According to Kant, the axioms of intuition, i.e. space and time, must provide an organization of the sensory experience. However, this first orderliness of empirical sensations seems to depend on a kind of faculty pertaining to subjectivity, rather than to the encounter of these same intuitions with the real properties of phenomena. Starting from an analysis of some very significant developments in mathematical and theoretical physics in the last decades, in which intuition played an important role, we argue that nevertheless (...) intuition comes into play in a fundamentally different way to that which Kant had foreseen: in the form of a formal or “categorical” yet not sensible intuition. We show further that the statement that our space is mathematically three-dimensional and locally Euclidean by no means follows from a supposed a priori nature of the sensible or subjective space as Kant claimed. In fact, the three-dimensional space can bear many different geometrical and topological structures, as particularly the mathematical results of Milnor, Smale, Thurston and Donaldson demonstrated. On the other hand, it has been stressed that even the phenomenological or perceptual space, and especially the visual system, carries a very rich geometrical organization whose structure is essentially non-Euclidean. Finally, we argue that in order to grasp the meaning of abstract geometric objects, as n-dimensional spaces, connections on a manifold, fiber spaces, module spaces, knotted spaces and so forth, where sensible intuition is essentially lacking and where therefore another type of mathematical idealization intervenes, we need to develop a new form of intuition. (shrink)

El artículo revela cómo la filosofía que desarrolló Karl Marx estuvo centrada en el tema de la vida. La esencia de la comprensión marxiana de la sociedad y la historia no radica en una primacía abstracta de lo económico, sino en el proceso real de producción y reproducción de la vida. Es la vida –y no la economía por sí misma– la que constituye el fundamento de la concepción materialista de la historia desarrollada por Marx.

The aim of this work is to elucidate the meaning of 'infinity' from a phenomenological perspective, especially within the framework of Husserl’s theory of knowledge and perception. In the first chapter I firstly sketch the basics of Husserl’s phenomenology of knowledge. Thereafter I delve into the questions concerning the reduction to the 'reellen Bestand', which is hold to be the ground of verification of purports in the "Logical Investigations". I then propose an interpretation of the categorial intuition as directed to (...) the laws an 'Auffassung' follows when it organizes the sensual contents related to an object. In the second chapter I briefly expound Husserl’s phenomenology of perception and I show how perception can be hold as an intentional experience. Afterwards I concentrate on the constitution of space and of thing (Ding). I show in which sense the structures of both constitutions are dependent on the sensations and kinesthesis (i.e. proprioceptions) experienced by the subject. In the third chapter I finally deal with the problem of infinity. I face some recent interpretations of Husserl’s theory of perception according to which infinity is somehow intertwined in and even intuited through thing-perception (Dingwahrnehmung). I claim that thing-perception can not be hold as an access to infinity, i.e. no thing-perception is a perception of something as infinite. Following I show how some other kinds of sensual experience can correspond to a perception of infinity. On the base of some Husserl’s manuscripts and through a brief confrontation with Kant’s Analytic of the Sublime I sustain that infinity can be sensually intuited in the senses of limitlessness and of formlessness. I then show that categorial intuition is necessary in order to constitute the meaning of mathematical infinity, i.e. an endless whole of discrete parts. In fact, the idea of such an “entity” is dependent on the capacity of grasping the law of a serial production. In the conclusion I establish that mathematical infinity is the only kind of infinity which can not find any sensual correlate. This is due to the fact that it is a meaning composed by two contradictory prescriptions: 'reach the limitless' and 'go on without an end'. I consequently argue that the idea of infinity is grounded on sensual experience and does not need any supernatural origin. (shrink)