In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.

Interpretations abound about Husserl’s understanding of the relationship between veridical perceptual experience and hallucination. Some read him as taking the two to share the same distinctive essential nature, like contemporary conjunctivists. Others find in Husserl grounds for taking the two to fall into basically distinct categories of experience, like disjunctivists. There is ground for skepticism, however, about whether Husserl’s view could possibly fall under either of these headings. Husserl, on the one hand, operates under the auspices of the phenomenological reduction, (...) abstaining from use of any epistemic commitments about mind-transcendent reality, whereas conjunctive and disjunctive accounts of perceptual experience, on the other hand, are both premised on some form of metaphysical realism. There seems to be a basic incompatibility between the former approach and the latter. I examine this line of thinking and argue that the incompatibility is only apparent. (shrink)

In this article I intend to show that certain aspects of the axiomatical structure of mathematical theories can be, by a phenomenologically motivated approach, reduced to two distinct types of idealization, the first-level idealization associated with the concrete intuition of the objects of mathematical theories as discrete, finite sign-configurations and the second-level idealization associated with the intuition of infinite mathematical objects as extensions over constituted temporality. This is the main standpoint from which I review Cantor’s conception of infinite cardinalities and (...) also the metatheoretical content of some later well-known theorems of mathematical foundations. These are, the Skolem-Löwenheim Theorem which, except for its importance as such, it is also chosen for an interpretation of the associated metatheoretical paradox (Skolem Paradox), and Gödel’s (first) incompleteness result which, notwithstanding its obvious influence in the mathematical foundations, is still open to philosophical inquiry. On the phenomenological level, first-level and second-level idealizations, as above, are associated respectively with intentional acts carried out in actual present and with certain modes of a temporal constitution process. (shrink)

This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to ...

This article is composed of three sections that investigate the epistemological foundations of Husserl’s idea of logic from the Logical Investigations . First, it shows the general structure of this logic. Husserl conceives of logic as a comprehensive, multi-layered theory of possible theories that has its most fundamental level in a doctrine of meaning. This doctrine aims to determine the elementary categories that constitute every possible meaning (meaning-categories). The second section presents the main idea of Husserl’s search for an epistemological (...) foundation for knowledge, science and logic. Their epistemological clarification can only be reached through a detailed analysis of the structure of those intentions that give us what is meant in our intentions. To reveal the intuitive giveness of logical forms is the ultimate aim of Husserl’s epistemology of logic. Logical forms and meaning-categories can only be given in a certain higher-order intuition that Husserl calls categorical intuition. The third section of this article distinguishes different kinds of categorical intuition and shows how the most basic logical categories and concepts are given to us in a categorical abstraction. (shrink)

In the present article, I address the issue of categorial representative contents, which, according to Husserl’s phenomenological theory, make knowledge possible by providing fullness to intuitive categorial acts. First, I discuss Husserl’s assertion that he no longer approves of his theory of categorial representation developed in Logical Investigations. I argue that the influential interpretation of Husserl’s self-criticism advanced by Dieter Lohmar is unfortunately misleading, as Husserl does not actually claim that categorial representatives are contents of reflection belonging to the realm (...) of inner sensibility, as Lohmar contends. After offering an alternative view of Husserl’s authentic position in Logical Investigations, I examine other possible reasons for his later dissatisfaction. These reasons relate to Husserl’s changing views on the role of categorial representatives in empty thinking acts—necessarily involved in cognition—and the necessity of spontaneously repeating the passive synthesis between the intentional matters that function as categorial representatives in the predicative activity yielding knowledge. (shrink)

There is a lot of misunderstanding and ignorance about Husserl’s philosophy among analytic philosophers. The present paper attempts to help correct that situation. It begins with some quotations of Husserl written around 1890, which clearly establish that he arrived at the distinction between sense and reference with independence from Frege. Then follows a brief survey of the most important themes of Husserl’s Logical Investigations, emphazising those that are of special interest to analytic philosophers. The paper concludes by mentioning other interesting (...) issues treated in later Husserlian writings, including his valuable conferences on ancient and modern logic from 1908-1909.Existen muchos malentendidos y mucha ignorancia acerca de la filosofía de Husserl entre los filósofos analíticos. El presente artículo intenta contribuir a corregir esa situacion. Él comienza con algunas citas de Husserl de aproximadamente 1890, que claramente establecen que Husserl obtuvo la distinción entre sentido y referente con independenica de Frege. Luego sigue un breve recuento de los más importantes temas de las Investigaciones Lógicas de Husserl, destacando aquéllos que son de particular interés para los filósofos analíticos. El artículo concluye haciendo référencia a otros temas tratados en escritos posteriores de Husserl, incluyendo sus valiosas conferencias acerca de lógica antigua y moderna de 1908-1909. (shrink)