Recent work on Mary Shepherd has largely focused on her metaphysics, especially as a response to Berkeley and Hume. However, relatively little attention has thus far been paid to the epistemological aspects of Shepherd’s program. What little attention Shepherd’s epistemology has received has tended to cast her as providing an unsatisfactory response to the skeptical challenge issued by Hume. For example, Walter Ott and Jeremy Fantl have each suggested that Shepherd cannot avoid Hume’s inductive skepticism even if she is (...) granted her metaphysics. In this paper, I examine Shepherd’s epistemology and argue that her response to Hume is more successful than the current literature suggests. In particular, I argue that, if Shepherd is granted her metaphysics, she can answer Hume’s demand for a rational justification of ordinary inductive inferences via a deductively justified uniformity principle and an appeal to parsimony. (shrink)

We discuss from a philosophical perspective the way in which the normal concept of time might be said to `emerge' in a quantum theory of gravity. After an introduction, we briefly discuss the notion of emergence, without regard to time. We then introduce the search for a quantum theory of gravity ; and review some general interpretative issues about space, time and matter. We then discuss the emergence of time in simple quantum geometrodynamics, and in the Euclidean approach. Section 6 (...) concludes. (shrink)

“Now, in calm weather, to swim in the open ocean is as easy to the practised swimmer as to ride in a spring-carriage ashore. But the awful lonesomeness is intolerable. The intense concentration of self in the middle of such a heartless immensity, my God! who can tell it? Mark, how when sailors in a dead calm bathe in the open sea—mark how closely they hug their ship and only coast along her sides.” (Herman Melville, Moby Dick, Chapter 94).

I discuss how modern cosmology illustrates under-determination of theoretical hypotheses by data, in ways that are different from most philosophical discussions. I emphasise cosmology's concern with what data could in principle be collected by a single observer ; and I give a broadly sceptical discussion of cosmology's appeal to the cosmological principle as a way of breaking the under-determination.I confine most of the discussion to the history of the observable universe from about one second after the Big Bang, as described (...) by the mainstream cosmological model: in effect, what cosmologists in the early 1970s dubbed the ‘standard model’, as elaborated since then. But in the closing Section 4, I broach some questions about times earlier than one second. (shrink)

Modest Infinitism -/- Jeremy Fantl -/- Abstract -/- Infinitism, a theory of justification most recently developed and defended by Peter Klein, is the view that justification is a matter of having an infinite series of non-repeating reasons for a proposition. I argue that infinitism is preferable to other theories (like foundationalism) in that only infinitism can plausibly account for two important features of justification: 1) that it admits of degrees and 2) that a concept of complete justification makes sense.

A notion called Herbrand saturation is shown to provide the model-theoretic analogue of a proof-theoretic method, Herbrand analysis, yielding uniform model-theoretic proofs of a number of important conservation theorems. A constructive, algebraic variation of the method is described, providing yet a third approach, which is finitary but retains the semantic flavor of the model-theoretic version.

In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. We survey implicit and explicit uses ofDirichlet characters in presentations of Dirichlet’s proof in the nineteenth and early twentieth centuries, with an eye toward understanding some of the pragmatic pressures that shaped the evolution of modern mathematical method.

In The Crane's Walk, Jeremy Barris seeks to show that we can conceive and live with a pluralism of standpoints with conflicting standards for truth--with the truth of each being entirely unaffected by the truth of the others. He argues that Plato's work expresses this kind of pluralism, and that this pluralism is important in its own right, whether or not we agree about what Plato's standpoint is.The longest tradition of Plato scholarship identifies crucial faults in Plato's theory of (...) Ideas. Barris argues that Plato deliberately displayed those faults, because he wanted to demonstrate that basic kinds of error or illogic have dimensions that are crucial to the establishing of truth. These dimensions legitimate a paradoxical coordination of logically incompatible conceptions of truth. Connecting this idea with emerging currents of Plato scholarship, he emphasizes, in addition to the dialogues' arguments, the importance of their nonargumentative features, including drama, myths, fictions, anecdotes, and humor. These unanalyzed nonargumentative features function rigorously, as a lever with which to examine the enterprise of rational argument itself, without presupposing its standards or illegitimately assimilating any position to the standards of another.Today, communities are torn apart by conflicts within and between a host of different pluralist and absolutist commitments. The possibility developed in this book-a coordination of absolute and relative truth that allows an understanding of some relativist and some absolutist positions as being fully legitimate and as capable of existing in a relation to their opposites-may contribute to perspectives for resolving these conflicts. (shrink)

Abstract: This paper assesses the Everettian approach to the measurement problem, especially the version of that approach advocated by Simon Saunders and David Wallace. I emphasise conceptual, indeed metaphysical, aspects rather than technical ones; but I include an introductory exposition of decoherence. In particular, I discuss whether---as these authors maintain---it is acceptable to have no precise definition of 'branch' (in the Everettian kind of sense). (A version of this paper will appear in a CTNS/Vatican Observatory volume on Quantum Theory and (...) Divine Action, ed. Robert Russell et al.). (shrink)

Abstract:Recently, the idea that every hypothetical imperative must somehow be ‘backed up’ by a prior categorical imperative has gained a certain influence among Kant interpreters and ethicists influenced by Kant. Since instrumentalism is the position that holds that hypothetical imperatives can by themselves and without the aid of categorical imperatives explain all valid forms of practical reasoning, the influential idea amounts to a rejection of instrumentalism as internally incoherent. This paper argues against this prevailing view both as an interpretation of (...) Kant and as philosophical understanding of practical reason. In particular, it will be argued that many of the arguments that claim to show that hypothetical imperatives must be backed up by categorical imperatives mistakenly assume that the form of practical reasoning must itself occur as a premise within the reasoning. An alternative to this assumption will be offered. I will conclude that while instrumentalism may well be false, there is no reason to believe it is incoherent. (shrink)

I discuss how modern cosmology illustrates underdetermination of theoretical hypotheses by data, in ways that are different from most philosophical discussions. I confine the discussion to the history of the observable universe from about one second after the Big Bang, as described by the mainstream cosmological model: in effect, what cosmologists in the early 1970s dubbed the ‘standard model’, as elaborated since then. Or rather, the discussion is confined to a (very!) few aspects of that history. I emphasize that despite (...) the underdetermination, a scientific realist can, and should, endorse this description. (shrink)

We analyze the pointwise convergence of a sequence of computable elements of L1 in terms of algorithmic randomness. We consider two ways of expressing the dominated convergence theorem and show that, over the base theory RCA0, each is equivalent to the assertion that every Gδ subset of Cantor space with positive measure has an element. This last statement is, in turn, equivalent to weak weak Königʼs lemma relativized to the Turing jump of any set. It is also equivalent to the (...) conjunction of the statement asserting the existence of a 2-random relative to any given set and the principle of Σ2 collection. (shrink)

What makes a veil of perception? Is it merely would-be objects of perceptual awareness, extraneous to the ‘environmental realities’ of which we judge? Or is it merely the presence of something extraneous along the route from perceptual awareness to awareness that our environment is thus and so? In his Mark Sacks lecture John McDowell seems to suppose something like the first answer. This essay argues for the second, thus that he himself imposes such a veil.

Arguing that journalism's traditional tenets--objectivity, fairness, accuracy--are no longer sufficient guidelines, journalist Jeremy Iggers challenges the dogmas that have shaped journalism for the last 100 years. He calls for a new code of ethics and a reexamination of the role of the news media in society.

This article argues that there is ultimately a very close convergence between prominent conceptions of being in mainstream Anglo‐American philosophy and mainstream postmodern Continental philosophy. One characteristic idea in Anglo‐American or analytic philosophy is that we establish what is meaningful and so what we can say about what is, by making evident the limits of sense or what simply cannot be meant. A characteristic idea in Continental philosophy of being is that being emerges through contrast and interplay with what it (...) is not, with what has no being at all and so is beyond sense. The two traditions consequently conceive being in significantly related ways. As a result, what the Continental tradition gets at with “the meaning of being as such and in general,” and how it gets at it, has much in common with what the Anglo‐American tradition gets at, and how it gets at it, by establishing “what can be meaningfully said.”. (shrink)

It is an underappreciated fact within the philosophical literature on laws of nature that many scientific laws require the aid of a supporting cast of additional modelling ingredients (such as boundary conditions, material parameters, interfacial stipulations, rigidity constraints, and so on) in order to perform their traditional role in scientific inquiry. In this paper, I suggest that this underappreciated fact spells trouble for some recent reformulations of David Lewis's Best Systems Account (BSA) of laws of nature. Under the auspices of (...) 'pragmatic Humeanism,' several philosophers have recently argued that the criteria of strength and simplicity that lay at the heart of Lewis's original formulation should be replaced with alternatives that are more sensitive to the role that laws play in scientific practice. Although the criteria that these philosophers put forward differ in a variety of ways, they are primarily concerned with the ability of laws to furnish us with predictions and encode information. This, I suggest, is a problem. If it is true that many scientific laws do not on their own perform some of the roles with which they are traditionally associated, then they are unlikely in isolation to make meaningful contributions to the predictive strength of a system or encode information about particular systems. Such laws are thus unlikely to end up in the best system, and so these accounts will have trouble conferring lawhood upon them. (shrink)

Time, along with concepts as space and matter, is bound to be a central concept of any physical theory. The chapter first discusses how time is treated similarly in quantum and classical theories. It then provides a few references on time‐reversal. The chapter discusses three chosen authors' (Paul Busch, Jan Hilgevoord and Jos Uffink) clarifications of uncertainty principles in general. Next, the chapter follows Busch in distinguishing three roles for time in quantum physics. They are external time, intrinsic time and (...) observable time. It also provides a brief discussion on time operators, in particular Pauli's influential proof. Finally, the chapter talks about time‐energy uncertainty principles with intrinsic times. (shrink)

In Section 2, I survey some of the ways that computers are used in mathematics. These raise questions that seem to have a generally epistemological character, although they do not fall squarely under a traditional philosophical purview. The goal of this article is to try to articulate some of these questions more clearly, and assess the philosophical methods that may be brought to bear. In Section 3, I note that most of the issues can be classified under two headings: some (...) deal with the ability of computers to deliver appropriate “evidence” for mathematical assertions, a notion that is explored in Section 4, while others deal with the ability of computers to deliver appropriate mathematical “understanding,” a notion that is considered in Section 5. Final thoughts are provided in Section 6. (shrink)

I reject Norton and Earman's hole argument that spacetime substantivalism is incompatible with determinism. I reconcile these both technically and philosophically. There is a technical definition of determinism that is not violated by pairs of models of the kind used in the hole argument. And technicalities aside, the basic idea of determinism is not violated if we claim that at most one of the two models represents a possible world. This claim can be justified either by metrical essentialism, or by (...) denying transworld identity for points: I prefer the latter. (shrink)

The increasing preponderance of opinion that some natural phenomena can be explained mathematically has inspired a search for a viable account of distinctively mathematical explanation. Among the desiderata for an adequate account is that it should solve the problem of directionality and the reversals of distinctively mathematical explanations should not count as members among the explanatory fold but any solution must also avoid the exclusion of genuine explanations. In what follows, I introduce and defend what I refer to as a (...) quasi-erotetic solution which provides a remedy to the problem in the form of an additional necessary condition on explanation. (shrink)

This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. More specifically, this paper argues against pointillisme about the structure of space and-or spacetime itself, especially a paper by Bricker (1993). (...) A companion paper argues against pointillisme in mechanics, especially about velocity; it focusses on Tooley, Robinson and Lewis. To avoid technicalities, I conduct the argument almost entirely in the context of ``Newtonian'' ideas about space and time. But both the debate and my arguments carry over to relativistic, and even quantum, physics. (shrink)

This paper discusses some of the modal involvements of analytical mechanics. I first review the elementary aspects of the Lagrangian, Hamiltonian and Hamilton-Jacobi approaches. I then discuss two modal involvements; both are related to David Lewis' work on modality, especially on counterfactuals. The first is the way Hamilton-Jacobi theory uses ensembles, i.e. sets of possible initial conditions. The structure of this set of ensembles remains to be explored by philosophers. The second is the way the Lagrangian and Hamiltonian approaches' variational (...) principles state the law of motion by mentioning contralegal dynamical evolutions. This threatens to contravene the principle that any actual truth, in particular an actual law, is made true by actual facts. Though this threat can be avoided, at least for simple mechanical systems, it repays scrutiny; not least because it leads to some open questions. (shrink)

The 1-consistency of arithmetic is shown to be equivalent to the existence of fixed points of a certain type of update procedure, which is implicit in the epsilon-substitution method.

We discuss the legacy of Alan Turing and his impact on computability and analysis.

This is a discussion of some themes in Max Tegmark’s recent book, Our Mathematical Universe. It was written as a review for Plus Magazine, the online magazine of the UK’s national mathematics education and outreach project, the Mathematics Millennium Project. Since some of the discussion---about symmetry breaking, and Pythagoreanism in the philosophy of mathematics---went beyond reviewing Tegmark’s book, the material was divided into three online articles. This version combines those three articles, and adds some other material, in particular a brief (...) defence of quidditism about properties. It also adds some references, to other Plus articles as well as academic articles. But it retains the informal style of Plus. (shrink)

Brian Earp and his colleagues argue in this issue’s target article that racial justice requires ending the War on Drugs. In this they are absolutely correct. Indeed, de...

The prime number theorem, established by Hadamard and de la Vallée Poussin independently in 1896, asserts that the density of primes in the positive integers is asymptotic to 1/ln x. Whereas their proofs made serious use of the methods of complex analysis, elementary proofs were provided by Selberg and Erdos in 1948. We describe a formally verified version of Selberg's proof, obtained using the Isabelle proof assistant.

Paradox and the Possibility of Knowledge argues that psychoanalytic theory has certain mostly unnoticed features that bring out, with unusual clarity, a logic that is true of conceptual thought generally. This logic is paradoxical in that it is deliberately and productively self-canceling. The general relevance of this logic to conceptual thought and to theory offers a solution to some fundamental epistemological problems. First, it allows a solution to the problem of the ultimate circularity or infinite regress of knowledge, by showing (...) how the circle or regress eliminates itself in a variety of successful knowledge-grounding ways. Second, it offers some resulting insights into issues involving politically troublesome dimensions of knowledge, specifically into the procedure of ethical political dialogue. The book is written in the contexts of both Anglo-American philosophy and Continental or European philosophy. The argument is largely Wittgensteinian, and at the same time proceeds through detailed reference to Freud's and Lacan's work. On the way it addresses theory construction in general, including the claims of phenomenology and deconstruction. (shrink)

Some recent philosophical debate about persistence has focussed on an argument against perdurantism that discusses rotating perfectly homogeneous discs. The argument has been mostly discussed by metaphysicians, though it appeals to ideas from classical mechanics, especially about rotation. In contrast, I assess the RDA from the perspective of the philosophy of physics. After introducing the argument and emphasizing the relevance of physics, I review some metaphysicians' replies to the argument, especially those by Callender, Lewis, Robinson and Sider. Thereafter, I argue (...) for three main conclusions. They all arise from the fact, emphasized in Section 2, that classical mechanics is both more subtle, and more problematic, than philosophers generally realize. The first conclusion is that the RDA can be formulated more strongly than is usually recognized: it is not necessary to ``imagine away'' the dynamical effects of rotation. The second is that in general relativity, the RDA fails because of frame-dragging. The third is that even setting aside general relativity, the strong formulation of the RDA can after all be defeated. Namely, by the perdurantist taking objects in classical mechanics to have only temporally extended, i.e. non-instantaneous, temporal parts: which immediately blocks the RDA. Admittedly, this version of perdurantism defines persistence in a weaker sense of `definition' than pointilliste versions that aim to define persistence assuming only instantaneous temporal parts. But I argue that temporally extended temporal parts: can do the jobs within the endurantism- perdurantism debate that the perdurantist wants temporal parts to do; and are supported by both classical and quantum mechanics. (shrink)

For the first time Entropy has been completely revised and updated to include a new subtitle which reflects the expanded focus on the greenhouse effect--the largest crisis ever to face mankind.

The paper proposes with Davidson that the talk of metaontology is literally meaningless, but with Wittgenstein that it is so in a way that grants a unique type of insight. More specifically, it argues both that Davidson’s arguments have a cogency that is hard to dismiss, and also that, since his own arguments are metaontological, they are self-referential, and consequently in turn undermine their own meaning as well. The paper argues further that metaontological statements cannot be avoided. Consequently, this kind (...) of statement constitutes an unavoidable self-referential paradox that means what it also excludes as capable of meaning. The result is a reinstatement of the meaning of ontological insight and in fact, the paper argues, a deep enrichment and also a particularly cogent justification of it. In addition, the logical peculiarity of the paradox involved has further useful consequences for the outcome of this justification, including a mutually illuminating commonality with some versions of metaethics. (shrink)

Pragmatic factors encroach on epistemic predicates not solely because the threshold for actionable belief may shift with an epistemic agent’s context, as an evidential Bayesian might insist, but also because what our inductive policy should be may shift with that context. I argue for this thesis in the context of imprecise probabilities, maintaining that the choice of the defining hyperparameter for an Imprecise Dirichlet Model for nonparametric predictive inference may correspond to the choice of an eager versus reticent inductive policy (...) in a way that can be sensitive to stakes and other practical circumstances. (shrink)

Volume 98, Issue 4, December 2020, Page 718-731.

This is a review of Hossenfelder’s book, Lost in Math: How Beauty Leads Physics Astray. The book gives a breezy exposition of the present situation in fundamental physics, and raises important questions: both about the content of the physics, and the way physics research is organized. I first state my main disagreements. Then, I mostly praise the book: I concentrate on Hossenfelder’s discussion of supersymmetry, naturalness and the multiverse.

Descartes’s causal theory is often taken to announce modernity by radically breaking with the Aristotelian past. Specifically, Descartes is often taken to reject the full Aristotelian causal theory in favor of the efficient causes characteristic of mechanistic physics and the activity of minds. In this chapter, I argue against this view by showing that Descartes endorses an avowedly Aristotelian notion of formal causation. First, I articulate Cartesian formal causation in light of its Aristotelian background, and I show that Descartes endorses (...) what Francisco Suárez termed metaphysical formal causal explanation. Then, I argue against taking formal causation to be a peripheral explanatory notion for Descartes by showing it to be both well-attested textually and part and parcel of his Platonic intellectualism. I conclude by suggesting some further contexts in which this Cartesian notion of formal causation could be profitably wielded. (shrink)

This paper gives a technically elementary treatment of some aspects of Hamilton -Jacobi theory, especially in relation to the calculus of variations. The second half of the paper describes the application to geometric optics, the optico-mechanical analogy and the transition to quantum mechanics. Finally, I report recent work of Holland providing a Hamiltonian formulation of the pilot-wave theory.