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.

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)

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)

Two or more attitudinal states are incoherent if and only if, necessarily, under conditions of full transparency, you are disposed to give up one of them. This is roughly the account of incoherence that has recently been put forward by Alex Worsnip (2018). In this paper, I argue that Worsnip’s account of incoherence is incorrect. Not only does it fail to be fully general (i.e., it does not allow us to assess the coherence of all combinations of attitudes), but it (...) also implies that an agent is necessarily incoherent just in virtue of being in one attitudinal state. (shrink)

In recent years, the science and the philosophy of consciousness has seen growing interest in structural questions about consciousness. This is the Editorial Introduction for a special volume for Philosophy and the Mind Sciences on “Structuralism in Consciousness Studies.”.

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)

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)

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 model-theoretic constructions that add sets to models are cited as evidence in favour of the latter. This paper informs this debate by developing a way for a Universist to interpret talk that (...) seems to necessitate the addition of sets 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 present a method of interpreting extension-talk (V-logic), and show how it captures satisfaction in `ideal' outer models and relates to impredicative class theories. We provide some reasons to regard the technique as philosophically virtuous, and argue that it opens new doors to philosophical and mathematical discussions for the Universist. (shrink)

La pertinence de la métaphysique analytique a fait l'objet de critiques : Ladyman et Ross, par exemple, ont suggéré d'abandonner ce domaine. French et McKenzie ont défendu la métaphysique analytique en affirmant qu'elle développe des outils qui pourraient s'avérer utiles pour la philosophie de la physique. Dans cet article, nous montrons dans un premier temps que cette défense heuristique de la métaphysique peut être étendue au domaine scientifique de l'ontologie appliquée, qui utilise des théories et outils issus de la métaphysique (...) analytique. Dans un deuxième temps, nous développons le parallèle que font French et McKenzie entre les mathématiques et la métaphysique pour montrer que l'ensemble du domaine de la métaphysique analytique, étant donné son utilité non seulement pour la philosophie mais également pour la science, devrait continuer à exister en tant que domaine largement autonome. (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)

Wie war es möglich? Diese mit Blick auf den Nationalsozialismus und die Zeit von 1933 bis 1945 unausweichliche Frage stellt sich für jede Generation aufs Neue – und auf unterschiedlichen Ebenen. Im Gegensatz zur detaillierten historischen Aufarbeitung der NS-Zeit ist die philosophisch-theoretische Analyse der normativen Grundlagen des NS Systems ein bislang vernachlässigtes Gebietder Forschung. Die hier edierte Sammlung von Originaltextenführender Juristen, Rechtstheoretiker und Rechtsphilosophen, die dem nationalsozialistischen Regime loyal gegenüberstanden und an der rechtlichen Um- und Neugestaltung mitarbeiteten, will diese Lücke (...) schließen helfen und einen Beitrag zur Analyse des nationalsozialistischen Herrschaftssystems aus dem Blickwinkel der Rechtstheorie und Rechtsphilosophie leisten. Die abgedruckten Originaltexte dokumentieren nicht nur die normativen Verschiebungen im Zuge der politischen Neuentwicklung, sondern zeigen auch, dass viele Maßnahmen des NS-Regimes, die in ihrer Radikalität und Unmenschlichkeit ohne Beispiel sind, eine gesetzliche Basis hatten und theoretisch vorbereitet waren. (shrink)

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)

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)

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.

Auf welchen normativen Grundlagen beruhte das NS-System? Mit welcher Rechtfertigung konnte der Führerwille dort zu einer Quelle des Rechts werden? Wie war es gemäß der NS-Strafgesetzgebung möglich, Handlungen zu bestrafen, die gegen kein geschriebenes Gesetz verstießen? Die in diesem Band versammelten und kommentierten Originaltexte geben Einblick in das Denken von Rechtstheoretikern, die mit dem Nationalsozialismus sympathisierten, und belegen deren Versuch, autoritäre und dem Rechtsstaat widersprechende Rechtsprinzipien zu legitimieren. Dabei zeigt sich ein überraschender und bis jetzt von der rechts- und moralphilosophischen (...) Forschung weitgehend unbeachteter Aspekt des NS-Unrechtssystems: der Versuch einer »Ethisierung« des Rechts und die damit verbundene Totalisierung des machtstaatlichen Einflusses. (shrink)

A main goal of the neuroscience of consciousness is: find the neural correlate to conscious experiences (NCC). When have we achieved this goal? The answer depends on our operationalization of “NCC.” Chalmers (2000) shaped the widely accepted operationalization according to which an NCC is a neural system with a state which is minimally sufficient (but not necessary) for an experience. A deeper look at this operationalization reveals why it might be unsatisfactory: (i) it is not an operationalization of a correlate (...) for occurring experiences, but of the capacity to experience; (ii) it is unhelpful for certain cases which are used to motivate a search for neural correlates of consciousness; (iii) it does not mirror the usage of “NCC” by scientists who seek for unique correlates; (iv) it hardly allows for a form of comparative testing of hypotheses, namely experimenta crucis. Because of these problems (i–iv), we ought to amend or improve on Chalmers's operationalization. Here, I present an alternative which avoids these problems. This “NCC2.0” also retains some benefits of Chalmers's operationalization, namely being compatible with contributions from extended, embedded, enacted, or embodied accounts (4E-accounts) and allowing for the possibility of non-biological or artificial experiencers. (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 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.

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)

The requirements of rationality are fundamental in practical and theoretical philosophy. Nonetheless, there exists no correct account of what constitutes rational requirements. This paper attempts to provide a correct constitutive account of ‘rationality requires’. I argue that rational requirements are grounded in ‘necessary explanations of subjective incoherence’, as I shall put it. Rationality requires of you to X if and only if your rational capacities, in conjunction with the fact that you not-X, explain necessarily why you have a non-maximal degree (...) of subjective coherence. (shrink)

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)

A pervasive thought in contemporary philosophy of mathematics is that in order to justify reflection principles, one must hold universism: the view that there is a single universe of pure sets. I challenge this kind of reasoning by contrasting universism with a Zermelian form of multiversism. I argue that if extant justifications of reflection principles using notions of richness are acceptable for the universist, then the Zermelian can use similar justifications. However, I note that for some forms of richness argument, (...) the status of reflection principles as axioms is left open for the Zermelian. (shrink)

This paper discusses whether rationality, morality or prudence impose process‐requirements upon us. It has been argued that process‐requirements fulfil two essential functions within a system of rational, moral or prudential requirements. These functions are considered to prove the existence of process‐requirements. First, process‐requirements are deemed necessary to ensure that rationality, morality or prudence can guide our deliberations and actions. Second, their existence is regarded as essential for the correctness of our ordinary explanations of why a person possesses a certain degree (...) of morality, rationality or prudence. However, I argue that these two functions are unable to show the existence of process‐requirements. Instead, I propose a different essential function for process‐requirements: they are necessary for attributing the correct degree of rationality, morality or prudence to a subject who is not entirely rational, moral or prudent. This function, I argue, necessitates the existence of process‐requirements. (shrink)

Can we employ the property of rationality in establishing what rationality requires? According to a central and formal thesis of John Broome’s work on rational requirements, the answer is ‘no’ – at least if we expect a precise answer. In particular, Broome argues that (i) the property of full rationality (i.e. whether or not you are fully rational) is independent of whether we formulate conditional requirements of rationality as having a wide or a narrow logical scope. That is, (ii) by (...) replacing a wide-scope requirement with a corresponding narrow-scope requirement (or vice versa), we do not alter the situations in which a person is fully rational. As a consequence, (iii) the property of full rationality is unable to guide us in determining whether a rational requirement has a wide or a narrow logical scope. We cannot resolve the wide/narrow scope debate by appealing to a theory of fully rational attitudes. This paper argues that (i), (ii) and (iii) are incorrect. Replacing a wide- with a corresponding narrow-scope requirement (or vice versa) can alter the set of circumstances in which a person is fully rational. The property of full rationality is therefore not independent of whether we formulate conditional requirements of rationality as having a wide or a narrow logical scope. As a consequence, the property of full rationality can guide us in determining what rationality requires – even in cases where we expect a precise answer. (shrink)

Three important 20th-century American films prominently feature a hotel as the site for morally ambiguous and sexually charged events depicted in the plot: Orson Welles's Touch of Evil (1958), Alfred Hitchcock's Psycho (1960), and Joel and Ethan Coen's Barton Fink (1991). While all three films have a multiplicity of elements that present how hotel spaces open horizons displaying human behaviors both normal and abnormal, moral and immoral, secret and public, sane and insane, the paper presents an extended argument (...) for seeing these particular cinematic efforts as being built around the same theme: that transgression (of a violent, misogynous nature) is the path to transcendence. (shrink)

A long tradition in theology holds that the divine is in some sense incomprehensible, ineffable, or indescribable. This is mirrored in the set-theoretic literature by those who hold that the universe of sets is incomprehensible, ineffable, or indescribable. In this latter field, set theorists often study reflection principles; axioms that posit indescribability properties of the universe. This paper seeks to examine a theological reflection principle, which can be used to deliver a very rich ontology. I argue that in analogy with (...) set-theoretic reflection principles, we should understand theological reflection via schematic commitment. (shrink)

We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \varphi(a) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model W \subset A. A stronger principle, the ground-model reflection principle, asserts that any such \varphi(a) true in V is also true in some non-trivial ground model of the universe with respect to set forcing. These principles each express a form of width (...) reflection in contrast to the usual height reflection of the Lévy–Montague reflection theorem. They are each equiconsistent with ZFC and indeed \Pi_2-conservative over ZFC, being forceable by class forcing while preserving any desired rank-initial segment of the universe. Furthermore, the inner-model reflection principle is a consequence of the existence of sufficient large cardinals, and lightface formulations of the reflection principles follow from the maximality principle MP and from the inner-model hypothesis IMH. We also consider some questions concerning the expressibility of the principles. (shrink)

Within the debate concerning reason and rationality, instrumental incoherence was for a long time conceived of as the paradigm of irrationality. However, with the emergence of the so-called ‘bootstrapping objection’ and the debate concerning the ‘scope’ of rational requirements, the innocuous status of the normative significance of (instrumental) coherence became subject to. This led to a paradigmatic shift in how to understand the relationship between rational requirements and normativity. While there now exists considerable doubt that rational requirements are normative, it (...) is commonly agreed that one’s normative point of view is a key feature of one’s rationality. Here the question is not only if one can hold a particular normative judgement and still be rational; what is significant too is whether your normative outlook coheres appropriately with your motivation. In fact, it is now commonly agreed that rationality requires us to intend to make the world fit with our first-personal ought beliefs. Enkrasia (i.e. coherence between your normative views and your motivation) is thus seen as a rational ideal and as a source of rational requirements. Nevertheless, many elementary questions regarding the application, content, and significance of an enkrasia-requirement remain unanswered, or subject to debate. This special issue on ‘The Nature of the Enkratic Requirement of Rationality’ aims to answer some of these fundamental questions. (shrink)

There is tension between commonly held views concerning phenomenal imagery on the one hand and our first-person epistemic access to it on the other. This tension is evident in many individual issues and experiments in philosophy and psychology (e.g. inattentional and change blindness, the speckled hen, dream coloration, visual periphery). To dissolve it, we can give up either (i) that we lack full introspective access to the phenomenal properties of our imagistic experiences, or (ii) that phenomenal imagery is fully determined, (...) or (iii) that phenomenal imagery does not exist. Which option is preferable? I explore the feasibility of option (ii) in more details by distinguishing between di erent kinds of indeterminacy. One of the most often proclaimed versions of indeterminacy is tied to Representationalism. However, I argue that in this context, Representationalism appears to be the least satisfying option, for which I give ten reasons. By abduction, we should reject Representationalism in favour of (i) or (iii)—the most parsimonious option being eliminativism, and the most conservative being the rejection of privileged access. The decision between these two, however, should be made on a case-by-case basis, depending on which is most adequate given the data. I illustrate this with the comparison between visual agnosia and Charles-Bonnet-Syndrome. (shrink)

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.

Is a phenomenal pain a conscious primitive or composed of more primitive phenomenal states? Are pain experiences necessarily or only contingently unpleasant? Here, I sketch how to answer such questions concerning intra-phenomenal metaphysics using the example of pain and unpleasantness. Arguments for a symmetrical metaphysical independence of phenomenal pain and unpleasant affect are presented, rejecting a composite view like the IASP definition and dimensional views. The motivating intuition of these views is explained by common binding mechanisms in consciousness and characterized (...) as fallacious if generalized. There are, however, underlying commonalities between pain perception and unpleasant affect, e.g. formal content or evolutionary ancestry. (shrink)

Hussain claims that ethical consumers are subject to democratic requirements of morality, whereas ordinary price/quality consumers are exempt from these requirements. In this paper, we demonstrate that Hussain’s position is incoherent, does not follow from the arguments he offers for it, and entails a number of counterintuitive consequences.

Let mathematical justification be the kind of justification obtained when a mathematician provides a proof of a theorem. Are Gettier cases possible for this kind of justification? At first sight we might think not: The standard for mathematical justification is proof and, since proof is bound at the hip with truth, there is no possibility of having an epistemically lucky justification of a true mathematical proposition. In this paper, I argue that Gettier cases are possible (and indeed actual) in mathematical (...) reasoning. By analysing these cases, I suggest that the Gettier phenomenon indicates some upshots for actual mathematical practice. (shrink)

Does a coherentist version of rationality issue requirements on states? Or does it issue requirements on processes? This paper evalu- ates the possibility of process-requirements. It argues that there are two possible definitions of state- and process-requirements: a satisfaction- based definition and a content-based definition. I demonstrate that the satisfaction-based definition is inappropriate. It does not allow us to uphold a clear-cut distinction between state- and process-requirements. We should therefore use a content-based definition of state- and pro- cess-requirements. However, a (...) content-based definition entails that ra- tionality does not issue process-requirements. Content-based process- requirements violate the principle that ‘rationality requires’ implies ‘can satisfy’. The conclusion of this paper therefore amounts to a radical re- jection of process-requirements of rationality. (shrink)

Suppose rationality requires you to A if you believe you ought to A. Suppose you believe that you ought to A. How can you satisfy this requirement? One way seems obvious. You can satisfy this requirement by A-ing. But can you also satisfy it by stopping to believe that you ought to A? Recently, it has been argued that this second option is not a genuine way of satisfying the above requirement. Conditional requirements of rationality do not have two ‘symmetric’, (...) but only one ‘asymmetric’ satisfaction condition. This paper explores the consequences of this argument for a theory of the requirements of rationality. I seek to show that thisview conflicts with another powerful intuition about the requirements of rationality, i.e. ‘rational consistency’: if rationality requires you to X, then it is not the case that rationality requires you to not-X. I shall conclude that ‘asymmetric’ satisfying is based on a misleading intuition, for which we should not sacrifice ‘rational consistency’. (shrink)

In this article, I survey some philosophical attitudes to talk concerning `the' universe of sets. I separate out four different strands of the debate, namely: (i) Universism, (ii) Multiversism, (iii) Potentialism, and (iv) Pluralism. I discuss standard arguments and counterarguments concerning the positions and some of the natural mathematical programmes that are suggested by the various views.

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)

The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper, I argue that whether or not large cardinal axioms count as maximality principles depends on prior commitments concerning the richness of the subset forming operation. In particular I argue that there is a conception of maximality through absoluteness, on which large cardinal axioms are restrictive. (...) I argue, however, that large cardinals are still important axioms of set theory and can play many of their usual foundational roles. (shrink)

Informal rigour is the process by which we come to understand particular mathematical structures and then manifest this rigour through axiomatisations. Structural relativity is the idea that the kinds of structures we isolate are dependent upon the logic we employ. We bring together these ideas by considering the level of informal rigour exhibited by our set-theoretic discourse, and argue that different foundational programmes should countenance different underlying logics (intermediate between first- and second-order) for formulating set theory. By bringing considerations of (...) perturbations in modal space to bear on the debate, we will suggest that a promising option for representing current set-theoretic thought is given by formulating set theory using quasi-weak second-order logic. These observations indicate that the usual division of structures into \particular (e.g. the natural number structure) and general (e.g. the group structure) is perhaps too coarse grained; we should also make a distinction between intentionally and unintentionally general structures. (shrink)

This paper argues that practical reasoning is a mental process which leads a person from a set of existent mental states to an intention. In Section 1, I defend this view against two other proposals according to which practical reasoning either concludes in an action itself or in a normative belief. Section 2 discusses the correctness of practical reasoning and explains how the correctness of instrumental reasoning can be explained by the logical relations that hold between the contents of the (...) mental states. In Section 3, I explore the correctness of normative practical reasoning. I conclude with the sceptical view that correct practical reasoning cannot require us to intend to do what we believe we ought to do. (shrink)

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a `structural' perspective (...) to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure. (shrink)

In Morals from Motives, Michael Slote proposed an agent-based approach to virtue ethics in which the morality of an action derives solely from the agent’s motives. Among the many objections that have been raised against Slote’s account, this article addresses two problems associated with the Kantian principle that ought implies can. These are the problems of “deficient” and “inferior” motivation. These problems arise because people cannot freely choose their motives. We cannot always choose to act from good motives; nor can (...) we always avoid acting from bad ones. Given this, Slote’s account implies that we sometimes cannot do what we ought to do, contrary to Kant’s principle. In this article, I propose an alternative agent-based account which, I argue, circumvents these problems. While people cannot choose their motives, they can choose their intentions. By characterizing virtuous action, as I do, in terms of good intentions rather than in terms of good motives, the conflict between what people can do and what they ought to do is resolved. (shrink)

In his _Being Known_ Peacocke sets himself the task of answering how we come to know about metaphysical necessities. He proposes a semantic principle-based conception consisting of, first, his Principles of Possibility which pro­vide necessary and sufficient conditions for a new concept 'admissibility', and second, characterizations of possibility and of necessity in terms of that new con­cept. I focus on one structural feature; viz. the recursive application involved in the specification of 'admissibility'. After sketching Peacocke’s proposal, I intro­duce a fictional (...) protagonist, Cautious Peacocke, whose coherence I claim shows that Peacocke s proposal cannot be made good. I conclude with the conjecture that similar failure will attend any such semantic-based attempts to ground the epistemology of metaphysical necessity. -/- Dans son livre intitulé Being Known, C. Peacocke se propose de repondre à la question de savoir comment nous en venons a connaitre des nécessités métaphysiques. Il développe une conception sémantique reposant sur des principes comprenant, d’une part, ses Principes de Possibilité — qui fournissent les conditions nécessaires et suffisantes pour un nouveau concept, « l’admissibilité » — et d’autre part des caractérisations de la possibilité et de la nécessité a l’aide de ce nouveau concept. Je me concentre sur une caractéristique structurelle, a savoir l’application récursive a l’œuvre dans la spécification de «l’admissibilité ». Apres avoir esquisse la proposition de Peacocke, j’introduis un personnage fictif, Peacocke-prudent. Je soutiens que la cohérence de ce personnage montre que la proposition de Peacocke ne peut pas être satisfaite. Je conclus en conjecturant qu’un échec similaire se présentera pour toutes les tentatives de fonder l’épistemologie de la nécessité métaphysique sur de telles bases semantiques. (shrink)

One question pursued in Buddhist studies concerns the classification of Buddhist ethics. Damien Keown has argued that Aristotelian virtue ethics provides a useful framework for understanding Buddhist ethics, but recently other scholars have argued that character consequentialism is more suitable for this task. Although there are similarities between the two accounts, there are also important differences. In this paper, I follow Keown in defending the aretaic interpretative model, although I do not press the analogy with Aristotelian ethics. Rather, I argue (...) that Buddhist ethics corresponds to a more generic, act-centered virtue ethics. Buddhist moral reasoning is often strikingly consequentialist, but I argue that this does not support the consequentialist interpretation. Analyzing the concept of right action must be distinguished from providing a justification for living a moral life and from formulating a procedure for making moral decisions. (shrink)

Can we find necessary and sufficient conditions for a mental state to be a pain state? That is, does pain have a nature? Or is the term ‘pain’ ambiguous? I argue here that our expression ‘pain’ lacks necessary use conditions if one considers a range of contexts. As use conditions constrain the reference class, I argue that ‘pain’ does not refer to a natural category, but binds together a bunch of loosely resembling phenomena. This leads to problems for scientific and (...) clinical discourse. To solve these, a method of explication is suggested, based on a discursive combination between analysis of first-person reports and theories of natural science. Lastly, I consider the ethical implications of this ambiguity that lead to a reformulation of the goal of pain science: Not alleviation of all pains ought to be our goal, but only manipulation of conscious and negatively emotionally charged pains. (shrink)