This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.

This dissertation is a contribution to formal and computational philosophy. -/- In the first part, we show that by exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. Case 1: Infinite lotteries. We discuss how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. The solution boils down to the introduction (...) of infinitesimal probability values, which can be achieved using non-standard analysis. Our solution can be generalized to uncountable sample spaces, giving rise to a Non-Archimedean Probability (NAP) theory. Case 2: Large but finite lotteries. We propose application of the language of relative analysis (a type of non-standard analysis) to formulate a new model for rational belief, called Stratified Belief. This contextualist model seems well-suited to deal with a concept of beliefs based on probabilities ‘sufficiently close to unity’. -/- The second part presents a case study in social epistemology. We model a group of agents who update their opinions by averaging the opinions of other agents. Our main goal is to calculate the probability for an agent to end up in an inconsistent belief state due to updating. To that end, an analytical expression is given and evaluated numerically, both exactly and using statistical sampling. The probability of ending up in an inconsistent belief state turns out to be always smaller than 2%. (shrink)

How much power does emotional dismissal have over the oppressed's ability to trust outlaw emotions, or to stand for such emotions before others? I discuss Sue Campbell's view of the interpretation of emotion in light of the political significance of emotional dismissal, in response, 1 suggest that feminist contentions of interpretation developed within dialogical communities are best suited to providing resources for expressing, interpreting, defining, and reflecting on our emotions.

This essay argues that ideals of cooperation or adversariality in argumentation are not equally attainable for women. Women in argumentation contexts face oppressive limitations undermining argument success because their authority is undermined by gendered norms of politeness. Women endorsing or, alternatively, transgressing feminine norms of politeness typically defend their authority in argumentation contexts. And yet, defending authority renders it less legitimate. My argument focuses on women in philosophy but bears the implication that other masculine dis- course contexts present similar double (...) binds that urge social and political change. (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)

Living in a culture of violence against women leads women to employ any number of avoidance and defensive strategies on a daily basis. Such strategies may be self protective but do little to counter women’s fear of violence. A pervasive fear of violence comes with a cost to integrity not addressed in moral philosophy. Restricting choice and action to avoid possibility of harm compromises the ability to stand for one’s commitments before others. If Calhoun is right that integrity is a (...) matter of standing for one’s commitments then fear for safety undermines integrity. This paper extends Calhoun’s view through arguing that integrity further requires resiliency to protect one’s commitments. My account shows that self-defense training is a key source of this resiliency because it cultivates self-confidence. The practical point is that self-defense training directly counters fear and other passive responses to violence that undermine integrity. The theoretical significance is that violence against women is a social condition threatening integrity. Hence, integrity requires self-protection for more socially minded reasons than moral theorists have previously recognized. (shrink)

Socialization enforces gendered standards of politeness that encourage men to be dominating and women to be deferential in mixed-gender discourse. This gendered dynamic of politeness places women in a double bind. If women are to participate in polite discourse with men, and thus to avail of smooth and fortuitous social interaction, women demote themselves to a lower social ranking. If women wish to rise above such ranking, then they fail to be polite and hence, open themselves to a wellspring of (...) social discord, dissention, and antagonism. The possibility for women’s politeness in mixed-gender conversation threatens more than cooperation, it undermines the possibility for self-respect and autonomy. (shrink)

Wright's _Truth and Objectivity_ seeks to systematise a variety of anti-realist positions. I argue that many objections to the system are avoided by transposing its talk of truth into talk of warrant. However, a problem remains about debates involving 'direction-of-fit'. -/- Dummett introduced 'anti-realism' as a philosophical view informed by mathematical intuitionism. Subsequently, the term has been associated with many debates, ancient and modern. _Truth and Objectivity_ proposes that truth admits of different characteristics; these various debates then concern which characteristics (...) truth has, in a given area. This pluralism of truth is at odds with deflationism. I find fault with Wright's argument against deflationism. However, transmission of warrant across the Disquotational Schema suffices to ground Wright's proposal, which survives as a pluralism of classes of warrant. -/- The two main debates concern whether truths are always knowable (Epistemic Constraint) and whether disagreements in an area must be down to some fault of one of those involved (Cognitive Command). I introduce Assertoric Constraint, relating to Epistemic Constraint, where truths cannot outstrip the availability of warrant for their assertion. I solve a structural problem by a comparison with a constitutive analysis of Moore's Paradox. The relativism of blameless disagreement is problematic. Wright's response invokes a sort of ignorance which he calls `Quandary'. I criticise this before proposing an alternative. -/- I agree with Wright that Dummett's original anti-realism does not belong among the positions which Wright seeks to systematise. However, two candidates show that the proposal suffers a weakness. Wright thinks Expressivism misguided, and implicitly rules out his earlier non-cognitivism about necessity. I argue that Expressivism has promise, and I endorse Wright's Cautious Man argument for non-cognitivism about necessity; both involve play with `direction-of-fit'. I conclude that this sort of anti-realist debate needs to be accommodated by the proposal. (shrink)

»Civil society« with its main elements of »social democratic citizenship« and subsidiarity is an analytical approach to the present situation of democracys and offers an perspective to surrender the democratic deficit and the crisis of the welfare state in the Member states of the European Union. The concept of »Civil society« bases on an active citizenship and give intermediary civil actors, especially the charitable social welfare associations and democratic movements, the chance to reflect on their position to the govemment on (...) the one side and to the citizen on the other side in order to take account of the citizen' s civil, political and social rights. (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)

Human freedom is in tension with nomological determinism and with statistical determinism. The goal of this paper is to answer both challenges. Four contributions are made to the free-will debate. First, we propose a classification of scientific theories based on how much freedom they allow. We take into account that indeterminism comes in different degrees and that both the laws and the auxiliary conditions can place constraints. A scientific worldview pulls towards one end of this classification, while libertarianism pulls towards (...) the other end of the spectrum. Second, inspired by Hoefer, we argue that an interval of auxiliary conditions corresponds to a region in phase space, and to a bundle of possible block universes. We thus make room for a form of non-nomological indeterminism. Third, we combine crucial elements from the works of Hoefer and List; we attempt to give a libertarian reading of this combination. On our proposal, throughout spacetime, there is a certain amount of freedom that can be interpreted as the result of agential choices. Fourth, we focus on the principle of alternative possibilities throughout and propose three ways of strengthening it. (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)

Many of us took pride in never feeling violent, never hitting. We had not thought deeply about our relationships to inflicting physical pain. Some of us expressed terror and awe when confronted with physical strength on the part of others. For us, the healing process included the need to learn how to use physical force constructively, to remove the terror—the dread. —bell hooks, Talking Back: Thinking Feminist, Thinking Black.

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.

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)

Der normative Gehalt des Subsidiaritätsprinzips und seine Bedeutung für die Politische und Soziale Union Europas (S. 201-203) 1. Die Entwicklung des Maßstabs normativer Subsidiarität im ersten Kapitel beruht auf der Erkenntnis, dass dem Subsidiaritätsprinzip insbesondere von seinen protestantischen Wurzeln und seiner Ausprägung in der katholischen Soziallehre her ein spezifisch normativer Kerngehalt innewohnt, der als Idee auch dem Grundgesetzt als zwar weltanschaulich neutraler, aber nicht wertneutraler politischer Ordnung zugrunde liegt. Ausgehend von einem Menschenbild, das christliche Personalität und gesellschaftliche Solidarität umfasst, setzt (...) der materiale Gehalt des Subsidiaritätsprinzip insofern Grenzen, "als die Legitimation einer politischen Gemeinschaft nur von der Einzelperson im Sinne des individualistischen Liberalismus erfolgen kann und als die Anwendung des Subsidiaritätspinzips der Solidarität sozialer Einheiten bedarf. 2. Das ursprünglich von den deutschen Ländern anvisierte Ziel einer Verankerung des Strukturprinzips des Föderalismus im Vorfeld des Maastrichter Vertrages, ergänzt um das Subsidiaritätsprinzip als Prinzip der Kompetenzausübung, scheiterte am Widerstand Großbritanniens. Die Briten setzten das föderative Prinzip mit einem zentralistischen Bundesstaat gleich, den sie auf jeden Fall verhindern wollten. Fortan verbanden die Deutschen, insbesondere die deutschen Länder und Bundesregierung mit Unterstützung der beiden großen Kirchen einschließlich der kirchlichen Wohlfahrtsverbände, mit dem Subsidiaritätsprinzip neben einer Föderalisierung der Europäischen Union auch das Ziel, die Gesundheits- und Sozialpolitik auf europäischer Ebene auszubauen. Wenig später, schon im Verlauf der der Ratifikation des Vertrages, wird das Subsidiaritätsprinzip seitens der Bundesregierung und der deutschen Länder auf den Vorrang der der unteren Ebene umgemünzt. 3. Parallel zum Subsidiaritätsstreit in den 60er Jahren wird die Nähe zur Person bzw. zum Bürger instrumentalisiert, um dem Subsidiaritätsbegriff den Inhalt zu geben, der aus machtpolitischen Interessen opportun erscheint. Im innerdeutschen Subsidiaritätssstreit der 60er Jahre wurde die funktionale Dimension des Prinzips in den Vordergrund gedrängt, wohingegen seit 1993 seitens der Bundesregierung und der deutschen Länder im europäischen Kontext die territoriale Dimension des Prinzips, die sich gegen europäische Institutionen als Inbegriff bürgerferner, nicht demokratisch legitimierter Politik richtet, hervorgehoben wird. In beiden Fällen geht die aus Gründen normativer Subsidiarität gebotene Balance zwischen Identität und Funktion, zwischen Demokratie und Effizienz, verloren. 4. In den 60er Jahren haben die Verbände der freien Wohlfahrtspflege ihre Freiheit gegen Staatsnähe eingetauscht. Daraus entstanden neo-korporatistische Strukturen, die die Verbände zu mächtigen Trägern sozialer Dienstleistungen werden ließen. Die Rolle der Verbände als intermediäres Bindeglied zwischen Bürger und Staat wurde vernachlässigt. 5. In den 90er Jahren im europäischen Kontext die funktionale Dimension des Subsidiaritätsprinzip auf den territorialen Rahmen der Mitgliedstaaten zurecht gestutzt. Im Vordergrund steht nicht die bestmögliche Lösung eines Problems. Man gibt sich mit der vermeintlich "ausreichenden" Lösung auf mitgliedsstaatlicher Ebene zufrieden. Die systematische Auslegung, die im Hinblick auf die Sicherung der Funktionsfähigkeit der Gemeinschaft von besonderer Bedeutung ist, ergibt hingegen, "dass das Subsidiaritätspinzip als Kompetenzausübungsprinzip verfasst ist und zweitens, dass eine Entscheidung sowohl auf der Ebene der Gemeinschaft als auch auf Ebene der Mitgliedstaaten bürgernah sein kann." Deutlich tritt hier die Kluft zwischen rechtlicher Konzeption, die Ausdruck universeller Geltung des Prinzips ist, und verfolgten politischen Eigeninteressen der Akteure hervor. 6. Wenngleich bei den Verbänden der freien Wohlfahrtspflege, insbesondere den kirchlichen, der Territorialaspekt des Subsidiaritätsprinzips dominiert, gibt es Anzeichen dafür, dass die Überzeugung wächst, dass ohne eine sachbezogene, auf weitere Integration gerichtete Europapolitik auch die drei Wohlfahrtspflege in Deutschland nicht aufrechtzuerhalten ist. So vertreten die kirchlichen Verbände im Rahmen einer von der Kommission initiierten Konsultation zu Armut und Ausgrenzung in Europa die Ansicht, dass eine Lösung auf mitgliedsstaatlicher Ebene nicht ausreichend sei. In welcher Form die sozialpolitische Verantwortung auf europäischer Ebene wahrgenommen werden soll, bleibt offen. 7. Weder das Hervorheben der Nation als die maßgebliche territoriale Größe, die ihren Bürgern Schutz und Sicherheit bieten kann, noch die Vorstellung, Europas Vielfalt durch die Mobilisierung der Selbstregulierungskräfte der Gesellschaft erhalten zu können, bieten Perspektiven, das Demokratie-Effizienz-Dilemma zu überwinden. 8. Der Erhalt europäischer Demokratien ist ohne das Herausbilden transnationaler Formen von Demokratie nicht denkbar. Denn der Nationalstaat allein kann die Substanz der Demokratie nicht gewährleisten. Der nationale Wohlfahrtsstaat wird ausgehöhlt. Übrig bleibt die leere Hülle nationaler Souveränität. 9. Aussicht bietet eine zivilgesellschaftliche Verschränkung von Politik und Gesellschaft. Repräsentative nationale Akteure kooperieren zur Erfüllung einer europäischen Aufgabe und entwickeln daraus eine europäische Identität. Aufgrund ihrer assoziativen Funktion sind hier vor allem zivilgesellschaftliche Akteure gefragt. Hier eröffnet sich den Wohlfahrtsverbänden die Chance, sich auf ihre Wurzeln zu besinnen und verstärkt ihre Rolle in der Gesellschaft wahrzunehmen, um sich so die Position der Repräsentativität nachhaltig zu sichern. 10. Eine gleichgewichtige funktionale Repräsentation wirtschaftlicher, sozialer und kultureller Interessen einschließlich Repräsentationsmonopol und Mitverantwortung für die ausgehandelten Ergebnisse kann einen Beitrag zur Behebung des europäischen Demokratiedefizit leisten. Dies setzt voraus, dass die Europäische Union staatsähnliche Eigenschaften ausbildet, die sie dazu befähigt, Verhandlungsgleichgewichte zwischen den Repräsentanten der verschiedenen Interessen herzustellen und autonom über Umverteilungsfragen zu entscheiden und eine entsprechende Politik auch durchzusetzen. (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)

Our position is that the threat and experience of violence that sex workers face is a crucial issue to address and should be considered in debates concerning the legalization of prostitution because even in countries where prostitution is legalized, prostitutes continue to experience violence. Our focus is to show that violence is crucially important to address because both the experience and the fear of physical, sexual or psychological harm erodes women ’s capacity to choose and act autonomously. We shall argue, (...) then, that despite differences between inside and outside prostitution, all women in prostitution suffer unacceptable levels of violence ; hence, we conclude that all forms of prostitution continue to be morally problematic. (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)

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)

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)

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 Continuum Hypothesis featured top of Hilbert's list of 23 problems in 1900. Today, we still consider the question, with various programmes pulling in different directions. This conceptual diversity raises a puzzle: In what sense do we disagree when we talk about it? A standard assumption takes it that the content of our thought about classes and the Continuum Hypothesis has not changed. Assuming a moderate view of how content is determined, I reject this assumption but also argue that whilst (...) the Continuum Hypothesis can have different content for different agents, it can also be determinate for certain programmes. In particular, I suggest that there is a fault line between those who think there are uncountable sets and recent countabilist programmes. (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)

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.

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)

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)

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.

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)

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)

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.

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)

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.

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)

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)

A number of concerns have been raised about the possible future use of pharmaceuticals designed to enhance cognitive, affective, and motivational processes, particularly where the aim is to produce morally better decisions or behavior. In this article, we draw attention to what is arguably a more worrying possibility: that pharmaceuticals currently in widespread therapeutic use are already having unintended effects on these processes, and thus on moral decision making and morally significant behavior. We review current evidence on the moral effects (...) of three widely used drugs or drug types: propranolol, selective serotonin reuptake inhibitors, and drugs that effect oxytocin physiology. This evidence suggests that the alterations to moral decision making and behavior caused by these agents may have important and difficult-to-evaluate consequences, at least at the population level. We argue that the moral effects of these and other widely used pharmaceuticals warrant further empirical research and ethical analysis. (shrink)

Following decades of maltreatment of women in obstetric care, professional respect for maternal autonomy in obstetric decision making and care have become codified in global and national professional ethical guidelines. Yet, using the example of birth after cesarean, identifiable threats to maternal autonomy in obstetrics continue. This paper focuses on how current scientific knowledge and obstetric practice patterns factor into restricted maternal autonomy as evidenced in three representative maternal accounts obtained prior and subsequent to birth after cesarean. Short- and long-term (...) remedies to improve the current state of restricted maternal autonomy in clinical practice surrounding decision making on birth after cesarean are provided. (shrink)

Response to commentary. We are grateful to Crockett and Craigie for their interesting remarks on our paper. We accept Crockett’s claim that there is a need for caution in drawing inferences about patient groups from work on healthy volunteers in the laboratory. However, we believe that the evidence we cited established a strong presumption that many of the patients who are routinely taking a medication, including many people properly prescribed the medication for a medical condition, have morally significant aspects of (...) their cognition and behavior modified in a way that is unintended and may sometimes be unwelcome. Crockett notes that in some cases the effects of long-term drug use may differ, sometimes markedly, from the effects of short-term use. However, if acute use of a drug affects a neural system involved in mediating moral cognition or behavior, this nevertheless provides some evidence that chronic use of the drug may affect that same system and thus have morally significant effects. It is also plausible, in some cases, that an acute moral effect would give rise to a chronic moral effect via cognitive mechanisms. ... (shrink)

A SECOND COMPLETELY REVISED EDITION OF THIS TEXTBOOK ON INTERDISCIPLINARY RESEARCH WAS PUBLISHED WITH AMSTERDAM UNIVERSITY PRESS IN 2022. Check out that version here and a PDF of its ToC and Introduction, as this first edition (AUP 2016) is no longer available. [This book (128 pp.) serves as an introduction and manual to guide students through the interdisciplinary research process. We are becoming increasingly aware that, as a result of technological developments and globalisation, problems are becoming so complex that they (...) can only be solved through cooperation between multiple disciplines. Healthcare, climate change, food security, energy, financial markets and quality of life are just a few examples of issues that require scientists and academics to work in a crossdisciplinary way. As a result of these developments, an interdisciplinary approach is becoming increasingly popular in higher education and must be considered an absolute necessity. Young academics are being called on to step beyond the boundaries of traditional disciplines in order to contribute to addressing fundamental problems and solving challenges facing society. There is a need for people who are not afraid to ask critical questions, who can work together well and can look beyond the boundaries of their own field. This means students need to learn more about how they can integrate and apply knowledge, methods and skills from different fields. Interdisciplinary research projects and practical training courses offer students more than one perspective on the same subject. Comparing and contrasting, connecting, adding and adapting concepts, theories and methodologies from different disciplines ultimately results in new insights and better answers to complex problems.]. (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)

LandryElaine, * ed. Categories for the Working Philosopher. Oxford University Press, 2017. ISBN 978-0-19-874899-1 ; 978-0-19-106582-8. Pp. xiv + 471.

Aims and objectives. Participant narratives from a feminist and queer phe- nomenological study aim to broaden current understandings of trauma. Examin- ing structural marginalisation within perinatal care relationships provides insights into the impact of dominant models of care on queer birthing women. More specifically, validation of queer experience as a key finding from the study offers trauma-informed strategies that reconstruct formerly disempowering perinatal relationships. Background. Heteronormativity governs birthing spaces and presents considerable challenges for queer birthing women who may also have (...) an increased risk of trauma due to structurally marginalising processes that create and maintain socially constructed differences. Design. Analysis of the qualitative data was guided by feminist and queer phe- nomenology. This was well suited to understanding queer women’s storied narra- tives of trauma, including disempowering processes of structural marginalisation. Methods. Semistructured and conversational interviews were conducted with a purposeful sample of thirteen queer-identified women who had experiences of birthing in rural Nova Scotia, Canada. Results. Validation was identified as meaningful for queer women in the context of perinatal care in rural Nova Scotia. Offering new perspectives on traditional models of assessment provide strategies to create a context of care that recon- structs the birthing space insofar as women at risk do not have to come out as queer in opposition to the expectation of heterosexuality. Conclusions. Normative practices were found to further the effects of structural marginalisation suggesting that perinatal care providers, including nurses, can challenge dominant models of care and reconstruct the relationality between queer women and formerly disempowering expectations of heteronormativity that govern birthing spaces. Relevance to clinical practice. New trauma-informed assessment strategies recon- struct the relationality within historically disempowering perinatal relationships through potentiating difference which avoids retraumatising women with re- experiencing the process of coming out as queer in opposition to the expectation of heterosexuality. (shrink)

Background: Previous studies assessing students’ learning outcomes and identifying contributing factors have often dwelt on the cognitive domain. Furthermore, school evaluation decisions are often made using scores from cognitive-based tests to rank students. This practice often skews evaluation results, given that education aims to improve the three learning domains. This study addresses this gap by assessing the contributions of four students’ input to their cognitive, affective and psychomotor skills (CAPs). Methods: A cross-section of senior secondary class II students (n = (...) 870), sampled through the multistage procedure, participated in a physical survey. Students’ Inputs Questionnaire (STIQ) and Learning Outcomes Questionnaire (LOQ) were used for data collection. Based on data obtained from a pilot sample (n = 412), principal axis factoring (PAF) was performed to assess the internal structure of the instruments following an oblique rotation. The KMO value of sampling adequacy were 0.88 and 0.94, while the Bartlett’s test of sphericity were significant χ2 (253) = 5,010; p < 0.001 and χ2 (105) = 3693.38, p < 0.001 for the STIQ and LOQ, respectively. Confirmatory factor analysis was used to assess the models’ acceptability based on the maximum likelihood estimation technique. The main study used hierarchical linear regression for data analysis. Results: Findings indicated that innate ability, health, motivation and social capital relatively and cumulatively predicted students’ overall, cognitive, affective and psychomotor learning outcomes. The proportion of variance explained by the predictors increased at different levels of the models with the addition of new variables. Students’ social capital reduced the effect of students’ innate ability regardless of their motivation and health status. Conclusion/implication: This study has provided evidence that the four students’ inputs are crucial predictors of their learning outcomes in the three domains. This result is helpful for school management to provide services aimed at improving the school climate for students’ motivation and social capital. The result can provide policymakers with a proper understanding of the constituents of learning outcomes and how policies can be aligned to secure quality student inputs for maximum productivity in education. (shrink)