Let's suppose you think that there are no uncountable sets. Have you adopted a restrictive position? It is certainly tempting to say yes---you've prohibited the existence of certain kinds of large set. This paper argues that this intuition can be challenged. Instead, I argue that there are some considerations based on a formal notion of restrictiveness which suggest that it is restrictive to hold that there are uncountable sets.

I provide an examination and comparison of modal theories for underwriting different non-modal theories of sets. I argue that there is a respect in which the `standard' modal theory for set construction---on which sets are formed via the successive individuation of powersets---raises a significant challenge for some recently proposed `countabilist' modal theories (i.e. ones that imply that every set is countable). I examine how the countabilist can respond to this issue via the use of regularity axioms and raise some questions (...) about this approach. I argue that by comparing them with the `standard' uncountabilist theory, a new approach that brings in arbitrariness rather than the strict controls of forcing is desirable. (shrink)

Feminist bioethicists of a variety of persuasions discuss the 2013 case of Marlise Munoz, a pregnant woman whose medical care was in dispute after she became brain dead.

How does our language relate to reality? This is a question that is especially pertinent in set theory, where we seem to talk of large infinite entities. Based on an analogy with the use of models in the natural sciences, we argue for a threefold correspondence between our language, models, and reality. We argue that so conceived, the existence of models can be underwritten by a weak notion of existence, where weak existence is to be understood as existing in virtue (...) of language. (shrink)

The relevance of analytic metaphysics has come under criticism: Ladyman & Ross, for instance, have suggested do discontinue the field. French & McKenzie have argued in defense of analytic metaphysics that it develops tools that could turn out to be useful for philosophy of physics. In this article, we show first that this heuristic defense of metaphysics can be extended to the scientific field of applied ontology, which uses constructs from analytic metaphysics. Second, we elaborate on a parallel by French (...) & McKenzie between mathematics and metaphysics to show that the whole field of analytic metaphysics, being useful not only for philosophy but also for science, should continue to exist as a largely autonomous field. (shrink)

This paper argues for the existence of a fourth positive generic value relation that can hold between two items beyond ‘better than’, ‘worse than’, and ‘equally good’: namely ‘on a par’.

In this article, I identify and critically examine 3 dogmas of normativity that support a commonly accepted ‘Passivist View' of rational agency. I raise some questions about these dogmas, suggest what we should believe in their place, and moot an alternative ‘Activist View' of what it is to be a rational agent that grows out of rejection of the 3 dogmas. Underwriting the dogmas and the Passivist View, I suggest, is a deeply held but mistaken assumption that the normative domain (...) is fundamentally akin to the nonnormative domain. Once we allow that the normative may be fundamentally unlike the nonnormative in certain key ways, a shift in our thinking about what it is to be rational becomes possible. I end by considering some implications of this paradigm shift in rationality from the passive to the active for various applied matters. (shrink)

This paper is the introduction to the volume. It gives an argumentative view of the philosophical landscape concerning incommensurability and incomparability. It argues that incomparability, not incommensurability, is the important phenomenon on which philosophers should be focusing and that the arguments for the existence of incomparability are so far not compelling.

Much of the discussion of set-theoretic independence, and whether or not we could legitimately expand our foundational theory, concerns how we could possibly come to know the truth value of independent sentences. This paper pursues a slightly different tack, examining how we are ignorant of issues surrounding their truth. We argue that a study of how we are ignorant reveals a need for an understanding of set-theoretic explanation and motivates a pluralism concerning the adoption of foundational theory.

Can quite different values be rationally weighed against one another? Can the value of one thing always be ranked as greater than, equal to, or less than the value of something else? If the answer to these questions is no, then in what areas do we find commensurability and comparability unavailable? And what are the implications for moral and legal decision making? This book struggles with these questions, and arrives at distinctly different answers.".

In virtue of what is something a reason for action? That is, what makes a consideration a reason to act? This is a metaphysical or meta-normative question about the grounding of reasons for action. The answer to the grounding question has been traditionally given in ‘pure’, univocal terms. This paper argues that there is good reason to understand the ground of practical normativity as a hybrid of traditional ‘pure’ views. The paper 1) surveys the three leading ‘pure’ answers to the (...) question of a normative ground, 2) examines one or two of the most difficult problems for each, proposing along the way a new objection to one, and 3) argues that a particular hybrid view about normative grounds –‘hybrid voluntarism’ – avoids each of the main problems faced by the three leading ‘pure’ views. (shrink)

This article articulates and assesses an imperatival approach to the foundations of mathematics. The core idea for the program is that mathematical domains of interest can fruitfully be viewed as the outputs of construction procedures. We apply this idea to provide a novel formalisation of arithmetic and set theory in terms of such procedures, and discuss the significance of this perspective for the philosophy of mathematics.

We explain and explore class-theoretic potentialism—the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning the relevant potentialist systems (in particular exhibiting failures of the $\mathsf {.2}$ and $\mathsf {.3}$ axioms). We then discuss the significance of these results for the different kinds of class-theoretic potentialists.

What makes a choice hard? I discuss and criticize three common answers and then make a proposal of my own. Paradigmatic hard choices are not hard because of our ignorance, the incommensurability of values, or the incomparability of the alternatives. They are hard because the alternatives are on a par; they are comparable, but one is not better than the other, and yet nor are they equally good. So understood, hard choices open up a new way of thinking about what (...) it is to be a rational agent. (shrink)

In this paper I adduce a new argument in support of the claim that IBE is an autonomous form of inference, based on a familiar, yet surprisingly, under-discussed, problem for Hume’s theory of induction. I then use some insights thereby gleaned to argue for the claim that induction is really IBE, and draw some normative conclusions.

The aim of this paper is to show that Shaftesbury’s thinking about liberty is best understood in terms of self-mastery. To examine his understanding of liberty, I turn to a painting that he commissioned on the ancient theme of the choice of Hercules and the notes that he prepared for the artist. Questions of human choice are also present in the so-called story of an amour, which addresses the difficulties of controlling human passions. Jaffro distinguishes three notions of self-control that (...) are present in the story of an amour. Although I agree with many aspects of Jaffro’s interpretation, I question his conclusion that self- control in the Stoic sense is best reserved for ‘moral heroes.’ I propose an alternative developmental interpretation, according to which all human beings are on an intellectual journey aimed at personal and moral improvement. My interpretation takes seriously that for Shaftesbury philosophy is meant to be practical and help improve our lives. I end by arguing that rather than trying to situate Shaftesbury’s concept of liberty within debates among compatibilists and incompatibilists it is more promising to understand it in terms of self- mastery and thus regard it as a version of positive liberty. (shrink)

Discussion of new axioms for set theory has often focused on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism (the view that any universe of a certain kind can be extended) and actualism (the view that there are universes that cannot be extended in particular ways) face (...) complementary problems. The latter view is unable to use maximality axioms that make use of extensions, where the former has to contend with the existence of extensions violating maximality axioms. An analysis of two kinds of multiversism, a Zermelian form and Skolemite form, leads to the conclusion that the kind of maximality captured by an axiom differs substantially according to background ontology. (shrink)

This Element offers the first detailed study of Catharine Trotter Cockburn's philosophy and covers her contributions to philosophical debates in epistemology, metaphysics, moral philosophy, and philosophy of religion. It examines not only Cockburn's view that sensation and reflection are the sources of knowledge, but also how she draws attention to the limitations of human understanding and how she approaches metaphysical debates through this lens. In the area of moral philosophy, this Element argues that it is helpful to take seriously Cockburn's (...) distinction between questions concerning the metaphysical foundation of morality and questions concerning the practice of morality. Moreover, this Element examines Cockburn's religious views and considers her understanding of the relation between morality and religion and her religious views concerning the resurrection and the afterlife. (shrink)

‘Normative powers’ are capacities to create normative reasons by our willing or say-so. They are significant, because if we have them and exercise them, then sometimes the reasons we have are ‘up to us’. But such powers seem mysterious. How can we, by willing, create reasons? In this paper, I examine whether normative powers can be adequately explained normatively, by appeal to norms of a practice, normative principles, human interests, or values. Can normative explanations of normative powers explain how an (...) exercise of the will can afford us special freedom in determining our reasons? I argue that normative approaches to answering this question prove to be inadequate. To vindicate the thought that normative powers can make our reasons ‘up to us’, we need an altogether different approach to understanding them, one that is located not in the normative but in the metaphysical. I end the paper by sketching a metaphysical explanation of normative powers. This metaphysical defence of normative powers provides a window into a different, more agent-centered way of thinking about rational agency. (shrink)

This paper investigates two puzzles in practical reason and proposes a solution to them. First, sometimes, when we are practically certain that neither of two alternatives is better than or as good as the other with respect to what matters in the choice between them, it nevertheless seems perfectly rational to continue to deliberate, and sometimes the result of that deliberation is a conclusion that one alternative is better, where there is no error in one’s previous judgment. Second, there are (...) striking differences between rational agents – some rational agents have most reason to pursue careers on Wall Street while others have most reason to take up a career in teaching, or scuba diving, or working for political causes. These differences aren’t plausibly explained by ‘passive’ facts about our psychology or their causal interaction with our environment; instead, these facts seem in some sense to ‘express who we are’. But what is this sense? These puzzles disappear if we adopt a novel view about the source of the normativity of reasons – some reasons are given to us and others are reasons in virtue of an act of will. We make certain considerations reasons through an act of will and thus sometimes make it true through an act of agency that we have most reason to do one thing rather than another. (shrink)

This article explores the main similarities and differences between Derek Parfit’s notion of imprecise comparability and a related notion I have proposed of parity. I argue that the main difference between imprecise comparability and parity can be understood by reference to ‘the standard view’. The standard view claims that 1) differences between cardinally ranked items can always be measured by a scale of units of the relevant value, and 2) all rankings proceed in terms of the trichotomy of ‘better than’, (...) ‘worse than’, and ‘equally good’. Imprecise comparability, which can be understood in terms of the more familiar notions of cardinality and incommensurability, rejects only the first claim while parity rejects both claims of the standard view. -/- I then argue that insofar as those attracted to imprecise comparability assume that all rankings are trichotomous, as Parfit appears to, the view should be rejected. This is because imprecise equality is not a form of equality but is a sui generis ‘fourth’ basic way in which items can be ranked. We should, I argue, understand imprecise equality as parity, and imprecise comparability as entailing ‘tetrachotomy’ – that if two items are comparable, one must better than, worse than, equal to, or on a par with the other. Thus those attracted to the idea that cardinality can be imprecise should abandon trichotomy and accept parity and tetrachotomy instead. -/- Finally, I illustrate the difference between Parfit’s trichotomous notion of imprecise comparability and parity by examining how each notion might be employed in different solutions to the problem posed by the Repugnant Conclusion in population ethics. I suggest that parity provides the arguably more ecumenical solution to the problem. (shrink)

This chapter argues that there is a particular kind of ‘internal’ commitment typically made in the context of romantic love relationships that has striking meta-normative implications for how we understand the role of the will in practical normativity. Internal commitments cannot plausibly explain the reasons we have in committed relationships on the usual model—as triggering reasons that are already there, in the way that making a promise triggers a reason via a pre-existing norm of the form ‘If you make a (...) promise to x, then you have a reason to x’. Instead, internal commitments are that in virtue of which one has the special reasons of committed relationships; they are the grounds of such reasons. In this way, the will is a source of practical normativity. (shrink)

This paper begins with a response to Josh Gert’s challenge that ‘on a par with’ is not a sui generis fourth value relation beyond ‘better than’, ‘worse than’, and ‘equally good’. It then explores two further questions: can parity be modeled by an interval representation of value? And what should one rationally do when faced with items on a par? I argue that an interval representation of value is incompatible with the possibility that items are on a par (a mathematical (...) proof is given in the appendix). I also suggest that there are three senses of ‘rationally permissible’ which, once distinguished, show that parity does distinctive practical work that cannot be done by the usual trichotomy of relations or by incomparability. In this way, we have an additional argument for parity from the workings of practical reason. (shrink)

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that seems (...) to necessitate the addition of subsets to V. We argue that despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We analyse extant interpretations of such talk, and analyse various tradeoffs in naturality that might be made. We conclude that the Universist has promising options for interpreting different forcing constructions. (shrink)

What sorts of consideration can be normative reasons for action? If we systematize the wide variety of considerations that can be cited as normative reasons, do we find that there is a single kind of consideration that can always be a reason? Desire-based theorists think that the fact that you want something or would want it under certain evaluatively neutral conditions can always be your normative reason for action. Value-based theorists, by contrast, think that what plays that role are evaluative (...) facts (or the facts that subvene them) about what you want, such as the fact that having it would be good in some way. This paper argues that value-based theorists are wrong; if we try to find a single kind of consideration that can always be normative reason, we find that sometimes our reason is the fact that we want something and not any corresponding evaluative fact. (shrink)

This introductory article describes the phenomena of incommensurability and incomparability, how they are related, and why they are important. Since incomparability is the more significant phenomenon, the paper takes that as its focus. It gives a detailed account of what incomparability is, investigates the relation between the incomparability of values and the incomparability of alternatives for choice, distinguishes incomparability from the related phenomena of parity, indeterminacy, and noncomparability, and, finally, defends a view about practical justification that vindicates the importance of (...) incomparability — assuming it exists — for practical reason. (shrink)

One of the most common judgments of normative life takes the following form: With respect to some things that matter, one item is better than the other, with respect to other things that matter, the other item is better, but all things considered – that is, taking into account all the things that matter – the one item is better than the other. In this paper, I explore how all-things-considered judgments are possible, assuming that they are. In particular, I examine (...) the question of how the different considerations relevant to an all-things-considered judgment come together in a way that gives each relevant consideration its proper due. I propose an answer which provides a unified account of all-things-considered judgments and highlights a deep connection between value and reason. My suggestion is that ‘all things considered’ is, in effect, a placeholder for a more comprehensive, sometimes nameless, value that includes the things considered as parts, and that this more comprehensive value determines how the things considered normatively relate. (shrink)

John Locke accepts that every perception gives me immediate and intuitive knowledge of my own existence. However, this knowledge is limited to the present moment when I have the perception. If I want to understand the necessary and sufficient conditions of my continued existence over time, Locke argues that it is important to clarify what ‘I’ refers to. While we often do not distinguish the concept of a person from that of a human being in ordinary language, Locke emphasizes that (...) this distinction is important if we want to engage with questions of identity over time. According to Locke, persons are thinking intelligent beings who can consider themselves as extended into the past and future and who are concerned for their happiness and accountable for their actions. Moreover, for Locke a self is a person, considered from a first-personal point of view. I show that the concept of self that he develops in the context of his discussion of persons and personal identity is richer and more complex than the I-concept that he invokes in his version of the cogito. I further argue that Locke’s moral and religious views explain why he emphasizes the need for a conceptual distinction between persons and human beings. In the final section I turn to the reception of Locke’s view by some of his early critics and defenders, including Elizabeth Berkeley Burnet, an anonymous author, and Catharine Trotter Cockburn. (shrink)

This paper presents an argument against the widespread view that ‘hard choices’ are hard because of the incomparability of the alternatives. The argument has two parts. First, I argue that any plausible theory of practical reason must be ‘comparativist’ in form, that is, it must hold that a comparative relation between the alternatives with respect to what matters in the choice determines a justified choice in that situation. If comparativist views of practical reason are correct, however, the incomparabilist view of (...) hard choices should be rejected. Incomparabilism about hard choices leads us to an implausible error theory about the phenomenology of hard choices, threatens an unattractive view of human agency, and leaves us in perplexity about what we are doing when we choose in hard choices. The second part of the argument explores the main competitor to comparativist views of practical reason, noncomparativist view, according tow which a choice is justified so long as it is not worse than any of the alternatives. This view is often assumed by rational choice theorists but has its best philosophical defense in work by Joseph Raz. On Raz’s view, incomparabilism about hard choices avoids the problems faced if comparativism is correct, but it faces different difficulties. I argue that Raz’s noncomparativist view mistakenly assimilates practical reason to more restricted normative domains such as the law. (shrink)

Heidegger argues that modern technology is quantifiably different from all earlier periods because of a shift in ethos from in situ craftwork to globalised production and storage at the behest of consumerism. He argues that this shift in technology has fundamentally shaped our epistemology, and it is almost impossible to comprehend anything outside the technological enframing of knowledge. The exception is when something breaks down, and the fault ‘shows up’ in fresh ways. Stiegler has several important addendums to Heidegger’s thesis. (...) Firstly, that Heidegger fails to fully appreciate the early Greek myth of Prometheus, and the technological depth that fire offers all human societies. Secondly, the fall, or failure, which is doubled in the myth of Prometheus, and shows up in epistemology accordingly. Thirdly the acceleration of technology since the onset of Information Technology, and the way this is disorientating our Being. I argue the fall in both Heidegger and early Stiegler has encaptured their imagination. In later work, Stiegler argues that acceleration is fused with algorithmic pretensions, that are distorting and undermining the creative political imaginary, and making it difficult to revalue the values that underpin the nihilist Anthropocene. The overcoming of the Anthropocene engages politics, economics, power, physics, and ecology. (shrink)

This paper proposes a way to understand transformative choices, choices that change ‘who you are.’ First, it distinguishes two broad models of transformative choice: 1) ‘event-based’ transformative choices in which some event—perhaps an experience—downstream from a choice transforms you, and 2) ‘choice-based’ transformative choices in which the choice itself—and not something downstream from the choice—transforms you. Transformative choices are of interest primarily because they purport to pose a challenge to standard approaches to rational choice. An examination of the event-based transformative (...) choices of L. A. Paul and Edna Ullman-Margalit, however, suggests that event-based transformative choices don’t raise any difficulties for standard approaches to rational choice. An account of choice-based transformative choices—and what it is to be transformed—is then proposed. Transformative choices so understood not only capture paradigmatic cases of transformative choice but also point the way to a different way of thinking about rational choice and agency. (shrink)

Hume’s theory of personal identity is developed in response to Locke’s account of personal identity. Yet it is striking that Hume does not emphasize Locke’s distinction between persons and human beings. It seems even more striking that Hume’s account of the self in Books 2 and 3 of the Treatise has less scope for distinguishing persons from human beings than his account in Book 1. This is puzzling, because Locke originally introduced the distinction in order to answer questions of moral (...) accountability and Hume’s discussion of the self in Book 2 provides the foundation of his moral theory in Book 3. In response to the puzzle I show that Locke and Hume hold different moral and religious views and these differences are important to explain why their theories of personal identity differ. (shrink)

Black holes are extremely relativistic objects. Physical processes around them occur in a regime where the gravitational field is extremely intense. Under such conditions, our representations of space, time, gravity, and thermodynamics are pushed to their limits. In such a situation philosophical issues naturally arise. In this chapter I review some philosophical questions related to black holes. In particular, the relevance of black holes for the metaphysical dispute between presentists and eternalists, the origin of the second law of thermodynamics and (...) its relation to black holes, the problem of information, black holes and hypercomputing, the nature of determinisim, and the breakdown of predictability in black hole space-times. I maintain that black hole physics can be used to illuminate some important problems in the border between science and philosophy, either epistemology and ontology. (shrink)

Shaftesbury’s major work Characteristicks of Men, Manners, Opinions, Times was one of the most influential English works in the eighteenth century. This paper focuses on his contributions to debates about persons and personal identity and shows that Shaftesbury regards metaphysical questions of personal identity as closely connected with normative questions of character development. I argue that he is willing to accept that persons are substances and that he takes their continued existence for granted. He sees the need to supplement metaphysical (...) debates of personal identity and believes that we have to turn to the character that is realized by a substance if we want to understand who we are. For Shaftesbury persons have a particular character, can act, and govern themselves. I propose that Shaftesbury’s approach to persons has a developmental dimension, which is meant to encourage personal development and improvement of character. The developmental dimension can be understood as an intellectual journey that invites us to search for our true self, to develop our character, and to seek happiness, which ultimately involves understanding our place as persons in the order of the universe. I show that my developmental interpretation is preferable to other existing interpretations. (shrink)

This encyclopedia entry urges what it takes to be correctives to common (mis)understandings concerning the phenomenon of incommensurability and incomparability and briefly outlines some of their philosophical upshots.

Multiverse Views in set theory advocate the claim that there are many universes of sets, no-one of which is canonical, and have risen to prominence over the last few years. One motivating factor is that such positions are often argued to account very elegantly for technical practice. While there is much discussion of the technical aspects of these views, in this paper I analyse a radical form of Multiversism on largely philosophical grounds. Of particular importance will be an account of (...) reference on the Multiversist conception, and the relativism that it implies. I argue that analysis of this central issue in the Philosophy of Mathematics indicates that Radical Multiversism must be algebraic, and cannot be viewed as an attempt to provide an account of reference without a softening of the position. (shrink)

Understanding climate change is becoming an urgent requirement for those in education. The normative values of education have long been closely aligned with the global, modernised world. The industrial model has underpinned the hidden and overt curriculum. Increasingly though, a new eco-centric orientation to economics, technology, and social organisation is beginning to shape up the post-carbon world. Unless education is up to date with the issues of climate change, the estate of education will be unable to meet its task of (...) knowledge transfer. This paper covers the basic science and ethical policy debates, and begins to outline the questions that will necessarily entangle education as we orientate ourselves to the new world that is upon us. (shrink)

Recently, some of the leading proponents of the view that there is widespread incommensurability among goods have suggested that the incommensurability of some goods is a constitutive feature of the goods themselves. So, for example, a friendship and a million dollars are incommensurable because it is part of what it is to be a friendship that it be incommensurable with money. According to these ‘constitutive incommensurabilists’ incommensurability follows from the very nature of certain goods. In this paper, I examine this (...) idea and argue that constitutive incommensurabilists have mistaken for constitutive incommensurability a particular emphatic kind of comparability. This examination involves an account of ‘higher’ and ‘lower’ goods and an explanation of how goods of different ‘types’ figure in practical conflict. (shrink)

This paper is not concerned with the (amply discussed) question as to the rational response to peer disagreement. Instead, it addresses a (considerably less often debated) problem to which many views about the (epistemic) significance of disagreement are vulnerable (to some extent or another): self-undermining. I reject several answers that have been proposed in the literature, defend one that has been offered (by meeting objections to it), and show that in its light, the prevalent assumption that the ‘equal-weight view’, a (...) prominent view about disagreement, rationally requires us to suspend judgement about contentious matters, is seen to be too pessimistic. (shrink)

This essay examines Locke’s chapter “Of Identity and Diversity” (Essay 2.27) in the context of the series of chapters on ideas of relations (Essay 2.25–28) that precede and follow it. I begin by introducing Locke’s account of how we acquire ideas of relations. Next, I consider Locke’s general approach to individuation and identity over time before I show how he applies his general account of identity over time to persons and personal identity. I draw attention to Locke’s claim that “person” (...) is a forensic term and analyse his arguments for why the sameness of a human being and the sameness of a substance or soul are neither necessary nor sufficient for personal identity. Instead, Locke argues that personal identity consists in sameness of consciousness. Locke regards persons as moral agents who are accountable for their actions. If a person now is held accountable for a past action it is important that the person now is the same person as the person who did the action. This means that moral accountability presupposes personal identity. Additionally, it will be important to consider whether the person deserves reward or punishment for the action. Locke’s account of moral relations, which he develops in Essay 2.28, addresses this issue and I show how it supplements his account of persons and personal identity. (shrink)

It is argued that quantum theory is best understood as requiring an ontological duality of res extensa and res potentia, where the latter is understood per Heisenberg’s original proposal, and the former is roughly equivalent to Descartes’ ‘extended substance.’ However, this is not a dualism of mutually exclusive substances in the classical Cartesian sense, and therefore does not inherit the infamous ‘mind-body’ problem. Rather, res potentia and res extensa are proposed as mutually implicative ontological extants that serve to explain the (...) key conceptual challenges of quantum theory; in particular, nonlocality, entanglement, null measurements, and wave function collapse. It is shown that a natural account of these quantum perplexities emerges, along with a need to reassess our usual ontological commitments involving the nature of space and time. (shrink)

In the contemporary philosophy of set theory, discussion of new axioms that purport to resolve independence necessitates an explanation of how they come to be justified. Ordinarily, justification is divided into two broad kinds: intrinsic justification relates to how `intuitively plausible' an axiom is, whereas extrinsic justification supports an axiom by identifying certain `desirable' consequences. This paper puts pressure on how this distinction is formulated and construed. In particular, we argue that the distinction as often presented is neither well-demarcated nor (...) sufficiently precise. Instead, we suggest that the process of justification in set theory should not be thought of as neatly divisible in this way, but should rather be understood as a conceptually indivisible notion linked to the goal of explanation. (shrink)

My chapter examines Isaac Watts’s and Catharine Trotter Cockburn’s views concerning the metaphysics of the mind and their underlying accounts of powers and substances. In Philosophical Essays on Various Subjects Watts criticizes Locke’s account of substances and argues for his own preferred account of substance. Watts argues that there is no need to postulate an unknown substratum, as Locke does. Instead, Watts searches for a better explanation of what substances are. His proposal is that bodily substance just is solid extension (...) and that mental substance is identical with the power of thinking. This means that Watts believes that some powers can be substances. I will show how Watts defends his account of substances against various objections. Cockburn was not satisfied by Watts’s account of substance and disagrees with Watts’s understanding of powers. She believes that Watts is too quick to draw metaphysical conclusions. Cockburn takes seriously the limitations of human understanding and emphasizes that humans are ignorant about many metaphysical truths. I end by assessing the strengths and weaknesses of Watts’s and Cockburn’s accounts of powers and substances. (shrink)

Catharine Trotter Cockburn challenges voluntarist views held by British moral philosophers during the first half of the eighteenth century. After introducing her metaphysics of morality, namely, her account of human nature, and her account of moral motivation, which for her is a matter concerning the practice of morality, I analyze her arguments against theological voluntarism. I examine, first, how Cockburn rejects the view that God can by an arbitrary act of will change what is good or evil; second, how she (...) challenges views that understand the initial creation of the world solely in terms of divine will and draws attention to the role that the divine understanding plays in God’s creation; and third, how she argues that moral obligation does not require a superior lawmaker. I conclude by highlighting how Cockburn’s arguments not only challenge voluntarist views, but also offer support for her moral fitness theory. (shrink)

Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...) work in numerical cognition and ontogenetic studies. (shrink)

This paper aims to reconstruct Francis Hutcheson's thinking about liberty. Since he does not offer a detailed treatment of philosophical questions concerning liberty in his mature philosophical writings I turn to a textbook on metaphysics. We can assume that he prepared the textbook during the 1720s in Dublin. This textbook deserves more attention. First, it sheds light on Hutcheson's role as a teacher in Ireland and Scotland. Second, Hutcheson's contributions to metaphysical disputes are more original than sometimes assumed. To appreciate (...) his independent thinking, I argue, it is helpful to take the intellectual debates in Ireland into consideration, including William King's defence of free will and discussions of Shaftesbury's views in Robert Molesworth's intellectual circle. Rather than taking a stance on the philosophical disputes about liberty, I argue that Hutcheson aims to shift the focus of the debates towards practical questions concerning control of desire, cultivation of habits, and character development. (shrink)

This paper takes a new look at Francis Hutcheson's moral sense theory and examines it in light of the views of his rationalist critics and opponents who claim that there has to be an antecedent moral standard prior to any sense or affections. I examine how Gilbert Burnet, Samuel Clarke, and Catharine Trotter Cockburn each argue for the priority of reason over a moral sense and how Hutcheson responds or could respond to their views. Furthermore, I consider the proposal that (...) rather than regarding Hutcheson's moral sense theory as fundamentally opposed to moral rationalism, Hutcheson and Clarke endorse a shared moral metaphysics, as argued by Patricia Sheridan. Although I consider this proposal as too broad and believe it overlooks relevant metaphysical differences between Clarke and Hutcheson, I argue that the dispute between Hutcheson and his critics and opponents will not be settled without taking their underlying moral metaphysics into consideration. (shrink)

Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive power (...) and meta-theoretic properties when comparing first-order and second-order logic. (shrink)