For forty years, Harvey Mansfield has been worth reading. Whether plumbing the depths of MachiavelliOs Discourses or explaining what was at stake in Bill ClintonOs impeachment, MansfieldOs work in political philosophy and political science has set the standard. In Educating the Prince, twenty-one of his students, themselves distinguished scholars, try to live up to that standard. Their essays offer penetrating analyses of Machiavellianism, liberalism, and America., all of them informed by MansfieldOs own work. The volume also includes a bibliography of (...) MansfieldOs writings. (shrink)

What were Shakespeare's final thoughts on history, tragedy, and comedy? Shakespeare's Last Plays focuses much needed scholarly attention on Shakespeare's "Late Romances." The work--a collection of newly commissioned essays by leading scholars of classical political philosophy and literature--offers careful textual analysis of Pericles, Prince of Tyre, Cymbeline, The Winter's Tale, The Tempest, All is True, and The Two Noble Kinsmen. The essays reveal how Shakespeare's thought in these final works compliments, challenges, fulfills, or transforms previously held conceptions of the playwright (...) and his political-philosophical views. (shrink)

Inspired by Cantor's Theorem (CT), orthodoxy takes infinities to come in different sizes. The orthodox view has had enormous influence in mathematics, philosophy, and science. We will defend the contrary view---Countablism---according to which, necessarily, every infinite collection (set or plurality) is countable. We first argue that the potentialist or modal strategy for treating Russell's Paradox, first proposed by Parsons (2000) and developed by Linnebo (2010, 2013) and Linnebo and Shapiro (2019), should also be applied to CT, in a way that (...) vindicates Countabilism. Our discussion dovetails with recent independently developed treatments of CT in Meadows (2015), Pruss (2020), and Scambler (2021), aimed at establishing the mathematical viability, and therefore epistemic possibility, of Countabilism. Unlike these authors, our goal isn't to vindicate the mathematical underpinnings of Countabilism. Rather, we aim to argue that, given that Countabilism is mathematically viable, Countabilism should moreover be regarded as true. After clarifying the modal content of Countabilism, we canvas some of Countabilism's many positive implications, including that Countabilism provides the best account of the pervasive independence phenomena in set theory, and that Countabilism has the power to defuse several persistent puzzles and paradoxes found in physics and metaphysics. We conclude that in light of its theoretical and explanatory advantages, Countabilism is more likely true than not. (shrink)

From David Brat, the college professor who made political headlines when he unseated Majority Leader Eric Cantor, comes his plan for restoring fiscal liberty for America. Congressman David Brat's odds-defying win against Eric Cantor--a triumph of a modest $200,000 campaign fund against a $5 million war chest--immediately brought David Brat, heretofore a liberal arts college economics professor, into the political limelight. Now, in his first book, AMERICAN UNDERDOG, Brat examines how we brought down the status quo by (...) tapping into moral and economic lessons as old as our civilization and discusses how Washington can learn from history instead of ignoring it. A fighter for children, he illuminates how our current fiscal policies are selling their future, and outlines new ways to move forward with a conservative agenda that provides fairer treatment for all. (shrink)

David Lowenthal offers a serious treatment of the idea that Shakespeare was a serious thinker, indeed a philosopher who chose to develop his ideas in dramatic form. Readers accustomed to contemporary Shakespeare criticism may be puzzled by Lowenthal’s book. He makes no effort to historicize his discussion of Shakespeare and never invokes the unholy trinity of race, class, and gender in analyzing the plays. Compared to new historicist, feminist, Marxist, and deconstructionist critics of Shakespeare, Lowenthal may seem to be (...) a naive reader; he is looking for what he can read out of the plays, not what he can read into them. Grounding himself in the older tradition of Shakespeare criticism, from Ben Jonson to Samuel Johnson, from Samuel Taylor Coleridge to A. C. Bradley, Lowenthal views the playwright as a source of genuine wisdom. He assumes that Shakespeare knew what he was doing and was fully in control of his dramatic material, shaping his plays into artistic wholes that allow him to raise fundamental questions about the human condition. (shrink)

In topological modal logic, it is well known that the Cantor derivative is more expressive than the topological closure, and the ‘elsewhere’, or ‘difference’, operator is more expressive than the ‘somewhere’ operator. In 2014, Kudinov and Shehtman asked whether the combination of closure and elsewhere becomes strictly more expressive when adding the Cantor derivative. In this paper we give an affirmative answer: in fact, the Cantor derivative alone can define properties of topological spaces not expressible with closure and elsewhere. To (...) prove this, we develop a novel theory of morphisms which preserve formulas with the elsewhere operator. (shrink)

It is standard in set theory to assume that Cantor's Theorem establishes that the continuum is an uncountable set. A challenge for this position comes from the observation that through forcing one can collapse any cardinal to the countable and that the continuum can be made arbitrarily large. In this paper, we present a different take on the relationship between Cantor's Theorem and extensions of universes, arguing that they can be seen as showing that every set is countable and that (...) the continuum is a proper class. We examine several principles based on maximality considerations in this framework, and show how some (namely Ordinal Inner Model Hypotheses) enable us to incorporate standard set theories (including ZFC with large cardinals added). We conclude that the systems considered raise questions concerning the foundational purposes of set theory. (shrink)

Dynamic Topological Logic ( $\mathcal{DTL}$ ) is a modal framework for reasoning about dynamical systems, that is, pairs 〈X, f〉 where X is a topological space and f: X → X a continuous function. In this paper we consider the case where X is a metric space. We first show that any formula which can be satisfied on an arbitrary dynamic topological system can be satisfied on one based on a metric space; in fact, this space can be taken to (...) be countable and have no isolated points. Since any metric space with these properties is homeomorphic to the set of rational numbers, it follows that any satisfiable formula can be satisfied on a system based on $\mathbb{Q}$ . We then show that the situation changes when considering complete metric spaces, by exhibiting a formula which is not valid in general but is valid on the class of systems based on a complete metric space. While we do not attempt to give a full characterization of the set of valid formulas on this class we do give a relative completeness result; any formula which is satisfiable on a dynamical system based on a complete metric space is also satisfied on one based on the Cantor space. (shrink)

It is a celebrated result of McKinsey and Tarski [28] thatS4is the logic of the closure algebraΧ+over any dense-in-itself separable metrizable space. In particular,S4is the logic of the closure algebra over the realsR, the rationalsQ, or the Cantor spaceC. By [5], each logic aboveS4that has the finite model property is the logic of a subalgebra ofQ+, as well as the logic of a subalgebra ofC+. This is no longer true forR, and the main result of [5] states that each connected (...) logic aboveS4with the finite model property is the logic of a subalgebra of the closure algebraR+.In this paper we extend these results to all logics aboveS4. Namely, for a normal modal logicL, we prove that the following conditions are equivalent: (i)Lis aboveS4, (ii)Lis the logic of a subalgebra ofQ+, (iii)Lis the logic of a subalgebra ofC+. We introduce the concept of a well-connected logic aboveS4and prove that the following conditions are equivalent: (i)Lis a well-connected logic, (ii)Lis the logic of a subalgebra of the closure algebra$\xi _2^ + $over the infinite binary tree, (iii)Lis the logic of a subalgebra of the closure algebra${\bf{L}}_2^ + $over the infinite binary tree with limits equipped with the Scott topology. Finally, we prove that a logicLaboveS4is connected iffLis the logic of a subalgebra ofR+, and transfer our results to the setting of intermediate logics.Proving these general completeness results requires new tools. We introduce the countable general frame property (CGFP) and prove that each normal modal logic has the CGFP. We introduce general topological semantics forS4, which generalizes topological semantics the same way general frame semantics generalizes Kripke semantics. We prove that the categories of descriptive frames forS4and descriptive spaces are isomorphic. It follows that every logic aboveS4is complete with respect to the corresponding class of descriptive spaces. We provide several ways of realizing the infinite binary tree with limits, and prove that when equipped with the Scott topology, it is an interior image of bothCandR. Finally, we introduce gluing of general spaces and prove that the space obtained by appropriate gluing involving certain quotients ofL2is an interior image ofR. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Taking Wittgenstein at his Word: A Textual StudyDavid SternRobert J. Fogelin. Taking Wittgenstein at his Word: A Textual Study. Princeton-Oxford: Princeton University Press. 2009. Pp. xviii + 181. Cloth, $35.00.This is an excellent book, which should be read widely. It is a short, lucid, and accessible introduction to Wittgenstein’s later philosophy, written by a leading expert. It is the ideal sequel to Saul Kripke’s Wittgenstein on Rules and (...) Private Language on a short list of required readings for a course on Wittgenstein. Part 1 concerns rule following and the conceivability of a private language, while part 2 discusses three topics in his philosophy of mathematics: the status of mathematical expressions, Wittgenstein’s treatment of Cantor on transfinite cardinals, and his approach to logical consistency. There is very little discussion of the secondary literature on any of these topics. Instead, apart from a few prefatory methodological [End Page 147] passages, almost all of the book is devoted to extensive quotations from Wittgenstein’s writing and to close reading of what he says there.Fogelin’s chief aim, to take Wittgenstein at his word, is in a sense a very modest one. Wittgenstein insisted throughout his career that he was not presenting philosophical theses, and that philosophy should not be a matter of defending theses. Indeed, Fogelin explicitly acknowledges that in taking Wittgenstein at his word, he is not presenting “a novel—hitherto unrecognized—way of understanding Wittgenstein’s later philosophy” (xii–xiii). Nevertheless, most interpreters have read Wittgenstein as failing to follow his own methodological precepts, and their interpretations have focused on the theses that they attribute to him. Instead, Fogelin lets “Wittgenstein speak for himself” (xi), not only quoting at length from his writings, but also from Wittgenstein’s “self-commentaries” (xi), passages where Wittgenstein helps us appreciate the philosophical significance he assigns to his words. Crucially, these quotations are held together by a close reading that provides a lucid and perceptive statement of what Wittgenstein is saying there and why, highlighting the intimate connection between Wittgenstein’s philosophical methods and his treatment of key topics in the philosophy of language and mathematics.A leading theme in Fogelin’s book is what he calls Wittgenstein’s “defactoist” approach to rule following. While he does not define this neologism, he does say that it involves “the rejection of appeals to rational processes where philosophers typically have attempted to find or supply them” (41). Furthermore, Fogelin connects it with the central role Wittgenstein gives to natural responses and training, the fact that the kind of training a creature can undergo depends on its natural or instinctive responses and Wittgenstein’s “rejection of the idea that training is merely an external device intended to induce in the trainee a grasp of the correctness, the legitimacy, of what he has been trained to do” (35–36).Although Fogelin never explicitly addresses the crucial question of which texts to draw on in taking Wittgenstein “at his word,” in practice he makes use of a wide range of publications from every stage of Wittgenstein’s career. The Tractatus, written during the First World War, is treated as belonging to an earlier stage of his thought, and some similarities to and differences from his later work are discussed. No such distinctions are drawn between material written in the early 1930s, editors’ reconstruction of lecture notes from the early 1930s and late 1930s, passages from the Philosophical Investigations, assembled in the mid-1940s, the different parts of the Remarks on the Foundations of Mathematics, from the mid-1930s to early 1940s, and selections from On Certainty, dating from the late 1940s and early 1950s. While Fogelin acknowledges that there was some development in Wittgenstein’s views during these years, he puts great weight on passages taken from manuscripts and student lecture notes from the 1930s. For instance, in his crucial opening chapter on rule following, he relies heavily on the words with which Wittgenstein first formulated his paradox of interpretation in the early 1930s (20–21) and on his statement of the connection between meaning and rules in his 1932 lectures (17). While these passages are attractive precisely because they... (shrink)

It is widely held that the paradox of Achilles and the Tortoise, introduced by Zeno of Elea around 460 B.C., was solved by mathematical advances in the nineteenth century. The techniques of Weierstrass, Dedekind and Cantor made it clear, according to this view, that Achilles’ difficulty in traversing an infinite number of intervals while trying to catch up with the tortoise does not involve a contradiction, let alone a logical absurdity. Yet ever since the nineteenth century there have been dissidents (...) claiming that the apparatus of Weierstrass et al. has not resolved the paradox, and that serious problems remain. It seems that these claims have received unexpected support from recent developments in mathematical physics. This support has however remained largely unnoticed by historians of philosophy, presumably because the relevant debates are cast in mathematical-technical terms that are only accessible to people with the relevant training. That is unfortunate, since the debates in question might well profit from input by philosophers in general and historians of philosophy in particular. Below we will first recall the Achilles paradox, and describe the way in which nineteenth century mathematics supposedly solved it. Then we discuss recent work that contests this solution, reiterating the dissident dogma that no mathematical approach whatsoever can even come close to solving the original Achilles. We shall argue that this dissatisfaction with a mathematical solution is inadequate as it stands, but that it can perhaps be reformulated in the light of new developments in mathematical physics. (shrink)

The widespread idea that infinitesimals were “eliminated” by the “great triumvirate” of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum (...) with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d’Alembert, Cauchy, and others. (shrink)

In his ‘Theory of Light and Colours’, presented to the Royal Society in November 1801, Thomas Young defended a mechanical explanation of the coloured fringes observed outside of the shadow of an opaque object – the so-called ‘colours by inflection’ – that was based on the hypothesis of an ethereal density gradient surrounding all material bodies. However, two years later, he publicly rejected that hypothesis, without giving much detail of his reasons. Although Geoffrey Cantor has demonstrated the crucial role of (...) mechanical and astronomical arguments in explaining the withdrawal of this fundamental hypothesis long ago, the purpose of this article is to draw deeper attention to a set of experiments performed by David Brewster on the inflection of light, described in a letter he addressed to the Royal Society in January 1802, but was retained by William Herschel, and finally was neither read before the Society, nor published in its Philosophical Transactions. For the hypothesis that will be evaluated here is that these unpublished experiments of Brewster’s were eventually known to Young through the mediation of Herschel, and eventually played a significant role in Young’s rejection of his ether distribution hypothesis. (shrink)

David Hilbert famously remarked, “No one will drive us from the paradise that Cantor has created.” This volume offers a guided tour of modern mathematics’ Garden of Eden, beginning with perspectives on the finite universe and classes and Aristotelian logic. Author Mary Tiles further examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor’s transfinite paradise; axiomatic set theory; logical objects and logical types; independence results and the universe of sets; and the constructs and reality of mathematical structure. Philosophers (...) and mathematicians will find an abundance of intriguing topics in this text, which is appropriate for undergraduate- and graduate-level courses. 1989 ed. 32 figures. (shrink)

David Hilbert’s early foundational views, especially those corresponding to the 1890s, are analysed here. I consider strong evidence for the fact that Hilbert was a logicist at that time, following upon Dedekind’s footsteps in his understanding of pure mathematics. This insight makes it possible to throw new light on the evolution of Hilbert’s foundational ideas, including his early contributions to the foundations of geometry and the real number system. The context of Dedekind-style logicism makes it possible to offer a (...) new analysis of the emergence of Hilbert’s famous ideas on mathematical existence, now seen as a revision of basic principles of the “naive logic” of sets. At the same time, careful scrutiny of his published and unpublished work around the turn of the century uncovers deep differences between his ideas about consistency proofs before and after 1904. Along the way, we cover topics such as the role of sets and of the dichotomic conception of set theory in Hilbert’s early axiomatics, and offer detailed analyses of Hilbert’s paradox and of his completeness axiom (Vollständigkeitsaxiom). (shrink)

David Kaplan observed in Kaplan that the principle \\) cannot be verified at a world in a standard possible worlds model for a quantified bimodal propositional language. This raises a puzzle for certain interpretations of the operator Q: it seems that some proposition p is such that is not possible to query p, and p alone. On the other hand, Arthur Prior had observed in Prior that on pain of contradiction, ∀p is Q only if one true proposition is (...) Q and one false proposition is Q. The two observations are related: ∀p is elusive in that it is not possible for the proposition to be uniquely Q. Kaplan based his model-theoretic observation on Cantor’s theorem, but there is a less well-known link between this simple set-theoretic observation and Prior’s remark. We generalize the link to develop a heuristic designed to move from Cantor’s theorem to the observation that a variety of sentences of the bimodal language express propositions that cannot be Q uniquely. We highlight the analogy between some of these results and some set-theoretic antinomies and suggest that the phenomenon is richer than one may have anticipated. (shrink)

The Forrest-Armstrong argument, as reconfigured by David Lewis, is a reductio against an unrestricted principle of recombination. There is a gap in the argument which Lewis thought could be bridged by an appeal to recombination. After presenting the argument, I show that no plausible principle of recombination can bridge the gap. But other plausible principles of plenitude can bridge the gap, both principles of plenitude for world contents and principles of plenitude for world structures. I conclude that the Forrest-Armstrong (...) argument, when fortified in one of these ways, demands that unrestricted recombination be rejected. The appropriate restriction comes from a consideration of what world structures are possible. I argue that, although there are too many worlds to form a set, for any world, the individuals at that world do form a set. To defend it I invoke a principle of Limitation of Size together with an iterative conception of structure. (shrink)

_ Convention_ was immediately recognized as a major contribution to the subject and its significance has remained undiminished since its first publication in 1969. Lewis analyzes social conventions as regularities in the resolution of recurring coordination problems-situations characterized by interdependent decision processes in which common interests are at stake. Conventions are contrasted with other kinds of regularity, and conventions governing systems of communication are given special attention.

Consciousness and Mind presents David Rosenthal's influential work on the nature of consciousness. Central to that work is Rosenthal's higher-order-thought theory of consciousness, according to which a sensation, thought, or other mental state is conscious if one has a higher-order thought that one is in that state. The first four essays develop various aspects of that theory. The next three essays present Rosenthal's homomorphism theory of mental qualities and qualitative consciousness, and show how that theory fits with and helps (...) sustain the HOT theory. A crucial feature of homomorphism theory is that it individuates and taxonomizes mental qualities independently of the way we're conscious of them, and indeed independently of our being conscious of them at all. So the theory accommodates the qualitative character not only of conscious sensations and perceptions, but also of those which fall outside our stream of consciousness. Rosenthal argues that, because this account of mental qualities makes no appeal to consciousness, it enables us to dispel such traditional quandaries as the alleged conceivability of undetectable quality inversion, and to disarm various apparent obstacles to explaining qualitative consciousness and understanding its nature. Six further essays build on the HOT theory to explain various important features of consciousness, among them the complex connections that hold in humans between consciousness and speech, the self-interpretative aspect of consciousness, and the compelling sense we have that consciousness is unified. Two of the essays, one an extended treatment of homomorphism theory, appear here for the first time. There is also a substantive introduction, which draws out the connections between the essays and highlights their implications. (shrink)

Epistemologists have recently proposed a number of norms governing rational inquiry. My aim in this paper is to unify and explain recently proposed norms of inquiry by developing a general account of the conditions under which inquiries are rational, analogous to theories such as evidentialism and reliabilism for rational belief. I begin with a reason-responsiveness conception of rationality as responding correctly to possessed normative reasons. I extend this account with a series of claims about the normative reasons for inquiry that (...) we possess. I apply the account to shed light on two classes of norms that have featured prominently in recent discussions: norms of clutter avoidance forbidding agents from engaging in trivial inquiries, and norms of logical non-omniscience governing properties such as the deductive closure and consistency of an agent's belief state. I conclude with a discussion of the sense in which norms of inquiry should be regarded as epistemic norms. (shrink)

This is a corrected version of the final proofs. I've fixed a number of typos, and corrected a blunder in chapter 4. In chapter 4 I say that 'this is this' is analytic, and 'this is not this' is antonymous. This is inconsistent with what I say in chapter 5, and not what I actually think. Rather, 'this is this' is taugologous, and 'this is not this' is contradictory. Analyticity and autnonmy are sense properties while tautologousness and contradictoriness are formal (...) logical properties. Heading, ToC and Index updated accordingly. (Oxford will make these corrections in their online version and in future print runs.). (shrink)

Do motivational limitations due to human nature constrain the demands of justice? Among those who say no, David Estlund offers perhaps the most compelling argument. Taking Estlund’s analysis of “ability” as a starting point, I show that motivational deficiencies can constrain the demands of justice under at least one common circumstance — that the motivationally-deficient agent makes a good faith effort to overcome her deficiency. In fact, my argument implies something stronger; namely, that the demands of justice are constrained (...) by what people are sufficiently likely to be motivated to do. Thus, contrary to the prevailing wisdom, it is the business of ideal theory — not just nonideal theory — to work with the motivational capacities people are likely enough to have. (See also Estlund's reply in the same issue of EJPT and my rejoinder on Philpapers.). (shrink)

We apply a familiar distinction from philosophy of language to a class of material artifacts that are sometimes said to “speak”: statues. By distinguishing how statues speak at the locutionary level versus at the illocutionary level, or what they say versus what they do, we obtain the resource for addressing two topics. First, we can explain what makes statues distinct from street art. Second, we can explain why it is mistaken to criticize—or to defend—the continuing presence of statues based only (...) on what they represent. Both explanations are driven by the same core idea: the significance of statues arises primarily from what they do, and not what they say. (shrink)

According to orthodoxy, our best physical theories strongly support Eternalism over Presentism. Our goal is to argue against this consensus, by arguing that a certain overlooked aspect of our best physical theories strongly supports Presentism over Eternalism.

I argue that it is metaphysically necessary that: (i) every fundamental entity is conscious, and (ii) every fundamental property is a phenomenal property.

This dialogue explores the question of whether intentionality—the “ofness”, “aboutness”, or “directedness” of mental states—is a relation. We explore three views: the Naive View, on which intentionality is a relation to ordinary, everyday objects, facts, and other such items; the Abstract Contents View, on which intentionality is a relation to mind-independent abstract entities that are our contents; and the Aspect View, on which intentionality is a matter of having intentional states with particular (non-relational) aspects that are our contents. We consider (...) the challenges facing these views, which include empirical challenges in accounting for all the contents our intentional states can represent, metaphysical challenges in making sense of how contents can be entertained or otherwise represented by us and how they can play a psychological role in the mental economy, and challenges in making sense of how intentionality connects us to the world—if at all. Along the way, we consider the question of how consciousness is related to intentionality and how this affects one’s choice of views. (shrink)

According to the Principle of Sufficient Reason, every fact has an explanation. An important challenge to this principle is that it risks being a counterexample to itself. What explains why everything needs to be explained? My first goal is to distinguish two broad kinds of answers to this question, which I call “Humean Rationalism” and “Non-Humean Rationalism”. My second goal will be to defend the prospects of Humean Rationalism.

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal (...) patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

The Right and the Good, a classic of twentieth-century philosophy by the great scholar Sir David Ross, is now presented in a new edition with a substantial introduction by Philip Stratton-Lake, a leading expert on Ross. Ross's book is the pinnacle of ethical intuitionism, which was the dominant moral theory in British philosophy for much of the nineteenth and early twentieth century. Intuitionism is now enjoying a considerable revival, and Stratton-Lake provides the context for a proper understanding of Ross's (...) great work today. (shrink)

There is a difference between merely thinking that P and really grasping that P. For example, Jackson's (1982) black-and-white Mary cannot (before leaving her black-and-white room) fully grasp what it means to say that fire engines are red, but she can perfectly well entertain the thought that fire engines are red. The contrast between merely thinking and grasping is especially salient in the context of certain moral decisions. For example, an individual who grasps the plight of starving children thanks to (...) evocative images seems much more likely to donate for the children's benefit than someone who is merely told about their plight. This paper offers a phenomenal account of grasping according to which grasping a content (whether a proposition or concept) consists in one's thoughts about the content being constituted by phenomenal experiences of constituents of the content. This account improves on earlier phenomenal accounts of grasping (Bourget 2017a, 2018) by allowing for partial grasping and generalizing to concepts. The paper also addresses objections to phenomenal accounts of grasping, including the objection that recent developments in AI technology show that consciousness is irrelevant to grasping and understanding. (shrink)

Christian pro-lifers often respond to Thomson’s defense of abortion that the violinist is allowed to die while the embryo is killed. Boonin and McMahan counter that this distinction does not provide an objection to extraction abortions that disconnect embryos and allow them to die. I disagree. I first argue that letting die and killing are not to be distinguished by differences between acts and omissions, moral and immoral motives, intentional or unintentional deaths, and causing or not causing a pathology. I (...) offer a taxonomy in which hysterotomies turn out to be killings. I then argue that if either the placenta is considered an organ of the embryo or the embryo is construed as a part of the pregnant woman, then abortion pills kill rather than allow death. So, assuming that killing people is morally worse than letting them die, extraction abortions can be condemned to the same degree as other abortions. (shrink)

Many philosophers of physics think that physical rates of change, like velocity or acceleration in classical physics, are extrinsic. Many philosophers of mind think that phenomenal properties, which characterize what it’s like to be an agent at a time, are intrinsic. I will argue that these two views can’t both be true. Given that these two views are in tension, we face an explanatory challenge. Why should there be any interesting connection between these physical quantities and consciousness in the first (...) place? In a speculative spirit, I close by developing a panpsychist view which promises to explain this connection in a particularly satisfying way. (shrink)

Suppose someone is brought up as an orthodox Jew, and so only eats kosher, is very conservative sexually, etc. Suppose they then find out that this Judaism stuff is just all a big mistake. If they then regret all the shrimp they could have eaten, all the sex!, this makes perfect sense. Not so, however, if someone finds out that moral realism is false, and they now regret all the fun they could have had hurting people’s feeling, etc. Even if (...) this does make sense, there’s a strong disanalogy between the moral and the religious case. This asymmetry, on a realist picture of morality, calls for explanation. This chapter tries to explain it. The discussion engages some topics familiar from objections to Robust realism—the why-be-moral challenge, the status of de-dicto moral motivation, and whether and why we should care about the moral properties, robustly realistically understood. (shrink)

Using as a starting point recent and apparently incompatible conclusions by Saunders and Knox, I revisit the question of the correct spacetime setting for Newtonian physics. I argue that understood correctly, these two versions of Newtonian physics make the same claims both about the background geometry required to define the theory, and about the inertial structure of the theory. In doing so I illustrate and explore in detail the view—espoused by Knox, and also by Brown —that inertial structure is defined (...) by the dynamics governing subsystems of a larger system. This clarifies some interesting features of Newtonian physics, notably the distinction between using the theory to model subsystems of a larger whole and using it to model complete universes, and the scale-relativity of spacetime structure. _1_ Introduction _2_ Newtonian Mechanics and Galilean Spacetime _3_ Vector Relationism and Maxwellian Spacetime _4_ Recovering the Galilei Group: Dynamics of Subsystems _5_ Knox on Inertial Structure _6_ Connections on Maxwellian Spacetime _7_ Knox on Newtonian Gravity _8_ Vector Relationism and Newton–Cartan Theory _9_ Inertial Structure in Newton–Cartan Gravity _10_ Reconciling Knox and Saunders _11_ Conclusions. (shrink)

This essay examines the philosophical significance of $\Omega$-logic in Zermelo-Fraenkel set theory with choice (ZFC). The categorical duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The hyperintensional profile of $\Omega$-logical validity can then be countenanced within a coalgebraic logic. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal and hyperintensional profiles of $\Omega$-logical validity correspond to those of second-order logical consequence, $\Omega$-logical validity is genuinely (...) logical. Second, the foregoing provides a hyperintensional account of the interpretation of mathematical and metamathematical vocabulary. (shrink)