Eudoxos versus Dedekind

• Authors: Piotr Błaszczyk

Title variants

PL

Eudoxos versus Dedekind

EN

Eudoxos versus Dedekind

• Languages of publication: PL

Abstracts

PL

All through the XXth century it has been repeated that "there is an exact correspondence, almost coincidence between Euclid's definition of equal ratios and the modern theory of irrational numbers due to Dedekind". Since the idea was presented as early as in 1908 in Thomas Heath's translation of Euclid's Elements as a comment to Book V, def. 5, we call it in the paper Heath's thesis. Heath's thesis finds different justifications so it is accepted yet in different versions. In the paper its historical and mathematical version is reconstructed. We next reconstruct Eudoxos' theory of proportions in an axiomatic fashion. Finally, we show that Heath's thesis both in the historical and mathematical version is false. To this end a counterexample is given; it is based upon a specific interpretation of the uniform distribution theorem.

• Publisher: University of Warsaw, Institute of Philosophy
• Journal: Filozofia Nauki
• Year: 2007
• Volume: 15
• Issue: 2
• Pages: 95-113

Dates

published

2007-06-01

Contributors

author

Piotr Błaszczyk