Some analyses of personal fission suggest that an informed subject should expect to have a distinct experience of each outcome simultaneously. Is rational provision for the future possible in such unfamiliar circumstances? I argue that, with some qualification, the subject can reasonably act as if faced with alternative possible outcomes with precise probabilities rather than multiple actual outcomes.

How does it come about then, that great scientists such as Einstein, Schrödinger and De Broglie are nevertheless dissatisfied with the situation? Of course, all these objections are levelled not against the correctness of the formulae, but against their interpretation. [...] The lesson to be learned from what I have told of the origin of quantum mechanics is that probable refinements of mathematical methods will not suffice to produce a satisfactory theory, but that somewhere in our doctrine is hidden a (...) concept, unjustified by experience, which we must eliminate to open up the road. (Born [ 1954 ], pp. 8, 11) It is truly surprising how little difference all this makes. Most physicists use quantum mechanics every day in their working lives without needing to worry about the fundamental problem of its interpretation. (Weinberg [ 1992 ], p. 66) I endorse the view that it may be of no relevance to the acceptability of the Everett interpretation of quantum mechanics as a physical theory whether or not an informed observer can be uncertain about the outcome of a quantum measurement prior to its having occurred. However, I suggest that the very possibility of post-measurement, pre-observation uncertainty has an essential role to play in both confirmation theory and decision theory in a branching universe. This is supported by arguments which do not appeal to van Fraassen’s Reflection Principle. (shrink)

Simon Saunders and David Wallace attempt to use a modified form of David Lewis's analysis of personal fission to ground the claim that prior to undergoing Everett branching an informed subject can be uncertain about which outcome s/he will observe. I argue that a central assumption of this seductive idea is questionable despite appearing innocuous and that at the very least further argument is needed in support of it. CiteULike Connotea Del.icio.us What's this?

Objective probability in quantum mechanics is often thought to involve a stochastic process whereby an actual future is selected from a range of possibilities. Everett’s seminal idea is that all possible definite futures on the pointer basis exist as components of a macroscopic linear superposition. I demonstrate that these two conceptions of what is involved in quantum processes are linked via two alternative interpretations of the mind-body relation. This leads to a fission, rather than divergence, interpretation of Everettian theory and (...) to a novel explanation of why a principle of indifference does not apply to self-location uncertainty for a post-measurement, pre-observation subject, just as Sebens and Carroll claim. Their Epistemic Separability Principle is shown to arise out of this explanation and the derivation of the Born rule for Everettian theory is thereby put on a firmer footing. (shrink)

Proposed derivations of the Born rule for Everettian theory are controversial. I argue that they are unnecessary but may provide justification for a simplified version of the Principal Principle. It’s also unnecessary to replace Everett’s idea that a subject splits in measurement contexts with the idea that subjects have linear histories which partition Many worlds? Everett, quantum theory, and reality, Oxford University Press, Oxford, pp 181–205, 2010; Wallace in The emergent multiverse, Oxford University Press, Oxford, 2012, Chapter 7; Wilson in (...) Br J Philos Sci 64:709–737, 2013; The nature of contingency: quantum physics as modal realism, Oxford University Press, Oxford, forthcoming). Linear histories were introduced to provide a concept of pre-measurement uncertainty and I explain why pre-measurement uncertainty for splitting subjects is after all coherent, though not necessary because Everett’s original fission interpretation of branching can arguably be rendered coherent without it, via reference to Vaidman, Tappenden, Sebens and Carroll and McQueen and Vaidman. A deterministic and probabilistic quantum mechanics can be made intelligible by replacing the standard collapse postulate with a no-collapse postulate which identifies objective probability with relative branch weight, supplemented by the simplified Principal Principle and some revisionary metaphysics. (shrink)

According to Sider’s stage theory a subject about to undergo personal fission should expect to experience each outcome simultaneously as distinct persons. How is the subject to make sense of this ? I argue that their most paradigmatically self-interested future-directed behaviour, betting for personal gain, ought to be exactly the same as in equivalent games of chance where the possible outcomes correspond to the fission output branches. So this novel form of expectancy, albeit strange, can be a reliable guide to (...) action. (shrink)

It is widely believed that the semantic contents of some linguistic and mental representations are determined by factors independent of a person’s bodily makeup. Arguments derived from Hilary Putnam’s seminal Twin Earth thought experiment have been especially influential in establishing that belief. I claim that there is a neglected version of the mind-body relation which undermines those arguments and also excludes the possibility of zombies. It has been neglected because it is counterintuitive but I show that it can nonetheless be (...) intelligibly worked out in detail and all obvious objections met. This suggests that we may be faced with a choice between embracing a counterintuitive interpretation of the mind-body relation or accepting that a currently very promising theory in cognitive science, Prediction Error Minimization, faces a fundamental problem. Furthermore, blocking that threat entails that any physicalist/materialst theory of mind is freed from the spectre of zombie worlds. The proposal also makes the ideas of personal teleportation of mind uploading more plausible. (shrink)

In the current debate on the concept of probability in the Everett interpretation of quantum mechanics Saunders and Wallace argue for a notion of pre-measurement uncertainty whilst Greaves and Myrvold attempt to do without uncertainty altogether. Both these approaches are controversial and I suggest a middle way. I develop in detail an argument which Wallace has hinted at and Greaves has seen as beside the point in order to show that Vaidman’s concept of post-measurement uncertainty has more relevance to pre-measurement (...) decision making than has hitherto been generally recognised. Further, Vaidman uncertainty leads naturally to another form of post-measurement uncertainty which clarifies the process of experimental confirmation of quantum mechanics in the Everett picture. I also stress the importance of Sider’s theory of transtemporal identity in making Everett’s multiverse intelligible. (shrink)

Murray Gell-Mann and James Hartle have made an original proposal for a version of decoherent histories quantum mechanics which is specifically tailored so as not to imply the emergence of multiple quasi-classical worlds. I argue that there is an explanatory gap in the proposal but that there remains an important insight which might be used to tackle what can be seen as an outstanding problem for Hugh Everett III’s “relative state” interpretation of quantum mechanics, if it is understood as giving (...) ontic priority to the wavefunction. The argument employs a recent novel analysis of self-location within any sort of multiverse. (shrink)

I continue to maintain that David Lewis’s concept of overlapping persons cannot yield pre-measurement uncertainty in the Everett interpretation of quantum mechanics in the way that Simon Saunders and David Wallace originally seemed to suggest. However, I argue that in their reply to me they make it clear that they do not wish to invoke overlap of persons after all. That makes it mysterious why they defended their interpretation of personal overlap in the first place and questionable what role overlap (...) has to play in their proposal. If Everettian branching can be understood to involve the divergence of distinct, non-overlapping worlds a concept of pre-measurement uncertainty is available. That idea was first proposed by David Deutsch but required an ad hoc postulate. Saunders has recently suggested that a similar scheme arises naturally out of the physics. If correct, that is important as it offers escape from some bizarre consequences of current alternative ways of understanding probability in the Everett interpretation. (shrink)

The contemporary popularity of semantic externalism has arisen from so-called Twin Earth thought experiments which suggest that the representational content of a natural kind term cannot be wholly determined by processes within a speaker's body. Such arguments depend on the intuition that the extensions of natural kind terms cannot have changed as the result of the scientific investigation of natural kinds' constitutions. I demonstrate that this externalist intuition depends on an assumption about the mentality of isomorphic doppelgangers which has never (...) been questioned but which is nonetheless arguably false. I develop an alternative view of the instantiation of mind which entails a revision of our understanding of the constitution of environmental objects. The picture seems to be fully coherent despite its oddity and I can find no good reason to reject it. The conclusion must be that the case for semantic externalism is thus less compelling than is often supposed. (shrink)

Paul Tappenden; The Roundsquare Copula: A Semantic Internalist's Rejoinder, Proceedings of the Aristotelian Society, Volume 96, Issue 1, 1 June 1996, Pages 395–.

It’s generally taken to be established that no local hidden-variable theory is possible. That conclusion applies if our world is a _thread_, where a thread is a world where particles follow trajectories, as in Pilot-Wave theory. But if our world is taken to be a _set_ of threads locality can be recovered. Our world can be described by a _many-threads_ theory, as defined by Jeffrey Barrett in the opening quote. Particles don’t follow trajectories because a particle in our world is (...) a set of _elemental_ particles following different trajectories, each in a thread. The “elements” of a superposition are construed as subsets in such a way that a particle in our world only has definite position if all its set-theoretic elements are at corresponding positions in each thread. Wavefunction becomes a 3D density distribution of particles’ subset measures, the stuff of an electron’s “probability cloud”. Current Pilot-Wave theory provides a non-relativistic dynamics for the elemental particles (approximated by Many Interacting Worlds theory). EPR-Bell nonlocality doesn’t apply because the relevant measurement outcomes in the absolute elsewhere of an observer are always in superposition. (shrink)

A selection of essays dedicated to Hans Herzberger with affection and gratitude for both his profound work and his lasting example. Contributors: I. Levi (on whether and how a rational agent should be seen as a maximizer of some cognitive value), C. Normore (on medieval accounts of logical validity), J. P. Tappenden (on the local influences on Frege's doctrines), A. Urquhart (on the inexpressible), A. C. Varzi (on dimensionality and the sense of possibility), and S. Yablo (on content and (...) carvings, and from there to mathematical realism). (shrink)

The options in a decision problem generally have outcomes with common features. Putting aside the common features simplifies deliberations, but the simplification requires a philosophical justification that this book provides.

The issues surrounding the Caesar problem are assumed to be inert as far as ongoing mathematics is concerned. This paper aims to correct this impression by spelling out the ways that, in their historical context, Frege's remarks would have had considerable resonance with work that other mathematicians such as Riemann and Dedekind were doing. The search for presentation‐independent characterizations of objects and global definitions was seen as bound up with fundamental methodological questions in complex analysis and number theory.

Schelling und Hegel benutzen in ihren philosophischen Texten mathematische und naturwissenschaftliche Modelle wie Unendlichkeit oder Gleichgewicht. Die Strukturen dieser Begriffe liefern einen Massstab fur den Vergleich der Positionen Schellings und Hegels, der fur Schellings Identitatsphilosophie und Hegels erste Jenaer Schriften durchgefuhrt wird. Als wichtigstes Resultat kann eine grundlegende Differenz zwischen beiden Positionen bereits um 1801 nachgewiesen und gezeigt werden, dass diese auf einer unterschiedlichen Auffassung der Rolle des Absoluten beruht.

Mathematical investigation, when done well, can confer understanding. This bare observation shouldn’t be controversial; where obstacles appear is rather in the effort to engage this observation with epistemology. The complexity of the issue of course precludes addressing it tout court in one paper, and I’ll just be laying some early foundations here. To this end I’ll narrow the field in two ways. First, I’ll address a specific account of explanation and understanding that applies naturally to mathematical reasoning: the view proposed (...) by Philip Kitcher and Michael Friedman of explanation or understanding as involving the unification of theories that had antecedently appeared heterogeneous. For the second narrowing, I’ll take up one specific feature (among many) of theories and their basic concepts that is sometimes taken to make the theories and concepts preferred: in some fields, for some problems, what is counted as understanding a problem may involve finding a way to represent the problem so that it (or some aspect of it) can be visualized. The final section develops a case study which exemplifies the way that this consideration – the potential for visualizability – can rationally inform decisions as to what the proper framework and axioms should be. The discussion of unification (in sections 3 and 4) leads to a mathematical analogue of Goodman’s problem of identifying a principled basis for distinguishing grue and green. Just as there is a philosophical issue about how we arrive at the predicates we should use when making empirical predictions, so too there is an issue about what properties best support many kinds of mathematical reasoning that are especially valuable to us. The issue becomes pressing via an examination of some physical and mathematical cases that make it seem unlikely that treatments of unification can be as straightforward as the philosophical literature has hoped. Though unification accounts have a grain of truth (since a phenomenon (or cluster of phenomena) called “unification” is in fact important in many cases) we are far from an analysis of what “unification” is.. (shrink)

I’ll use an extension of the “smidget” example Soames sets out on pages 165-172 to bring out the point. Groups A and B are disjoint and satisfy certain regularity conditions. Recall that the extension and anti-extension are specified by a pair of sufficient conditions. We specify: every member of group A is a smidget and every member of group B is not a smidget. No decision is made about persons that are outside groups A and B. It is, of course, (...) crucial that the smidgethood of the indeterminate cases is genuinely left open. What is the cash value of the difference between leaving a case unsettled and settling a case as indeterminate? Here is one difference: when a case is left unsettled, speakers of the language can resolve it later, if there is some reason to do so. This provides a simple model of key features of legal stipulations, at least in circumstances like U.S. constitutional law, where a single body can introduce an expression and stipulate how it is to be interpreted. (shrink)

There was a methodological revolution in the mathematics of the nineteenth century, and philosophers have, for the most part, failed to notice.2 My objective in this chapter is to convince you of this, and further to convince you of the following points. The philosophy of mathematics has been informed by an inaccurately narrow picture of the emergence of rigour and logical foundations in the nineteenth century. This blinkered vision encourages a picture of philosophical and logical foundations as essentially disengaged from (...) ongoing mathematical practice. Frege is a telling example: we have misunderstood much of what Frege was trying to do, and missed the intended significance of much of what he wrote, because our received stories underestimate the complexity of nineteenth-century mathematics and mislocate Frege’s work within that context. Given Frege’s perceived status as a paradigmatic analytic philosopher, this mislocation translates into an unduly narrow vision of the relation between mathematics and philosophy. This chapter surveys one part of a larger project that takes Frege as a benchmark to fix some of the broader interest and philosophical significance of nineteenth-century developments. To keep this contribution to a manageable.. (shrink)

I’ll use an extension of the “smidget” example Soames sets out on pages 165-172 to bring out the point. Groups A and B are disjoint and satisfy certain regularity conditions. Recall that the extension and anti-extension are specified by a pair of sufficient conditions. We specify: every member of group A is a smidget and every member of group B is not a smidget. No decision is made about persons that are outside groups A and B. It is, of course, (...) crucial that the smidgethood of the indeterminate cases is genuinely left open. What is the cash value of the difference between leaving a case unsettled and settling a case as indeterminate? Here is one difference: when a case is left unsettled, speakers of the language can resolve it later, if there is some reason to do so. This provides a simple model of key features of legal stipulations, at least in circumstances like U.S. constitutional law, where a single body can introduce an expression and stipulate how it is to be interpreted. (shrink)

This paper uses the strengthened liar paradox as a springboard to illuminate two more general topics: i) the negation operator and the speech act of denial among speakers of English and ii) some ways the potential for acceptable language change is constrained by linguistic meaning. The general and special problems interact in reciprocally illuminating ways. The ultimate objective of the paper is, however, less to solve certain problems than to create others, by illustrating how the issues that form the topic (...) of this paper are more intricate than previously realised, and that they are related in delicate and somewhat surprising ways. (shrink)

A cluster of recent papers on Frege have urged variations on the themethat Frege’s conception of logic is in some crucial way incompatible with‘metatheoretic’ investigation. From this observation, significant consequencesfor our interpretation of Frege’s understanding of his enterprise are taken tofollow. This chapter aims to critically examine this view, and to isolate whatI take to be the core of truth in it. However, I will also argue that once wehave isolated the defensible kernel, the sense in which Frege was committedto (...) rejecting ‘metatheory’ is too narrow and uninteresting to support the con-clusions drawn from the thesis by its proponents. (shrink)

This paper develops some respects in which the philosophy of mathematics can fruitfully be informed by mathematical practice, through examining Frege's Grundlagen in its historical setting. The first sections of the paper are devoted to elaborating some aspects of nineteenth century mathematics which informed Frege's early work. (These events are of considerable philosophical significance even apart from the connection with Frege.) In the middle sections, some minor themes of Grundlagen are developed: the relationship Frege envisions between arithmetic and geometry and (...) the way in which the study of reasoning is to illuminate this. In the final section, it is argued that the sorts of issues Frege attempted to address concerning the character of mathematical reasoning are still in need of a satisfying answer. (shrink)

The first book-length study of a leading tenth-century Ismaili theoretician Abu Ya'qub al-Sijistani.

Zusammenfassungen der Referate in französischer Sprache.

An agent often does not have precise probabilities or utilities to guide resolution of a decision problem. I advance a principle of rationality for making decisions in such cases. To begin, I represent the doxastic and conative state of an agent with a set of pairs of a probability assignment and a utility assignment. Then I support a decision principle that allows any act that maximizes expected utility according to some pair of assignments in the set. Assuming that computation of (...) an option's expected utility uses comprehensive possible outcomes that include the option's risk, no consideration supports a stricter requirement. (shrink)

A cluster of recent papers on Frege have urged variations on the theme that Frege’s conception of logic is in some crucial way incompatible with ‘metatheoretic’ investigation. From this observation, significant consequences for our interpretation of Frege’s understanding of his enterprise are taken to follow. This chapter aims to critically examine this view, and to isolate what I take to be the core of truth in it. However, I will also argue that once we have isolated the defensible kernel, the (...) sense in which Frege was committed to rejecting ‘metatheory’ is too narrow and uninteresting to support the con-. (shrink)

There are currently several versions of Everett's relative state interpretation of quantum mechanics, responding to a number of perceived problems for the original proposal. One of those problems is whether Everett's idea is in accord with the standard 'probabilistic' interpretation implicit in the Born rule. I argue in defence of what appears to be Everett's original view on this. The contribution I aim to make is a more complete discussion of the central issues of the identity of objects and observers (...) over time and how the concept of expectation can be applied when all 'possible' outcomes of a measurement process are regarded as actually occurring. (shrink)

The centrality of death rituals has in anthropologically informed studies of Buddhism been little documented. The current volume brings together a range of perspectives on Buddhist death rituals including ethnographic, textual, historical and theoretically informed accounts, and presents the diversity of the Buddhist funeral cultures of mainland Southeast Asia and China. It arises out of the University of Bristol's Centre for Buddhist Studies research project Buddhist Death Rituals in Southeast Asia and China, funded by the United Kingdom's Arts and Humanities (...) Research Council. This project involved extensive new research in Thailand, Laos and China. Other items from that project included several public exhibitions, extensive stills photographs, and several video films. The project-team produced two 30 minutes films on the ghost festival in Laos and China, one on urban funerals in Chiang Mai (Thailand) and several shorter clips dealing with funeral cultures in Laos, Thailand and China. Most of this material (and an extensive bibliography on the topic) is available free of charge from the project website located at the webpage of the Department of Theology and Religious Studies (Centre for Buddhist Studies) at the University of Bristol. (shrink)