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)

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.

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)

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)

Shared activity is often simply willed into existence by individuals. This poses a problem. Philosophical reflection suggests that shared activity involves a distinctive, interlocking structure of intentions. But it is not obvious how one can form the intention necessary for shared activity without settling what fellow participants will do and thereby compromising their agency and autonomy. One response to this problem suggests that an individual can have the requisite intention if she makes the appropriate predictions about fellow participants. I argue (...) that implementing this predictive strategy risks derailing practical reasoning and preventing one from forming the intention. My alternative proposal for reconciling shared activity with autonomy appeals to the idea of acting directly on another's intention. In particular, I appeal to the entitlement one sometimes has to another's practical judgment, and the corresponding authority the other sometimes has to settle what one is to do. (shrink)

Some of the reasons one acts on in joint action are shared with fellow participants. But others are proprietary: reasons of one’s own that have no direct practical significance for other participants. The compatibility of joint action with proprietary reasons serves to distinguish the former from other forms of collective agency; moreover, it is arguably a desirable feature of joint action. Advocates of “team reasoning” link the special collective intention individual participants have when acting together with a distinctive form of (...) practical reasoning that purports to put individuals in touch with group or collective reasons. Such views entail the surprising conclusion that one cannot engage in joint action for proprietary reasons. Suppose we understand the contrast between minimal and robust forms of joint action in terms of the extent to which participants act on proprietary reasons as opposed to shared reasons. Then, if the team reasoning view of joint intention and action is correct, it makes no sense to talk of minimal joint action. As soon as the reason for which one participates is proprietary, then one is not, on this view, genuinely engaged in joint action. (shrink)

The reasons for which I act are normally my reasons; I represent goal states and the means to attaining them, and these guide me in action. Can your reason ever be the reason why I act? If I haven’t yet taken up your reason and made it mine by representing it for myself, then it may seem mysterious how this could be possible. Nevertheless, the paper argues that sometimes one is entitled to another’s reason and that what one does is (...) to be explained in terms of it. The case for this draws on aspects of the interplay between reasons and intentions in individual agency that have not received the attention they deserve. The paper closes by exploring the limits of interpersonal entitlement to reasons by formulating a hypothesis about which reasons one might be entitled to, and by considering how defeaters can undermine entitlement. (shrink)

What is it for a duty or obligation to be directed? Thinking about paradigmatic cases such as the obligations generated by promises will take us only so far in answering this question. This paper starts by surveying several approaches for understanding directed duties, as well as the challenges they face. It turns out that shared agency features something similar to the directedness of duties. This suggests an account of directedness in terms of shared agency – specifically, in terms of the (...) so-called practical intimacy that holds between individuals when they act together. The final section addresses a challenge to the shared agency approach posed by legal wronging in tort law. (shrink)

There is a way of talking that would appear to involve ascriptions of purpose, goal directed activity, and intentional states to groups. Cases are familiar enough: classmates intend to vacation in Switzerland, the department is searching for a metaphysician, the Democrats want to minimize losses in the upcoming elections, and the US intends to improve relations with such and such country. But is this talk to be understood just in terms of the attitudes and actions of the individuals involved? Is (...) the talk, to take an overly simple proposal as an example, a mere summary of familiar individual attitudes of the group members? Or is the ascription of attitudes and actions to groups to be taken more literally, as suggesting that the group for example believes that P, or intends to A, over and above what the members individually think and do? In short, are there groups with minds of their own? Philip Pettit has deployed the “discursive dilemma” to defend the thesis that there are such group minds. In what follows, I explore the relationship between the group allegedly with a mind of its own and the individuals it comprises, and I consider just how this relationship must be understood in order to give Pettit’s argument for group minds its best chance for success. As I understand it, the discursive dilemma has to be used in conjunction with what might be called an indispensability argument for group minds. It is useful to distinguish two forms of this argument. The explanatory version of the indispensability argument is, very schematically, as follows: there is a compelling explanatory theory T concerning the social, certain indispensable elements of T entail the group mind thesis, so the group mind thesis is true. Several questions immediately arise: What sort of theory is T? In what sense is it indispensable? Are there other forms of indispensability? I don’t have definitive answers to these questions. But how we settle them will have implications for the interaction and support the discursive dilemma provides the indispensability argument. In particular, using the discursive dilemma to defend what I characterize below as a practical version of the indispensability argument commits us to the rationality of individual participants in a way that the explanatory version of the indispensability argument does not. My point in the first part of the paper is that if Pettit wants to avoid the weaknesses of the explanatory indispensability argument and pursue the practical version, then he owes us a story about the rationality of individual participation in groups. Pettit also owes us a story about the agency an individual exercises as part of a group. If it takes the actions of individuals to execute the intentions of the group, how are we to understand those actions in order for the group to count as having a mind of its own? How must group intentions figure in the practical or deliberative perspective of individuals who execute those intentions? I will argue that the proponent of the group mind thesis must proceed with some care here, because some natural ways of answering these questions will undermine the thesis. But in the end, I think that these questions are interesting independently of whether Pettit is right to think that groups do have minds of their own. That’s because investigating Pettit’s arguments might lead to new ideas about how the rationality and agency of individuals can be exercised, and suggests new ways of understanding how individuals can act together, irrespective of whether the groups they compose ever have minds of their own. (shrink)

What makes public history more than just another hill to fight over in culture war politics? In this paper I propose a novel way of understanding the political significance of how public history creates and shapes identities: a contractarian one. I argue that public history can be sensibly understood as representing groups as a society’s contracting parties. One particular value of the contractarian approach is that it helps to elucidate the phenomenon of “signing on,” where a marginalized or oppressed group (...) is offered membership in a society without the social order being meaningfully changed. (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)

What are the implications for agency – and in particular, the idea of acting for reasons – if we are to take seriously the notion of collective responsibility? My thesis is that some cases of individuals subject to a collective form of responsibility and blame will force us to make sense of how it is that an individual can be entitled to collective reasons for action, i.e. entitled to a reason had in the first place by a plurality of individuals (...) together rather than any one of them alone. This entitlement makes it possible for the collective reason to be a reason for which one acts, even if one’s contribution on its own makes little or no difference in the collective effort. Although a full defense of this entitlement cannot be undertaken here, I will gesture at how this might work by suggesting that intentions function to preserve reasons for action. . (shrink)

When an agent suffers in their capacity as a knower, they are a victim of epistemic injustice. Varieties of epistemic injustices have been theorised. A salient feature across these theories is that perpetrators and victims of epistemic injustice belong to different social groups. In this paper, I argue for a form of epistemic injustice that could occur between members of the same social group. This is a form of epistemic injustice where the knower is first a victim of historical and (...) continuing oppression. Secondly, they internalise and appreciate the systems that harm them as a knower. This is possible because the victim subscribes to perniciously formed epistemic systems. This form of epistemic injustice is a valuable explanatory tool for non-standard and obscure instances of epistemic injustice where the victim a) accepts and appreciates the injustice they experience and b) is even the seeming perpetrator of the injustice against themselves. (shrink)

Why should we decolonise knowledge? One popular rationale is that colonialism has set up a single perspective as epistemically authoritative over many equally legitimate ones, and this is a form of...

There has recently been a focus on the question of statue removalism. This concerns what to do with public history statues that honour or otherwise celebrate ethically bad historical figures. The specific wrongs of these statues have been understood in terms of derogatory speech, inapt honours, or supporting bad ideologies. In this paper I understand these bad public history statues as history, and identify a distinctive class of public history-specific wrongs. Specifically, public history plays an important identity-shaping role, and bad (...) public history can commit specifically ontic injustice. Understanding bad public history in terms of ontic injustice helps understand not just to address bad public history statues, but also understand the value of public history more broadly. (shrink)

Instances of epistemic injustice elicit resistance, anger, despair, frustration or cognate emotional responses from their victims. This sort of response to the epistemic injustices that accompanied historical systems of oppression such as colonialism, for example, is normal. However, if their victims have internalised these oppressive situations, we could get the counterintuitive response of appreciation. In this paper, I argue for the phenomenon of appreciative silencing to make sense of instances like this. This is a form of epistemic silencing that happens (...) when the accepted hegemonic intuitions of the oppressed are formed/influenced by the ideologies of the oppressors over time. Here, we have a resilient, oppressive and hegemonic epistemic system. Put together, it creates a variant of epistemic injustice and silencing that is obscure since its victims are neither resistant nor aware of the injustice they face but are appreciative. (shrink)

In this thesis I provide an account of the unpleasantness of pain. In doing this, I shed light on the nature of pain and unpleasantness. I propose to understand the unpleasantness of pain based on the determinable-determinate distinction. Unpleasantness is a determinable phenomenal property of mental states that entails badness. I propose that an unpleasant pain experience has two phenomenal properties: i) the phenomenal property of being a pain, and ii) a phenomenal determinate property (u1, u2, u3, etc.) of the (...) unpleasantness determinable. According to this theory unpleasant pains feel bad, and this explains why we are motivated and justified in avoiding them. This explains, for example, why we are motivated and justified to take painkillers. This theory allows us to account for the heterogeneity of unpleasantness, i.e., we can explain how different unpleasant experiences feel unpleasant even if they feel so different. -/- The thesis is organised into seven chapters and divided by three main themes: i) what the unpleasantness of pain consists in, ii) how we can account for the great phenomenal diversity among experiences of unpleasantness, and iii) which cases suggest that there could be pains that are not unpleasant. Broadly, the first two chapters deal with the first theme, where I analyse two reductive accounts of unpleasantness: the content theories and the desire theories. I deal with the second theme in the third and fourth chapter, where I analyse different theories that try to account for the phenomenal property of unpleasantness. In the fifth and sixth chapter, I focus on the third theme, where I consider different cases that suggest the existence of pains that are not unpleasant. In the final chapter, I offer a conclusion of the three main themes by providing my own view on the unpleasantness of pain. (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)

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)

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)

Journal of Applied Philosophy, EarlyView.

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.

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.

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)

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)

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)

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)

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)

While Plantinga has famously argued that acceptance of neo-Darwinian theory commits one to the rejection of naturalism, Plantinga’s argument is vulnerable to an objection developed by Evan Fales. Not only does Fales’ objection undermine Plantinga’s original argument, it establishes a general challenge which any attempt to revitalize Plantinga’s argument must overcome. After briefly laying out the contours of this challenge, we attempt to meet it by arguing that because a purely naturalistic account of our etiology cannot explain the correlation between (...) our preference for simplicity and simplicity’s ability to serve as a veridical method of theory selection, the scientific realist is committed to the rejection of naturalism. (shrink)

My concern here is to motivate some theses in the philosophy of mind concerning the interpersonal character of intentions. I will do so by investigating aspects of shared agency. The main point will be that when acting together with others one must be able to act directly on the intention of another or others in a way that is relevantly similar to the manner in which an agent acts on his or her own intentions. What exactly this means will become (...) clearer once we understand what it is to act directly on one’s own intentions. But I take it to be a fundamental assumption of the prevailing individualism of the theory of action— one at the core of its conception of the separateness of individuals— that one person cannot act directly on another’s intention. I agree that there is an important way in which we are or can be separate and autonomous thinkers and agents. But the way the individualist tries to capture this separateness is misguided. (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)

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)

Accepting a promise is normatively significant in that it helps to secure promissory obligation. But what is it for B to accept A’s promise to φ? It is in part for B to intend A’s φ-ing. Thinking of acceptance in this way allows us to appeal to the distinctive role of intentions in practical reasoning and action to better understand the agency exercised by the promisee. The proposal also accounts for rational constraints on acceptance, and the so-called directedness of promissory (...) obligation. Finally, the proposal, conjoined with Cognitivism about intentions, addresses recent criticism of Scanlon’s expectation-based view of promissory obligation. (shrink)

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)

Immanuel Kant (1724-1804), the German philosopher, is considered as the father of modern ethics and one of the great philosophers in the history of philosophy. He wanted to establish a firm foundation for moral philosophy. He contributed something new to modern ethics which was not attempted by earlier ethicists. He wanted to show by using reason that morality is based on a single supreme universal principle, which is binding to all rational beings. Precisely, Kant wanted to establish the first principle (...) of morality which neglects all consideration of self-interest and even particular human problems. In the Groundwork of the Metaphysics of Morals, Kant claimed that his intention is to seek out and establish the supreme principle of morality, and that supreme principle is the categorical imperative. He puts the supreme principle of morality or the categorical imperative in at least five ways. These are formula of universal law (FUL), formula of universal law (FLN), formula of humanity (FH), formula of humanity (FA), and formula of realm of ends (FRE). However, Kant affirms that there is one canonical and general formulation of the categorical imperative and it is the FUL. For him, the other formulas are not distinct ethical principles; rather they are the reformulations or variant formulations of the single categorical imperative. Kant put this position in his works, The Groundwork of the Metaphysics of Morals. So, in this paper, I will mainly concentrate on the fundamental doctrine of the Groundwork of the Metaphysics of Morals. As I have tried to make clear before, Kant’s aim in the Groundwork of the Metaphysics of Morals is to search for and establish the supreme principle of morality (i.e., categorical imperative). He attempted to do this at the end of the Groundwork of the Metaphysics of Morals. But, to me, the way he attempted to justify the categorical imperative is problematic. Thus, in this paper, I argue that Kant did not put the categorical imperative or morality on a solid ground. (shrink)

I have developed transcendental arguments to refute several versions of Nick Bostrom’s simulation hypothesis. I called some of these arguments the SIM-style argument. In this paper, I have four main aims. First, I employ the SIM-style argument to remedy a defect in Hilary Putnam’s Brain-in-vat argument. Second, I show that the most radical skepticism, which Tim Button called the nightmarish Cartesian skepticism, can be refuted by the SIM-style argument or by another transcendental argument I develop here. Third, I compare my (...) approach to radical skepticisms with Donald Davidson’s, as it is often regarded as an exemplar of transcendental arguments. Fourth, I explain how the prominent objections, mainly developed by Barry Stroud, to transcendental arguments can incur two undesirable results: psychologism and Kantian skepticism. (shrink)

Does trust play a significant role in the appreciation of art? If so, how does it operate? We argue that it does, and that the mechanics of trust operate both at a general and a particular level. After outlining the general notion of ‘art-trust’—the notion sketched is consistent with most notions of trust on the market—and considering certain objections to the model proposed, we consider specific examples to show in some detail that the experience of works of art, and the (...) attribution of art-relevant properties or characterisations to works of art, very often involves the notion of trust; in such cases—perhaps most or even, implicitly, all—the question ‘Do I trust the artist (or art-maker)?’, is inescapable. (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)

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)

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)

As a site of colonial conquest, sub-Saharan Africa has experienced colonialism’s historic and continuing harms. One of the aspects of this harm is epistemic. In the analytic philosophical tradition, this harm can partly be theorised in line with the literature on epistemic injustice, although it does not fit squarely. I show this by arguing for what can be understood as a colonial state’s specific manifestation of epistemic injustice. This manifestation takes into account the historical context of colonisation and the continuing (...) coloniality of sub-Saharan African countries. From this, I argue for an approach to remediating this epistemic injustice that relies on the fair-minded pursuit of knowledge. This approach, I briefly argue, gains valuable insights from African epistemological traditions and can be beneficial to other epistemic injustice instances that result specifically from historical cases of oppression. (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)

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)

One important thesis Ásta defends in Categories We Live By is that social properties and categories are somehow dependent on our thoughts, attitudes, or practices—that they are inventions of the mind, projected onto the world. Another important aspect of her view is that the social properties are related to certain base properties; an individual is placed in a category when the relevant base properties are thought to hold of them. I see the relationship between the social and the base as (...) connected to the problem of explaining how the social properties are sufficiently stable so as to be taken seriously, both in theoretical endeavors as well as in practical matters of how we relate to each other. In this light, I identify stability constraints for an adequate account of social categories. I argue that certain distinctive aspects of Ásta's conferralist view of social categories, such as the radical contextualism in her account of gender, undermine the stability of categories and are at odds with taking social categories seriously. I end with the suggestion that a distinctive “sheltered” form of normativity might help us do justice to Ásta's insights while avoiding some of the destabilizing elements of conferralism. (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.

Nick Bostrom considered a number of simulations and contended that the probability that we are living in one of them is high or at least nonzero. I present arguments to refute the claim that we are or might be in any one of them. -/- Here is a highly dense reasoning why we are not in the simulation: -/- Suppose Simon is in the simulation, and he entertains the idea that he is in the simulation. And he thinks about the (...) word 'apple'. But since he is always in the simulation, he has never interacted with an actual apple, which the word 'apple' refers to. -/- Then Simon must think that "if I am in the simulation, then I never interact with an actual apple, and my understanding about the word 'apple' can only be given by the simulator. And this means I never exercise my reason to gain the understanding about the word 'apple', and never exercise my reason to apply the word 'apple'. Consequently, since what I am thinking right now (namely, this entire thought within the double quotation marks) involves the word 'apple', I am not using reason to think what I am thinking." -/- By denying he is using reason to think, Simon is being incoherent in thinking the preceding thought. To avoid being incoherent, Simon must reject the idea that he is in the simulation. -/- For the similar reason, if we think we are in the simulation, we are being incoherent. More simply, to think that we are in the simulation is to be incoherent. Therefore we cannot actually think that we are in the simulation. Hence, we are not in the simulation. -/- The whole paper is to flesh out the reasoning above. (shrink)