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)

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)

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.

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)

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)

[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)

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)

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)

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)

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)

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.

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)

Y a-t-il des Idées et peut-on démontrer qu’elles existent ? Parmi les protagonistes anciens de la controverse qui a opposé partisans et adversaires des Idées, Aristote mérite une attention toute particulière. De fait, si – au moment où Aristote intervient dans le débat autour de l’hypothèse des Idées – ce débat a déjà une histoire, c’est avec lui que cette histoire atteint une maturité qui est à la fois d’ordre doctrinal et doxographique. De fait, non seulement Aristote est le premier (...) à avoir défini certaines au moins des propriétés de ce qui est et se dit en commun de plusieurs, mais encore a-t-il pris soin d’inscrire ces définitions dans la continuité de l’héritage socratique dont il s’est explicitement revendiqué tout en dénonçant sa dérive aux mains des successeurs de Socrate. L’objectif principal du cycle de conférences a été d’étudier les objections qu’Aristote a formulées à l’encontre des partisans des Idées en prenant comme fil conducteur la notion de substance que sa discussion des Formes platoniciennes tantôt présuppose, tantôt mobilise explicitement. Pour ce faire, nous avons procédé à une lecture détaillée d’un certain nombre de documents, tirés aussi bien de ses écrits d’école que des vestiges de ses traités perdus, où Aristote rejette la notion d’un universel substantiel (autant dire, en l’occurrence, séparé) et s’efforce de mettre à mal les arguments que ses partisans avançaient pour prouver son existence. (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)

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)

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)

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)

El presenta trabajo describe y caracteriza de manera breve y concisa lo que podría ser una ontología del arte. En la primera sección se presentan las dificultades actuales, así como las nociones y preguntas principales de la ontología. En la sección segunda, se bosquejan las definiciones y caracterizaciones actuales de la ontología, se hace especial hincapié, en la ontología aplicada. En la tercera, cuarta y quinta sección se caracteriza y configura lo que podría ser una ontología del arte, se evidencian (...) sus limitaciones así́ como sus perspectivas y trazabilidad para hacer viable dicha ontología; adicionalmente se abordan los aportes del realismo anglosajón a la cuestión. El propósito de esta caracterización es hacer evidente que es plausible dar un tratamiento integral al problema de la realidad y su configuración y desarrollo en los mundos regionales, como, el mundo del arte. (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.

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)

This article presents a reconstruction of the scientific policies established in Ecuador in the years between 1979 and 2007. The purpose is double: on the one hand, it seeks to understand the process of institutionalization of the System of Science and Technology, on the other hand analysing the achievements of three scientific policies established during this period. Hence, the reconstruction is split into three stages: from 1979 to 1994 when the first scientific policy was in place; from 1994 to 2004 (...) the second policy; and between 2005 and 2007 the third policy. To obtain the objective, some of the most relevant normative aspects during each stage are reviewed, as well as institutional statistical records related to Science and Technology. (shrink)

La noción de mundos posibles, sostiene que nuestro mundo es un mundo entre otros, un subconjunto de todas las cosas que existen. Esto implica aceptar que existen mundos estructuralmente equivalentes con sus propios lenguajes [formales], que entre sí no tienen ningún estatuto privilegiado, p.e., el mundo y lenguaje del arte o el mundo y lenguaje de la física; no obstante, la idea de aceptar otros mundos equivalentes como mundos posibles epistémica y ontológicamente legítimos para acceder y expresar lo cognoscible del (...) mundo no goza de gran aceptación. En este sentido, de entre las múltiples dimensiones de la noción de mundos posibles anotada, su dimensión lógica, es una de las más extendidas, ésta se entiende como un posible estado de cosas o un posible curso de eventos. Empero, esta concepción es la más restrictiva de la noción de mundos posibles, no sólo porque dicha noción transmuta en una especie de «técnica predictiva» que nos permite analizar y visualizar posibles escenarios de un estado de cosas o un curso de eventos, sino porque fundamentalmente, la noción de mundos posibles pierde gran parte de su potencia conceptual. Hablar de proposiciones como conjuntos de mundos posibles, no es un error, pero es limitar innecesariamente el alcance y campo de acción de la noción de mundos posibles. Si entendemos dicha noción en la versión primaría de Lewis [«Nuestro mundo actual es sólo un mundo entre otros»], sería plausible recuperar, entre otras, las dimensiones ontológica y epistémica de la noción de mundos posibles, y por ende la posibilidad objetiva de indagar en formas alternativas y legitimas de acceder y expresar lo cognoscible del mundo; en este sentido, en este trabajo me propongo: (1) retomar la noción primaria de mundos posibles de Lewis, para analizar y explicitar brevemente sus limitaciones, virtudes y requerimientos; (2) examinar las condiciones de posibilidad de un mundo; y, (3) sugerir los lineamientos epistémicos que deberían considerarse y explicitarse cuando se habla de y desde un mundo posible a la hora de expresar un enunciado. (shrink)

This collection highlights the new trend away from rationalism and toward empiricism in the epistemology of modality. Accordingly, the book represents a wide range of positions on the empirical sources of modal knowledge. Readers will find an introduction that surveys the field and provides a brief overview of the work, which progresses from empirically-sensitive rationalist accounts to fully empiricist accounts of modal knowledge. Early chapters focus on challenges to rationalist theories, essence-based approaches to modal knowledge, and the prospects for naturalizing (...) modal epistemology. The middle chapters present positive accounts that reject rationalism, but which stop short of advocating exclusive appeal to empirical sources of modal knowledge. The final chapters mark a transition toward exclusive reliance on empirical sources of modal knowledge. They explore ways of making similarity-based, analogical, inductive, and abductive arguments for modal claims based on empirical information. Modal epistemology is coming into its own as a field, and this book has the potential to anchor a new research agenda. (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)

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)

[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)

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)

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.

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)

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)

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)

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.

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)

[ES] Este trabajo, realiza una sumarísima revisión histórica, a través de algunas conjeturas epistemológicas, sobre las reflexiones filosóficas acerca del mundo del arte, su estatuto, desarrollo y «funcionamiento» con el propósito de allanar el camino para una ulterior descripción de la problemática acerca de la noción del mundo del arte. [EN] This writing makes a brief historical review, through some epistemological assumptions, on the philosophical reflections on the art world, its status, development and «functioning» in order to pave the way (...) for a further description of the problems about the notion of the art world. (shrink)

[ES] En este trabajo, ofreceré una reconstrucción sucinta de los argumentos sobre el significado de la noción de mundo del arte, así como de sus implicaciones en la ontología del arte. En primer lugar, describiré de manera esquemática los principios básicos de la noción de mundo del arte de Danto, y a partir de estos principios delinearé su influencia en la teoría institucional del arte de George Dickie. Sobre esta base, apoyado en la crítica al rol de la teoría en (...) estética de Morris Weitz, intentaré evidenciar las dificultades de lo que se ha dado en llamar la teoría institucional del arte al momento definir lo que es el arte. En la parte final del trabajo, presentaré algunas sugerencias que podrían tomarse en consideración al momento de abordar la relación entre el mundo del arte y la ontología del mundo del arte. [EN] In this paper, I will offer a succinct reconstruction of the arguments about the meaning of the notion of the world of art, as well as its implications in the ontology of art. First, I will outline the basic principles of Danto's notion of the art world, and from these principles I will outline its influence on George Dickie's institutional theory of art. On this basis, supported by Morris Weitz's critique to the role of the theory of aesthetics, I will try to highlight the difficulties of what has been called the institutional theory of art at the moment of defining what art is. In the final part of the paper, I will present some suggestions that could be taken into account when considering the relation between the world of art and the artworld ontology. (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)

[ES] En este trabajo propedéutico, a través de los propios textos de Kant, intentaré ofrecer una descripción equilibrada y una reconstrucción sucinta de los argumentos que ofrece Kant acerca de la posibilidad e imposibilidad de la metafísica. En primer lugar presentaré algunas críticas a la metafísica, luego visualizaré la noción kantiana de metafísica, así como sus razones y momentos constitutivos; y finalmente, analizaré que tipo de conocimiento es la metafísica y las características y naturaleza de esta para que sea viable (...) dicha «ciencia». Para realizar este cometido, asumiré la hipótesis de que la metafísica para Kant, en correspondencia con la resolucion de la tercera cuestion del conocimiento, es una ciencia que integra razón práctica y teórica en un sistema universal que busca la transcendencia. Si la metafísica tiene alguna posibilidad, ésta probablemente sería la vía. [EN] In this propaedeutic work, through Kant’s own texts, I will try to offer a balanced description and a succinct reconstruction of Kant’s arguments about the possibility and impossibility of Metaphysics. In the first place I will present some criticisms of Metaphysics, then I will visualize the Kantian notion of Metaphysics, as well as its constitutive reasons and moments; and finally, I will analyze what kind of knowledge is Metaphysics and the characteristics and nature of it, so that this «science» is viable. In order to carry out this task, I will assume the hypothesis that Kant’s Metaphysics, in correspondence with the resolution of the third question of knowledge, is a science that integrates practical and theoretical reason into a universal system that seeks transcendence. If Metaphysics has any chance, this would probably be the way. (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)

The tenth volume of the Frontiers of Japanese Philosophy focuses on the theme of “transition,” dealing with transitory and intermediary phenomena and practices such as translation, transmission, and transformation. Written in English, German and Japanese, the contributions explore a wide range of topics, crossing disciplinary borders between phenomenology, linguistics, feminism, epistemology, aesthetics, political history, martial arts, spiritual practice and anthropology, and bringing Japanese philosophy into cross-cultural dialogue with other philosophical traditions. As exercises in “thinking in transition,” the essays reveal novel (...) modes of doing philosophy as a way of boundary crossing that takes transition not only as an object of inquiry, but also as a method of philosophical practice itself. (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.

Aristotle, in his Metaphysics, not only tries to establish a relationship that is direct, coherent, inter-operational and "precise" between this science, its name as a science, and its object of study, but also begins an indignation that tries to set a science — materially adequate and formally correct — to study τὸ ὂν ᾗ ὂν. In order to complete this task, Aristotle does an in-focus strategy that consists on the diffusion of τὸ ὄν in its categories, that allows Aristotle the (...) possibility of formulate a science ἐπιστήμη to study τὸ ὂν ᾗ ὂν at the same time that supports the diffusion of τὸ ὄν in the "different categories or supreme genres" of τὸ ὄν. Due to this argumentation, Aristotle distinguishes the ἐπιστήμη σοφία of any other type of knowledge: the former is fundamentally an enquiry "about the first causes (πρῶτα αἴτια) and the principles (ἀρχὰς)". With this conception in mind, Aristotle was able to characterize several related forms of the ἐπιστήμη σοφία which, as a whole, eventually allow him to establish a science of the principles and causes "maximally universal and referred to…everything real", and in consequence, to "that that is, as long as something is". In this work, I will try to reconstruct such arguments, and offer some observations and conjectures referred to these notions that plausibly incline the scale in favor of an ontological reading of Aristotle’s Metaphysics, in order to contribute to clarify the confusion that exists between the aim of the discipline with the justification to establish the existence of its own object. (shrink)

There is some cost to you in voting. While it may be small for some, it is significant for others. Some people go to a great deal of effort just to vote. What return do they get for this effort? Zilch! A single vote can only impact an election when there is a tie, which has essentially zero chance of happening in a state or national election. The typical response to this is "Well, what if everyone did that?" Of course, (...) that would be a disaster. But we are not talking about everyone, we are talking about ONE individual. (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)

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)

Este volumen contiene los trabajos presentados en el I Simposio de Pensamiento Contemporáneo, celebrado en la Universidad Técnica Particular de Loja (UTPL) durante los días 23 y 24 de enero de 2019 y cuyo tema central fue las «Nuevas Tecnologías en la Educación» (SPC–NTE). Este Simposio tuvo como objetivo fomentar la interacción entre personas de diferentes formaciones e intereses en la discusión de problemas y soluciones relevantes para la educación en la era digital, a fin de intercambiar ideas sobre prácticas (...) e investigaciones que busquen comprender, mejorar y ampliar el uso de las nuevas tecnologías en los procesos de enseñanza–aprendizaje en los más diferentes contextos de enseñanza. 28 trabajos analizan abordan temáticas de especial interés para los futuros docentes, así como para quienes ya se desempeñan como tales en los diversos niveles educativos. Estos textos son instantáneas breves, ágiles y claras de las contribuciones teóricas o de experiencias pedagógicas que tratan sobre ambientes, softwares y hardwares para apoyar la enseñanza y aprendizaje; TIC en la educación universitaria; técnicas y estrategias lúdicas en educación; experiencias pedagógicas con las TIC y humanidades digitales en la educación. (shrink)

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)

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)

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)