Abstract

CARVALHO, Tadeu Fernandes de  and  D'OTTAVIANO, Itala Maria Loffredo. Calculus infinitesimalis: uma teoria entre a razão e o mito?. Ciência educ. [online]. 2012, vol.18, n.04, pp.981-996. ISSN 1516-7313.

In this paper we go through the historical, logical and mathematical paths which join infinitesimal calculus to the non-standard analysis of Abraham Robinson, and this to paraconsistent differential calculus - a calculus proposed by Newton da Costa, supported by paraconsistent logic and paraconsistent set theory. We present for this calculus, some unpublished concepts and properties, including a transfer theorem establishing the conditions under which a given formula is a theorem of classical calculus if, and only if, there is an "interpretation" of the same which is a theorem of paraconsistent calculus. We conclude the paper with some considerations about the teaching of Calculus with emphasis on use of infinitesimal approach.

Keywords : Calculus Infinitesimalis; Paraconsistent Calculus; Non-Standard Analysis; History; Costa, Newton da.

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