Let M be an o-minimal expansion of a real closed field. Let G be a definably compact definably connected abelian n-dimensional group definable in M. We show the following: the o-minimal fundamental group of G is isomorphic to ℤn; for each k>0, the k-torsion subgroup of G is isomorphic to n, and the o-minimal cohomology algebra over ℚ of G is isomorphic to the exterior algebra over ℚ with n generators of degree one.

We prove that if G is a group definable in a saturated o-minimal structure, then G has no infinite descending chain of type-definable subgroups of bounded index. Equivalently, G has a smallest type-definable subgroup G00 of bounded index and G/G00 equipped with the “logic topology” is a compact Lie group. These results give partial answers to some conjectures of the fourth author.

Necessitism about individuals claims that necessarily every individual necessarily exists. An analogous necessitist thesis attributes necessary existence to properties and relations. Both theses have been defended by Williamson. Furthermore, Williamson specifically argues against the hybrid conjunction of first-order contingentism and higher-order necessitism; a combination that would bring about additional drawbacks. I work out a defence of the hybrid combination, including some replies to Williamson’s additional objections. Considerations of ontological parsimony and pre-theoretical intuitions favour the hybrid view over necessitism at all (...) orders. (shrink)

I deal here with one of Boghossian’s arguments against content externalism, related to ourinferential rationality(to use his term). According to his reasoning, the apriority of our logical abilities is inconsistent with certain externalist assumptions. Nevertheless, the problem constitutes an important challenge foranytheory of content, not just for externalism. Furthermore, when we examine what internalists may propose to solve the problem, we see that externalists have at their disposal a more promising repertoire of possible replies than internalists. In that sense, insofar (...) as Boghossian’s scenario is relevant to the debate externalism/internalism, it can be seen (against Boghossian’s original intention) as providing additional evidence for content externalism. (shrink)

We develop an intersection theory for definable Cp-manifolds in an o-minimal expansion of a real closed field and we prove the invariance of the intersection numbers under definable Cp-homotopies . In particular we define the intersection number of two definable submanifolds of complementary dimensions, the Brouwer degree and the winding numbers. We illustrate the theory by deriving in the o-minimal context the Brouwer fixed point theorem, the Jordan-Brouwer separation theorem and the invariance of the Lefschetz numbers under definable Cp-homotopies. A. (...) Pillay has shown that any definable group admits an abstract manifold structure. We apply the intersection theory to definable groups after proving an embedding theorem for abstract definably compact Cp-manifolds. In particular using the Lefschetz fixed point theorem we show that the Lefschetz number of the identity map on a definably compact group, which in the classical case coincides with the Euler characteristic, is zero. (shrink)

Models of normal open induction are those normal discretely ordered rings whose nonnegative part satisfy Peano's axioms for open formulas in the language of ordered semirings. (Where normal means integrally closed in its fraction field.) In 1964 Shepherdson gave a recursive nonstandard model of open induction. His model is not normal and does not have any infinite prime elements. In this paper we present a recursive nonstandard model of normal open induction with an unbounded set of infinite prime elements.

In [E. Baro, M. Otero, On o-minimal homotopy, Quart. J. Math. 15pp, in press ] o-minimal homotopy was developed for the definable category, proving o-minimal versions of the Hurewicz theorems and the Whitehead theorem. Here, we extend these results to the category of locally definable spaces, for which we introduce homology and homotopy functors. We also study the concept of connectedness in -definable groups — which are examples of locally definable spaces. We show that the various concepts of connectedness associated (...) to these groups, which have appeared in the literature, are non-equivalent. (shrink)

Let M be an o-minimal expansion of an ordered field. Let φ be a formula in the language of ordered domains. In this note we establish some topological properties which are transferred from $\varphi^M$ to $\varphi^R$ and vice versa. Then, we apply these transfer results to give a new proof of a result of M. Edmundo-based on the work of A. Strzebonski-showing the existence of torsion points in any definably compact group defined in an o-minimal expansion of an ordered field.

Hume argued that inductive inferences do not have rational justification. My aim is to reject Hume’s argument. The discussion is partly motivated by an analogy with Carroll’s Paradox, which concerns deductive inferences. A first radically externalist reply to Hume (defended by Dauer and Van Cleve) is that justified inductive inferences do not require the subject to know that nature is uniform, though the uniformity of nature is a necessary condition for having the justification. But then the subject does not have (...) reasons for believing what she believes. I defend a moderate externalist account that seeks to partly accommodate that objection to the radical externalist proposal. It is based on an extension of Peacocke’s theory of concepts: possession conditions for predicative concepts standing for natural properties include (fallible) dispositions to project them to new cases in accordance with inductive inferential patterns. (shrink)

Let G be a definably compact group in an o-minimal expansion of a real closed field. We prove that if dim(G\X) < dim G for some definable ${X \subseteq G}$ then X contains a torsion point of G. Along the way we develop a general theory for the so-called G-linear sets, and investigate definable sets which contain abstract subgroups of G.

A common view about Moore’s Proof of an External World is that the argument fails because anyone who had doubts about its conclusion could not use the argument to rationally overcome those doubts. I agree that Moore’s Proof is—in that sense—dialectically ineffective at convincing an opponent or a doubter, but I defend that the argument (even when individuated taking into consideration the purpose of Moore’s arguing and, consequently, the preferred addressee of the Proof) does not fail. The key to my (...) defence is to conceive the Proof as addressed to subjects with a different epistemic condition. To sustain this view I formulate some hypothesis about the common general purpose of arguing and I defend that it can be fulfilled even when the addressee of an argument is not someone who disbelieves or doubts its conclusion. (shrink)

Según Williamson, saber y creer son estados mentales, pero creer algo verdadero y creer justificadamente algo verdadero no lo son. Ese tratamiento discriminatorio es relevante para la epistemología de Williamson. Su principal tesis epistemológica negativa y su principal tesis epistemológica positiva están en peligro si su teoría metafísica sobre lo mental es incorrecta. Presento aquí un problema para dicha teoría: impone limitaciones implausibles a los posibles usos de conceptos y expresiones lingüísticas. Describiré algunas opciones que tendría Williamson para evitar el (...) problema; pero sostendré que acarrean cierta dosis de arbitrariedad. (shrink)

I present an epistemological puzzle about perceptual knowledge and its relation to the evaluation of probabilities. It involves cases, concerning a given subject S and a proposition P in a determinate context, where apparently: S has perceptual knowledge of P; the epistemic justification S has for believing Not-P is much greater than her epistemic justification for believing P. If those two theses were true, the following very plausible epistemological principle would fail: If S knows P, then the epistemic justification S (...) has for believing Not-P is not greater than her epistemic justification for believing P. I offer a solution to the puzzle, which is compatible with basic intuitions and theses of orthodox Bayesianism. (shrink)

This paper argues for a conditional claim concerning a famous argument—developed by Church in elucidation of some remarks by Frege to the effect that the bedeutung of a sentence is the sentence’s truth-value—the Frege–Gödel–Church argument, or FGC for short. The point we make is this :if, and just to the extent that, Arthur Smullyan’s argument against Quine's use of FGC is sound, then essentially the same rejoinder disposes also of Davidson's use of FGC against ‘correspondence’ theories of truth. We thus (...) dispute a contention by Professor Davidson that it is coherent to accept that Smullyan’s rejoinder takes away the force of Quine’s version of FGC, while still consistently using FGC to establish that if true sentences (or utterances) correspond to anything, they all correspond to the same thing. We show that the differences between the cases discussed by Smullyan and Davidson’s version of FGC on which Davidson relies for his contention are irrelevant to the point under dispute. (shrink)

Timothy Williamson has defended the claim that any philosophically satisfying conception of modality that encompasses possible worlds semantics (PWS) commits us to the Barcan Formula. His argument depends on the assumption that the domain of what there is (the domain of the actual world) has to be identified with the domain D(@), where @ is the index or possible world that in PWS represents , or stands for , the actual world. I work out an interpretation of the relation between (...) PWS and possible worlds terminology that makes it plausible to reject that assumption. (shrink)

E. Machery and some collaborators have used survey data to criticize Kripke’s anti-descriptivism about proper names. I highlight a number of drawbacks in the tests of Machery et al. Some of my objections concern their ambiguity. In particular, the responses that–according to them–reveal descriptivist intuitions can be interpreted as anti-descriptivist responses. Furthermore, their vignettes are inconsistent. I also discuss other issues related to the role of intuitions in philosophy; Machery et al.’s theses depends on an unjustified assumption: there is not (...) expertise regarding intuitions. (shrink)

Tanto la Fórmula Barcan como la postulación de possibilia contradicen los juicios intuitivos preteóricos de la mayoría de los sujetos, favorables al actualismo sobre la naturaleza de los mundos posibles. En este artículo discuto y rechazo dos argumentos que pretenderían contrarrestar tales juicios, y que conciben erróneamente la relación entre la semántica de mundos posibles y nuestros lenguajes naturales modales. El argumento más importante asume que el dominio de todas las entidades es idéntico al dominio de @. Desarrollo una interpretación (...) de la SMP conforme a la cual esa tesis no está suficientemente justificada. /// Barcan Formula and the postulation of possibilia contradict the pretheoretical intuitive judgments of most people, which favour actualism about possible worlds. In this paper I discuss and reject two arguments against such judgments, both of which conceive wrongly the relation between possible worlds semantics and modal natural languages. The more important argument assumes that the domain of the actual world is identical to the domain of @. I develop an interpretation of PWS which elucidates why that thesis is unwarranted. (shrink)

Kripke formula cuatro objeciones en contra de una solución disposicionalista simple al enigma wittgensteiniano sobre seguir una regla. En este trabajo presento dos propuestas parcialmente disposicionalistas diferentes a la teoría disposicionalista simple que Kripke discute y defiendo que aquellas cuatro objeciones no les afectan. Una de esas dos propuestas puede atribuirse, con cierta precaución, al propio Wittgenstein. La otra, que me parece preferible, invoca una noción teleológica de disposición. Ambas propuestas apelan al concepto de simplicidad, o —alternativamente— al concepto de (...) similitud natural. Rechazo también ciertas críticas que Kripke hace del uso de tales conceptos para solucionar el enigma sobre seguir una regla. (shrink)

We consider IOpen, the subsystem of PA (Peano Arithmetic) with the induction scheme restricted to quantifier-free formulas. We prove that each model of IOpen can be embedded in a model where the equation x 2 1 + x 2 2 + x 2 3 + x 2 4 = a has a solution. The main lemma states that there is no polynomial f(x,y) with coefficients in a (nonstandard) DOR M such that $|f(x,y)| for every (x,y) ∈ C, where C is (...) the curve defined on the real closure of M by C: x 2 + y 2 = a and $a > 0$ is a nonstandard element of M. (shrink)

En este artículo discuto el supuesto compromiso de la lógica modal cuantificada con el esencialismo. Entre otros argumentos, Quine, el más emblemático de los críticos de la modalidad, ha objetado a la lógica modal cuantificada que ésta se compromete con una doctrina filosófica usualmente considerada sospechosa, el esencialismo: la concepción que distingue, de entre los atributos de una cosa, aquellos que le son esenciales de otros poseidos sólo contingentemente. Examino en qué medida Quine puede tener razón sobre ese punto explorando (...) una analogía entre la lógica modal y la logica clásica de primer orden. Con ello se pretende proporcionar una visión clarificadora sobre el estatus de la lógica modal y su relación con la lógica en general.In this paper I discuss the alleged commitment of quantified modal logic to philosophical essentialism. Besides some other more or less related arguments against quantified modal logic, Quine (its more prominent critic) objects to it by claiming its commitment to a philosophical doctrine usually regarded as suspicious, essentialism: the view that some of the attributes of a thing are essential to it, and others are accidental. I study to what extent Quine can be right about this specific issue. I defend some of his views by exploring an analogy between modal logic and standard first order logic. That serves to get a better understanding of the status of modal logic and its relation with logic in general. (shrink)

Los servidores públicos no siempre actúan en función del interés de la comunidad a pesar de las amenazas y sanciones establecidas en el derecho; es necesario encontrar nuevas vías de actuación para resolver tan importante problema. En ese sentido, este artículo busca fundamentar los principios que deben regir la actuación de los mismos. Para ello, en primer lugar, se intenta establecer un método que permita la creación de estos principios, basándose en la teoría del valor de Luis Villoro y en (...) la ética de Immanuel Kant. Posteriormente, se identifica el interés público como aquel valor que se busca por él mismo sin necesidad de acudir a otros valores para cuyo fin esté dispuesto. A continuación, se derivan los valores de responsabilidad, objetividad, imparcialidad, razonabilidad, publicidad, solidaridad, prudencia e instrumentalidad, a partir de los cuáles se construyen principios éticos que puedan, posteriormente, ser positivizados en el derecho. (shrink)

Is parental involvement a relevant factor in explaining academic performance in the most disadvantaged socioeconomic contexts? This article examines the effect of parental involvement on the Langua...

En las últimas décadas se ha producido un cambio radical en el concepto de museo hacia la valorización de la experiencia como vía de adquisición de conocimiento. Este cambio ha generado un entorno propicio para la entrada de instalaciones digitales interactivas que aúnan información y educación con una perspectiva lúdica que, con frecuencia, le lleva a trasladar elementos y características de los videojuegos para una experiencia más atractiva, inmersiva y memorable. El objeto del presente artículo ha sido redefinir elementos del (...) diseño de videojuegos y su intersección con el diseño centrado en el usuario para su aplicación en el contexto museístico. (shrink)

Kripke argued for the existence of necessary a posteriori truths and offered different accounts of why certain necessary truths seem to be contingent. One of these accounts was used by Kripke in an argument against the psychophysical identity thesis. I defend the claim that the explanatory force of Kripke's standard account of the appearance of contingency relies on the explanatory force of one of the more general accounts he also offers. But the more general account cannot be used to undermine (...) the psychophysical identity thesis. Specifically, a crucial feature in Kripke's standard account, which is needed to argue for dualism, is explanatorily superfluous. Alternative accounts that are similar to Kripke's original one but lack that trait would also explain the phenomenon. Consequently, the Kripkean dualist argument is blocked. /// Kripke ha argumentado que existen verdades necesarias a posteriori, y ha ofrecido diferentes explicaciones de por qué ciertas verdades necesarias parecen contingentes. Una de esas explicaciones se usaba en un argumento con el que Kripke criticaba la tesis de la identidad psicofísica. En este trabajo sostengo que la fuerza explicativa de la explicacion kripkeana estándar de la apariencia de contingencia depende de la fuerza explicativa de una de las otras explicaciones que Kripke también propone. Pero esa otra explicación, más general, no sirve para rechazar la identidad psicofísica. Con-cretamente, un rasgo crucial de la explicación kripkeana estandar resulta explicativamente superfluo. Explicaciones alternativas, similares a la de Kripke pero que carezcan de ese rasgo, explicarían también el fenómeno. Como consecuencia, el argumento dualista kripkeano queda bloqueado. (shrink)

I present some puzzling cases regarding knowledge and its relation to rational credence. They seem to entail a failure of an apparently correct principle: if S knows P, then the epistemic justi...

In John Etchemendy's book, The Concept of Logical Consequence, several arguments are put forth against the standard model‐theoretic account of logical consequence and logical truth. I argue in this article that crucial parts of Etchemendy's attack depend on a failure to distinguish two senses of logic and two correlative senses of being something a logical question. According to one of these senses, the logic of a language, L, is the set of logical truths of L. In the other sense, logic (...) is a theoretical discipline whose aim is to characterize logical properties and it can be identified with the set of sentences on what, and why, the extension of the set of logical truths of a particular language is. Some particular claims by Etchemendy about the status assigned to the axiom of infinity in the model‐theoretic account are criticized and shown to be erroneous because of that conflation. (shrink)

In John Etchemendy's book, The Concept of Logical Consequence, several arguments are put forth against the standard model‐theoretic account of logical consequence and logical truth. I argue in this article that crucial parts of Etchemendy's attack depend on a failure to distinguish two senses of logic and two correlative senses of being something a logical question. According to one of these senses, the logic of a language, L, is the set of logical truths of L. In the other sense, logic (...) is a theoretical discipline whose aim is to characterize logical properties and it can be identified with the set of sentences on what, and why, the extension of the set of logical truths of a particular language is. Some particular claims by Etchemendy about the status assigned to the axiom of infinity in the model‐theoretic account are criticized and shown to be erroneous because of that conflation. (shrink)

Kripke argued for the existence of necessary a posteriori truths, and tried to explain why some of them seem to be contingent. His main explanation motivated two philosophical proposals: the attempt - linked to some interpretations of two-dimensionalism - to analyse the epistemic concept of a priori truth using metaphysical modal concepts; the argument for psychophysical dualism worked out by Kripke relying on his explanation of the appearances of contingency. I point out several difficulties for , and argue that can (...) oe blocked because of the existence of alternative accounts of the phenomenon. (shrink)