Daniel Isaacson has advanced an epistemic notion of arithmetical truth according to which the latter is the set of truths that we grasp on the basis of our understanding of the structure of natural numbers alone. Isaacson’s thesis is then the claim that Peano Arithmetic (PA) is the theory of finite mathematics, in the sense that it proves all and only arithmetical truths thus understood. In this paper, we raise a challenge for the thesis and show how it can be (...) overcome. We introduce the concept of purity for theories of arithmetic: a theory of arithmetic is pure when it only proves arithmetical truths. Then, we argue that, under Isaacson’s thesis, some PA-provable truths—including transfinite induction claims for infinite ordinals and some consistency statements—are seemingly not arithmetical in Isaacson’s sense, and hence that Isaacson’s thesis might entail the impurity of PA. Nonetheless, we conjecture that the advocate of Isaacson’s thesis can avoid this undesirable consequence: the arithmetical nature, as understood by Isaacson, of all contentious PA-provable statements can be justified. As a case study, we explore how this is done for transfinite induction claims with infinite ordinals below ε0. To this end, we show that the PA-proof of such claims employs exclusively resources from finite mathematics, and that ordinals below ε0 are finitary objects despite being infinite. (shrink)

This paper is concerned with the claim that supervaluationist consequence is not classical for a language including an operator for definiteness. Although there is some sense in which this claim is uncontroversial, there is a sense in which the claim must be qualified. In particular I defend Keefe's position according to which supervaluationism is classical except when the inference from phi to Dphi is involved. The paper provides a precise content to this claim showing that we might provide complete (and (...) sound) systems of deduction for supervaluationist consequence in which proofs are completely classical with the exception of a single last step (involving the above mentioned inference). (shrink)

To what degree can language be acquired from linguistic input alone? This question has vexed scholars for millennia and is still a major focus of debate in the cognitive science of language. The complexity of human language has hampered progress because studies of language–especially those involving computational modeling–have only been able to deal with small fragments of our linguistic skills. We suggest that the most recent generation of Large Language Models (LLMs) might finally provide the computational tools to determine empirically (...) how much of the human language ability can be acquired from linguistic experience. LLMs are sophisticated deep learning architectures trained on vast amounts of natural language data, enabling them to perform an impressive range of linguistic tasks. We argue that, despite their clear semantic and pragmatic limitations, LLMs have already demonstrated that human-like grammatical language can be acquired without the need for a built-in grammar. Thus, while there is still much to learn about how humans acquire and use language, LLMs provide full-fledged computational models for cognitive scientists to empirically evaluate just how far statistical learning might take us in explaining the full complexity of human language. (shrink)

Topics in Cognitive Science, Volume 14, Issue 3, Page 634-645, July 2022.

In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, (...) which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases. (shrink)

This paper presents and defends a way to add a transparent truth predicate to classical logic, such that and A are everywhere intersubstitutable, where all T-biconditionals hold, and where truth can be made compositional. A key feature of our framework, called STTT (for Strict-Tolerant Transparent Truth), is that it supports a non-transitive relation of consequence. At the same time, it can be seen that the only failures of transitivity STTT allows for arise in paradoxical cases.

The incredible success of quantum theory as a mathematical model makes it especially frustrating that we cannot agree on a plausible philosophical or metaphysical description of it. Some philosophers of science have noticed certain parallels between quantum theory and the philosophy of Thomas Aquinas, and these parallels are deepened and strengthened if the “observer” of modern physics is associated with the “intellect” of scholastic ontology. In this case we are talking about a human observer. But this type of observer has (...) a unique quality that is not considered at all by either physics or scholastic philosophy—the human observer is mimetic and therefore “interdividual.” By taking this fundamental anthropological fact into account, it turns out that the critical gaps still separating Aquinas from modern physicists can be effectively closed, reconciling the realism of Aquinas with the empirical evidence of quantum mechanics. This book explores this new bridge between the physical and the human—a bridge essentially designed by scholastic theory, clarified by mimetic theory, and built by quantum theory—and the path it opens to that metaphysical understanding for which philosophers of modern science have been striving. It is an understanding, not merely of the physical but of physics in the fuller sense of what is real and what is true. Here the reader will find a physics that describes the natural world and our place as mimetic observers within it. (shrink)

Substructural approaches to paradoxes have attracted much attention from the philosophical community in the last decade. In this paper we focus on two substructural logics, named ST and TS, along with two structural cousins, LP and K3. It is well known that LP and K3 are duals in the sense that an inference is valid in one logic just in case the contrapositive is valid in the other logic. As a consequence of this duality, theories based on either logic are (...) tightly connected since many of the arguments for and objections against one theory reappear in the other theory in dual form. The target of the paper is making explicit in exactly what way, if any, ST and TS are dual to one another. The connection will allow us to gain a more fine-grained understanding of these logics and of the theories based on them. In particular, we will obtain new insights on two questions concerning ST which are being intensively discussed in the current literature: whether ST preserves classical logic and whether it is LP in sheep’s clothing. Explaining in what way ST and TS are duals requires comparing these logics at a metainferential level. We provide to this end a uniform proof theory to decide on valid metainferences for each of the four logics. This proof procedure allows us to show in a very simple way how different properties of inferences (unsatisfiability, supersatisfiability and antivalidity) that behave in very different ways for each logic can be captured in terms of the validity of a metainference. (shrink)

Michel Janssen and Harvey Brown have driven a prominent recent debate concerning the direction of an alleged arrow of explanation between Minkowski spacetime and Lorentz invariance of dynamical laws in special relativity. In this article, I critically assess this controversy with the aim of clarifying the explanatory foundations of the theory. First, I show that two assumptions shared by the parties—that the dispute is independent of issues concerning spacetime ontology, and that there is an urgent need for a constructive interpretation (...) of special relativity—are problematic and negatively affect the debate. Second, I argue that the whole discussion relies on a misleading conception of the link between Minkowski spacetime structure and Lorentz invari-ance, a misconception that in turn sheds more shadows than light on our understand-ing of the explanatory nature and power of Einstein’s theory. I state that the arrow connecting Lorentz invariance and Minkowski spacetime is not explanatory and uni-directional, but analytic and bidirectional, and that this analytic arrow grounds the chronogeometric explanations of physical phenomena that special relativity offers. (shrink)

What is infinity? It's reading the last line of a book and imagining the rest. No, wait, it's the instruction manual for the machine that operates the sun and the stars. In unexpected observations, captivating images, and even some equations, celebrated Argentinian author-illustrator Pablo Bernasconi, finalist for the 2018 Hans Christian Andersen Award, offers up verses about what infinity could mean to all of us. Winner of the Grand Prize from the Asociación de Literatura Infantil y Juvenil de la (...) Argentina (ALIJA) in 2018, Infinity is a book children and adults alike will find endlessly fascinating. (shrink)

When we speak about different interpretations of quantum mechanics it is suggested that there is one single quantum theory that can be interpreted in different ways. However, after an explicit characterization of what it is to interpret quantum mechanics, the right diagnosis is that we have a case of predictively equivalent rival theories. I extract some lessons regarding the resulting underdetermination of theory choice. Issues about theoretical identity, theoretical and methodological pluralism, and the prospects for a realist stance towards quantum (...) theory can be properly addressed once we recognize that interpretations of quantum mechanics are rival theories. (shrink)

Se presenta una reflexión antropológica y epistemológica de la situación actual de la Psicología clínica y de la Psiquiatría. Partiendo de los hechos y datos clínicos se plantea la necesidad de explicitar el fundamento filosófico (antropológico y ético) de estas disciplinas, y abrir estas áreas del saber a dimensiones no contempladas por las ciencias positivas. La equiparación de estas materias a las ciencias naturales lleva irremediablemente a un reduccionismo cientificista, que a su vez nos conduce a unas aporías clínicas insalvables, (...) originando distorsiones en nuestro modo de concebir y tratar los trastornos mentales. Se enfatiza en la noción central de naturaleza como referente obligado para una recta comprensión de nuestro quehacer profesional. (shrink)

El problema de determinar cuál es el método de la Ciencia de la Información ha sido objeto de distintos abordajes y propuestas metodológicas. En este trabajo defendemos que dichos problemas usualmente se han planteado de manera errónea, y que su planteo no contribuye a una mejora del campo. Comenzamos con un recorrido por diferentes propuestas metodológicas, señalando el consenso existente sobre el impacto de la indagación metodológica en el status científico de la disciplina. Luego rastreamos la influencia del positivismo en (...) la metodología de la CI, sosteniendo que la concepción positivista del método científico aún sigue gobernando de forma implícita la autopercepción epistemológica de la disciplina. Finalmente ensayamos una lectura de algunos problemas metodológicos basada en la filosofía de Thomas Kuhn, enfatizando que no es la reflexión metodológica, sino el desarrollo de una tradición exitosa de resolución de problemas lo que consolida el status científico. (shrink)

En este artículo discuto la relevancia que tiene el autorrespeto en la teoría de la justicia de Rawls. Para alcanzar dicho objetivo, en primer lugar examino las nociones de valor moral y mérito y su vinculación con el autorrespeto como forma de autovaloración. En segundo lugar, especifico las bases que sustentan el autorrespeto al interior de su teoría. Finalmente, discuto la función que tiene el autorrespeto en la justificación de los principios de la justicia como equidad.

En este artículo discuto la importancia que tiene para la teoría de la justicia de Rawls el desarrollo del sentido de la justicia como condición para la estabilidad social. Para cumplir con dicho objetivo analizo la interpretación que Rawls ofrece de nuestra psicología moral con la finalidad de evaluar su rol en la aceptación de los principios de justicia, así como las razones para fundar dicha estabilidad en determinados sentimientos morales. El análisis anterior me permitirá concluir que la búsqueda de (...) bases naturales para fundar los sentimientos morales constituye para Rawls una vía alternativa tanto al deductivismo moral, así como a cualquier forma de fundamentación metafísica de los principios que guían nuestras prácticas sociales. (shrink)

This paper analyzes Davidson´s classical version of the principle of charity,in order to suggest a reformulation from which it is possible to extractsome consequences regarding the nature of understanding. Thus, it is putforward an abandonment of the intencionalist hermeneutics as well as theCartesi..