Cantorian Theory of Transfinite Numbers: Its Relation with Analogical-Geometric Thought
DOI:
https://doi.org/10.15448/1984-6746.2016.2.25652Keywords:
Set theory. Geometric intuition. G. Cantor. Exiom of constructability. K. Gödel.Abstract
In this short article, I analyze how geometric intuition was present in the seminal development of Cantor’s set theory. From this fact, it follows that the notion of set or transfinite number was not treated by Cantor as something worthy of a logical foundation. The paradoxes that have arisen in Cantor's theory are the result of such initial disengagement, and subsequent attempts to solve them have resulted in intuitive and expected aspects on sets or the infinite being lost. In particular, we see here the “non geometric” consequences of Gödel´s axiom of constructible sets.
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