Pasch’s Empiricism as Methodological Structuralism
2020 ◽
pp. 88-105
This chapter presents Pasch’s structuralist methodology within his empiricist philosophy. Two criteria for a minimal version of methodological structuralism are proposed, and it is argued that they are met in Pasch’s work on projective geometry and the foundations of arithmetic, despite the fact that Pasch firmly held an empiricist standpoint according to which only empirical objects can ultimately serve as a foundation for mathematics. What drove Pasch toward his version of structuralism were his focus on rigorous deductions, the duality of projective geometry, and the independence of arithmetical results from the referents of numerals.
Keyword(s):
1993 ◽
Vol 54
(2)
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pp. 191-206
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Keyword(s):
1908 ◽
Vol s2-6
(1)
◽
pp. 224-239
Keyword(s):
Keyword(s):
1983 ◽
Vol 15
(1)
◽
pp. 31-34
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Keyword(s):
1991 ◽
Vol 11
(5-6)
◽
pp. 549-578
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Keyword(s):
1969 ◽
Vol 44
(1)
◽
pp. 310-315
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