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)

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.

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)

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)

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

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

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)

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)

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 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.

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

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

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)

Anydomainofscientificresearchhasitssustainingorthodoxy. Thatis, research on a problem, whether in astronomy, physics, or biology, is con- ducted against a backdrop of broadly shared assumptions. It is these as- sumptionsthatguideinquiryandprovidethecanonofwhatisreasonable-- of what "makes sense." And it is these shared assumptions that constitute a framework for the interpretation of research results. Research on the problem of how we see is likewise sustained by broadly shared assump- tions, where the current orthodoxy embraces the very general idea that the business of the visual system is to (...) create a detailed replica of the visual world, and that it accomplishes its business via hierarchical organization and by operatingessentiallyindependently of other sensorymodalitiesas well as independently of previous learning, goals, motor planning, and motor execution. (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.

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.

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.

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)

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

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)

ABSTRACT: Why would someone concerned with heresy, who defined it as private opinion that flew in the face of doctrine sanctioned by the public person, harbor such a detailed interest in heterodoxy? Hobbes's religious beliefs ultimately remain a mystery, as perhaps they were meant to: the private views of someone concerned to conform outwardly to what his church required of him, and thereby avoid to heresy, while maintaining intellectual autonomy. The hazard of Hobbes's particular catechism is that he and his (...) supporters could never avoid the suspicion of insincerity. His preparedness to believe whatever the prince demanded of him smacked of heresy in the more usual sense, despite elaborate biblical exegesis designed to prove his orthdoxy. Undoubtedly he realized it even as he wrote the last lines of Leviathan, expressing the hope that "I cannot think it will be condemned at this time, either by the Publique Judge of Doctrine, or by any that desires the continuance of Publique Peace/7 Indicating an intention to return to science, he continued, "I hope the Novelty will as much please, as in the Doctrine of this Artificiall Body it useth to Offend" (Lev, Rev. and conclusion, 491). (shrink)

This paper brings new work to bear on the perennial question about Hobbes's atheism to show that as a debate about scepticism it is falsely framed. Hobbes, like fellow members of the Mersenne circle, Descartes and Gassendi, was no sceptic, but rather concerned to rescue physics and metaphysics from radical scepticism by exploring corporealism. In his early letter of November 1640, Hobbes had issued a provocative challenge to Descartes to abandon metaphysical dualism and subscribe to a ?corporeal God?; a provocation (...) to which the Frenchman angrily responded, but was perhaps importantly influenced. Hobbes's minimal realism was consonant with atheism, to which Descartes felt he was being forced. Moreover, Hobbes was unrelenting in his battle against Cartesian dualism, for which he saw Robert Boyle's experimental science as a surrogate. (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 is a critical discussion of Simon Blackburn’s recent work on lust. Blackburn develops a view on which lust is decent only when part of a pure mutuality in sex, and is best left alone—we ought not tamper with its “freedom of flow.” I argue that this treatment, which I believe reflects commonly held views, fails in several ways. First, it does not square with the fact that we pursue lust as a good in itself. Second, pure mutuality is (...) hard to come by and almost impossible to recognize, so Blackburn’s account is more restrictive than it may seem. Third, on such a view, masturbation is morally sanctioned only insofar as it mimics real sex; this doesn’t seem right. Finally, such a perspective fits ill with some recent research on the biology of lust in women. (shrink)

Buddhist philosophy asserts that human suffering is caused by ignorance regarding the true nature of reality. According to this, perceptions and thoughts are largely fabrications of our own minds, based on conditioned tendencies which often involve problematic fears, aversions, compulsions, etc. In Buddhist psychology, these tendencies reside in a portion of mind known as Store consciousness. Here, I suggest a correspondence between this Buddhist Store consciousness and the neuroscientific idea of stored synaptic weights. These weights are strong synaptic connections built (...) in through experience. Buddhist philosophy claims that humans can find relief from suffering through a process in which the Store consciousness is transformed. Here, I argue that this Buddhist 'transformation at the base' corresponds to a loosening of the learned synaptic connections. I will argue that Buddhist meditation practices create conditions in the brain which are optimal for diminishing the strength of our conditioned perceptual and behavioural tendencies. (shrink)

Hegel's interpretation of Sophocles' play Antigone is central to an understanding of woman's role in the Hegelian system. Hegel is fascinated by this play and uses it in both the Phenomenology and the Philosophy of Right to demonstrate that familial ethical life is woman's unique responsibility. Antigone is revealed as the paradigmatic figure of womanhood and family life in both the ancient and modern worlds, although there are fundamental differences between these two worlds for Hegel. Through an immanent critique of (...) both the Phenomenology and the Philosophy of Right which focuses on the role of woman as presented by Hegel in the figure of Antigone, my analysis reveals the limitations of Hegel’s dialectical theory. (shrink)

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

A 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)

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)

Despite considerable growth in understanding of various aspects of sporting and exercise embodiment over the last decade, in-depth investigations of embodied affectual experiences in running remain limited. Furthermore, within the corpus of literature investigating pleasure and the hedonic dimension in running, much of this research has focused on experiences of pleasure in relation to performance and achievement, or on specific affective states, such as enjoyment, derived after completing a run. We directly address this gap in the qualitative literature on sporting (...) and exercise embodiment by contributing novel insights on the mind-body pleasures of running via focusing analytic attention towards the pleasures recalled by runners as experienced during positive, rewarding running experiences. Applying conceptual insights drawn from sociological phenomenology, we analyse data from an in-depth, event-focused interview study with distance runners who reported positive, rewarding experiences in recent recreational runs. Through reflexive thematic analysis, we present findings in relation to three themes: (1) ‘running feels like it should’; (2) sensory engagements; and (3) time out. The study contributes fresh perspectives, both conceptually and in relation to data-collection approach, to a small literature on the lived experience of pleasure in sport, exercise and physical cultures. (shrink)

Marx in his early Critique of Hegel's Philosophy of Right (1843) declared "Democracy is human existence, while in other political forms man has only legal existence". In the Grundrisse and his late Ethnological Notebooks he studied the emergence of "the political" from primordialism, or the rule of family, tribe and clan .

Hobbes's interest in the power of the Image was programmatic, as suggested by his shifts from optics, to sensationalist psychology, to the strategic use of classical history, exemplified by Thucydides and Homer. It put a great resource at the disposal of the state-propaganda machine, with application to the question of state-management and crowd control.

Quentin Skinner’s dedication to investigating Hobbes’s concept of liberty in a number of essays and books has born some unusual fruit. Not only do we see the enormous problems that Hobbes set himself by proceeding as he did, but Skinner’s careful analysis allows us to chart Hobbes’ ingenuity as he tried to steer a path between the Charybdis of determinism and the Scylla of voluntarism – not very successfully, as we shall see. The upshot is a theory of individual freedom (...) and civil liberty to challenge the classical republican traditionThis Article does not have an abstract. (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)

Reformation commentators were well aware of the allegorical referents for Leviathan and Behemoth in the book of Job, representing the powerful states of Ancient Egypt and Assyria, but played them down. Hobbes did not.

ABSTRACT: Hobbes belonged to philosophical and scientific circles grappling with the big question at the dawn of modern physics: materialism and its consequences for morality. ‘Matter in motion’ may be a core principle of this materialism but it is certainly inadequate to capture the whole project. In wave after wave of this debate the Epicurean view of a fully determined universe governed by natural laws, that nevertheless allows to humans a sphere of libertas, but does not require a creator god (...) or teleology to explain it, comes up against monotheism and its insistence on the incoherence of an ordered world in the absence of a God and his purposes. The following questions were central to this debate: Can we understand the universe as law-governed in the absence of a god? If so, what room is there in a fully determined mechanical universe for human freedom? If humans do enjoy freedom, does the same hold for other animals? Is this freedom compatible with standard views of morality? (shrink)

The development of the Functional Genomics Investigation Ontology (FuGO) is a collaborative, international effort that will provide a resource for annotating functional genomics investigations, including the study design, protocols and instrumentation used, the data generated and the types of analysis performed on the data. FuGO will contain both terms that are universal to all functional genomics investigations and those that are domain specific. In this way, the ontology will serve as the “semantic glue” to provide a common understanding of data (...) from across these disparate data sources. In addition, FuGO will reference out to existing mature ontologies to avoid the need to duplicate these resources, and will do so in such a way as to enable their ease of use in annotation. This project is in the early stages of development; the paper will describe efforts to initiate the project, the scope and organization of the project, the work accomplished to date, and the challenges encountered, as well as future plans. (shrink)

It is unclear that United States schools are doing sufficient work to identify and protect the interests of their LGB students this analysis, we rely on certain public-health research in social epidemiology to show that discrimination against LGB adolescents imposes morally significant harms to both adolescents and community. We apply "trust” and “social capital” to educational standards and practices as foundations for educational practices that work toward full equality of LGB students in regard to opportunity and other primary social goods.

Hobbes in Leviathan, chapter xv, 4, makes the startling claim: “The fool hath said in his heart, ‘there is no such thing as justice,’” paraphrasing Psalm 52:1: “The fool hath said in his heart there is no God.” These are charges of which Hobbes himself could stand accused. His parable of the fool is about the exchange of obedience for protection, the backslider, regime change, and the tyrant; but given that Hobbes was himself likely an oath-breaker, it is also self-reflexive (...) and self-justificatory. For, Hobbes’s fool is not a windbag, or one of the dumb mob, led astray by priests. He is, in the terminology of Psalm 52, an insipiens, a madman or raving lunatic, whose rebellion against God the King is his own destruction and that of his people. A long iconographic tradition portraying the fool as insipiens, Antichrist, heretical impostor and tyrant king, was at Hobbes’s disposal. (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)

BioPortal is a Web portal that provides access to a library of biomedical ontologies and terminologies developed in OWL, RDF(S), OBO format, Protégé frames, and Rich Release Format. BioPortal functionality, driven by a service-oriented architecture, includes the ability to browse, search and visualize ontologies (Figure 1). The Web interface also facilitates community-based participation in the evaluation and evolution of ontology content.

This paper focuses on the interpretation of the Italian approximative adverb quasi 'almost' by primarily looking at cases in which it modifies temporal connectives, a domain which, to our knowledge, has been largely unexplored thus far. Consideration of this domain supports the need for a scalar account of the semantics of quasi (close in spirit to Hitzeman's semantic analysis of almost, in: Canakis et al. (eds) Papers from the 28th regional meeting of the Chicago Linguistic Society, 1992). When paired with (...) suitable analyses of temporal connectives, such an account can provide a simple explanation of the patterns of implication that are observed when quasi modifies locational (e. g. quando 'when'), directional (e. g. fino 'until' and da 'since'), and event-sequencing temporal connectives (e. g. prima 'before' and dopo ' after'). A challenging empirical phenomenon that is observed is a contrast between the modification of fino and da by quasi, on the one hand, and the modification of prima and dopo by the same adverb, on the other. While quasi fino and quasi da behave symmetrically, a puzzling asymmetry is observed between quasi prima and quasi dopo. To explain the asymmetry, we propose an analysis of prima and dopo on which the former has the meaning of the temporal comparative più presto 'earlier', while the latter is seen as an atomic predicate denoting temporal succession between events (Del Prete, Nat Lang Semantics 16: 157-203, 2008). We show that the same pattern of implication observed for quasi prima is attested when quasi modifies overt comparatives, and propose a pragmatic analysis of this pattern that uniformly applies to both cases, thus providing new evidence for the claim that prima is underlyingly a comparative. A major point of this paper is a discussion of the notion of scale which is relevant for the semantics of quasi', in particular, we show that the notion of Horn (entailment-based) scale is not well-suited for handling modification of temporal connectives, and that a more general notion of scale is required in order to provide a uniform analysis of quasi as a cross-categorial modifier. (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.

This essay, published in Political Theory in 1975, was one of the first to address the subject of the last two long books of Hobbes's Leviathan on religion. It addresses the purpose of these books and the relation between Hobbes's philosophy, ecclesiology and theology and the problems they raise.