Agents know some but not all logical consequences of what they know. Agents seem to be neither logically omniscient nor logically incompetent. Yet finding an intermediate standard of minimal rationality has proven difficult. In this paper, I take suggestions found in the literature (Lewis, 1988; Hawke, Özgün and Berto, 2020; Plebani and Spolaore, 2021) and join the forces of subject matter and impossible worlds approaches to devise a new solution to this quandary. I do so by combining a space of (...) FDE worlds (Berto and Jago, 2019) with a Lewisian (1988) understanding of subject matters as partitions. By doing so, I show how subject matters impose some order in the anarchic space of FDE worlds, while the worlds allow for distinctions between contents which would not otherwise be available. Combining the two approaches, then, brings us closer to the desired closure principles for knowledge of minimally rational agents. (shrink)

Agents know some but not all logical consequences of what they know. Agents seem to be neither logically omniscient nor logically incompetent. Yet finding an intermediate standard of minimal rationality has proven difficult. In this paper, I take suggestions found in the literature (Lewis, 1988; Hawke, Özgün and Berto, 2020; Plebani and Spolaore, 2021) and join the forces of subject matter and impossible worlds approaches to devise a new solution to this quandary. I do so by combining a space of (...) FDE worlds (Berto and Jago, 2019) with a Lewisian (1988) understanding of subject matters as partitions. By doing so, I show how subject matters impose some order in the anarchic space of FDE worlds, while the worlds allow for distinctions between contents which would not otherwise be available. Combining the two approaches, then, brings us closer to the desired closure principles for knowledge of minimally rational agents. (shrink)

The reward system of science is the priority rule. The first scientist making a new discovery is rewarded with prestige, while second runners get little or nothing. Michael Strevens, following Philip Kitcher, defends this reward system, arguing that it incentivizes an efficient division of cognitive labor. I argue that this assessment depends on strong implicit assumptions about the replicability of findings. I question these assumptions on the basis of metascientific evidence and argue that the priority rule systematically discourages replication. My (...) analysis leads us to qualify Kitcher and Strevens’s contention that a priority-based reward system is normatively desirable for science. (shrink)

This research examined the management of financial and non-financial resources by Calabar Metropolis’ public secondary school principals in relation to the fulfillment of institutional goals. Null hypotheses were developed based on the two specific objectives guiding the study. The study used the ex-post facto research design under the quantitative research framework. A census approach was adopted in enumerating all the 69 school managers (24 principals and 45 vice principals) in Calabar Metropolis, Nigeria. A validated questionnaire, with a reliability index of (...) .90, was used for data collection. It was shown that there is a considerable association between the management of financial resources by school leaders and the fulfillment of institutional goals. A significant relationship was also established between principals’ management of non-financial resources (such as school libraries, school records and human resources) and the fulfillment of institutional goals in secondary schools. It is argued that to fulfil educational goals, financial and non-financial resources’ management in public secondary schools are critical. Policy and theoretical implications for successful educational management were discussed in light of this result. (shrink)

Some metaphysicians believe that metaphysical modality is explainable by the essences of objects. In §II, I spell out the definitional view of essence, and in §III, a working notion of metaphysical explanation. Then, in §IV, I consider and reject five natural ways to explain necessity by essence: in terms of the principle that essential properties can't change, in terms of the supposed obviousness of the necessity of essential truth, in terms of the logical necessity of definitions, in terms of Fine's (...) logic of essence, and in terms of the theory of real definitions. I will conclude that the present evidence favours rejecting the hypothesis that modality is explainable by essence. (shrink)

I present a discussion of some issues in the ontology of spacetime. After a characterisation of the controversies among relationists, substantivalists, eternalists, and presentists, I offer a new argument for rejecting presentism, the doctrine that only present objects exist. Then, I outline and defend a form of spacetime realism that I call event substantivalism. I propose an ontological theory for the emergence of spacetime from more basic entities. Finally, I argue that a relational theory of pre-geometric entities can give rise (...) to substantival spacetime in such a way that relationism and substantivalism are not necessarily opposed positions, but rather complementary. In an appendix I give axiomatic formulations of my ontological views. (shrink)

Black holes are arguably the most extraordinary physical objects we know in the universe. Despite our thorough knowledge of black hole dynamics and our ability to solve Einstein’s equations in situations of ever increasing complexity, the deeper implications of the very existence of black holes for our understanding of space, time, causality, information, and many other things remain poorly understood. In this paper I survey some of these problems. If something is going to be clear from my presentation, I hope (...) it will be that around black holes science and metaphysics become more interwoven than anywhere else in the universe. (shrink)

Black holes are extremely relativistic objects. Physical processes around them occur in a regime where the gravitational field is extremely intense. Under such conditions, our representations of space, time, gravity, and thermodynamics are pushed to their limits. In such a situation philosophical issues naturally arise. In this chapter I review some philosophical questions related to black holes. In particular, the relevance of black holes for the metaphysical dispute between presentists and eternalists, the origin of the second law of thermadynamics and (...) its relation to black holes, the problem of information, black holes and hypercomputing, the nature of determinsim, and the breakdown of predictability in black hole space-times. I maintain that black hole physics can be used to illuminate some important problems in the border between science and philosophy, either epistemology and ontology. (shrink)

I present a formal ontological theory where the basic building blocks of the world can be either things or events. In any case, the result is a Parmenidean worldview where change is not a global property. What we understand by change manifests as asymmetries in the pattern of the world-lines that constitute 4-dimensional existents. I maintain that such a view is in accord with current scientific knowledge.

On a highly influential way to think of modality, that I call ‘relationalism’, the modality of a state is explained by its being composed of properties, and these properties being related by a higher-order and primitively modal relation. Examples of relationalism are the Dretske-Tooley-Armstrong account of natural necessity, many dispositional essentialist views, and Wang’s incompatibility primitivism. I argue that relationalism faces four difficulties: that the selection between modal relations is arbitrary, that the modal relation cannot belong to any logical order, (...) that to explain how the modal relation can relate properties of different adicities additional ideological complexity has to be introduced, and that not all modal constraints are relational. From the discussion, I will extract desiderata for a successor theory of modality. (shrink)

A supertask consists in the performance of an infinite number of actions in a finite time. I show that any attempt to carry out a supertask will produce a divergence of the curvature of spacetime, resulting in the formation of a black hole. I maintain that supertaks, contrarily to a popular view among philosophers, are physically impossible. Supertasks, literally, collapse under their own weight.

I argue that there are no physical singularities in space–time. Singular space–time models do not belong to the ontology of the world, because of a simple reason: they are concepts, defective solutions of Einstein’s field equations. I discuss the actual implication of the so-called singularity theorems. In remarking the confusion and fog that emerge from the reification of singularities I hope to contribute to a better understanding of the possibilities and limits of the theory of general relativity.

The Kalam Cosmological Argument is perhaps the most solid and widely discussed argument for a caused creation of the universe. The usual objections to the argument mainly focus on the second premise. In this paper we discuss the dependency of the first premise on the topological structure of the space-time manifold adopted for the underlying cosmological model. It is shown that in chronology-violating space-times the first premise can also be violated. The chronology-violation, in turn, requires a massive violation of the (...) so-called energy conditions which might have observational effects that are briefly discussed here. Hence, astronomical observations could be relevant for the validity of the metaphysical argument. In this sense, it is possible to talk of “observational theology”. (shrink)

There has been much debate recently on the question whether essence can explain modality. Here, I examine two routes to an essentialist account of modality. The first is Hale's argument for the necessity of essence, which I will argue is — notwithstanding recent attempted defences of it — invalid by its very structure. The second is the proposal that it is essential to essential truth that it is necessary. After offering three possible versions of the view, I will argue that (...) each fails to provide a metaphysical explanation of necessity in terms of essence. (shrink)

This is the introduction to the special issue of Crítica on the metaphysics of physics, featuring papers by Valia Allori, Tim Maudlin and Gustavo Esteban Romero.

This brief review of Mario Bunge’s research on physics begins with an analysis of his masterpiece Foundations of Physics, and then it discusses his other contributions to the philosophy of physics. Following that is a summary of his more recent reactions to scientific discoveries in physics and a discussion of his position about non-locality in quantum mechanics, as well as his changing opinions on the nature of spacetime. The paper ends with a brief assessment of Bunge’s legacy concerning the foundations (...) of physics. (shrink)

La filosofía científica es filosofía informada por la ciencia, que usa herramientas exactas como la lógica y la matemática, y proporciona a la actividad científica de un marco donde dirimir las cuestiones más generales sobre la naturaleza, el lenguaje que usamos para describirla, y el conocimiento que de ella obtenemos. Muchas teorías de la filosofía científica pueden ser contrastadas y evaluadas utilizando evidencia científica. En este artículo me concentro en caracterizar a la filosofía científica y en discutir los límites de (...) la ciencia. (shrink)

Transformar el modo de vida individual es necesario para abordar la crisis ecosocial, y resulta perentorio que las políticas comprometidas con su resolución promocionen una capacidad individual de acción ecosocial. Sin embargo, parece que cierta brecha motivacional está obstaculizando la transformación del modo de vida individual. A fin de dar respuesta a esta brecha, ensayamos una mixtura del enfoque de las capacidades con las teorías de Hartmut Rosa. Argumentamos que la resonancia natural funge de factor personal de conversión necesario, si (...) bien no suficiente, para la capacidad de acción ecosocial; y que una política que promocione la resonancia natural se adecuaría también a los requisitos impuestos al desarrollo humano tanto por el enfoque de las capacidades como por la sostenibilidad. (shrink)

This essay discusses the idea that trust is a pre-rational, other-oriented emotion and it is constitutive of friendship practices regardless of the type of friendship. In particular, what we call ‘social friendship’ refers to a distinctive set of loose but lasting and cohesive bonds both among citizens within society (horizontal dimension) and between them and the state (vertical dimension), triggering solidarity and altruism. The other-oriented emotion of trust underpinning these social bonds–social friendship–in turn, is necessary for social justice to be (...) supported, legitimized, and furthermore demanded by society. (shrink)

This article considers friendship as a channel for education and as one of its objectives, as it is a necessary ingredient for a fulfilled life. This requires an initial study of interpersonal relationships in the postmodern context, considering their opportunities and risks. Our aim is to draw a topography of these relationships by analysing texts by major thinkers of the last four decades. The result of this analysis is the core of the article, namely, that there are four categories which (...) seem to give a proper account of the characteristics of interpersonal relationships in postmodernity and are relevant in education: 1) the questioning of the individual; 2) the appearance of the internet; 3) the recoveryof emotions; and, finally; 4) the extension of the feminine space. As a conclusion, they may all be said to have an ambivalent character that requires central issues in education to be reconsidered: the awareness and emotional regulation; the new constitution of identity and intimacy on the internet; education for male-female relationships, which now exist outside the sexual sphere, and preventing violence in these relationships; as well as how to educate for cooperation in an individualistic society. (shrink)

The idea of a moving present or ‘now’ seems to form part of our most basic beliefs about reality. Such a present, however, is not reflected in any of our theories of the physical world. I show in this article that presentism, the doctrine that only what is present exists, is in conflict with modern relativistic cosmology and recent advances in neurosciences. I argue for a tenseless view of time, where what we call ‘the present’ is just an emergent secondary (...) quality arising from the interaction of perceiving self-conscious individuals with their environment. I maintain that there is no flow of time, but just an ordered system of events. (shrink)

Democratization process has become the global demand of the present century. The Millennium Development Goal (MDG) gave credence to this development. Nigeria and South Africa have had checkered history of dictatorship under military rule and obnoxious apartheid policy respectively. Both countries embraced the current wave in the 1990s. The exploration of this development is our central focus. To do this, the paper examined the following: the relationship between type of electoral system and the conduct of elections in Nigeria and South (...) Africa; and the efficacy of majoritarian and proportional representation systems as applied in both countries. Our findings indicated that majoritarian system accounted for electoral irregularities while proportional representation contributed to wide acceptance of polls. The data were generated from the secondary source. We recommended the adoption of the proportional electoral system as practiced in South Africa and absolute constitutionalism for both countries so as to engender the principles of rule of law. (shrink)

I discuss the ontological assumptions and implications of General Relativity. I maintain that General Relativity is a theory about gravitational fields, not about space-time. The latter is a more basic ontological category, that emerges from physical relations among all existents. I also argue that there are no physical singularities in space-time. Singular space-time models do not belong to the ontology of the world: they are not things but concepts, i.e. defective solutions of Einstein’s field equations. I briefly discuss the actual (...) implication of the so-called singularity theorems in General Relativity and some problems related to ontological assumptions of Quantum Gravity. (shrink)

It is a remarkable fact that all processes occurring in the observable universe are irre- versible, whereas the equations through which the fundamental laws of physics are formu- lated are invariant under time reversal. The emergence of irreversibility from the funda- mental laws has been a topic of consideration by physicists, astronomers and philosophers since Boltzmann's formulation of his famous \H" theorem. In this paper we shall discuss some aspects of this problem and its connection with the dynamics of space-time, (...) within the framework of modern cosmology. We conclude that the existence of cosmological horizons allows a coupling of the global state of the universe with the local events deter- mined through electromagnetic processes. (shrink)

I offer a theory of art that is based on science. I maintain that, as any other human activity, art can be studied with the tools of science. This does not mean that art is scientific, but aesthetics, the theory of art, can be formulated in accord with our scientific knowledge. I present elucidations of the concepts of aesthetic experience, art, work of art, artistic movement, and I discuss the ontological status of artworks from the point of view of scientific (...) philosophy. (shrink)

I present a condensed exposé of systemic materialism, a synthesis of materialism and systemism originally proposed by Mario Bunge. Matter is identified with mutability of propertied particulars, and a concrete or material system is defined as an object with composition, structure, mechanism, and environment. I review different aspects of this ontology, and discuss some of its implications for epistemology, ethics, and aesthetics. I also try to identify some problems of this view and offer some ways to overcome the difficulties. I (...) conclude that systemic materialism is a promising philosophical project still in the making. (shrink)

Cuento ganador en la categoría "Mini ficción" de la compilación "El covid no es un cuento".

En este artículo discuto cómo es que la idea intuitiva de que las cosas podrían cambiar, combinada con principios excesivamente plausibles, nos lleva a la paradoja de Chisholm. Arguyo que la mejor respuesta a esta paradoja –pues efectúa la menor mutilación a nuestros principios teóricos y asunciones intuitivas– es la postura esencialista. Primero expongo algunas motivaciones para hacer una teoría metafísica que explique la modalidad de re. Luego reviso los principios a los que estaremos regresando en el curso del artículo. (...) Entonces muestro cómo ellos, conjuntamente, implican la paradoja de Chisholm. Después reviso las posibles fuentes de esta paradoja, rechazando varias salidas posibles. Argumento que la fuente de la paradoja está en que nuestros principios teóricos son demasiado liberales, y que la opción esencialista subsana este defecto. (shrink)

The ontology behind quantum mechanics has been the subject of endless debate since the theory was formulated some 100 years ago. It has been suggested, at one time or another, that the objects described by the theory may be individual particles, waves, fields, ensembles of particles, observers, and minds, among many other possibilities. I maintain that these disagreements are due in part to a lack of precision in the use of the theory’s various semantic designators. In particular, there is some (...) confusion about the role of representation, reference, and denotation in the theory. In this article, I first analyze the role of the semantic apparatus in physical theories in general and then discuss the corresponding ontological implications for quantum mechanics. Subsequently, I consider the extension of the theory to quantum fields and then analyze the semantic changes of the designators with their ontological consequences. In addition to the classical arguments to rule out a particle ontology in the case of non-relativistic quantum field theory, I show how the existence of black holes makes the proposal of a particle ontology in general spacetimes unfeasible. I conclude by proposing a provisional pluralistic ontology of fields and spacetime and discussing some prospects for possible future ontological economies. (shrink)

The concept of ideology is central to the understanding of the many political, economic, social, and cultural processes that have occurred in the last two centuries. And yet, what is the nature of the different ideologies remains a vague, open, and much disputed question. Many political, sociological, and ideological studies have been devoted to ideology. Very little, on the other hand, has been done from the philosophical field. And this despite the fact that there are undoubtedly many philosophical questions related (...) to ideology and its role in modern industrialized societies. Just a few examples of ideology-related philosophical questions suffice to prove the point: What objects do ideologies deal with? Are the ideologies testable? Are there true ideologies? Do they evolve? How are ideologies related to societies? Is the existence of ideologies inevitable in modern societies? What is the relation of ideology to science? Is science just another kind of ideology? Are we, as human beings, innately predisposed to believe in ideologies? Or, instead, ideologies proliferate through indoctrination and propaganda? Are ideologies necessarily harmful?...and much more. In this article I try to answer some of these questions from a philosophical point of view, taking a materialist approach. I begin by characterizing ideology as a complex, multi-layered concept. Then, I briefly discuss the material systems on which ideological movements operate, that is, societies and concrete human groups. I identify at least 11 different elements that seem to be present in most ideologies, and I compare these characteristics with those of contemporary science and technology. Although some superficial similarities can be identified, there are deep differences that make ideology completely different from science. The similarities, however, are stronger with technology. Ideologies continually evolve with technological advances, social changes, and even with mere fashion. The current fragmentation of ideologies caused by the widespread use of new technologies and social networks has given rise to new phenomena of ideological propagation which, in my opinion, are very dangerous, particularly for open societies. I discuss these processes, within the context of the nature vs nurture debate, along with the question of whether we can get rid of ideologies. (shrink)

Después de introducir el artículo (§1), repasaré los aspectos más generales y centrales de la literatura sobre la fundamentación (§2); esta tarea me parece valiosa ya que no existen revisiones generales y actualizadas en español sobre el tema. Después, argumentaré que la fundamentación no es una medida de complejidad física, y que, sin un vínculo necesario con la complejidad, quedan pocas razones para pensar que la fundamentación une a los diferentes estratos de la realidad física, que es una de las (...) motivaciones más importantes para introducir relaciones de dependencia (§3). (shrink)

It is common in psychiatry and other sciences to describe an individual or a type of individual in terms of its disposition to manifest specific effects in a particular range of circumstances. According to one understanding, dispositions are statistical regularities of an individual or type of individual in specific circumstances. According to another understanding, dispositions are properties of individuals in virtue of which such regularities hold. This entry considers a number of ways of making each of these senses of disposition (...) more precise while discussing a number of dangers lurking in careless use of the concept of a disposition. (shrink)

La representación científica del mundo se construye sobre un tejido de teorías en las cuales hay enunciados generales que representan leyes naturales. Estas leyes son patrones de sucesos regulares. Un presupuesto básico de la ciencia es que todo acontecimiento es legal: ocurre regido por leyes que son fijas. ¿Es compatible esa legalidad con la libertad de elección que creemos tener? ¿Cuáles son las implicaciones para la libertad política que debemos esperar en una sociedad organizada y racional? ¿Cuál es el rol (...) de la ética en todo esto? Trataré de responder a estas preguntas aquí, defendiendo la concepción de una sociedad abierta, democrática y plural, que maximice la libertad de elección y acción de las personas que la forman. (shrink)

A chapter of the book Elogio del Cientificismo.

En "Paraconsistencia y fundamentación de las matemáticas" se reformula un aspecto del programa formalista de Hilbert, problema clásico dentro del panorama de la filosofía de las matemáticas. Lo anterior se hace desde un enfoque no clásico de la lógica, particularmente desde LP de Priest. Finalizando el articulo se rescatan las virtudes de la reformulación de este problema clásico y se evalúa hasta qué punto puede ser posible hablar del programa formalista desde la luz de la aritmética inconsistente de Priest.

There are several types of truths. In this paper I focus on semantic truths, and within these on factual truths. These truths are attributed to statements. I review the theory of the truth proposed by Bunge and discuss some problems that it presents. I suggest that a theory of truth of factual statements should be complemented by a theory of relevance, and propose the basic tenets of it. Finally, I briefly discuss the nature of propositions and the problem of scientific (...) truth in the light of the presented semantic theory. (shrink)

I present a discussion of some open issues in the philosophy of space-time theories. Emphasis is put on the ontological nature of space and time, the relation between determinism and predictability, the origin of irreversible processes in an expanding Universe, and the compatibility of relativity and quantum mechanics. In particular, I argue for a Parmenidean view of time and change, I make clear the difference between ontological determinism and predictability, propose that the origin of the asymmetry observed in physical processes (...) is related to the existence of cosmological horizons, and present a non-local concept of causality that can accommodate both special relativity and quantum entanglement. (shrink)

En este artículo se presenta una caracterización del concepto de falacia, con énfasis en la llamada ‘falacia de apelación a lo natural’. Se explica el alcance de esta falacia, y su peligrosidad, en particular en el ámbito de las ciencias de la salud y de alimentos.

En este texto deseamos hacer una presentación global del pensamiento de Schelling a partir de su idea de absoluto en conexión con el concepto de Dios y la enigmática “B” que significa lo “real” en sus diferentes sistemas. Para ello mostramos las principales ideas de lo absoluto y cómo se articulan, de manera problemática, con lo real, lo efectivo y lo singular, conceptos diferentes pero entrelazados y resumidos en esa letra “B” que aparecerá en sus ecuaciones del absoluto.

I argued against relationalism with four objections. One of those was that, under reasonable assumptions, relationalism's modal relation needs to be what I called an `extra order' relation. I recently came to notice that the objection could have been posed with much less substantive assumptions. In particular, I recently noticed that order-dissonant predications are not required for the objection; therefore, noncumulativism is not relevant for my argument.

A nadie sorprende decir que lenguaje y dinero son sistemas simbólicos o sistemas de intercambio de información. Tampoco sorprende a nadie resaltar el hecho de que las computadores funcionan esencialmente con la versión más formalizada del lenguaje. Pero si hiciésemos las conexiones no opondríamos el lenguaje a la técnica, reservando la poesía para el primero y la técnica al segundo. El lenguaje posee un elemento estructural, formal, “maquínico” que le permite copiarse en toda una población. Éramos ya máquina antes de (...) inventar una. Pero este acontecimiento de producir una máquina fuera de nosotros, de darle energía a un “inconsciente” es un acto inédito. Si entendiéramos cómo es que el capitalismo contemporáneo se realiza a través de la virtualidad informática comenzaríamos a contemplar la posibilidad de que ahora sean los algoritmos y no la ambición subjetiva lo que producirá las nuevas burbujas inmobiliarias. O al menos entenderíamos que mientras más extendemos el mundo hacia regiones virtuales, el capital lo sigue para crear ahí nuevos nichos de mercado. Y viceversa, la expansión virtual del dinero exige la creación de nuevos programas, algoritmos, portales de inversión y de consumo. (shrink)

Este artículo ofrece una evaluación de la relevancia de los conceptos de biopolítica y biopoder en la obra de Michel Foucault. Un análisis exhaustivo de la obra de Foucault es esencial para una evaluación de los diversos aspectos del concepto de biopolítica. Esto permite que sea posible concluir que la biopolítica pueda considerarse fundamental en el interior del marco conceptual de Foucault.

The importance of education in boosting the manpower of an economy cannot be overemphasized. This critical sector has been bastardized, relegated and put in a dust bin position through paltry figures usually allocated to it by the Federal Government of Nigeria. This paper presents a holistic trend of budgetary activities in Nigeria with a particular focus on the allocation to the Education sector using times series approach from 2009-2018. Two research questions were answered using secondary data gathered from the Central (...) Bank of Nigeria's Statistical Bulletin, 2018. Collected data were analyzed using descriptive statistics, while the results of the analysis showed that, the total allocation to the education sector from 2009 – 2018 is N4,038,115,000,000. The results further revealed a difference of N 10,311,805,000,000 between UNESCO benchmark of 26% and the actual allocation to the education sector for the same time period. It was concluded that the total allocation made to the education sector within the time period of 2009-2018 is generally low, and below the UNESCO benchmark. Based on the findings, it was recommended amongst others that the Federal Government of Nigeria should adequately fund the educational sector by allocating at least 26% of her budget to the education sector as prescribed by UNESCO. (shrink)

Diariamente vemos noticias sobre políticos irresponsables que rechazan el consejo que los expertos basan en los modelos científicos, o nos encontramos con notas periodísticas que distorsionan los hechos o las teorías. En México, diariamente somos testigos —tanto que se ha vuelto un chiste recurrente— de la evidente incapacidad de la comunidad periodística para cubrir informes técnicos, así como de la dificultad que tienen muchos columnistas para comprender incluso los más básicos conceptos de la estadística. Además, muchas veces nos preguntamos por (...) qué los científicos y las organizaciones de salud parecen estar cambiando constantemente de opinión, contradiciéndose entre sí, o no terminan de ponerse de acuerdo. (shrink)

Las teorías que usamos para representar el mundo pueden ser extremadamente complejas. Abordan temas tales como electrones, campos cuánticos, estrellas de neutrones, materia oscura, redes neuronales, mercados económicos, la atmósfera y muchas otras entidades que suponemos existen en el universo. Al formular nuestras teorías, recurrimos a lenguajes exactos que nos permiten minimizar la vaguedad y expresarnos lo más precisa y cuantitativamente posible. Recurrimos a la matemática. Cuando formulamos nuestras teorías fácticas en lenguaje matemático, estas se refieren no solamente a objetos (...) que nosotros interpretamos como materiales, tales como partículas o personas, sino también a entidades más raras de un mundo abstracto: conjuntos, números, funciones, espacios algebraicos, variedades, topologías, y otras entidades similares. Estos objetos no son materiales en el sentido en que nosotros decimos que una manzana es material. Ellos no existen en el espacio-tiempo, no interactúan, no cambian o evolucionan. Sin embargo, allí están, profundamente arraigados en nuestras teorías más apreciadas acerca del mundo. (shrink)

Ensayo introductorio para mi traducción del influyente artículo "Essence and Modality" de Kit Fine.