This paper examines two alleged limitations in the use of formal languages: on the one hand, the trade-offs between expressive and inferential power, and on the other, the phenomenon of system imprisonment. After reconceptualizing the issue, we consider the role played by modality in the understanding of certain aspects of mathematical structures and argue for its centrality.

Although number sentences are ostensibly simple, familiar, and applicable, the justification for our arithmetical beliefs has been considered mysterious by the philosophical tradition. In this paper, I argue that such a mystery is due to a preconception of two realities, one mathematical and one nonmathematical, which are alien to each other. My proposal shows that the theory of numbers as properties entails a homogeneous domain in which arithmetical and nonmathematical truth occur. As a result, the possibility of arithmetical knowledge is (...) simply a consequence of the possibility of ordinary knowledge. (shrink)

In this paper, we examine two conceptions of the application of logic and assess their comparative merits. The first is a platonist monist conception that characterizes the logical consequence relation as an abstract relation among propositions. We argue that this proposal, which insists on logic’s topic neutrality, accommodates very well the objectivity of logic. From this perspective, there are no constraints on particular topics. As a result, we have the universality that allows us to go through a wide scope of (...) contexts where logic is applied. In contrast, a non-platonist pluralist conception is examined, and it characterizes the variety of logical consequence relations as concrete, context-dependent in particular cases, and topic-dependent. As will become clear, this conception is particularly well suited to make room for the applications of logic. We conclude that, in order to solve the ontological debate about logic, we need to go beyond its applications. (shrink)

José Ferreirós y Abel Lasalle Casanave, El árbol de los números: cognición, lógica y práctica matemática, Editorial Universidad de Sevilla, Sevilla, 2015, 256 pp.

Este es un libro que nace de nuestro compromiso por señalar las contribuciones de las filósofas a partir de la pregunta vital: ¿Quiénes nos formaron? Como resultado, se presenta este diálogo a doce voces; reunidas para dialogar, desde distintos lugares en América Latina, sobre nuestra formación teórica, profesional y humana desde una plataforma equitativa y franca. Concebido, en medio de la pandemia por SARS-CoV-2, queremos construir un espacio abierto a nuevas ideas, propuestas e identidades en la Filosofía. Más aún, queremos (...) invitar a nuestros alumnxs a vislumbrar las posibilidades de un cambio radical en la forma en que concebimos y hacemos filosofía. (shrink)