Lior Rabi
Published Online: 30 Apr 2016
Page range: 46 – 70
Abstract
Ortega y Gasset is known for his philosophy of life and his effort to proposean alternative to both realism and idealism. The goal of this article is to focus onan unfamiliar aspect of his thought. The focus will be given to Ortega’s interpreta-tion of the advancements in modern mathematics in general and Cantor’s theory oftrans”nite numbers in particular. The main argument is that Ortega acknowledgedthe historical importance of the Cantor’s Set Theory, analyzed it and articulated aresponse to it. In his writings he referred many times to the advancements in mo-dern mathematics and argued that mathematics should be based on the intuition ofcounting. In response to Cantor’s mathematics Ortega presented what he de”nedas an ‘absolute positivism’. In this theory he did not mean to naturalize cognitionor to follow the guidelines of the Comte’s positivism, on the contrary. His aim wasto present an alternative to Cantor’s mathematics by claiming that mathematiciansare allowed to deal only with objects that are immediately present and observable tointuition. Ortega argued that the in”nite set cannot be present to the intuition andtherefore there is no use to differentiate between cardinals of different in”nite sets.
Cite
Rabi, Lior. “Ortega y Gasset on Georg Cantor’s Theory of Transfinite Numbers” Kairos. Journal of Philosophy & Science, vol.15, no.1, 2016, pp.46-70. https://doi.org/10.1515/kjps-2016-0003