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The British journal for the philosophy of science, 2016-06, Vol.67 (2), p.579-615
Ort / Verlag
Oxford: Oxford University Press
Erscheinungsjahr
2016
Link zum Volltext
Quelle
Oxford Journals 2020 Humanities
Beschreibungen/Notizen
Neologicists have sought to ground mathematical knowledge in abstraction. One especially obstinate problem for this account is the bad company problem. The leading neologicist strategy for resolving this problem is to attempt to sift the good abstraction principles from the bad. This response faces a dilemma: the system of 'good' abstraction principles either falls foul of the Scylla of inconsistency or the Charybdis of being unable to recover a modest portion of Zermelo—Fraenkel set theory with its intended generality. This article argues that the bad company problem is due to the 'static' character of abstraction on the neologicist's account and develops a 'dynamic' account of abstraction that avoids both horns of the dilemma.