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 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)

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)

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)

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)

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)

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)

This paper is a review and critical discussion of John Broome’s Rationality Through Reasoning. In particular, it engages critically with Broome’s view on the independence of normative reasons and rationality, his construal of the capacity, property, and requirement senses of “rationality”, and his account of reasoning as a conscious, rule-following operation on mental contents.

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)

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)

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)

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)

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)

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)

One popular line of argument put forward in support of the principle that the right is prior to the good is to show that teleological theories, which put the good prior to the right, lead to implausible normative results. There are situa- tions, it is argued, in which putting the good prior to the right entails that we ought to do things that cannot be right for us to do. Consequently, goodness cannot (always) explain an action's rightness. This indicates that (...) what is right must be determined independently of the good. In this paper, I argue that these purported counterexamples to teleology fail to establish that the right must be prior to the good. In fact, putting the right prior to the good can lead to sets of ought statements which potentially con- flict with the principle that ‘ought’ implies ‘can’. I argue that no plausible ethical theory can determine what is right independently of a notion of value or goodness. Every plausible ethical theory needs a mapping from goodness to rightness, which implies that right cannot be prior to the good. (shrink)

Animal rights activists are often accused of caring more about animals than about human beings. How, it is asked, can activists condemn the use of animals in biomedical research—research that improves human health and saves human lives? In this article, I argue that even if animal experimentation might eventually provide cures for many serious diseases, given the present state of the world, we are not justified supporting this research; rather, we ought to devote our limited resources to other forms of (...) humanitarian assistance. (shrink)

I argue that the understanding of "pain" as presented in the official medical definition by the IASP is ambiguous and likely a cluster concept.

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)

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)

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)

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)

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.

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)

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.

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)

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.”.

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)

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)

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.

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)

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)

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)

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)

Unter einigenWissenschaftlern ist die Vorstellung verbreitet, dass Paradoxien Anzeichen von Fortschritt sein können. Es ist jedoch unklar, wie dies zu deuten ist. Dieser Essay stellt ein subjekt-relatives Verständnis von Paradoxikalität vor, das Paradoxien als »Dissonanzen der Zustimmung« (Rescher 2001) charakterisiert und dadurch erlaubt, sie als Katalysator wissenschaftlichen Fortschritts zu rekonstruieren: Durch ihre Struktur haben Problemstellungen in Form von Paradoxien wenigstens fünf fortschrittsfördernde Eigenschaften, die sie Problemstellungen in Form von Fragen voraushaben. Dadurch können Paradoxien als Angelpunkte theoretischen Fortschritts gesehen werden. Dies (...) legt eine Forderung nahe: Wenn wir theoretischen Fortschritt in den Wissenschaften fördern wollen, so sollten wir den Bau von Paradoxien aktiv verfolgen, gemäß dem Credo: Progress by Paradox! (shrink)

This paper is a review and critical discussion of John Broome’s Rationality Through Reasoning. In particular, it engages critically with Broome’s view on the independence of normative reasons and rationality, his construal of the capacity, property, and requirement senses of “rationality”, and his account of reasoning as a conscious, rule-following operation on mental contents.

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.

Der Arktikel beschreibt die Logik des "eingefrorenen" Konflikts zwischen der Republik Moldau und der selbsternannten „Pridnestrowische Moldauischen Republik“ ("Transnistrien"). Bezugnehmend auf die strategischen Optionen der beteiligten Akteure wird erklärt warum der seit 1992 bestehende Konflikt zu keiner Lösung findet.

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)

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)

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)

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)

One important foundation of Buddhist ethics is a commitment to nonviolence. My aim in this paper is to work out the implications of this commitment with regard to the treatment of offenders. Given that punishment involves the intentional infliction of harm, I argue that the practice of punishment is incompatible with the principle of nonviolence. The core moral teaching of the Buddha is to conquer evil with goodness, and it is reconciliation, rather than punishment, that conforms to this teaching. I (...) argue that a commitment to nonviolence requires not only that we refrain from inflicting intentional harm, but that we refrain from inflicting unnecessary harm, and that this has important implications concerning the practice of incapacitation. I analyze the concept of harm and argue that the Buddhist understanding of this notion leads to the conclusion that none of the standard justifications for punishment are compatible with the principle of nonviolence, properly understood. (shrink)