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Author: Burt C. Hopkins

, 2005, 2006), and Lisa Sha- bel (1998) have done important work on the historical context that informed Kant's understanding of mathematics. They have shown that in addition to Euclid's writings on geometry and the general theory of arithmetical and geomet- rical proportions, Kant's understanding of

In: The Philosophy of Edmund Husserl
Author: Martin Pleitz

paradigmatic example of Euclid’s axiomatic treatment of geometry, the axioms of a theory are truths about the subject matter of the theory which are so basic that they entail everything the theory has to say about its subject matter (and thus are ideally suited to organize the body of knowledge constituted by

In: Logic, Language, and the Liar Paradox
Author: Peter M. Simons

suitable variable, or if there are too few. Take for example Euclid's statement [9] There are infinitely many prime numbers and assurne it is true. On the face-value interpretation this requires the exis- tence of infinitely many prime numbers. On the substitutional interpretation, for it to have the

In: Reflections on Free Logic

modal notions. But there are pertinent examples that suggest otherwise (see Baker/Hacker 1985: ch. VIII). Statements that were once regarded as paradigms of necessary truth, such as Euclid’s 5th axiom or the claim that there cannot be negative numbers have not just been stripped of their necessary

In: The A Priori and Its Role in Philosophy

einer Definition erforderlich ist. Euclid’s Definition von Parallellinien ist von der Art. 1Anmerkung in der Akademie-Ausgabe. 2Bei Textpassagen mit vorangestelltem 𝑔 handelt es sich um Zusätze Kants aus derselben Schriftphase. 3In eckigen Klammern [ ] stehen von Kant ausgestrichene Wörter und

In: Kant zur Philosophie der Mathematik

represent the same figure, a circle, but whereas the first is simply a genetic version of Euclid’s definition and his corresponding postulate, Euclid demanded a demonstration in the case of the second. (See On Universal Synthesis and Analysis, or the Art of Discovery and Judgment [PPL 230].) 40 P 4:316, KrV

In: From Leibniz to Kant

. Whittaker, E. (1958) From Euclid to Eddington, New York: Dover Publications. Wilson,]. (2006) Jorge Luis Borges, London: Reaktion Books. Wingenstein, L. (1993) Tractatus Logico-Philosophicus, London: Routledge. Wingenstien, L. (1958) Philosophical Investigations, Oxford: Basil Blackwell. Zammito, ]. H

In: Kant: Here, Now and How

proved in this way. The second way is to show “how such a thing could come into being”, since “if we know how something could come into being, we may no more doubt as to whether it could be”. Wolff explains that Euclid “proves in this way that an equilateral triangle is possible when he shows how [such a

In: From Leibniz to Kant

AnPo 1.4-5, see 1.4, 73b32-4 and my 2006a. 322 Pieter Sjoerd Hasper References Acerbi, F. 2008. Euclid's Pseudaria. Archive o[ the History o[ the Exad Sciences 62, 511-551. Bolton, R. 1990. The Epistemological Basis of Aristotelian Dialectic. In: Devereux, D./ Pellegrin, P. (eds.). Biologie

In: Fallacious Arguments in Ancient Philosophy