Abstract
Having gone into some detail on the structural (i.e. semantical and syntactical) moments of a mathematical theory, we shall now broaden our scope and show how mathematical theories are related to more general philosophical, especially epistemological but also some ontological, questions. This broadening of the terrain will require, however, some knowledge of questions of a philosophical nature.To plunge into the present discussions on the philosophy of mathematics immediately would be somewhat premature. Our procedure shall be first to look back in time and see how the present problems have arisen, thereby allowing ourselves to gain valuable insight into the origin of present discussions, while at the same time letting related philosophical problems come to the fore. In this manner the discussions on the philosophy of mathematics will be seen against their historical background while the related philosophical questions will lose some of their unfamiliarity.
-ξύν νόωι λέγοντας ίσχυρίζεσϑαι χρή τώι ξυνώι πάντων, őκωσπερ νόμωι πόλις, καί πολύ ίσχυροτέρως
Heraclitos, DK B frgmnt 114.
[Those who speak with reasonable insight should reinforce themselves with that which is common to all, just as a town becomes strong by its legislation, and even stronger (than a town).]
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© 1977 Springer Science+Business Media Dordrecht
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Kuyk, W. (1977). Epistemological Aspects of Mathematics in Historical Perspective. In: Complementarity in Mathematics. Mathematics and Its Applications, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7624-6_2
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DOI: https://doi.org/10.1007/978-94-015-7624-6_2
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