In this talk I want to present Robinson’s monad as the essence of nonstandard analysis from a phenomenological point of view.
Husserl centered his systematic introduction to phenomenology of 1929, although titled Cartesian meditations, on a version of the Leibnizian notion of monad. In a letter of January 5, 1917, to his former student, Dietrich Mahnke, Husserl confessed that ‘I am in fact, a monadologist myself’. (As appears in Mark Van Atten and Juliette Kennedy 2003, 456(. The importance of monads for Husserl is brought out in the fourth meditation, where it is explained that all phenomenology is essentially a study of the monadic ego. The monadically concrete ego also includes the whole of its actual and potential existence. Although Husserl credits Leibniz for his insights, he faults him for not working them out systematically. The method that Husserl supplied, is the method of the phenomenological reduction of epoch which includes what Husserl calls the ‘eidetic reduction’ which is supposed to help us clarify the essence of the phenomena to be studied.
According to Robinson’s philosophical point of view logic is the basis of epistemology, since Logic according to Robinson deals, among other things, with the question of what makes sense in the eyes of the mathematician and there is a connection between that and what is understandable. According to Robinson’s philosophy of mathematics, there is harmony between epistemology and ontology; what is understandable also exists and therefore logic influences also the ontology of mathematics. The actual acts of consciousness can only come up with contingent truths, for example, the thought that we can talk about the standard real numbers as if they are unique up to isomorphism is an illusion. Robinson was not interested in the way that the real numbers appear to us, he was interested in their ontology and essences. Monad is a central concept in Robinson’s nonstandard analysis. Using reflection principle Robinson showed that everything that ‘is’, in nonstandard analysis, can in the final analysis be reduced to monads and vice versa, that monads reflect everything. Thus Robinson’s monad can be considered as the essence of nonstandard analysis.
Conference | Paper
Robinson's Monad from a Phenomenological Point of View
Tali Leven
Thursday 6th December 2018
16:40 - 17:40