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.

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)

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)

Algunas de las preguntas fundamentales de la filosofía del arte son: 1) ¿Qué es una obra de arte?, 2) ¿Qué es Arte?, 3) ¿Qué es el arte? Responderlas es determinar el sentido del arte. Este tipo de preguntas están planteadas bajo la fórmula ¿Qué es X?, es decir, preguntas en las cuales en lo simple esta lo complejo, preguntas en donde lo simple no quiere decir que sean sencillas; son preguntas que traen dentro de si su naturaleza y carácter metafísico-ontológico-gnoseológico, (...) y hasta axiológico. No es el propósito de este trabajo hacer frente o resolver estos problemas, sino proporcionar una aproximación al concepto de “obra de arte” en la época actual y como podría entenderse en relación a ciertos problemas ontológicos y epistemológicos actuales. -/- [Extended Version of: Vélez León, Paulo (2006). «Aproximaciones a la ¿obra de arte?». En Políticas al borde. Una investigación sobre el arte contemporáneo cuencano en los discursos políticos actuales, editado por Paulo Vélez León y Hernán Pacucuru. Cuenca: Universidad de Cuenca/Bienal Internacional de Cuenca, 2006, pp. 1-12]. (shrink)

The prologue of the Sophistici elenchi is as close an Aristotelian text gets to dealing with language as a subject matter in its own right, only in reverse. Language and its features bear consideration to the extent that they account for some major predicaments discursive reasoning is prone to, both as a separate and as a common endeavour. That being said, the linguistic pitfalls that trick us into thinking that whatever is the case for words and word-compounds is also the (...) case for the things and facts linguistic items stand for reveal as much about good linguistic habits and sound argumentation as they themselves are revealed by the principles and rules our argumentation goes by. In this connection, Aristotle resorted to a curious (or not so curious) analogy between words and counters which played a major role in explaining why language is such a powerful source of illusion and deception. As it happens, Aristotle accounting analogy is a case in point for showcasing the level of sophistication medieval Latin literature on fallacies achieved as early as the first half of the twelfth century. As a matter of fact, Western commentators managed to build compelling cases both in favour of and against the understanding that was to become and still is the standard story – which, of course, speaks volumes about their exegetical proficiency and technical expertise. On the one hand, trusting implicitly Boethius’ translation and well aware of his views on disputational hazards as opposed to computational reliability, they usually understood Aristotle’s comparison as if it was an analogy in name only. On the other hand, despite Boethius’ translation put them at a considerable disadvantage, Latin commentators were able to construe Aristotle’s analogy as bringing together two sets of symbolic variables (words and counters) that are neither entirely free nor entirely bound – which expose them to subtle but critical shifts in value and meaning. (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)

El proceso de aprehensión de lo cognoscible, en la filosofía contemporánea, ha sido tratado desde diversas perspectivas, entre ellas la fenomenológica y la analítica. Cada una de estas perspectivas aportan unos presupuestos filosóficos y procesos metodológicos que nos proporcionan marcos de trabajo para indagar en las vías de aprehensión del conocimiento; sin embargo, empleadas por separado son insuficientes y limitadas. En absoluto se trata de procurar un método universal, sino de integrar e indagar sobre diversos presupuestos, procesos, patrones y estructuras (...) para avanzar en la indagación de la aprehensión del conocimiento. En este sentido, en la primera parte, abordaremos la necesidad de tener reglas (definitorias y estratégicas) para ser parte y avanzar en cualquier «juego», en especial el del conocimiento. En la segunda y tercera, describiremos los «métodos» desarrollados por José Ferrater Mora (operaciones filosóficas) y Nicolai Hartmann (pensar sistemático), los que pueden ser un punto de partida, vías a considerar en este proceso. En la parte final, a modo de contraste, se ofrece en un gráfico un esquema metodológico de los dos métodos analizados. (shrink)

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often model-theoretic constructions that add sets to models are cited as evidence in favour of the latter. This paper informs this debate by developing a way for a Universist to interpret talk that (...) seems to necessitate the addition of sets to V. We argue that, despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We present a method of interpreting extension-talk (V-logic), and show how it captures satisfaction in `ideal' outer models and relates to impredicative class theories. We provide some reasons to regard the technique as philosophically virtuous, and argue that it opens new doors to philosophical and mathematical discussions for the Universist. (shrink)

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that seems (...) to necessitate the addition of subsets to V. We argue that despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We analyse extant interpretations of such talk, and analyse various tradeoffs in naturality that might be made. We conclude that the Universist has promising options for interpreting different forcing constructions. (shrink)

Discussion of new axioms for set theory has often focused on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism (the view that any universe of a certain kind can be extended) and actualism (the view that there are universes that cannot be extended in particular ways) face (...) complementary problems. The latter view is unable to use maximality axioms that make use of extensions, where the former has to contend with the existence of extensions violating maximality axioms. An analysis of two kinds of multiversism, a Zermelian form and Skolemite form, leads to the conclusion that the kind of maximality captured by an axiom differs substantially according to background ontology. (shrink)

Let's suppose you think that there are no uncountable sets. Have you adopted a restrictive position? It is certainly tempting to say yes---you've prohibited the existence of certain kinds of large set. This paper argues that this intuition can be challenged. Instead, I argue that there are some considerations based on a formal notion of restrictiveness which suggest that it is restrictive to hold that there are uncountable sets.

This article articulates and assesses an imperatival approach to the foundations of mathematics. The core idea for the program is that mathematical domains of interest can fruitfully be viewed as the outputs of construction procedures. We apply this idea to provide a novel formalisation of arithmetic and set theory in terms of such procedures, and discuss the significance of this perspective for the philosophy of mathematics.

We explain and explore class-theoretic potentialism—the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning the relevant potentialist systems (in particular exhibiting failures of the $\mathsf {.2}$ and $\mathsf {.3}$ axioms). We then discuss the significance of these results for the different kinds of class-theoretic potentialists.

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

Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...) work in numerical cognition and ontogenetic studies. (shrink)

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

I provide an examination and comparison of modal theories for underwriting different non-modal theories of sets. I argue that there is a respect in which the `standard' modal theory for set construction---on which sets are formed via the successive individuation of powersets---raises a significant challenge for some recently proposed `countabilist' modal theories (i.e. ones that imply that every set is countable). I examine how the countabilist can respond to this issue via the use of regularity axioms and raise some questions (...) about this approach. I argue that by comparing them with the `standard' uncountabilist theory, a new approach that brings in arbitrariness rather than the strict controls of forcing is desirable. (shrink)

Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive power (...) and meta-theoretic properties when comparing first-order and second-order logic. (shrink)

The metaphysics of gender and race is a growing area of concern in contemporary analytic metaphysics, with many different views about the nature of gender and race being submitted and discussed. But what are these debates about? What questions are these accounts trying to answer? And is there real disagreement between advocates of differ- ent views about race or gender? If so, what are they really disagreeing about? In this paper I want to develop a view about what the debates (...) in the metaphysics of gender and race are about, namely, a version of metaphysical deflationism, according to which these debates are about how we actually use or should use the terms ‘gender’ and ‘race’ (and other related terms), where moral and political considerations play a central role. I will also argue that my version of the view can overcome some recent and powerful objections to metaphysical deflationism of- fered by Elizabeth Barnes (2014, 2017). (shrink)

[ES] En recientes décadas se ha observado un renovado interés por algunos de los temas clásicos de la ontología, desde áreas de conocimiento externas a la filosofía, sin embargo, este renacimiento ontológico ha «estimulado» una multiplicidad y diversidad de teorías y concepciones «ontológicas» que ha dado como consecuencia una proliferación de «ontologías» y de interminables batallas para determinar qué tipo de «entidades» estudian sus respectivos «dominios», que a su vez se consideran autónomos e independientes entre sí, inclusive de la propia (...) ontología. En este sentido, el propósito de este trabajo es caracterizar y representar de manera adecuada estas «ontologías», dentro del marco general del debate acerca de la naturaleza de la ontología. Es así que, en la primera sección haré un diagnostico de la ontología contemporánea; en la segunda proporcionaré algunas definiciones y caracterizaciones de las principales concepciones, en especial de las denominadas «ontologías aplicadas»; y en la tercera analizaré sí estas concepciones pueden ser consideradas diversos tipos de ontología o simplemente son diversos niveles de ontología. El marco de la discusión no se centrará en confrontar todas estas nociones, sino en describirlas y analizarlas para ofrecer un enfoque sobre el estado actual de la ontología y sus problemas. [EN] In recent decades there has been a renewed interest in some of the classic themes of ontology, from areas of knowledge external to philosophy; however, this ontological revival has «stimulated» a multiplicity and diversity of «ontological» theories and concepts that has resulted in a proliferation of «ontologies» and endless battles to determine what kind of «entities» study their respective «domains», which in turn are considered autonomous and independent, even of ontology itself. In this sense, the purpose of this work is to adequately characterize and represent these «ontologies», within the general framework of the debate about the nature of ontology. Thus, in the first section I will make a diagnosis of contemporary ontology; in the second I will provide some definitions and characterizations of the main concepts, especially the so-called «applied ontologies»; and in the third I will analyze whether these concepts can be considered different types of ontology or simply are different levels of ontology. The framework of the discussion will not center on confronting all these notions, but to describe and analyze them to provide a focus on the current state of ontology and its problems. (shrink)

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

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

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 paper I present an overview of the doctrine known as Positive Aesthetics regarding aesthetic judgements about nature. According to this view, all pristine nature is always beautiful and, generally, although not necessarily, human intervention tends to introduce ugliness in nature. One of the strong practical motivations behind this claim is an attempt to ground our reasons to preserve natural environments in aesthetic reasons. Positive Aesthetics has been defended within contrary approaches to nature appreciation such as the cognitivists and (...) the anti-cognitivist. Recently, the possibility of real ugliness in nature has been defended; at the same time, it is argued that the presence of ugly items in nature does not lead necessarily to the idea that they are not aesthetically valuable. Hence, natural ugliness can be a reason to preserve nature. In this sense, the denial of the Positive Aesthetics claim is shown to be compatible with the appeal to aesthetic negative qualities as a source of reasons for preserving natural environments. (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’s constitutive of classical theism that there is a necessarily existent personal god who is also the creator of the universe, where the latter claim includes at least the following three theses: (i) God is wholly distinct from the natural world; (ii) God is the originating or sustaining cause of the natural world; and (iii) God created the natural world ex nihilo, i.e., without the use of pre-existing materials. Call this tripartite component of classical theism the classical view of creation. (...) In this paper, I offer a new argument against classical theism. In particular, I argue that creation ex nihilo is prima facie impossible, and that since the doctrine of creation ex nihilo is constitutive of classical theism, classical theism is false. (shrink)

Scholarly dissatisfaction with Aristotle’s fallacy of accident has traditionally focused on his examples, whose compatibility with the fallacy’s definition has been doubted time and again. Besides a unified account of the fallacy of accident itself, the paper provides a formalized analysis of its several examples in Aristotle’s Sophistici elenchi. The most problematic instances are dealt with by means of an internal reconstruction of their features as conveyed by Aristotle’s text and an extensive survey of their interpretation in the Byzantine and (...) Latin exegetical tradition. Carefully handled a doxographical approach, as opposed to rapid results oriented practices, proves to be most effective in that it supplies both useful albeit ordinarily overlooked insights and a comprehensive framework of reference for further investigations. (shrink)

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

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

It is standard in set theory to assume that Cantor's Theorem establishes that the continuum is an uncountable set. A challenge for this position comes from the observation that through forcing one can collapse any cardinal to the countable and that the continuum can be made arbitrarily large. In this paper, we present a different take on the relationship between Cantor's Theorem and extensions of universes, arguing that they can be seen as showing that every set is countable and that (...) the continuum is a proper class. We examine several principles based on maximality considerations in this framework, and show how some (namely Ordinal Inner Model Hypotheses) enable us to incorporate standard set theories (including ZFC with large cardinals added). We conclude that the systems considered raise questions concerning the foundational purposes of set theory. (shrink)

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

What does it mean to say that some features, such as gender, race and sexual orientation, are socially constructed? Many scholars claim that social constructionism about a kind is a version of realism about that kind, according to which the corresponding kind is a social construction, that it, it is constituted by social factors and practices. Social constructionism, then, is a version of realism about a kind that asserts that the kind is real, and puts forward a particular view about (...) the nature of the kind, namely, that it is constituted by social factors and practices. Social constructivists about human kinds such as gender, race and sexual orientation often make an additional claim, namely, that these kinds are social constructions but they are typically believed to be biological kinds (that is, people are typically wrong about the nature of these kinds). Ron Mallon (2017) calls social constructions that are (falsely) taken to be biological kinds covert social constructions. This paper is about how we could have terms in our natural language that come to refer to covert social constructions. (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.

Marjorie Perloff is a distinguished commentator on the literature of this century, best known for her work on Futurism, one of the pre-First War international and inter-art avant garde movements. Radical Artifice takes on the avant garde since 1960, observed from the angle of the institutions of popular culture -- in particular television talk shows, and graphic advertisements. The project of the book is to respond to Charles Bernstein's decree: "There is no natural look or sound to a poem. Every (...) element is intended, chosen. That is what makes a thing a poem" (qtd. 35). "Why, Perloff asks, "is the natural now regarded with such suspicion?" (35). (shrink)

W. J. T. Mitchell's "Spatial Form in Literature: Toward a General Theory" (Critical Inquiry 6 [Spring 1980]: 539-67) raises some fundamental questions about the concept of form itself and makes some large claims for the centrality of spatial form not only in modern criticism but in our entire culture. I wish to address a few of the questions raised by his discussion. First, Mitchell posits an identity between spatial form and "synchronic structural models" as if all explanatory models abstracted from (...) temporal alteration were necessarily spatial. (shrink)

My title is derived from Heidegger's 1936-37 lectures, The Will to Power as Art, and my discussion is keyed to two of the Nietzschean remarks on art which Heidegger discusses. The first is: "The phenomenon 'artist' is still the most perspicuous" (Nietzsche 69), and the second is: "The will to semblance, to illusion, to deception, to becoming and change is deeper, more 'metaphysical,' than the will to truth, to reality, to Being" (Nietzsche 74). Heidegger reformulates them respectively as: "Art is (...) the most perspicuous and familiar configuration of will to power," and "Art is worth more than the truth" (75). I propose to tease out what these aphorisms imply for Heidegger's answer to the panel question: "What is a work of art?/Was ist ein Kunstwerk? (shrink)

Selected Bibiliography and Overview of Japanese Philosophy by reference to major Japanese Anthologies of Traditional and Modern Japanese Thought / Philosophy, listing a wide range of Japanese philosophers and thinkers from ancient times to the present.

In this paper, I try to show how Japanese practices of self-cultivation found in the so-called “ways” can be interpreted as embodied forms of “caring for oneself ” and, therefore, as part of a philosophical Lebenskunst or art of living. To this end, I refer to phenomenological accounts of the body as well as to a unique notion of practice found in the writings of Dōgen Kigen, a thirteenth-century Japanese Zen master. Central to this essay is a concern with embodying (...) kata or pre-defined patterns of movement and posture used in nearly all practices of self-cultivation in Japan. To approach this question, I look at the etymological roots of the term kata and its use in the writings of Zeami, the foremost representative of classical Noh theater, both as author and as actor. This is followed by an analysis of certain aspects of the embodiment of kata and the way it is described in Japanese literature. (shrink)

[ES] Nicolai Hartmann es uno de los filósofos más significativos en la filosofía contemporánea; empero, en la actualidad es poco conocido por nuestro mundo filosófico, posiblemente debido a que el esplendor de su filosofía coincidió con el naciente giro lingüístico y con el apogeo del existencialismo, los cuales, como se sabe, absorbieron gran parte de la atención y del quehacer filosófico de la época. Lo anterior, de una u otra manera ha dificultado el conocimiento objetivo de su obra. Es por (...) este motivo, que en este breve trabajo, me propongo presentar en forma esquemática una apostilla sobre su vida y su obra —y no una biografía completa—, que nos permita sentar las bases histórico-filosóficas para una primera aproximación a algunas de sus preocupaciones filosóficas. Esta aproximación se completa, en la parte final del trabajo, con una breve relación bibliográfica de algunos estudios introductorios a su vida y obra. [EN] Nicolai Hartmann is one of the most significant philosophers in contemporary philosophy; however, today is little known by our philosophical world, possibly because the splendor of his philosophy coincided with the nascent linguistic turn and the heyday of existentialism, which, as is known, absorbed much of the attention and philosophical work of the time. This, in one way or another has hindered the objective knowledge of his work. It is for this reason that in this short paper, I intend to present in schematic form a commentary on his life and his work —and not a full biography—, that allows us to lay the historical and philosophical foundations for a first approach to some of its philosophical concerns. This approach is completed at the end of the work, with a brief bibliographical note with some introductory studies to his life and work. (shrink)

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.

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)

Original title : 「歴史的身体」『西田幾多郎全集』[Nishida Kitarō Gesamtausgabe], 3. Auflage, Tokyo, Iwanami Shoten, Bd. 14: 265–92.

Relying on evidence from fifteen epigraphic collections and sixty-odd ancient sources as well as discussing a literature of over five hundred titles, the essay’s highly unorthodox conclusions are a case in point of the micrological ideal of achieving novelty on any given subject by way of transcribing and studying first-hand all relevant materials – edited and unedited alike. The paper’s ambition was to shed new light on one of the most intriguing analogies of the whole Aristotelian corpus, namely the comparison (...) between words and pebbles. A review of all material evidence and virtually all extant sources made short work of two related, albeit mutually exclusive, misconception about ancient reckoning boards and their workings: (1) the idea that – for all practical purposes – the abacus’ arrangement mirrored the decimal system, its columns and rows conveniently matching units, tens, hundreds, thousands, etc. (2) the idea that the inscriptions on several surviving counting boards were a nuisance to the extent that, being inconsistent to a fault with the decimal system itself, they made actual calculations harder than they already were (as opposed to making them easier, as one would expect). The paper demonstrated that the first assumption – the « decimal » bias – is simply mistaken and betrays little or no awareness of the epigraphic and archaeological evidence. The paper also demonstrated that the second assumption – the « abacus riddled with complications » bias – simply defeats the purpose of resorting to the abacus in the first place and betrays a poor understanding of its practical vocation which, most assuredly, was not to add to the very problem it was meant to solve. After bulldozing its way through both misunderstandings, the essay focused on the abacus most distinctive features, that is positionality (i.e. the abacus being a positional system through and through) and hybridity (i.e. the abacus’ place value system being monetary in nature and purpose, as opposed to it being abstract and homogeneous). The final result is an interpretation that moves away from the received views by showing that the prologue of the Sophistici elenchi offers no support to the notion that, when Aristotle referred to counters, he was leaning on a kinship of sorts – or any kinship, for that matter – between abstract calculation and speech. Once we turns the pebble’s simile on its head and set it back upon its feet (Aristotle’s pebble analogy is about pebbles, what else?), it becomes clear that it presupposed numeracy all right, but it was not about numeracy itself. Moreover its goal was not to explain why computational and linguistic symbolisms succeed, but to explain how they fail – failure being the whole point; in this particular instance, failure to detect and prevent abusive value shifts affecting words and counters alike. (shrink)

Quelque nombreuses et quelque influentes qu'elles soient par ailleurs, les vues d'Aristote sur le langage se caractérisent à la fois par leur hétérogénéité et par leur marginalité. Sans faire nulle part du langage et de la signification l'objet d'une investigation autonome et méthodique, Aristote multiplie les remarques et les digressions à leur sujet, que ce soit dans ses écrits d'éthique et de politique ou dans ses traités d'histoire et de philosophie naturelle, ou encore dans ses manuels de dialectique, de poétique (...) et de rhétorique. Face à l'abondance de ces matériaux et aux difficultés qu'ils présentent du fait de s'offrir au lecteur en ordre quelque peu dispersé, «Le langage. Lectures d'Aristote» fait le choix d'indexer l'étude du langage chez Aristote sur des passages précis du corpus en ne posant aux textes aristotéliciens d'intérêt linguistique que les questions auxquelles ces mêmes textes - tantôt pris isolément, tantôt mis en relation les uns avec les autres - apportent une réponse. (shrink)

Celebrated as the equal to the great philosophers of old, namely Plato and Aristotle, whom – as Cassiodorus put it – he taught to speak Latin better than they spoke Greek, Boethius aspired to fully emancipate Roman culture from its Greek models through translations and exegesis so faithful they would leave nothing more to be desired from the original. The essay focuses on Boethius philhellenism, without complexes insofar as it had little to do either with the mixed feelings of his (...) Roman predecessors or with the plundering agenda of his Christian contemporaries. Special attention is paid to the close relationship Boethius established between word for word translations and multi-layered commentaries which he thought of and – albeit partially – carried out as part of the same scholarly endeavour. Devoid of literary pretentions as well as free from aspirations to autonomy, Boethius literal rendering and scrupulous interpretation were meant to be completely self-sufficient. Together they stand out as both the most innovative and the most conservative features of his ambitious cultural project. -/- Célébré comme l’égal des grands philosophes du passé, auxquels il aurait appris à parler Latin mieux qu’ils ne parlaient Grec, Boèce a caressé le rêve d’une émancipation radicale de la culture romaine vis-à-vis des modèles grecs qu’il se proposait de traduire et interpréter assez fidèlement pour que la comparaison avec les sources ne soit plus nécessaire. De son effort de livrer un Aristote et un Platon latins à la hauteur des originaux grecs, nous étudions l’étroite solidarité qui relie la traduction mot-à-mot des textes grecs et la restitution scrupuleuse de leur sens. Cette double tâche, que Boèce a conçue et menée d’un seul tenant, nous est dès lors apparue comme le reflet d’un philhellénisme sans complexes, tout aussi éloigné des sentiments ambivalents que nourrissaient vis-à-vis des hellènes ses devanciers romains que des efforts visant à domestiquer l’héritage classique auxquels se livraient certains de ses contemporains de même confession que lui. Affranchis de tout rêve d’autonomie, les traductions et les commentaires de Boèce se conçoivent comme parfaitement autosuffisants. Ensemble ils constituent ce qu’il y a à la fois de franchement novateur et de profondément conservateur dans son projet de faire parler Latin les sources grecques. (shrink)

Few arguments from the past have stirred up as much interest as Aristotle’s “Third man” and not so many texts have received as much attention as its account in chapter 22 of the Sophistici elenchi. And yet, several issues about both remain highly controversial, starting from the very nature of the argument at stake and the exact signification of some of its features. The essay provides a close commentary of the text, dealing with its main difficulties and suggesting an overall (...) interpretation of Aristotle’s discussion of the “Third Man” argument. (shrink)

This bibliographical guide gives a comprehensive overview of the historiography of philosophy and thought in the Japanese language through an extensive and thematically organized collection of relevant literature. Comprising over one thousand entries, the bibliography shows not only how extensive and complex the Japanese tradition of philosophical and intellectual historiography is, but also how it might be structured and analyzed to make it accessible to a comparative and intercultural approach to the historiography of philosophy worldwide. The literature is categorized and (...) organized according to thematic focus areas such as geographical regions and continents, nations or peoples, religious traditions and philosophical teachings such as Buddhism, Islam, Shintō, and Confucianism, as well as disciplines such as ethics, aesthetics, and political thought. The bibliography is accompanied by an introduction outlining the research method as well as quantitative and qualitative approaches to analyzing the material, followed by a chronological overview of the historiography of philosophy and thought in the Japanese language and of the Japanese tradition of writing “world histories of philosophy.” As a first step towards a “history of the historiography of philosophy” in non-European languages, we hope that this guide will provide a useful tool for interculturally oriented scholarship aimed at a non-Eurocentric and diversified historiography of philosophy in a global perspective. (Open access, see link below.). (shrink)