It has been widely discussed whether the existence of other universes than the known universe is a purely metaphysical consideration. This paper argues to the contrary that the existence of other universes is a meaningful hypothesis, which can be tested based on observable data. The paper applies the perspective of observer bias as an approach for assigning probabilities to the mutually excluding hypotheses of universe vs. multiverse, i.e., whether the known universe is the only universe, or just one universe in (...) an ensemble of universes, a so-called multiverse. The basic idea of the paper relies on the following consideration. In a multiverse, the vast majority of observers would live in universes that are more life friendly. Thus, conditional on there being a multiverse, we should expect to find ourselves in a universe with values of the fundamental parameters that provide particularly fertile grounds for life. In contrast, if there is only a single universe, it may well be the case that there is still a few observers even if the parameters are far from ideal for life, and in that case, those observers will find values of the parameters that are not ideal for intelligent life. It may well be the case that, among all parameter configurations that allow life at least somewhere, those that are not ideal for life far outnumber those that are ideal for life. Based on this elementary consideration, the paper proceeds to propose a quantitative framework to determine probabilities for either hypothesis. In particular, it is described how a future ab initio determination of some of the factors in the Drake equation may be used to infer which one of the two hypotheses is the more likely. A quantitative approach to this end is proposed. Expressing these factors of the Drake equation in the context of the two hypotheses, a general likelihood approach is first described. Then, to support intuition, example computations are provided, illustrating how an actual hypothesis test would work in practice. (shrink)

The study of continuous group actions is ubiquitous in mathematics, and perhaps the most general kinds of actions for which we can hope to prove theorems in just ZFC are those where a Polish group acts on a Polish space.For this general class we can find works such as [29] that build on ideas from ergodic theory and examine actions of locally compact groups in both the measure theoretic and topological contexts. On the other hand a text in model theory, (...) such as [12], will typically consider issues bearing on the actions by the symmetric group of all permutations of the integers. More generally [1] shows that the orbit equivalence relations induced by closed subgroups of the infinite symmetric group can be reduced to the isomorphism relation on corresponding classes of countable models.This paper considers a third category formed by the continuous actions of separable Banach spaces on Polish spaces. These examples cannot be subsumed under the two earlier headings, and it is known from [10] that theBorel cardinalitiesof the quotient spaces that arise from such actions are incomparable with the equivalence relations induced by the symmetric group or any locally compact Polish group action.One of the first things to be addressed concerns the complexity of these equivalence relations. This question forappears in [1]. (shrink)

We reformulate, in the context of continuous logic, an oscillation theorem proved by G. Hjorth and give a proof of the theorem in that setting which is similar to, but simpler than, Hjorth's original one. The point of view presented here clarifies the relation between Hjorth's theorem and first-order logic.

S. Adams, W. Ambrose, A. Andretta, H. Becker, R. Camerlo, C. Champetier, J.P.R. Christensen, D.E. Cohen, A. Connes. C. Dellacherie, R. Dougherty, R.H. Farrell, F. Feldman, A. Furman, D. Gaboriau, S. Gao, V. Ya. Golodets, P. Hahn, P. de la Harpe, G. Hjorth, S. Jackson, S. Kahane, A.S. Kechris, A. Louveau,, R. Lyons, P.-A. Meyer, C.C. Moore, M.G. Nadkarni, C. Nebbia, A.L.T. Patterson, U. Krengel, A.J. Kuntz, J.-P. Serre, S.D. Sinel'shchikov, T. Slaman, Solecki, R. Spatzier, J. Steel, D. Sullivan, (...) S. Thomas, A. Valette, V.S. Varadarajan, B. Velickovic, B. Weiss, J.D.M. Wright, R.J. Zimmer. (shrink)

A Polish group G is tame if for any continuous action of G, the corresponding orbit equivalence relation is Borel. When [Formula: see text] for countable abelian [Formula: see text], Solecki [Equivalence relations induced by actions of Polish groups, Trans. Amer. Math. Soc. 347 (1995) 4765–4777] gave a characterization for when G is tame. In [L. Ding and S. Gao, Non-archimedean abelian Polish groups and their actions, Adv. Math. 307 (2017) 312–343], Ding and Gao showed that for such G, the (...) orbit equivalence relation must in fact be potentially [Formula: see text], while conjecturing that the optimal bound could be [Formula: see text]. We show that the optimal bound is [Formula: see text] by constructing an action of such a group G which is not potentially [Formula: see text], and show how to modify the analysis of [L. Ding and S. Gao, Non-archimedean abelian Polish groups and their actions, Adv. Math. 307 (2017) 312–343] to get this slightly better upper bound. It follows, using the results of Hjorth et al. [Borel equivalence relations induced by actions of the symmetric group, Ann. Pure Appl. Logic 92 (1998) 63–112], that this is the optimal bound for the potential complexity of actions of tame abelian product groups. Our lower-bound analysis involves forcing over models of set theory where choice fails for sequences of finite sets. (shrink)

§ 1. Introduction. In this communication we present some recent results on the classification of Polish metric spaces up to isometry and on the isometry groups of Polish metric spaces. A Polish metric space is a complete separable metric space.Our first goal is to determine the exact complexity of the classification problem of general Polish metric spaces up to isometry. This work was motivated by a paper of Vershik [1998], where he remarks : “The classification of Polish spaces up to (...) isometry is an enormous task. More precisely, this classification is not ‘smooth’ in the modern terminology.” Our Theorem 2.1 below quantifies precisely the enormity of this task.After doing this, we turn to special classes of Polish metric spaces and investigate the classification problems associated with them. Note that these classification problems are in principle no more complicated than the general one above. However, the determination of their exact complexity is not necessarily easier.The investigation of the classification problems naturally leads to some interesting results on the groups of isometries of Polish metric spaces. We shall also present these results below.The rest of this section is devoted to an introduction of some basic ideas of a theory of complexity for classification problems, which will help to put our results in perspective. Detailed expositions of this general theory can be found, e.g., in Hjorth [2000], Kechris [1999], [2001]. (shrink)

In this book William G. Lycan offers an epistemology of philosophy itself, a partial method for philosophical inquiry. The epistemology features three ultimate sources of justified philosophical belief. First, common sense, in a carefully restricted sense of the term-the sorts of contingentpropositions Moore defended against idealists and skeptics. Second, the deliverances of well confirmed science. Third and more fundamentally, intuitions about cases in a carefully specified sense of that term. The first half of On Evidence in Philosophy expounds a version (...) of Moore's method and applies it to each of several issues. This version is shown to resist all the standard objections to Moore; most of them do not even apply. It is argued, in Chapters 5 and 6, that philosophical method is far lesspowerful than most have taken it to be. In particular, deductive argument can accomplish very little, and hardly ever is an opposing position refuted except by common sense or by science. The final two chapters defend the evidential status of intuitions and the Goodmanian method of reflectiveequilibrium; it is argued that philosophy always and everywhere depends on them. The method is then set within a more general explanatory-coherentist epistemology, which is shown to resist standard forms of skepticism.In sum, William G. Lycan advocates a picture of philosophy as a very wide explanatory reflective equilibrium incorporating common sense, science, and our firmest intuitions on any topic-and nothing more, not ever. (shrink)

Fichte assigns ‘intellectual intuition’ a new meaning after Kant. But in 1799, his doctrine of intellectual intuition is publicly deemed indefensible by Kant and nihilistic by Jacobi. I propose to defend Fichte’s doctrine against these charges, leaving aside whether it captures what he calls the ‘spirit’ of transcendental idealism. I do so by articulating three problems that motivate Fichte’s redirection of intellectual intuition from being to acting: (1) the regress problem, which states that reflecting on empirical facts of consciousness leads (...) only to further facts and so cannot yield a first principle; (2) the rhapsody problem, which states that the categories form a haphazard set and so lack necessity unless they derive from a first principle; and (3) the nihilism problem, which states that a first principle cannot lie outside our cognition of it, lest it be the cause of our cognition and, being first, the cause of all our actions, reducing us to machines. Crucially, Fichte’s three motivating problems are in fact aspects of a single problem. Leaving any aspect unsolved spoils putative solutions to the other two. Consequently, Fichte requires a single unified solution to all three, which his doctrine of intellectual intuition provides. (shrink)

Throughout his career, Schelling assigns knowledge of the absolute first principle of philosophy to intellectual intuition. Schelling's doctrine of intellectual intuition raises two important questions for interpreters. First, given that his doctrine undergoes several changes before and after his identity philosophy, to what extent can he be said to “hold onto” the same “sense” of it by the 1830s, as he claims? Second, given that his doctrine of intellectual intuition restricts absolute idealism to what he calls a “science of reason”, (...) which he says cannot prove the absolute’s existence, what other doctrine does he require in order to prove this? I will answer these questions by tracing the shifts in Schelling’s doctrine of intellectual intuition from the 1790s to the 1830s and drawing out its evolving methodological role within his science of intelligibility. (shrink)

This chapter contains section titled: I II III IV V VI VII VIII IX X XI XII Coda Appendix Acknowledgements.

In the Freedom essay, Schelling charges that (1) idealism fails to grasp human freedom’s distinctiveness and that (2) this failure undermines idealism's attempt to refute pantheism, as exemplified by Spinoza. This raises two questions, which I will answer in turn: what, for Schelling, is distinctive of human freedom; and how does the idealists’ failure to grasp it render them unable to refute pantheism? To answer these questions, I will reconstruct Schelling’s argument that freedom has the distinctness of being the unconditioned (...) condition of the world’s intelligibility. My reconstruction will illustrate how Schelling’s notion of freedom as primal will grounds the alleged primacy of practical reason as Kant and Fichte conceive it. I will then consider three objections to Schelling’s argument. Throughout, I will develop the Schellingian idea that freedom is enacted in an unprethinkable decision that cannot be anticipated by any law or principle. (shrink)

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

The COVID-19 pandemic revealed numerous weaknesses in pandemic preparedness and response, including underfunding, inadequate surveillance, and inequitable distribution of countermeasures. To overcome these weaknesses for future pandemics, WHO released a zero draft of a pandemic treaty in February, 2023, and subsequently a revised bureau's text in May, 2023. COVID-19 made clear that pandemic prevention, preparedness, and response reflect choices and value judgements. These decisions are therefore not a purely scientific or technical exercise, but are fundamentally grounded in ethics. The latest (...) treaty draft reflects these ethical considerations by including a section entitled Guiding Principles and Approaches. Most of these principles are ethical—they establish core values that undergird the treaty. Unfortunately, the treaty draft's set of principles are numerous, overlapping, and show inadequate coherence and consistency. We propose two improvements to this section of the draft pandemic treaty. First, key guiding ethical principles should be clearer and more precise than they currently are. Second, the link between ethical principles and policy implementation should be clearly established and define boundaries on acceptable interpretation, ensuring that signatories abide by these principles. (shrink)

We study a natural subclass of continuous actions of Polish groups on Polish spaces which we call eventually open actions. We prove that this property characterizes the actions endowed with a complete system of hereditarily countable invariant structures introduced by Hjorth as a generalization of Scott sentences.

Information can be public among a group. Whether or not information is public matters, for example, for accounts of interdependent rational choice, of communication, and of joint intention. A standard analysis of public information identifies it with (some variant of) common belief. The latter notion is stipulatively defined as an infinite conjunction: for p to be commonly believed is for it to believed by all members of a group, for all members to believe that all members believe it, and so (...) forth. This analysis is often presupposed without much argument in philosophy. Theoretical entrenchment or intuitions about cases might give some traction on the question, but give little insight about why the identification holds, if it does. The strategy of this paper is to characterize a practical-normative role for information being public, and show that the only things that play that role are (variants of) common belief as stipulatively characterized. In more detail: a functional role for “taking a proposition for granted” in non-isolated decision making is characterized. I then present some minimal conditions under which such an attitude is correctly held. The key assumption links this attitude to beliefs about what is public. From minimal a priori principles, we can argue that a proposition being public among a group entails common commitment to believe among that group. Later sections explore partial converses to this result, the factivity of publicity and publicity from the perspective of outsiders to the group, and objections to the aprioricity of the result deriving from a posteriori existential presuppositions. (shrink)

Philosophers and logicians have long debated how best to understand conditional or hypothetical sentences. William G. Lycan has a distinctive approach to this debate, attending not just to the semantics of such sentences, but equally to their syntax. He shows how insights from linguistic theory help to illuminate problems about the meaning and function of conditionals. For instance, philosophers and logicians have had problems analysing the locutions 'only if', 'unless', and 'even if'. Lycan sets out a general semantic theory of (...) conditionals which works for all such sentences; he assigns meanings to them in a way that explains how and why those meanings depend upon features of utterance context. According to Lycan's theory the 'if'-clauses refer to items called 'events', 'circumstances', or 'conditions'.Real Conditionals gives at last the definitive presentation of this original approach to a topic at the intersection of philosophy, logic, and linguistics. Lycan's characteristically lively and witty expository style ensures that it can be enjoyed by readers from all three disciplines. (shrink)

Disjunctivism about perceptual appearances, as I conceive of it, is a theory which seeks to preserve a na.

‘Facticity’ is a concept that classical phenomenologists like Heidegger use to denote the radically contingent or underivably brute conditions of intelligibility. Yet Fichte coins the term, to which he gives the opposing use of denoting unacceptably brute conditions of intelligibility. For him, radical contingency is a problem to be solved by deriving such conditions from reason. Heidegger rejects Fichte's recoil from facticity with his hermeneutics of facticity, supplanting Fichte's metaphor of our always being in reason's hand with the metaphor of (...) our always having been thrown. How does Heidegger inherit and diametrically repurpose Fichte's neologism? Whence the reversed meaning of ‘facticity’ in post-Kantian thought? The answer is Lask's doctoral thesis, which exerts an acknowledged impact on Heidegger's habilitation thesis. Lask interprets ‘facticity’ as Fichte's term for the individuality problem, that is, the resistance of the material particularity of individuals to explanation by the categories genetically deduced from reason. On his interpretation, ‘facticity’ denotes radical contingency in the guise of haecceity, that is, the brute uniqueness of individuals. Lask credits Fichte with registering the problem of individuality, which highlights the world's irreducibly precategorial character. But how is ‘facticity’ transmitted from Lask to Heidegger, given their opposing interpretations of how Fichte understands its meaning? I argue that (1) Lask misreads Fichte as a proponent of facticity, that is, one whose accommodation of radical contingency deflates the Wissenschaftslehre's systematic ambitions, and (2) Lask's misreading, without deceiving Heidegger regarding the sincerity of Fichte's ambitions, encourages Heidegger's own hermeneutics of facticity. (shrink)

Quantum mechanics, which describes the behavior of subatomic particles, seems to challenge common sense. Waves behave like particles; particles behave like waves. You can tell where a particle is, but not how fast it is moving--or vice versa. An electron faced with two tiny holes will travel through both at the same time, rather than one or the other. And then there is the enigma of creation ex nihilo, in which small particles appear with their so-called antiparticles, only to disappear (...) the next instant in a tiny puff of energy. Since its inception, physicists and philosophers have struggled to work out the meaning of quantum mechanics. Some, like Niels Bohr, have responded to quantum mechanics' mysteries by replacing notions of position and velocity with probabilities. Others, like Einstein and Penrose, have disagreed and think that the entire puzzle reflects not a fundamental principle of nature but our own ignorance of basic scientific processes. Sneaking a Look at God's Cards offers the general reader a deep and real understanding of the problems inherent to the interpretation of quantum mechanics, from its inception to the present. The book presents a balanced overview of current debates and explores how the theory of quantum mechanics plays itself out in the real world. Written from the perspective of a leading European physicist, the book looks extensively at ideas from both sides of the Atlantic and also considers what philosophers have contributed to the scientific discussion of this field. Sneaking a Look at God's Cards sets out what we know about the endlessly fascinating quantum world, how we came to this understanding, where we disagree, and where we are heading in our quest to comprehend the seemingly incomprehensible. (shrink)

This book, published in 1986, addresses questions concerned with a central normative principle in contemporary assessments of economic policies and systems. What does 'consumer sovereignty' mean? Is consumer sovereignty an appropriate principle for the optimization and evaluation of the design and performance of economic policies, institutions and systems? If not, what is a more appropriate principle? The author argues that the conception of consumer sovereignty has to be broadened so that it is not limited to the market mechanism but includes (...) environmental, work and social preferences. However, even this version runs into serious difficulties as the principle of consumer sovereignty still relies on too subjectivist a conception of the interests of individuals to be suitable for the evaluation of economic institutions. An alternative basis for such evaluation is 'human interests' that are not contingent on particular economic systems, After considering various possibilities, a basic-needs approach is proposed and its use in economic evaluation illustrated. (shrink)

Kant’s science of the conditions of intelligibility leaves post-Kantians with a question: can a science of intelligibility tolerate brute facts? ‘Facticity’ is associated with phenomenology, for which the concept denotes underivable or brute conditions of intelligibility like temporality, sociality, and embodiment. While this suggests an affirmative answer to the post-Kantian question, scholars overlook that ‘facticity’ is a concept from German idealism, whose proponents answer the question in the negative. Fichte coins ‘facticity’ to denote the intolerable bruteness of conditions that are (...) putatively presupposed by, and hence inexplicable limitations on, reason. A science of intelligibility must eliminate putative bruteness if it is to be systematic, as Fichte says, or presuppositionless, as Hegel says. Moreover, eliminating putative bruteness requires a new logic for deriving conditions of intelligibility from reason’s own contradictions, a dialectical logic that Fichte invents and Hegel develops. German idealism’s logical revolution subsequently provokes Heidegger’s phenomenological objection that dialectic presupposes brute conditions of the dialectician’s lived experience, conditions whose facticity dialectic inevitably reproduces and hence can only interpret hermeneutically. The heretofore untold history of the concept of facticity thus contains the deepest parting of the ways after Kant. On the one hand, Hegel eliminates vestigial facticity in Fichte’s system in his final step toward a presuppositionless science of intelligibility, although Schelling charges Hegel with presupposing both the value of science and the existence that science renders intelligible. On the other hand, Lask’s otherwise misleading reading of Fichte inspires Heidegger to reject the very idea of presuppositionlessness on behalf of a hermeneutics of facticity. The trajectory from German idealism via neo-Kantianism to phenomenology is accordingly one in which facticity begins as the obstacle to the science of intelligibility and ends as the character of the situation in which this science is possible in the first place. Within this trajectory and up to our own time, reason is fated to transform from the hand that unconditionally holds the world to the thrown activity of being in the world. (shrink)