Axel Barceló

Pronpongo una nueva manera de concebir la aceptación de proposiciones y su relación con la creencia y la inferencia. Argumento además que adoptar esta propuesta nos permite resolver de manera relativamente sencilla algunas paradojas aparentemente tan disímbolas cómo la del prefacio, la lotería y el sorites. Según esta propuesta, el error detrás de la paradoja sorítica es pensar que quién cree que hay una línea divisoria entre lo que cae dentro de la extensión de un término y lo que cae fuera de él debe creer también de algún lugar que ahí se encuentra dicha línea divisoria. Espero convencerlos de que no es así, y que por lo tanto, nuestros juicios de sentido común no nos llevan a ninguna contradicción.

This dissertation looks to make sense of the role 'grammar' plays in Wittgenstein's philosophy of mathematics during the middle period of his career. It constructs a formal model of Wittgenstein's notion of grammar as expressed in his writings of the early thirties, addresses the appropriateness of that model and then employs it to test Wittgenstein's claim that mathematical propositions are ultimately grammatical. ;In order to test Wittgenstein's claim that mathematical propositions are grammatical, the dissertation provides a formalized theory of grammatical analysis and applies it to a portion of language big enough to contain numerical expressions. It attempts to prove that, if the object language contains the appropriate numerical expressions, the resulting grammar will include at least some rules with a natural mathematical interpretation. In particular, it tries to show that Wittgenstein's grammatical analysis of the ordinary use of numerical expressions yields familiar theorems of arithmetic. ;The dissertation also endeavors to extend these results to a coherent picture of Wittgenstein's peculiar view of mathematics as grammar. It fits the formal results into the larger picture of Wittgenstein's philosophy of mathematics during this period. A large portion of the dissertation explains how, by combining the notions of grammar and mathematics, Wittgenstein allowed himself to offer original answers to some central questions in the philosophy of mathematics. In this regard, the dissertation pays special attention to four main issues: Wittgenstein's use of the term 'grammar' in his philosophical writings of this period, in comparison with traditional understandings of 'grammar', mathematics as part of the syntax of language, his explanation of mathematical application, and Wittgenstein's account of mathematical necessity. Taking these points in consideration situates the dissertation's results in the larger philosophical discussion of these themes

El objetivo de este artí­culo es clarificar el sentido en el cual el proyecto semántico de Frege, Russell y Carnap puede llamarse correctamente de análisis semántico. Para ello, delineo brevemente la historia del concepto de análisis en la intersección de la filosofí­a y las matemáticas modernas, teniendo como hipótesis que el análisis semántico en la filosofí­a analí­tica temprana pertenece a una larga tradición de adoptar metodologí­as geométricas a la solución de problemas filosóficos. En particular, este tipo de análisis adapta la formalización cartesiana como mecanismo de representación analí­tica, a problemas de semántica.The goal of this article is to clarify the sense in which the semantic project of Frege, Russel and Carnap may be correctly described as a kind of semantic analysis. To this goal, I briefly trace the history of the term analysis in modern philosophy and mathematics, under the guiding hypothesis that semantic analysis in early analytic philosophy belongs to a long tradition of adopting geometrical methodologies to the solution of philosophical problems. In particular, it adapts Descartes"™ development of formalization as a mechanism of analytic representation, for its application in semantics

La lógica matemática es matemática en cuanto que usa herramientas matemáticas. En este sentido, la lógica matemática es matemática en el mismo sentido que lo es, digamos, la mecánica newtoniana. En ambos casos, el método es matemático, pero las ciencias mismas no lo son, pues su objeto de estudio pertenece a una realidad objetiva e independiente. En particular, las herramientas matemáticas que usa la lógica simbólica contemporánea —tanto en su simbolismo como en su cálculo— se crearon originalmente para el desarrollo algebraico de la geometría, y luego fueron adaptadas al resto de las matemáticas y la lógica. A estas herramientas se les llama formales, pues permiten el cálculo con formas generales.

Without a doubt, one of the main reasons Platonsim remains such a strong contender in the Foundations of Mathematics debate is because of the prima facie plausibility of the claim that objectivity needs objects. It seems like nothing else but the existence of external referents for the terms of our mathematical theories and calculations can guarantee the objectivity of our mathematical knowledge. The reason why Frege – and most Platonists ever since – could not adhere to the idea that mathematical objects were mental, conventional or in any other way dependent on our faculties, will or other historical contingencies was that objects whose properties of existence depended on such contingencies could not warrant the objectivity required for scientific knowledge. This idea gained currency in the second half of the 19th Century and remains current for the most part today. However, it was not always like that. Objectivity, after all, has a history, and according to its historians (Daston 2001), the view that scientific knowledge need be objective is a fairly recent one. Up until mid-19th Century, science was not so much concerned with objectivity, as it was concerned with truth. Before the rise of the modern university and the professional scientist, science had the discovery of truths as its ultimate goal. In contrast, modern science now aims at the production and acquisition of objective knowledge. The difference might seem..

Para concretar el proyecto naturalista de Penelope Maddy, sería necesario, pues, contar con un criterio que nos permita decidir cuándo la argumentación es en favor o en contra de revisar los criterios de existencia y justificación en matemáticas es ella misma matemática y cuando es más bien filosófica o metafísica. Esto pone a Maddy en una posición particularmente difícil. Por un lado, quiere que la matemática sea considerada tan científica como para merecer el mismo tipo de autonomía epistémica, pero no tan científica como para requerir el mismo tipo de justificación. Esto la hace blanco de críticas tanto de parte de naturalistas (quienes criticarían la autonomía que le otorga a la matemática), como de positivistas (quienes cuestionarían el carácter científico de la matemática).

Is there a notion of domain specificity which affords genuine insight in the context of the highly modular mind, i.e. a mind which has not only input modules, but also central ‘conceptual’ modules? Our answer to this question is no. The main argument is simple enough: we lay out some constraints that a theoretically useful notion of domain specificity, in the context of the highly modular mind, would need to meet. We then survey a host of accounts of what domain specificity is, based on the intuitive idea that a domain specific mechanism is restricted in the kind of information that it processes, and show that each fails at least one of those constraints.

The similarities between the philosophical debates surrounding assessment sensitivity and moral luck run so deep that one can easily adapt almost any argument from one debate, change some terms, adapt the examples, and end up with an argument relevant to the other. This article takes Brian Rosebury's strategy for resisting moral luck in “Moral Responsibility and ‘Moral Luck' ” (1995) and turns it into a strategy for resisting assessment sensitivity. The article shows that one of Bernard Williams's examples motivating moral luck is very similar to one of the examples John MacFarlane uses to motivate the assessment sensitivity of epistemic modals, and in particular the assessment sensitivity of the auxiliary verb “might.” This means that, if Rosebury is right and we do not actually need moral luck to explain Williams's example, we may not need assessment sensitivity to account for the semantic behaviour of the epistemic modal verb “might” either

En "Elementos esenciales de una hermenéutica analógica", Mauricio Beuchot trata de ubicar su hermenéutica analógica como una posición intermedia entre lo que él llama el univocismo y la hermenéutica alegórica. En este comentario busco mostrar, tomando como punto de partida que los objetivos teóricos de la hermenéutica no se encuentran muy distantes de los de las teorías analíticas de la interpretación, que el debate sobre el papel de los elementos extralingüísticos en la interpretación es mucho más complejo de lo que el trilema de Beuchot sugiere. In "Essential Elements for an Analogical Hermeneutics", Mauricio Beuchot seeks to place his analogical hermeneutics in a position between what he calls univocism and allegorical hermeneutics. In this commentary I intend to show, taking into account that the theoretical goals of hermeneutics are not so different from those of analytical theories of interpretation, that the debate over the role played by extralinguistic elements in interpretation is much more complex than what Beuchot's trilemma suggests.

Using conjunction as an example, I show a technical and philosophical problem when trying to conciliate the currently prevailing views on the meaning of logical connectives: the inferientialist (also called 'syntactic') one based on introduction and elimination rules, and the representationalist (also called 'semantic') one given through truth tables. Mostly I show that the widespread strategy of using the truth theoretical definition of logical consequence to collapse both definitions must be rejected by inferentialists. An important consequence of my argument is that there are different notions of conjunction at play in standard first order logic, and that the technical and philosophical connections between them are far from well established.

Alvin I. Goldman has argued that since one must count epistemic rules among the factors that help to fix the justificational status of agents (generally called J-factors), not all J-factors are internalist, that is, intrinsic to the agent whose justificational status they help to fix. After all, for an epistemic rule to count as a genuine J-factor, it must be objectively correct and, therefore, “independent of any and all minds.” Consequently, it cannot be intrinsic to any particular epistemic agent. In this brief commentary, I will argue that Goldman’s argument misunderstands what it takes for epistemic justification to be internalist and, therefore, fails to guarantee his externalist conclusion. In particular, I want to demonstrate that Goldman’s argument trivializes the difference between intrinsic and extrinsic properties that lays at the basis of the internalist/externalist debate. I will show that, if sound, simple variations on Goldman’s argument could be used to prove the absurd conclusion that all properties are extrinsic. Now, since the intrinsic/extrinsic distinction is fundamental to debates in several areas of philosophy, not only the internalist/externalist debate in epistemology, I conclude that Goldman’s argument cannot be sound.