Resumen: En la actualidad uno de los libros más usados para dar lógica elemental es el de Irving Copi y Carl Cohen (Introducción a la lógica, 2001), allí se presentan unas reglas para decidir la validez de los silogismos categóricos de forma estándar. Pero en tal texto ni en ninguno que nosotros conozcamos se ofrece una fundamentación de las mismas. Es decir, una demostración de que ellas son realmente una condición necesaria y suficiente de la validez de un silogismo categórico (...) de forma estándar, lo único que hemos leído es su motivación como condición necesaria. El objetivo de este trabajo es ofrecer una fundamentación de las mismas usando la noción de conjunto (o clase) y la técnica de diagramas de Venn, un concepto y una técnica que están expuestos en los principales textos de lógica elemental, incluyendo el referido anteriormente. -/- Abstract: Currently, one of the most widely used textbooks in elementary logic is the one by Irving Copi and Carl Cohen (Introduction to Logic, 2001). They offer rules for deciding the validity of standard categorical syllogisms. But neither that textbook, nor any other we know of, provides the foundations of these rules; that is to say, the demonstration that they are a necessary and sufficient condition for the validity of a standard categorical syllogism. We have only found motivations for the necessary condition. The main goal of this work is to provide a foundation of these rules using the notion of set as well as Venn diagrams, a concept and a technique exposed in the main textbooks of logic, including the aforementioned. (shrink)

The objective of this document is to present three introductory notes on set theory: The first note presents an overview of this discipline from its origins to the present, in the second note some considerations are made about the evaluation of reasoning applying the first-order Logic and Löwenheim's theorems, Church Indecidibility, Completeness and Incompleteness of Gödel, it is known that the axiomatic theories of most commonly used sets are written in a specific first-order language, that is, they are developed within (...) the framework of first-order logic, so this note is relevant; and the third note refers to the presence of mathematical platonism in the axioms of ZFC and in the axioms of "complete ordered field", it is known that the last axioms mentioned characterize (except isomorphism) the real number system and are currently used to develop the real Analysis in the context of set theory. It is hoped that this article will be of pedagogical utility for students interested in set theory and in the philosophy of mathematics (that are beginning in the subject). (shrink)

Sebastian Schmidt (Zürich) fragt in seinem Beitrag »Wie vernünftig sind Verschwörungstheoretiker?«, wie es um die Vernunft derjenigen steht, die einer Verschwörungstheorie über die Corona-Pandemie anhängen. Im Umgang mit Corona scheint sich zu bestätigen, was die Psychologie seit Jahrzehnten lehrt: Menschen unterliegen in ihrem Denken kognitiven Fehlern und Verzerrungen. Doch ist verschwörungstheoretisches Denken, das solche Fehler ebenfalls begeht, deshalb irrational? Schmidt warnt davor, einander zu leichtfertig als irrational zu betrachten, und verweist auf die wichtige Rolle, die intellektuelles Vertrauen in Wissensgemeinschaften (...) spielt. Am Beispiel des sogenannten Bestätigungsfehlers führt er aus, dass Menschen, die ihre Überzeugungen nicht fortwährend kritisch prüfen, in diesem Verhalten durchaus rational sein können. (shrink)

En el ámbito de la lógica matemática existe un problema sobre la relación lógica entre dos versiones débiles del Axioma de elección (AE) que no se ha podido resolver desde el año 2000 (aproximadamente). Tales versiones están relacionadas con ultrafiltros no principales y con Propiedades Ramsey (Bernstein, Polarizada, Subretículo, Ramsey, Ordinales flotantes, etc). La primera versión débil del AE es la siguiente (A): “Existen ultrafiltros no principales sobre el conjunto de los números naturales (ℕ)”. Y la segunda versión débil del (...) AE es la siguiente (B): “Existen ultraflitros sobre ℕ”. Se sabe que A implica B, pero se desconoce si B implica A. Di Prisco y Henle conjeturan en los artículos ([1], [2]) que esto no ocurre, es decir, conjeturan que B no implica A, en otras palabras, conjeturan que A es más fuerte estrictamente que B, que A es independiente de B, pero esto no se ha podido demostrar todavía aunque se ha intentado hacer desde hace aproximadamente 21 años. Una descripción detallada de este problema abierto puede encontrarse en esta ponencia (dictada en el marco del Día Mundial de la Lógica 14-01-2022) y en el artículo [3]. [1] C. Di Prisco y H. Henle. “Doughnuts, Floating Ordinals, Square Brackets, and Ultraflitters”. Journal of Symbolic Logic 65 (2000) 462-473. [2] C. Di Prisco y H. Henle. “Partitions of the reals and choice”. En “Models, algebras and proofs”. X. Caicedo y C.M. Montenegro. Eds. Lecture Notes in Pure and Appl. Math, 203, Marcel Dekker, 1999. [3] F. Galindo. “Tópicos de ultrafiltros”. Divulgaciones Matemáticas. Vol. 21, No 1-2, 2020. (shrink)

In having an experience one is aware of having it. Having an experience requires some form of access to one's own state, which distinguishes phenomenally conscious mental states from other kinds of mental states. Until very recently, Higher-Order (HO) theories were the only game in town aiming at offering a full-fledged account of this form of awareness within the analytical tradition. Independently of any objections that HO theories face, First/Same-Order (F/SO) theorists need to offer an account of such access to (...) become a plausible alternative. My aim in this paper is twofold. In the first place, I wish to widen the logical space of the discussion among theories of consciousness by offering a distinction, orthogonal to that between F/SO and HO theories, between what I will call 'Self-Involving' (SI) and 'Mental-State-Involving' (MSI) theories and argue in favor of the former one. In the second place, I will present the basics of a characterization of such a Self-Involving theory in Same-Order terms. (shrink)

This paper analyzes the concept of a spirituality without religion. I argue that spirituality is best understood as a specific attitude that a subject has towards the totality of existence, characterized by a certain emotional, evaluative and noetic quality. The spiritual attitude typically involves a shift in the way a subject interprets their relation to themselves and to the whole of reality. Understood this way, religious and non-religious spiritualities are varieties of the same core phenomenon. Religious beliefs are compatible with, (...) but not necessary for spiritual attitudes. (shrink)

What should we believe when epistemic and practical reasons pull in opposite directions? The traditional view states that there is something that we ought epistemically to believe and something that we ought practically to (cause ourselves to) believe, period. More recent accounts challenge this view, either by arguing that there is something that we ought simpliciter to believe, all epistemic and practical reasons considered (the weighing view), or by denying the normativity of epistemic reasons altogether (epistemic anti‐normativism). I argue against (...) both accounts and defend the traditional view. An agent can be blameworthy in doxastic dilemmas for complying with their practical but not their epistemic reasons. This reveals how epistemic reasons are normative: the concept of epistemic blame helps us track epistemic normativity. (shrink)

El objetivo de este artículo es presentar una demostración de un teorema clásico sobre álgebras booleanas y ordenes parciales de relevancia actual en teoría de conjuntos, como por ejemplo, para aplicaciones del método de construcción de modelos llamado “forcing” (con álgebras booleanas completas o con órdenes parciales). El teorema que se prueba es el siguiente: “Todo orden parcial se puede extender a una única álgebra booleana completa (salvo isomorfismo)”. Donde extender significa “sumergir densamente”. Tal demostración se realiza utilizando cortaduras de (...) Dedekind siguiendo el texto “Set Theory” de Jech, y otras ideas propias del autor de este artículo. Adicionalmente, se formulan algunas versiones débiles del axioma de elección relacionadas con las álgebras booleanas, las cuales son también de gran importancia para la investigación en teoría de conjuntos y teoría de modelos, pues estas son poderosas técnicas de construcción de modelos, como por ejemplo, el teorema de compacidad (permite construir modelos no estándar, etc) y el teorema del ultrafiltro, que permite construir ultraproductos (pueden ser usados para investigar problemas de cardinales grandes, etc). Se presentan algunas referencias de problemas abiertos sobre el tema. -/- The objective of this paper is to present a demonstration of a classical theorem on boolean algebras and partial orders of current relevance in set theory, as for example, for applications of model construction method called forcing" (with boolean algebras complete or with partial orders). The theorem to be proved is as follows: Any partial order can be extended to a single complete boolean algebra (up to isomorphism)". Where to extend means embed densely". Such a demonstration is done using Dedekind's cuts following the text Set Theory" of Jech, and other ideas of the author of this article. In addition, some weak versions of the axiom of choice related to boolean algebras are formulated, which are also of great importance for the research in set theory and model theory, since this are powerful model construction techniques, such as the compactness theorem (allows the construction of non-standard models, etc.) and the ultralter theorem, which allows the construction of ultraproducts (can be used to investigate problems of large cardinals, etc). Some references of open problems on the subject are presented. (shrink)

Saying that x is ineffable seems to be paradoxical – either I cannot say anything about x, not even that it is ineffable – or I can say that it is ineffable, but then I can say something and it is not ineffable. In this article, I discuss Alston’s version of the paradox and a solution proposed by Hick which employs the concept of formal and substantial predicates. I reject Hick’s proposal and develop a different account based on some passages (...) from Pseudo-Dionysius’ Mystica Theologia. ‘God is ineffable’ is a metalinguistic statement concerning propositions about God: not all propositions about God are expressible in a human language. (shrink)

It is often argued that there are no practical reasons for belief because we could not believe for such reasons. A recent reply by pragmatists is that we can often believe for practical reasons because we can often cause our beliefs for practical reasons. This paper reveals the limits of this recently popular strategy for defending pragmatism, and thereby reshapes the dialectical options for pragmatism. I argue that the strategy presupposes that reasons for being in non-intentional states are not reducible (...) to reasons to act. Pragmatists who want to preserve a motivational constraint on reasons therefore have exactly two options: either arguing that there are irreducible reasons for being in non-intentional states ; or arguing that we can believe directly for practical reasons. I argue that the prospects for the former option are dim because irreducible reasons to be in states are hard to square with the motivational constraint on reasons. Returning to the more traditional route of arguing for pragmatism by defending a version of doxastic voluntarism therefore seems to be the more promising way for pragmatists to go. (shrink)

ABSTRACT The difference between perception and cognition seems introspectively obvious in many cases. Perceiving and thinking have also been assigned quite different roles, in epistemology, in theories of reference and of mental content, in philosophy of psychology, and elsewhere. Yet what is the nature of the distinction? In what way, or ways, do perception and cognition differ? The paper reviews recent work on these questions. Four main respects in which perception and cognition have been held to differ are discussed. First, (...) their phenomenal character, such as the often-remarked vivacity or immediacy of perception. Second, the way in which they represent the world, e.g. the non-propositional nature of the contents, or non-discursive character of the vehicles, that have been held to characterise perceptual representation. Third, their place in cognitive architecture, i.e., roughly, in the information-flow of the mind, such as their alleged (non-)modularity. Fourth, their mind-world relations, e.g. the way in which perceptions seem to be tightly causally linked with distal or proximal stimuli. Against this background, we distinguish some main options for an account of the perception/cognition distinction, in particular concerning whether there is one, several, or no interesting and principled distinction(s) to be drawn here. (shrink)

This paper argues for the normative significance of attention. Attention plays an important role when describing an individual’s mind and agency, and in explaining many central facts about that individual. In addition, many in the public want answers and guidance with regard to normative questions about attention. Given that attention is both descriptively central and the public cares about normative guidance with regard to it, attention should be central also in normative philosophy. We need an ethics of attention: a field (...) of study of which normative pressures, if any, govern attention. Like the ethics of belief, the ethics of attention will connect those normative questions to issues regarding the nature of attention, i.e. to what is subject to such normative pressures. Philosophers should develop an ethics of attention that helps to provide normative guidance and that is commensurate in its richness to the descriptive significance of attention. The second half of the paper sketches a framework that may help us to get started at developing the ethics of attention. (shrink)

Meta-ethical expressivism was traditionally seen as the view that normative judgements are not beliefs. Recently, quasi-realists have argued, via a minimalist conception of “belief”, that expressivism is fully compatible with normative judgements being beliefs. This maneuver is successful, however, only if quasi-realists have really offered an expressivist-friendly account of belief that captures all platitudes characterizing belief. But, quasi-realists’ account has a crucial gap, namely how to account for the propositional contents of normative beliefs in an expressivist-friendly manner. In particular, quasi-realists (...) haven’t yet developed their preferred option, a “minimalist” or “deflationist” account of such contents. This paper aims to close that gap. I argue that expressivists who accepts conceptual role semantics and use an account of that-clauses in their use in belief-attributions based on Wilfrid Sellars’ work can give a deflationary account of the contents of beliefs that is compatible with normative judgements being beliefs, even if expressivism is true. (shrink)

El objetivo principal de este artículo es presentar la demostración directa del Teorema de compacidad de la Lógica de primer orden (Gama tiene un modelo si y sólo si cada subconjunto finito de Gama tiene un modelo) que se realiza utilizando el Método de construcción de modelos llamado "Ultraproductos" que, a su vez, usa "Ultrafiltros". Actualmente es más común demostrar el Teorema de compacidad como un corolario del Teorema de completitud de Gödel y usar el método de reducción al absurdo (...) para probarlo. Sin embargo, vale la pena estudiar también esta prueba directa que usa Ultraproductos porque dicha técnica tiene importantes aplicaciones en investigaciones contemporáneas de matemáticas, por ejemplo en la Teoría de conjuntos y en el Análisis. Al final del artículo se realiza un breve comentario sobre Compacidad, Ultraproductos, Cardinales grandes y Modelos no estándar. (shrink)

Conceptual engineering is the enterprise of evaluating and improving our representational devices. But how should we conduct this enterprise? One increasingly popular answer to this question proposes that conceptual engineering should proceed in terms of the functions of our representational devices. In this paper, we argue that the best way of understanding this suggestion is in terms of normative functions, where normative functions of concepts are, roughly, things that they allow us to do that matter normatively (for example, things in (...) virtue of which we have normative reasons to have these concepts). Not only does this introduce a novel view about functions to the literature. This proposal also fits more naturally than the alternatives with conceptual engineering as a normative enterprise, and it allows functions to play all of the explanatory roles assigned to them in the conceptual engineering literature. Our discussion of the explanatory advantages of normative functions also advances the understanding of the ways in which concepts can be authoritative, what this means for conceptual engineering, and highlights the importance of political philosophy for thinking about conceptual engineering in practice. Furthermore, the paper explicates what kind of role considerations about function can and should actually play in conceptual engineering. (shrink)

Cognitive theories claim, whereas non-cognitive theories deny, that cognitive access is constitutive of phenomenology. Evidence in favor of non-cognitive theories has recently been collected by Block and is based on the high capacity of participants in partial-report experiments compared to the capacity of the working memory. In reply, defenders of cognitive theories have searched for alternative interpretations of such results that make visual awareness compatible with the capacity of the working memory; and so the conclusions of such experiments remain controversial. (...) Instead of entering the debate between alternative interpretations of partial-report experiments, this paper offers an alternative line of research that could settle the discussion between cognitive and non-cognitive theories of consciousness. Here I relate the neural correlates of cognitive access to empirical research into the neurophysiology of dreams; cognitive access seems to depend on the activity of the dorsolateral prefrontal cortex. However, that area is strongly deactivated during sleep; a period when we entertain conscious experiences: dreams. This approach also avoids the classic objection that consciousness should be inextricably tied to reportability or it would fall outside the realm of science. (shrink)

It has been argued that rationality consists in responding correctly to reasons. Recent defenses of the normativity of rationality assume that this implies that we always ought to be rational. However, this follows only if the reasons rationality requires us to correctly respond to are normative reasons. Recent meta-epistemological contributions have questioned whether epistemic reasons are normative. If they were right, then epistemic rationality wouldn’t provide us with normative reasons independently of wrong-kind reasons to be epistemically rational. This paper spells (...) out this neglected challenge for the normativity of epistemic rationality by connecting the two bodies of literature. Moreover, it generalizes this challenge to the rationality of desire, intention, and emotion. The upshot is that we can only answer the normative question about rationality if we debate about blame and accountability for holding different kinds of irrational attitudes, as well as about the sources of mental normativity. (shrink)

Ultrafilters are very important mathematical objects in mathematical research [6, 22, 23]. There are a wide variety of classical theorems in various branches of mathematics where ultrafilters are applied in their proof, and other classical theorems that deal directly with ultrafilters. The objective of this article is to contribute (in a divulgative way) to ultrafilter research by describing the demonstrations of some such theorems related (uniquely or in combination) to topology, Measure Theory, algebra, combinatorial infinite, set theory and first-order logic, (...) also formulating some updated open problems of set theory that refer to non-principal ultrafilters on N, the Mathias’s model and the Solovay’s model. -/- Resumen: Los ultrafiltros son objetos matemáticos muy importantes en la investigación matemática [6, 22, 23]. Existen una gran variedad de teoremas clásicos en diversas ramas de la matemática donde se aplican ultrafiltros en su demostración, y otros teoremas clásicos que tratan directamente sobre ultrafiltros. El objetivo de este artículo es contribuir (de una manera divulgativa) con la investigación sobre ultrafiltros describiendo las demostraciones de algunos de tales teoremas relacionados (de manera única o combinada) con topología, teoría de la medida, álgebra, combinatoria infinita, teoría de conjuntos y lógica de primer orden, formulando además algunos problemas abiertos actuales de la teoría de conjuntos que se refieren a ultrafiltros no principales sobre N, al Modelo de Mathias y al Modelo de Solovay. (shrink)

El estudio de los "cardinales grandes" es uno de los principales temas de investigación de la teoría de conjuntos y de la teoría de modelos que ha contribuido con el desarrollo de dichas disciplinas. Existe una gran variedad de tales cardinales, por ejemplo cardinales inaccesibles, débilmente compactos, Ramsey, medibles, supercompactos, etc. Tres valiosos teoremas clásicos sobre cardinales medibles son los siguientes: (i) compacidad débil, (ii) Si κ es un cardinal medible, entonces κ es un cardinal inaccesible y existen κ cardinales (...) inaccesibles menores que κ , y (iii) Si existe un cardinal medible, entonces el axioma de constructibilidad (V=L) es falso. El objetivo de este artículo es presentar una demostración de cada uno de estos tres teoremas en el contexto de la teoría de modelos usando ideas del texto de Chang y Keisler (Model Theory). Tales demostraciones tienen en común el uso del método de construcción de modelos llamado ultraproductos, de lógicas infinitarias o fragmentos de la lógica de segundo orden, y del axioma de elección. Cardinales grandes y/o ultraproductos son importantes en teoría de conjuntos, teoría de modelos, análisis matemático, teoría de la medida, probabilidades, topología, análisis funcional, física, teoría de números, finanzas, etc. (shrink)

Para matemáticos interesados en problemas de fundamentos, lógico-matemáticos y filósofos de la matemática, el axioma de elección es centro obligado de reflexión, pues ha sido considerado esencial en el debate dentro de las posiciones consideradas clásicas en filosofía de la matemática (intuicionismo, formalismo, logicismo, platonismo), pero también ha tenido una presencia fundamental para el desarrollo de la matemática y metamatemática contemporánea. Desde una posición que privilegia el quehacer matemático, nos proponemos mostrar los aportes que ha tenido el axioma en varias (...) áreas fundamentales de la matemática, su aplicación en la lógica de primer orden, así como una breve descripción de las pruebas de consistencia relativa debidas a Gödel y Cohen, las cuales establecieron su independencia del sistema axiomático Zermelo-Fraenkel (ZF). Con todo lo anterior mostraremos cómo el quehacer matemático contemporáneo se adscribe al platonismo matemático en los términos de Bernays y Ferreirós. Revisaremos también los argumentos de Zermelo y Cantor para permitir el uso de asunciones en la matemática, los cuales se acercan a los planteamientos de la investigación científica y esbozan relaciones con la filosofía de la práctica matemática. Finalmente, justificamos el uso del axioma de elección en la contemporaneidad, abogando por unas relaciones de equidad entre la matemática y la filosofía, presentando además su plena vigencia, a través de la referencia a algunos problemas abiertos en la actualidad que vinculan el axioma de elección con la teoría de Ramsey. (shrink)

En este artículo se presentan dos demostraciones del teorema de interpolación: Una para la lógica proposicional y otra para la lógica de primer orden. Ambas se realizan en el contexto de la teoría de modelos. El teorema de interpolación afirma que si A y B son fórmulas, donde A no es una contradicción, B no es válida, y B es una consecuencia lógica de A, entonces existe una fórmula C que esta escrita en el lenguaje común al de A y (...) de B, tal que C es una consecuencia lógica de A y B es una consecuencia lógica de C. El teorema de interpolación fue demostrado por primera vez para la lógica de primer orden por William Craig en 1957, y desde entonces se ha investigado la posibilidad de generalizarlo o aplicarlo. Dicho teorema tiene generalizaciones o aplicaciones en teoría de la demostración, teoría de modelos abstracta, ciencias de la computación, lógica modal, lógica intuicionista, etc. Se presentan ejemplos de aplicaciones o generalizaciones de la propiedad de interpolación relacionados con lógicas infinitarias, cuantificadores generalizados, segundo orden, no clásicas, abstractas, etc. También se ofrecen referencias de problemas abiertos sobre interpolación en el contexto de la teoría de modelos abstracta. (shrink)

En este artículo realizamos una reconstrucción del Programa original de Hilbert antes del surgimiento de los teoremas limitativos de la tercera década del siglo pasado. Para tal reconstrucción empezaremos por mostrar lo que Torretti llama los primeros titubeos formales de Hilbert, es decir, la defensa por el método axiomático como enfoque fundamentante. Seguidamente, mostraremos como estos titubeos formales se establecen como un verdadero programa de investigación lógico-matemático y como dentro de dicho programa la inquietud por la decidibilidad de los problemas (...) matemáticos y en específico la decidibilidad de la Lógica de primer orden cobra peso. Luego pasamos a analizar como la inquietud por la decibilidad toma lugar dentro del pensamiento filosófico-matemático de Hilbert presentándose como uno de los grandes problemas a los cuales la metamatemática debe encontrar una solución, esto lo hacemos mostrando un contraste con autores, como John von Neumann y Roberto Torretti, quienes de alguna u otra manera no interpretan el problema de la decidibilidad de la Lógica de primer orden como un problema de peso dentro del programa original de Hilbert. Finalmente argumentamos que el resultado meta-teórico de Church puede entenderse como una refutación del optimismo intelectual que permea a todo el programa original de Hilbert. (shrink)

We study several perfect set properties of the Baire space which follow from the Ramsey property ω→(ω) ω . In particular we present some independence results which complete the picture of how these perfect set properties relate to each other.

¿Qué ha pasado con el problema del cardinal del continuo después de Gödel (1938) y Cohen (1964)? Intentos de responder esta pregunta pueden encontrarse en los artículos de José Alfredo Amor (1946-2011), "El Problema del continuo después de Cohen (1964-2004)", de Carlos Di Prisco , "Are we closer to a solution of the continuum problem", y de Joan Bagaria, "Natural axioms of set and the continuum problem" , que se pueden encontrar en la biblioteca digital de mi blog de Lógica (...) Matemática y Fundamentos de la Matemática (ver). También en la entrada "The Continuum Hypothesis" de la web de Enciclopedia de Filosofía de la Universidad de Stanford existe información importante y actualizada al respecto. En esta breve nota se comenta sobre el tema de una manera divulgativa. (shrink)

El objetivo de este trabajo es presentar en un solo cuerpo tres maneras de relativizar (o generalizar) el concepto de conjunto constructible de Gödel que no suelen aparecer juntas en la literatura especializada y que son importantes en la Teoría de Conjuntos, por ejemplo para resolver problemas de consistencia o independencia. Presentamos algunos modelos resultantes de las diferentes formas de relativizar el concepto de constructibilidad, sus propiedades básicas y algunas formas débiles del Axioma de Elección válidas o no válidas en (...) ellas. (shrink)

The objective of this article is to present an original proof of the following theorem: Thereis a generic extension of the Solovay’s model L(R) where there is a linear order of P(N)/fin that extends to the partial order (P(N)/f in), ≤*). Linear orders of P(N)/fin are important because, among other reasons, they allow constructing non-measurable sets, moreover they are applied in Ramsey's Theory .

El objetivo principal de este trabajo es presentar el sistema lógico que resulta de extender, de una manera natural, a la Silogística con la Lógica proposicional, y demostrar que tal extensión se puede caracterizar como un sistema axiomático. Los axiomas que se utilizan son los de Jan Łukasiewicz , y la completitud de tal sistema de axiomas se prueba utilizando un método análogo al método del conjunto maximal consistente con testigos de Henkin, siguiendo algunas ideas que utiliza John Corcoran para (...) probar que su sistema de reglas de inferencia para la Silogística es completo. (shrink)

Eva Schmidt argues that facts about incoherent beliefs can be non-evidential epistemic reasons to suspend judgment. In this commentary, I argue that incoherence-based reasons to suspend are epistemically superfluous: if the subjects in Schmidt’s cases ought to suspend judgment, then they should do so merely on the basis of their evidential reasons. This suggests a more general strategy to reduce the apparent normativity of coherence to the normativity of evidence. I conclude with some remarks on the independent interest that reasons-first (...) epistemology might have within an evidentialist framework. (shrink)

El objetivo de este artículo es presentar dos tópicos de Lógica matemática y sus fundamentos: El primer tópico es una actualización de la demostración de Alonzo Church del Teorema de completitud de Gödel para la Lógica de primer orden, la cual aparece en su texto "Introduction to Mathematical Logic" (1956) y usa el procedimientos efectivos de Forma normal prenexa y Forma normal de Skolem; y el segundo tópico es una demostración de que la propiedad de partición (tipo Ramsey) del espacio (...) topológico de Baire llamada "Propiedad de partición polarizada" es falsa en el Modelo Básico de Cohen. (shrink)

Introduction to edited volume on vitalism and/in the life sciences, 1800-2010.

I argue that the problem of responsibility for attitudes is best understood as a puzzle about how we are responsible for responding to our object-given reasons for attitudes – i.e., how we are responsible for being (ir)rational. The problem can be solved, I propose, by understanding the normative force of reasons for attitudes in terms of blameworthiness. I present a puzzle about the existence of epistemic and mental blame which poses a challenge for the very idea of reasons for attitudes. (...) We are left with three options: denying that there are any reasons for attitudes, opting for pragmatism about reasons for attitudes, or arguing that the challenge rests on a misunderstanding of the normative force of reasons for attitudes. I finally suggest a version of the last strategy. We can understand the normative force of reasons for attitudes, and thereby solve the problem of mental responsibility, by acknowledging that the way we blame each other for failing to respond correctly to our reasons for attitudes is different from the way we blame each other when one failed to respond correctly to reasons for action. (shrink)

I argue that believing at will – i.e. believing for practical reasons – is in some sense possible and in some sense impossible. It is impossible insofar as we think of belief formation as a re-sult of our exercise of certain capacities (perception, memory, agency). But insofar as we think of belief formation as an action that might lead to such a result (i.e. a deliberation or an in-quiry), believing at will is possible. First I present and clarify the problem (...) and its philosophical relevance (section 1). I then argue that a belief formation as an immediate reaction to practical reasons is not necessarily equivalent to believing at will because the causal mechanism that leads to the formation might be deviant (section 2). Finally, I explain the difference between the two above mentioned meanings of “belief formation” in order to clarify the possibility and impossibility of believing at will (section 3). (shrink)

In this paper, I analyze the concept of ineffability: what does it mean to say that something cannot be said? I begin by distinguishing ineffability from paradox: if something cannot be said truly or without contradiction, this is not an instance of ineffability. Next, I distinguish two different meanings of ‘saying something’ which result from a fundamental ambiguity in the term ‘language’, viz. language as a system of symbols and language as a medium of communication. Accordingly, ‘ineffability’ is ambiguous, too, (...) and we should make a distinction between weak and strong ineffability. Weak ineffability is rooted in the deficiencies of a particular language while strong ineffability stems from the structure of a particular cognitive system and its capacities for conceptual mental representation. Mental contents are only sayable if we are able to conceptualize them and then create signs to represent them in communication. (shrink)

Broome takes the debate on rationality to be concerned with the ordinary use of 'rational'. I argue that this is at best misleading. For the object of current theories of rationality is determined by a specific use of 'rational' that is intimately connected to blame and praise. I call the property it refers to 'rationalityRESP'. This focus on rationalityRESP, I argue, has two significant implications for Broome's critique of theories of rationality as reasons-responsiveness. First, rationalityRESP is plausibly conceived of as (...) a kind of reasons-responsiveness. Secondly, Broome's dispute with internalists about normativity as well as his dispute with externalists about rationality both hinge on questions regarding the concept of responsibility. I conclude that philosophers should integrate discussions about responsibility in their debates about rationality. (shrink)

Representations are not only used in our folk-psychological explanations of behaviour, but are also fruitfully postulated, for example, in cognitive science. The mainstream view in cognitive science maintains that our mind is a representational system. This popular view requires an understanding of the nature of the entities they are postulating. Teleosemantic theories face this challenge, unpacking the normativity in the relation of representation by appealing to the teleological function of the representing state. It has been argued that, if intentionality is (...) to be explained in teleological terms, then the function of a state cannot depend on its phylogenetical history, given the metaphysical possibility of a duplicate of an intentional being that lacks an evolutionary history. In this paper, I present a method to produce, according to our current knowledge in genetic engineering, human-like individuals who are not the product of natural selection in the required sense. This variation will be used to shed light on the main replies that have been offered in the literature to the Swampman thought experiment. I argue that these replies are not satisfactory: representations should better not depend on natural selection. I conclude that a non-etiological notion of function is to be preferred for characterizing the relation of representation. (shrink)

In this review, we present a rigorous construction of an algebraic method for quantum unstable states, also called Gamow states. A traditional picture associates these states to vectors states called Gamow vectors. However, this has some difficulties. In particular, there is no consistent definition of mean values of observables on Gamow vectors. In this work, we present Gamow states as functionals on algebras in a consistent way. We show that Gamow states are not pure states, in spite of their representation (...) as Gamow vectors. We propose a possible way out to the construction of averages of observables on Gamow states. The formalism is intended to be presented with sufficient mathematical rigor. (shrink)

Many of our attitudes are non-culpable: there was nothing that we should have done to avoid holding them. I argue that we can still be blameworthy for non-culpable attitudes: they can impair our relationships in ways that make our full practice of apology and forgiveness intelligible. My argument poses a new challenge to indirect voluntarists, who attempt to reduce all responsibility for attitudes to responsibility for prior actions and omissions. Rationalists, who instead explain attitudinal responsibility by appeal to reasons-responsiveness, can (...) make sense of blameworthiness for non-culpable attitudes. In response, voluntarists could propose a revision of our actual practices. This would lead us into a quite different debate. (shrink)

Higher-Order Thought (HOT) theories of consciousness maintain that the kind of awareness necessary for phenomenal consciousness depends on the cognitive accessibility that underlies reporting. -/- There is empirical evidence strongly suggesting that the cognitive accessibility that underlies the ability to report visual experiences depends on the activity of the dorsolateral prefrontal cortex (dlPFC). This area, however, is highly deactivated during the conscious experiences we have during sleep: dreams. HOT theories are jeopardized, as I will argue. I will briefly present HOT (...) theories in the first section. Section 2 offers empirical evidence to the effect that the cognitive accessibility that underlies the ability to report depends on the dorsolateral prefrontal cortex: dlPFC is the neural correlate of HOTs. Section 3 shows the evidence we have of the deactivation of this brain area during dreams and, in section 4, I present my argument. Finally, I consider and rejoin two possible replies that my opponent can offer: the possibility of an alternative neural correlate of HOTs during dreams and the denial that we have phenomenally conscious experiences during sleep. (shrink)

How can we be responsible for our attitudes if we cannot normally choose what we believe, desire, feel, and intend? This problem has received much attention during the last decades, both in epistemology and ethics. Yet its connections to discussions about reasons and rationality have been largely overlooked. This book develops the foundations of an ethics of mind by investigating the responsibility that is presupposed by the requirements of rationality that govern our attitudes. It has five main goals. First, it (...) reinterprets the problem of responsibility for attitudes as a problem about the normativity of rationality. Second, it connects substantive and structural rationality by drawing on debates about responsibility. Third, it supports recent accounts of the normativity of rationality by explicitly defending the view that epistemic reasons and other ‘right-kind’ reasons are genuine normative reasons. Fourth, it breaks the stalemate between rationalist and voluntarist accounts of mental responsibility by proposing a hybrid view. Finally, it argues that irrationality can warrant moral blame, thus revealing an unnoticed normative force of rational requirements. Length of manuscript: 85,000 words. (shrink)

Higher-order thought theories of consciousness attempt to explain what it takes for a mental state to be conscious, rather than unconscious, by means of a HOT that represents oneself as being in the state in question. Rosenthal Consciousness and the self: new essays, Cambridge University Press, Cambridge, 2011) stresses that the way we are aware of our own conscious states requires essentially indexical self-reference. The challenge for defenders of HOT theories is to show that there is a way to explain (...) the required reference-fixing mechanisms that is compatible with the theory. According to Rosenthal, the reference to oneself as such is grounded in the disposition to identify the individual the HOT refers to as the individual who has that HOT. I argue that this leads to a vicious infinite regress on the more than plausible assumption that our cognitive capacities are limited. This leaves such theories without a foundation, since self-reference is thought essential to consciousness. (shrink)

En este trabajo matemático-filosófico se estudian cuatro tópicos de la Lógica matemática: El método de construcción de modelos llamado Ultraproductos, la Propiedad de Interpolación de Craig, las Álgebras booleanas y los Órdenes parciales separativos. El objetivo principal del mismo es analizar la importancia que tienen dichos tópicos para el estudio de los fundamentos de la matemática, desde el punto de vista del platonismo matemático. Para cumplir con tal objetivo se trabajará en el ámbito de la Matemática, de la Metamatemática y (...) de la Filosofía de la matemática. El desarrollo de la investigación arrojó como resultado que tales tópicos son muy importantes para el estudio de los fundamentos de la matemática, desde el punto de vista del platonismo matemático, y en el trabajo se explica detalladamente con abundantes ejemplos el porqué (al final de cada sección y al final del mismo). (shrink)

Es conocido que el método de forcing es una de las técnicas de construcción de modelos más importantes de la Teoría de conjuntos en la actualidad, siendo el mismo muy útil para investigar problemas de matemática y/o de fundamentos de la matemática. El destacado matemático Joan Bagaria afirma lo siguiente sobre el método de forcing en su artículo "Paul Cohen y la técnica del forcing" (Gaceta de la Real Sociedad Matemática Española, Vol. 2, Nº 3, 1999, págs 543-553) : "Aunque (...) Cohen recibió la medalla Fields por su demostración de la independencia de la hipótesis del continuo y del axioma de elección, su contribución va mucho más allá de estos problemas. Su nuevo método, el forcing, no sólo ha permitido resolver un sinfín de problemas importantes en prácticamente todas las áreas de las matemáticas, si no que ha cambiado para siempre nuestra concepción de la matemática como ciencia". El objetivo principal del siguiente trabajo es estudiar el método de forcing describiendo algunas de sus aplicaciones (forcing de Cohen, forcing aleatorio, forcing de Mathias, forcing de Sacks, forcing de Silver, etc.), y ofreciendo una aproximación a sus fundamentos metamatemáticos. Se aspira que estas notas sirvan de apoyo para aprender dicho método. (shrink)

Es conocido que el Teorema de Completitud de Gödel, el Teorema del Colapso Transitivo de Mostowski y el Principio de Reflexión son resultados muy útiles en las investigaciones de Lógica matemática y/o los Fundamentos de la matemática. El objetivo de este trabajo es presentar algunas demostraciones clásicas de tales resultados: Dos del Teorema de Completitud de Gödel, una del Teorema del Colapso Transitivo de Mostowski y una del Principio de Reflexión. Se aspira que estas notas sean de utilidad para estudiar (...) dichas pruebas. Vale la pena resaltar que entre los métodos matemáticos que se utilizan en tales demostraciones se encuentran: (1) La técnica de construcción de modelos a partir de constantes (o "método del conjunto maximal consistente con un conjunto de testigos" de Henkin) y (2) el Principio de inducción matemática en varias versiones [ (2.1) Inducción matemática sobre los números naturales y (2.2) Inducción transfinita ((2.2.1) Inducción transfinita sobre conjuntos bien ordenados cualesquiera, por ejemplo sobre un cardinal infinito Alef_alfa, (2.2.2) Inducción transfinita sobre una clase de conjuntos bien ordenada, por ejemplo sobre la "clase de todos los ordinales, finitos o infinitos", y (2.2.3) Inducción transfinita sobre relaciones bien fundamentadas, por ejemplo sobre la "relación de pertenencia" entre conjuntos)]. (shrink)

La siguiente ponencia-taller tiene por finalidad explicar cómo podría aplicarse el Método de George Polya para resolver problemas (matemáticos) en el contexto de la Lógica Matemática, especialmente en la lógica Matemática elemental (la lógica de primer orden con identidad). Es una propuesta pedagógica experimental (además de las ya existentes) que tal vez pueda ser útil para la enseñanza de la lógica matemática en ciencias o en humanidades. Dicha ponencia se presentó (vía web) con motivo de la celebración del Día Mundial (...) de Lógica 2022 en dos ocasiones: En la Universidad Central de Venezuela (Venezuela) y en la Universidad Mayor de San Andrés (Logic & Analytics Group - La Paz y La Sociedad Científica de Filosofía de la UMSA, Bolivia). Es un proyecto pedagógico en construcción. (shrink)

Wenn wir Peter Singers Konklusion in „Famine, Affluence, and Morality“ (1972) akzeptieren, dann handeln wir im Alltag sehr viel häufiger falsch, als es uns lieb ist. Anstatt über die Natur von Altruismus zu philosophieren, könnten wir auch möglichst effektiv Hungerleidenden helfen. Ist es daher etwa moralisch verwerflich – weil egoistisch – zu philosophieren? In diesem Beitrag beleuchte ich die Gründe, die wir haben, Philosophie in den Mittelpunkt unseres Lebens zu stellen. Ich argumentiere, dass Philosophieren – genauso wie die Beschäftigung mit (...) Kunst und Wissenschaft – nur dann gerechtfertigt sein kann, wenn es praktische Gründe jenseits von Gründen des persönlichen Nutzens und der Moral gibt. Dabei schliesse ich an Susan Wolfs Idee an, dass diese Tätigkeiten ein Leben mit Sinn erfüllen können. Es bleibt jedoch offen, ob in einer Welt voller Ungerechtigkeit die moralischen Gründe gegen das Philosophieren (und für andere Handlungsoptionen) nicht dennoch überwiegen. (shrink)

The well-known distinction between access consciousness and phenomenal consciousness has moved away from the conceptual domain into the empirical one, and the debate now is focused on whether the neural mechanisms of cognitive access are constitutive of the neural correlate of phenomenal consciousness. In this paper, I want to analyze the consequences that a negative reply to this question has for the cognitive phenomenology thesis – roughly the claim that there is a “proprietary” phenomenology of thoughts. If the mechanisms responsible (...) for cognitive access can be disentangled from the mechanisms that give rise to phenomenology in the case of perception and emotion, then the same disentanglement is to be expected in the case of thoughts. This, in turn, presents, as I argue, a challenge to the cognitive phenomenology thesis: either there are thoughts with cognitive phenomenology we lack cognitive access to or there are good reasons to doubt that there is such a thing as cognitive phenomenology. I discuss a... (shrink)

This chapter locates our overall approach within the dialectic of contemporary philosophical debates and provides an overall framework for discussion. First, I introduce the problem of mental normativity. I show how this problem poses a prima facie threat to the common assumption in epistemology and metaethics that beliefs and other attitudes are governed by robust normative requirements. Secondly, I motivate philosophical inquiry about an ethics of mind by tracing this field back to recent debates in the ethics of belief. I (...) characterize the ethics of mind as being concerned with two main questions: 1. How can we be responsible for our attitudes? 2. What attitudes should we have? Finally, I give an overview over the structure of the book and summarize the chapters. (shrink)

It has been argued that the explanation of self-control requires positing special motivational powers. Some think that we need will-power as an irreducible mental faculty; others that we need to think of the active self as a dedicated and depletable pool of psychic energy or – in today more respectable terminology – mental resources; finally, there is the idea that self-control requires postulating a deep division between reason and passion – a deliberative and an emotional motivational system. This essay argues (...) that no such special motivational powers are necessary. Yet, at the same time, self-control does powerfully illustrate the importance of a feature of the mind. What it illustrates, I argue, is the importance of the mental activity of attention in the control of all action. It is by appeal to this mental activity that we can dispense with special motivational powers. If we think of Humeanism as the view that there is fundamentally only one kind of motivational system and that all action is based in that system, then this essay contributes to a defense of Humeanism. On the other hand, the essay also shows that any model of agency in terms of only beliefs and desires, motivational and representational states, or preferences and credences is incomplete. A different conception of Humeanism as the view that every mental state is either motivational, representational, or a combination of them, is false. (shrink)

The traditional approach in cognitive sciences holds that cognition is a matter of manipulating abstract symbols followingcertain rules. According to this view, the body is merely an input/output device, which allows the computationalsystem—the brain—to acquire new input data by means of the senses and to act in the environment following its com-mands. In opposition to this classical view, defenders of embodied cognition (EC) stress the relevance of the body inwhich the cognitive agent is embedded in their explanation of cognitive processes. (...) From a representationalist frameworkregarding our conscious experience, in this article, I will offer a novel argument in favor of EC and show that cognitionconstitutively—and no merely causally—depends upon body activity beyond that in the brain. In particular, I will arguethat in order to solve the problem derived from the empirical evidence in favor of the possibility of shifted spectrum,representationalist should endorse the view that experiences concern its subject: the content of experience isde se.Ishow that this claim perfectly matches the phenomenological observation and helps explaining the subjective characterof the experience. Furthermore, I argue that entertaining this kind of representation constitutively depends on bodilyactivity. Consequently, insofar as cognition depends on consciousness, it is embodied. (shrink)

The author defends the claim that there are cases in which we should promote irrationality by arguing (1) that it is sometimes better to be in an irrational state of mind, and (2) that we can often influence our state of mind via our actions. The first claim is supported by presenting cases of irrational _belief_ and by countering a common line of argument associated with William K. Clifford, who defended the idea that having an irrational belief is always worse (...) than having a rational one. In support of the second claim, the author then explains how the control we have over our beliefs could look like. In conclusion, the author suggests that the argument of this essay is not restricted to the irrationality of beliefs, but can be applied to irrational states of mind in general. In an outlook on the “ethics of belief” debate, the author points out that the argument of this essay need not conflict with evidentialism, but does so when combined with another plausible claim about the meaning of doxastic ought-statements. (shrink)