Abstract
‘Mathematics is the science of the infinite, its goal the symbolic comprehension of the infinite with human, that is finite, means.’ Along this line, in The Open World, Hermann Weyl contrasted the desire to make the infinite accessible through finite processes, which underlies any theoretical investigation of reality, with the intuitive feeling for the infinite ‘peculiar to the Orient,’ which remains ‘indifferent to the concrete manifold of reality.’ But a critical analysis may acknowledge a valuable dialectical opposition. Struggling to spell out the infinity of real numbers mathematicians come to see the active role of emptiness. Pondering over the essence of self-awareness, the Japanese philosopher Nishida Kitarō comes to see the ‘place’ where it abides as absolute nothingness. Thus, the two ways of seeing coalesce into a perspective in which infinity and nothingness mirror each other.
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Notes
For more, see in particular Kemp (1990).
For a thorough analysis, see Friedman (2012).
In his Geometrie der Lage (Nürnberg 1847).
For more, see Stillwell (2018), pp. 14–16.
See My Philosophical Path (1939), in Yusa (2002), p. 301.
For an insightful discussion, see Ghilardi (2009).
For a deeper analysis, see Maraldo (2006).
For more, see Yusa (2002), p. 203.
Aristotle De anima 429A 27–29; quoted in Nishida (2012), p. 6.
For an insightful discussion, see Tremblay (2000).
For more details, see Dalissier (2008).
‘Here I made the point of departure of my philosophy’ (Nishida 1987b, p. 67).
For more details, see Stillwell (2013), p. 82.
On the origin of zero and the logic of the Prajnaparamitra Sutra, see Matsuo (1987).
In contrast with the measure argument for the uncountability of real numbers (mentioned above), Cantor constructed a real number x unequal to each member of a given countable set S = {x1, x2, x3, x4, ...} of real numbers (and therefore, not in S). For more details, see Stillwell (2013), pp. 70–72.
For a thoughtful analysis, see Weyl (2009).
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Acknowledgements
I thank Agustín Jacinto Zavala, Masato Mitsuda, and Jacynthe Tremblay for reading an earlier draft of this article, and John Stillwell for corrections and helpful comments.
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Lupacchini, R. A Philosophical Path from Königsberg to Kyoto. SOPHIA 60, 851–868 (2021). https://doi.org/10.1007/s11841-020-00776-7
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DOI: https://doi.org/10.1007/s11841-020-00776-7