<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Ortega y Gasset is known for his philosophy of life and his effort to propose an alternative to both realism and idealism. The goal of this article is to focus on an unfamiliar aspect of his thought. The focus will be given to Ortega’s interpretation of the advancements in modern mathematics in general and Cantor’s theory of transfinite numbers in particular. The main argument is that Ortega acknowledged the historical importance of the Cantor’s Set Theory, analyzed it and articulated a response to it. In his writings he referred many times to the advancements in modern mathematics and argued that mathematics should be based on the intuition of counting. In response to Cantor’s mathematics Ortega presented what he defined as an ‘absolute positivism’. In this theory he did not mean to naturalize cognition or to follow the guidelines of the Comte’s positivism, on the contrary. His aim was to present an alternative to Cantor’s mathematics by claiming that mathematicians are allowed to deal only with objects that are immediately present and observable to intuition. Ortega argued that the infinite set cannot be present to the intuition and therefore there is no use to differentiate between cardinals of different infinite sets.</p></abstract>

Ortega y Gasset is known for his philosophy of life and his effort to propose an alternative to both realism and idealism. The goal of this article is to focus on an unfamiliar aspect of his thought. The focus will be given to Ortega’s interpretation of the advancements in modern mathematics in general and Cantor’s theory of transfinite numbers in particular. The main argument is that Ortega acknowledged the historical importance of the Cantor’s Set Theory, analyzed it and articulated a response to it. In his writings he referred many times to the advancements in modern mathematics and argued that mathematics should be based on the intuition of counting. In response to Cantor’s mathematics Ortega presented what he defined as an ‘absolute positivism’. In this theory he did not mean to naturalize cognition or to follow the guidelines of the Comte’s positivism, on the contrary. His aim was to present an alternative to Cantor’s mathematics by claiming that mathematicians are allowed to deal only with objects that are immediately present and observable to intuition. Ortega argued that the infinite set cannot be present to the intuition and therefore there is no use to differentiate between cardinals of different infinite sets.

Ortega y Gasset on Georg Cantor’s Theory of Transfinite Numbers

Kairos. Journal of Philosophy & Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Ortega y Gasset on Georg Cantor\u2019s Theory of Transfinite Numbers"}

Ortega y Gasset is known for his philosophy of life and his effort to propose an alternative to both realism and idealism. The goal of this article is to focus...

Ortega y Gasset on Georg Cantor’s Theory of Transfinite Numbers

Published Online: Apr 30, 2016

Page range: 46 - 70

DOI: https://doi.org/10.1515/kjps-2016-0003

Keywords
Ortega y Gasset, Georg Cantor, Galileo, infinite set, intuitionism

© 2016 Lior Rabi, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Ortega y Gasset on Georg Cantor’s Theory of Transfinite Numbers

Published Online: Apr 30, 2016

Page range: 46 - 70

DOI: https://doi.org/10.1515/kjps-2016-0003

KeywordsOrtega y Gasset, Georg Cantor, Galileo, infinite set, intuitionism

© 2016 Lior Rabi, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Ortega y Gasset, Georg Cantor, Galileo, infinite set, intuitionism