Abstract
This essay argues that Jan Patočka ’s ‘Galileo Galilei and the End of the Ancient Cosmos’ goes beyond Husserl ’s fragmentary account of Galileo in The Crisis of European Sciences and Transcendental Phenomenology to present an account of the a priori eidetic structure of the foundation of a strand of the modern, scientific mathematisation of nature that is informed by actual history. In conjunction with this, Patočka adumbrates the eidetic structure of the concomitant limits on human meaning imposed by this historically dated conceptual foundation, insofar as the human being becomes a part of the mechanised world that Galileo’s accomplishment makes possible.
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Notes
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Published as “Beilage III” in Die Krisis der europäischen Wissenschaften und die transzendentale Phänomenologie. Eine Einleitung in die phänomenologische Philosophie (Husserl 1954). English translation: “The Origin of Geometry”, in The Crisis of European Sciences and Transcendental Phenomenology (Husserl 1970a). Henceforth, English and [German Husserliana Vol.] page numbers, respectively.
- 3.
Jan Patočka , ‘Galileo Galilei and the End of the Ancient Cosmos’, unpublished translation by Erika Abrams and Martin Pokorný (Patočka in press). Original publication: Patočka 1954.
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English and [German Husserliana Vol.] page numbers, respectively.
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As the following quote demonstrates, Kurt Gödel likewise recognised the contradiction the Ancient Greeks saw at the heart of arithmetic: “A set is a unity of which its elements are the constituents. It is a fundamental property of the mind to comprehend multitudes into unities. Sets are multitudes which are also unities. A multitude is the opposite of a unity. How can anything be both a multitude and a unity? Yet a set is just that. It is a seemingly contradictory fact that sets exist. It is surprising that the fact that multitudes are also unities leads to no contradictions: this is the main fact of mathematics . Thinking [a plurality] together seems like a triviality: and this appears to explain why we have no contradiction. But ‘many things for one’ is far from trivial” (Wang 1996: 254).
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NB: The standard translation of ἀρχή as ‘first principle’ occludes the distinction, crucial not just for Greek arithmetic but for any science of numbers, made by the Pythagoreans between the Form of numbers and the numbers themselves. ‘One’, as the ἀρχή of number, is precisely not a concept or principle (first or otherwise) of number but its most basic element; as such, it belongs not to its Form but to its numerical being.
- 7.
German edition: Klein 1936; 1934. See also Hopkins 2011: Ch. 19.
- 8.
Francisci Vietae , In Artem Analyticem (sic) Isagoge, Seorsim excussa ab opere restituate Mathematicae Analyseo, seu, Algebra Nova (Introduction to the Analytical Art, excerpted as a separate piece from the opus of the restored Mathematical Analysis, or The New Algebra [Tours, 1591]). English translation: Vietae 1992.
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Thus the attempt, for instance Patočka ’s, to capture the difference between the ancient and modern concepts of number in terms of “the much more abstract character” (Patočka in press) of the modern concept falls short of the mark of the difference in question; which, as we have seen, cannot be measured in terms of degrees of abstraction but only captured in terms of the transformation of the basic unit of arithmetic from a determinate multitude to the concept of such a multitude.
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German edition: Kant 2001: A140/B179.
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Hopkins, B.C. (2015). Nostalgia and Phenomenon: Husserl and Patočka on the End of the Ancient Cosmos. In: Učník, Ľ., Chvatík, I., Williams, A. (eds) The Phenomenological Critique of Mathematisation and the Question of Responsibility. Contributions To Phenomenology, vol 76. Springer, Cham. https://doi.org/10.1007/978-3-319-09828-9_5
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