Abstract
This essay draws inspiration from Thomas Seebohm’s remarks on the origins of mathematical thinking in the lifeworld in his History as a Science and the System of Sciences. It argues that the crux of the phenomenological account of the origins of mathesmatics lies in the temporal constitution of mathematical idealities, above all with regard to phenomena associated with measurement. Such an account in turn promises to provide a sound basis for a nuanced conception of mathematical thinking that is well-suited to articulating problems germane to modern mathematics and the philosophy of mathematics.
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Notes
- 1.
“Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk.” The mathematician Heinrich Weber attributes this to Kronecker in his eulogy “Leopold Kronecker” (1891/1892, 19).
- 2.
The principle of which is “All intuitions are extensive magnitudes.” See Kant 1902, A162/B202–A166/B207.
- 3.
Seebohm cites Lohmar 1989 and Tieszen 1989. We can add the more recent volume edited by Mirja Hartimo (2010), which includes contributions from several scholars working on the phenomenological foundations of mathematics (and logic), including Guillermo Rosado-Haddock, Claire Ortiz Hill, Robert Hanna, and Olav Wiegand.
- 4.
This role of geometry is presented in detail in Boyer 1949.
- 5.
One of the best recent studies of the history and horizon of Hilbert’s Program is Sieg 2013.
- 6.
See Tieszen 2011, who provides an interesting and detailed elaboration of Gödel’s Platonism on phenomenological grounds.
References
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———. 2011. After Gödel. Oxford: Oxford University Press.
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Dodd, J. (2020). Mathesis and Lifeworld: Some Remarks on Thomas Seebohm’s History as a Science and the System of the Sciences. In: Nenon, T. (eds) Thomas Seebohm on the Foundations of the Sciences. Contributions to Phenomenology, vol 105. Springer, Cham. https://doi.org/10.1007/978-3-030-23661-8_8
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