Mehrtens' unsourced claim that Hilbert was interested in production rather than meaning appears to stem from Mehrtens' marxist leanings. Among Klein's credits is helping launch the career of Abraham Fraenkel, and advancing the careers of Sophus Lie, Emmy Noether, and Ernst Zermelo, all four surely of impeccable modernist credentials. Klein and Hilbert were equally interested in the axiomatisation of physics. Hilbert's views on intuition are closer to Klein's views than Mehrtens is willing to allow. Klein's Goettingen lecture and other texts shed light on Klein's modernism. We argue that Klein and Hilbert, both at Goettingen, were not adversaries but rather modernist allies in a bid to broaden the scope of mathematics beyond a narrow focus on arithmetized analysis as practiced by the Berlin school. Some of Mehrtens' conclusions have been picked up by both historians (Jeremy Gray) and mathematicians (Frank Quinn). Historian Herbert Mehrtens sought to portray the history of turn-of-the-century mathematics as a struggle of modern vs countermodern, led respectively by David Hilbert and Felix Klein. the Archimedean property, corroborating the non-Archimedean construal of the Leibnizian calculus. In a pair of 1695 texts Leibniz made it clear that his incomparable magnitudes violate Euclid's Definition V.4, a.k.a. ) currently in the process of digitalisation, sheds light on the nature of Leibnizian inassignable infinitesimals. A newly released 1705 manuscript by Leibniz (Puisque des personnes. We analyze a hitherto unnoticed objection of Rolle's concerning the lack of justification for extending axioms and operations in geometry and analysis from the ordinary domain to that of infinitesimal calculus, and reactions to it by Saurin and Leibniz. A careful examination of the evidence leads us to the opposite conclusion from Arthur's.
Of particular interest is evidence stemming from Leibniz's work Nouveaux Essais sur l'Entendement Humain as well as from his correspondence with Arnauld, Bignon, Dagincourt, Des Bosses, and Varignon. Leibniz's own views, expressed in his published articles and correspondence, led Bos to distinguish between two methods in Leibniz's work: (A) one exploiting classical 'exhaustion' arguments, and (B) one exploiting inassignable infinitesimals together with a law of continuity. The position of Bos and Mancosu contrasts with that of Ishiguro and Arthur. What kind of fictions they were exactly is a subject of scholarly dispute. Leibniz used the term fiction in conjunction with infinitesimals.
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