Abstract

Paradoxos, o infinito e a intuição geométrica. Educação e Filosofia [online]. 2011, vol.25, n.50, pp.717-739. ISSN 1982-596X.

This paper studies some mathematical results formerly characterized as opposed to the intuition and also carries out a query for the possible causes of this counter-intuitive feature. In this sense, both Tarski-Banach and Galileo’s paradoxes are discussed and Cantor’s proof that the segment and the square have the same number of points is analyzed. In particular, it is examined the role that the concept of infinity and such principles as “the whole is greater than the part” have in these paradoxes. Furthermore, the effect that geometrical intuitions have on some paradoxes as well as the relationship between these intuitions and the concept of geometry of the Erlanger Programm of Felix Klein are discussed.

Keywords : Paradox; Intuition; Erlanger Programm.

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