Two Models of Radical Revelation in Austrian Philosophy

In this paper I highlight two opposing models of the notion of divine revelation: the propositional and the radical. The propositional understanding of revelation was central to theology and philosophy until the 19th century. Since then, a number of other models of revelation have emerged. I define as radical the understanding of revelation which emphasizes two features of revelation: (1) God’s existence is per se revelatory; (2) God’s revelation is per se self-revelation. I propose too an assessment of the notion of propositional revelation as presented by Richard Swinburne. And I offer detailed analyses of two representatives of the early understanding of divine revelation as self-revelation: the views of Bernard Bolzano and Anton Günther. Bolzano, the renowned mathematician, was also a philosopher of religion; and Günther, one of the most ingenious writers in Austrian philosophy, was not only a theologian but also a philosopher comparable to the important figures of 19th-century G

Avicenna's Philosophy of Mathematics

I discuss four different aspects of Avicenna’s philosophical views on mathematics, as scattered across his various works. I first explore the negative aspect of his ontology of mathematics, which concerns the question of what mathematical objects (i.e., numbers and geometrical shapes) are not. Avicenna argues that mathematical objects are not independent immaterial substances. They cannot be fully separated from matter. He rejects what is now called mathematical Platonism. However, his understanding of Plato’s view about the nature of mathematical objects differs from both Plato’s actual view and the view that Aristotle attributes to Plato. Second, I explore the positive aspect of Avicenna’s ontology of mathematics, which is developed in response to the question of what mathematical objects are. He considers mathematical objects to be specific properties of material objects actually existing in the extramental world. Mathematical objects can be separated, in mind, from all the specific kinds of matter to which they are actually attached in the extramental word. Nonetheless, inasmuch as they are subject to mathematical study, they cannot be separated from materiality itself. Even in mind they should be considered as properties of material entities. Third, I scrutinize Avicenna’s understanding of mathematical infinity. Like Aristotle, he rejects the infinity of numbers and magnitudes. But he does so by providing arguments that are much more sophisticated than their Aristotelian ancestors. By analyzing the structure of his Mapping Argument against the actuality of infinity, I show that his understanding of the notion of infinity is much more modern than we might expect. Finally, I engage with Avicenna’s views on the epistemology of mathematics. He endorses concept empiricism and judgment rationalism regarding mathematics. He believes that we cannot grasp any mathematical concepts unless we first have had some specific perceptual experiences. It is only through the ineliminable and irreplaceable operation of the faculties of estimation and imagination upon some sensible data that we can grasp mathematical concepts. By contrast, after grasping the required mathematical concepts, independently from all other faculties, the intellect alone can prove mathematical theorems. Other faculties, and in particular the cogitative faculty, can assist the intellect in this regard; but the participation of such faculties is merely facilitative and by no means necessary

Heideggerian Marxism

An extended review of the English collection of Marcuse's essays and interviews on Heidegger that addresses the philosophical basis of a synthesis of Marx and Heidegger

Early numerical cognition and mathematical processes

In this paper I study the development of arithmetical cognition with the focus on metaphorical thinking. In an approach developing on Lakoff and Núñez (2000), I propose one particular conceptual metaphor, the Process → Object Metaphor (POM), as a key element in understanding the development of mathematical thinking.; En este artículo estudio el desarrollo de la cognición aritmética enfocado en el pensamiento metafórico. En una propuesta que se desarrolla desde la de Lakoff y Núñez (2000), propongo una metáfora particular conceptual, la Metáfora Proceso → Objeto (POM), como un elemento clave para comprender el desarrollo del pensamiento matemátic

Early numerical cognition and mathematical processes

In this paper I study the development of arithmetical cognition with the focus on metaphorical thinking. In an approach developing on Lakoff and Núñez (2000), I propose one particular conceptual metaphor, the Process → Object Metaphor (POM), as a key element in understanding the development of mathematical thinking.; En este artículo estudio el desarrollo de la cognición aritmética enfocado en el pensamiento metafórico. En una propuesta que se desarrolla desde la de Lakoff y Núñez (2000), propongo una metáfora particular conceptual, la Metáfora Proceso → Objeto (POM), como un elemento clave para comprender el desarrollo del pensamiento matemátic