity is given that suffices for the result, and the condition is proved to be optimal. (shrink)

Bayesian epistemology has struggled with the problem of regularity: how to deal with events that in classical probability have zero probability. While the cases most discussed in the literature, such as infinite sequences of coin tosses or continuous spinners, do not actually come up in scientific practice, there are cases that do come up in science. I shall argue that these cases can be resolved without leaving the realm of classical probability, by choosing a probability measure that preserves “enough” regularity. (...) This approach also provides a resolution to the McGrew, McGrew and Vestrum normalization problem for the fine-tuning argument. (shrink)

Few studies have examined how trait emotion dysregulation relates to momentary affective experiences and the emotion regulation strategies people use in daily life. In the current study, 112 c...

Scoring rules measure the accuracy or epistemic utility of a credence assignment. A significant literature uses plausible conditions on scoring rules on finite sample spaces to argue for both probabilism—the doctrine that credences ought to satisfy the axioms of probabilism—and for the optimality of Bayesian update as a response to evidence. I prove a number of formal results regarding scoring rules on infinite sample spaces that impact the extension of these arguments to infinite sample spaces. A common condition in the (...) arguments for probabilism and Bayesian update is strict propriety: that according to each probabilistic credence, the expected accuracy of any other credence is worse. Much of the discussion needs to divide depending on whether we require finite or countable additivity of our probabilities. I show that in a number of natural infinite finitely additive cases, there simply do not exist strictly proper scoring rules, and the prospects for arguments for probabilism and Bayesian update are limited. In many natural infinite countably additive cases, on the other hand, there do exist strictly proper scoring rules that are continuous on the probabilities, and which support arguments for Bayesian update, but which do not support arguments for probabilism. There may be more hope for accuracy-based arguments if we drop the assumption that scores are extended-real-valued. I sketch a framework for scoring rules whose values are nets of extended reals, and show the existence of a strictly proper net-valued scoring rules in all infinite cases, both for f.a. and c.a. probabilities. These can be used in an argument for Bayesian update, but it is not at present known what is to be said about probabilism in this case. (shrink)

The "Supplement" transmitted as the second book of "On the Soul" by Alexander of Aphrodisias is a collection of short texts on a wide range of topics from psychology, including the general hylomorphic account of soul and its faculties, and the theory of vision; questions in ethics ; and issues relating to responsibility, chance and fate. One of the texts in the collection, "On Intellect", had a major influence on medieval Arabic and Western thought, greater than that of (...) class='Hi'>Alexander's "On the Soul" itself. The treatises may all be by Alexander himself; certainly the majority of them are closely connected with his other works. Many of them, however, consist of collections of arguments on particular issues, collections which probably incorporate material from earlier in the history of the Peripatetic school. This translation is from a new edition of the Greek text based on a collation of all known manuscripts and comparison with medieval Arabic and Latin translations. (shrink)

Sceptical theism claims that we have vast ignorance about the realm of value and the connections, causal and modal, between goods and bads. This ignorance makes it reasonable for a theist to say that God has reasons beyond our ken for allowing the horrendous evils we observe. But if so, then does this not lead to moral paralysis when we need to prevent evils ourselves? For, for aught that we know, there are reasons beyond our ken for us to allow (...) the evils, and so we should not prevent them. This paralysis argument, however, shall be argued to rest on a confusion between probabilities and expected utilities. A connection between this paralysis argument and Lenman's1 discussion of the butterfly effect and chaos will be drawn, and the solution offered will apply in both cases. (shrink)

Clinical trials aim to minimise participant risk and generate new clinical knowledge for the wider population. Many military agencies are now investing efforts in pushing towards developing new treatments involving Brain-Computer Interfaces, Gene Therapy and Stem Cells interventions. These trials are targeting smaller disease groups, as such they give rise to novel participant risks of harms that are largely not accommodated by existing practice. This is of most concern with irreversible harms at early trial stages, where participants may forfeit any (...) future therapy, and in personalised medicine, where the individual participant assumes all of the trial risk. Given these new experimental interventions involve high risk of irreversible harms, how much risk should patients be exposed to when participating in experimental testing of innovative technologies? Designing clinical trials which better balance risk/benefit ratios for participants is crucial. The aim of this book chapter is to suggest a new stratified risk framework aimed at minimising the risk-benefit ratio to participants in clinical trials associated with high risk of irrevocable harms. We will argue it demands a higher-level of clinical data capture at earlier trial stages than predicated by current trial doctrine; it also requires publication of all trial data to minimise risk to participants of any future trial. (shrink)

The Adams Thesis holds for a conditional → and a probability assignment P if and only if P=P whenever P>0. The restriction ensures that P is well defined by the classical formula P=P/P. Drawing on deep results of Maharam on measure algebras, it is shown that, notwithstanding well-known triviality results, any probability space can be extended to a probability space with a new conditional satisfying the Adams Thesis and satisfying a number of axioms for conditionals. This puts significant limits on (...) how far triviality results can go. (shrink)

This important philosophical reflection on love and sexuality from a broadly Christian perspective is aimed at philosophers, theologians, and educated Christian readers. Alexander R. Pruss focuses on foundational questions on the nature of romantic love and on controversial questions in sexual ethics on the basis of the fundamental idea that romantic love pursues union of two persons as one body. _One Body_ begins with an account, inspired by St. Thomas Aquinas, of the general nature of love as constituted by (...) components of goodwill, appreciation, and unitiveness. Different forms of love, such as parental, collegial, filial, friendly, fraternal, or romantic, Pruss argues, differ primarily not in terms of goodwill or appreciation but in terms of the kind of union that is sought. Pruss examines romantic love as distinguished from other kinds of love by a focus on a particular kind of union, a deep union as one body achieved through the joint biological striving of the sort involved in reproduction. Taking the account of the union that romantic love seeks as a foundation, the book considers the nature of marriage and applies its account to controversial ethical questions, such as the connection between love, sex, and commitment and the moral issues involving contraception, same-sex activity, and reproductive technology. With philosophical rigor and sophistication, Pruss provides carefully argued answers to controversial questions in Christian sexual ethics. "This is a terrific—really quite extraordinary—work of scholarship. It is quite simply the best work on Christian sexual ethics that I have seen. It will become the text that anyone who ventures into the field will have to grapple with—a kind of touchstone. Moreover, it is filled with arguments with which even secular writers on sexual morality will have to engage and come to terms." —_Robert P. George, Princeton University __ "_One Body_ is an excellent piece of philosophical-theological reflection on the nature of sexuality and marriage. This book has the potential to become a standard go-to text for professors and students working on sex ethics issues, whether in philosophy or theology, both for the richness of its arguments, and the scope of its coverage of cases. " — Christopher Tollefsen, University of South Carolina_ "Alexander Pruss here develops sound and humane answers to the whole range of main questions about human sexual and reproductive choices. His principal argument for the key answers is very different from the one I have articulated over the past fifteen years. But his argumentation is at every point attractively direct, careful, energetic in framing and responding to objections, and admirably attentive to realities and the human goods at stake." —_John Finnis, University of Oxford _. (shrink)

A nested mode ontology allows one to make sense of apparently contradictory Christological claims such as that Christ knows everything and there are some things Christ does not know.

Popper functions allow one to take conditional probabilities as primitive instead of deriving them from unconditional probabilities via the ratio formula P=P/P. A major advantage of this approach is it allows one to condition on events of zero probability. I will show that under plausible symmetry conditions, Popper functions often fail to do what they were supposed to do. For instance, suppose we want to define the Popper function for an isometrically invariant case in two dimensions and hence require the (...) Popper function to be rotationally invariant and defined on pairs of sets from some algebra that contains at least all countable subsets. Then it turns out that the Popper function trivializes for all finite sets: P=1 for all A ) if B is finite. Likewise, Popper functions invariant under all sequence reflections can’t be defined in a way that models a bidirectionally infinite sequence of independent coin tosses. (shrink)

The book takes the reader on a vivid, imaginative journey towards unraveling the mysteries of our existence, roles in society, and personal loyalties. The book melds science with philosophy and theology and highlights the people who dedicated their lives in pursuit of the seven riddles of the universe.

Introduction : the computer as a mode of mediation -- The unworkable interface -- Software and ideology -- Are some things unrepresentable? -- Disingenuous informatics -- Postscript : we are the gold farmers.

The strict dominance principle that a wager always paying better than another is rationally preferable is one of the least controversial principles in decision theory. I shall show that (given the Axiom of Choice) there is a contradiction between strict dominance and plausible isomorphism or symmetry conditions, by showing how in several natural cases one can construct isomorphic wagers one of which strictly dominates the other. In particular, I will show that there is a pair of wagers on the outcomes (...) of a uniform spinner which differ simply in where the zero degrees point of the spinner is defined to be but where one wager dominates the other. I shall also argue that someone who accepts Williamson’s famous argument that the probability of an infinite sequence of heads is zero should accept the symmetry conditions, and thus has reason to weaken the strict dominance principle, and I shall propose a restriction of the principle to “implementable” wagers. Our main result also has implications for social choice principles. (shrink)

Consider the regularity thesis that each possible event has non-zero probability. Hájek challenges this in two ways: there can be nonmeasurable events that have no probability at all and on a large enough sample space, some probabilities will have to be zero. But arguments for the existence of nonmeasurable events depend on the axiom of choice. We shall show that the existence of anything like regular probabilities is by itself enough to imply a weak version of AC sufficient to prove (...) the Banach–Tarski Paradox on the decomposition of a ball into two equally sized balls, and hence to show the existence of nonmeasurable events. This provides a powerful argument against unrestricted orthodox Bayesianism that works even without AC. A corollary of our formal result is that if every partial order extends to a total preorder while maintaining strict comparisons, then the Banach–Tarski Paradox holds. This yields an argument that incommensurability cannot be avoided in ambitious versions of decision theory. (shrink)

_Laruelle_ is one of the first books in English to undertake in an extended critical survey of the work of the idiosyncratic French thinker François Laruelle, the promulgator of non-standard philosophy. Laruelle, who was born in 1937, has recently gained widespread recognition, and Alexander R. Galloway suggests that readers may benefit from colliding Laruelle’s concept of the One with its binary counterpart, the Zero, to explore more fully the relationship between philosophy and the digital. In _Laruelle_, Galloway argues that (...) the digital is a philosophical concept and not simply a technical one, employing a detailed analysis of Laruelle to build this case while referencing other thinkers in the French and Continental traditions, including Alain Badiou, Gilles Deleuze, Martin Heidegger, and Immanuel Kant. In order to explain clearly Laruelle’s concepts such as the philosophical decision and the principle of sufficient philosophy, Galloway lays a broad foundation with his discussions of “the One” as it has developed in continental philosophy, the standard model of philosophy, and how philosophers view “the digital.” Digital machines dominate today’s world, while so-called digital thinking—that is, binary thinking such as presence and absence or self and world—is often synonymous with what it means to think at all. In examining Laruelle and digitality together, Galloway shows how Laruelle remains a profoundly non-digital thinker—perhaps the only non-digital thinker today—and engages in an extensive discussion on the interconnections between media, philosophy, and technology. (shrink)

We shall use Gödel’s Second Incompleteness Theorem to show that consistency is not possibility, and then argue that the argument does serious damage to some theories of modality where consistency plays a major but not exclusive role.

Always connect—that is the imperative of today’s media. But what about those moments when media cease to function properly, when messages go beyond the sender and receiver to become excluded from the world of communication itself—those messages that state: “There will be no more messages”? In this book, Alexander R. Galloway, Eugene Thacker, and McKenzie Wark turn our usual understanding of media and mediation on its head by arguing that these moments reveal the ways the impossibility of communication is (...) integral to communication itself—instances they call excommunication. In three linked essays, _Excommunication_ pursues this elusive topic by looking at mediation in the face of banishment, exclusion, and heresy, and by contemplating the possibilities of communication with the great beyond. First, Galloway proposes an original theory of mediation based on classical literature and philosophy, using Hermes, Iris, and the Furies to map out three of the most prevalent modes of mediation today—mediation as exchange, as illumination, and as network. Then, Thacker goes boldly beyond Galloway’s classification scheme by examining the concept of excommunication through the secret link between the modern horror genre and medieval mysticism. Charting a trajectory of examples from H. P. Lovecraft to Meister Eckhart, Thacker explores those instances when one communicates or connects with the inaccessible, dubbing such modes of mediation “haunted” or “weird” to underscore their inaccessibility. Finally, Wark evokes the poetics of the infuriated swarm as a queer politics of heresy that deviates from both media theory and the traditional left. He posits a critical theory that celebrates heresy and that is distinct from those that now venerate Saint Paul. Reexamining commonplace definitions of media, mediation, and communication, _Excommunication_ offers a glimpse into the realm of the nonhuman to find a theory of mediation adequate to our present condition. (shrink)

Unter Bezugnahme auf Philosophie und Mathematik schlägt dieser Artikel allgemeine Formeln für das Digitale und das Analoge vor, wobei das Digitale als das Verhältnis der diskreten Terme (a/b), das Analoge als eine Verhältnisgleichung (a/b = c/d) definiert sind. Mit diesen allgemeinen Formeln zur Hand werden wir in der Lage sein, zwei der häufigsten operativen Ontologien (Digitalität und das Analoge) zu erforschen und gleichzeitig ein ontologisches Szenario zu enthüllen, in dem keines der beiden zutrifft. Taking into account both philosophy and maths, (...) this article suggests general formulas for both the digital sphere and the analogue, defining the digital sphere as a relation of discrete terms (a/b) whereas the analogue is described as a proportion (a/b = c/d). Falling back on those general formulas, one will be able to study two of the most frequently used operative ontologies (the digitality and the analogue) while at the same time unveiling an ontological scenario to which none of the aforementioned ontologies apply. (shrink)

Taking into account both philosophy and maths, this article suggests general formulas for both the digital sphere and the analogue, defining the digital sphere as a relation of discrete terms (a/b) whereas the analogue is described as a proportion (a/b = c/d). Falling back on those general formulas, one will be able to study two of the most frequently used operative ontologies (the digitality and the analogue) while at the same time unveiling an ontological scenario to which none of the (...) aforementioned ontologies apply. (shrink)

A serious error in the proof of a recent characterization of the existence of full conditional probabilities invariant under symmetries is corrected.

It is widely thought that it can be permissible to persuade someone set on a greater evil to commit a lesser evil instead, though the question is not without controversy. I argue that a version of this kind of Principle of Counseling Lesser Evil can be derived from the Principle of Double Effect and some considerations about the way human choices work. As an application, I argue that giving bribes to officials who otherwise would not do their job might be (...) considered a special case of this counseling principle. (shrink)

I shall offer some very plausible assumptions for the measure of confirmation and show that they imply that E confirms H relative to background K to degree f/PK), where f is a strictly increasing function. An additional assumption about how measures of confirmation combine then makes f be proportional to a logarithm.

The Principle of Sufficient Reason says that all contingent facts must have explanation. In this 2006 volume, which was the first on the topic in the English language in nearly half a century, Alexander Pruss examines the substantive philosophical issues raised by the Principle Reason. Discussing various forms of the PSR and selected historical episodes, from Parmenides, Leibnez, and Hume, Pruss defends the claim that every true contingent proposition must have an explanation against major objections, including Hume's imaginability argument (...) and Peter van Inwagen's argument that the PSR entails modal fatalism. Pruss also provides a number of positive arguments for the PSR, based on considerations as different as the metaphysics of existence, counterfactuals and modality, negative explanations, and the everyday applicability of the PSR. Moreover, Pruss shows how the PSR would advance the discussion in a number of disparate fields, including meta-ethics and the philosophy of mathematics. (shrink)

This chapter contains sections titled: Introduction The PSR Nonlocal CPs Toward a First Cause The Gap Problem Conclusions and Further Research References.

According to the Russo-Williamson Thesis, causal claims in the health sciences need to be supported by both difference-making and mechanistic evidence. In this article, we attempt to determine whether Evidence-based Medicine can be improved through the consideration of mechanistic evidence. We discuss the practical composition and function of each RWT evidence type and propose that exposure-outcome evidence provides associations that can be explained through a hypothesis of causation, while mechanistic evidence provides finer-grained associations and knowledge of entities that ultimately explains (...) a causal hypothesis. We suggest that mechanistic evidence holds untapped potential to add value to the assessment of evidence quality in EBM and propose initial recommendations for the integration of mechanistic and exposure-outcome evidence to improve EBM by robustly leveraging available evidence in support of good medical decisions. (shrink)

Regularity is the thesis that all contingent propositions should be assigned probabilities strictly between zero and one. I will prove on cardinality grounds that if the domain is large enough, a regular probability assignment is impossible, even if we expand the range of values that probabilities can take, including, for instance, hyperreal values, and significantly weaken the axioms of probability.

Consider the reasonable axioms of subjunctive conditionals if p → q1 and p → q2 at some world, then p → at that world, and if p1 → q and p2 → q at some world, then → q at that world, where p → q is the subjunctive conditional. I show that a Lewis-style semantics for subjunctive conditionals satisfies these axioms if and only if one makes a certain technical assumption about the closeness relation, an assumption that is probably (...) false. I will then show how Lewisian semantics can be modified so as to assure and even when the technical assumption fails, and in fact in one sense the semantics actually becomes simpler then. (shrink)

We show that infinitesimal probabilities are much too small for modeling the individual outcome of a countably infinite fair lottery.