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Important reference School of Aristotle
Eudemus of Rhodes edited by Istv?n Bodn?r and William W. Fortenbaugh (Rutgers University Studies in Classical Humanities, Volume XI: Transaction Publishers) Eudemus of Rhodes (2nd half of 4th cent. BCE.), was a pupil of Aristotle in the second half of the fourth century BCE. This volume is composed entirely of articles that discuss Eudemus from a variety of viewpoints.
In a charming story in Aulus Gellius (13.5), when Aristotle was dying, he chose Theo?phrastus over Eudemus as his successor in the Lyceum. Eudemus apparently returned to Rhodes on Aristotle's death and founded his own. school; Simplicius (In Phys. 923.9-15) mentions an exchange of letter between him and Theophrastus on a textual question in Aristotle's Physics. Simplicius also (924.13) mentions a biography of Eudemus by one Damas, of whom nothing else is known.
There are ascribed to Eudemus in various places two books of Analytics, a Categories, On Expression, On the Angle, Physics, and histories of geometry, arithmetic, and astronomy. Simpli?cius refers to Eudemus as "the most genuine of Aristotle's comrades" (In Phys. 411.15-16) and says that he "follows Aristotle in all things" (133.. 22). Though not entirely true, this appears not far off.
In logic, Eudemus and Theophrastus (who are always mentioned to?gether in this connection) made various modifications to Aristotle's syl?logistic; Alexander, in his commentary on the Prior Analytics, cites the following Alexander is echoed by the other commentators on most a, these points): (i) Theophrastus and Eudemus devised a direct proof of the convertibility of universal negative propositions (Alexander 31.4-10; contrast Ar. APri. 1.2, 25a14-17). (ii) They adopted the peiorem rule in modal logic: "that the conclusion is always assimilated to the lesser and weaker of the premises" (Alexander 124.13-14; by contrast Aristotle al?lowed certain combinations of necessary and assertoric premises to yield necessary conclusions, as in APri. 1.9). (iii) They defended the convert- ibility of universal negative problematic propositions (Alexander 220.9- 16, against Ar. APri. 1.17, 36b35-37a31). (iv) They also did extensive work on hypothetical syllogisms (Alexander 389.31-390.3; Philoponus, In APri. 242.18-19, speaks of "treatises of many lines" on the subject).
Eudemus is said to have claimed in On Expression (Alexander In APri. 16.15-17, scholium in APri. ed. Brandis [in Aristotelis Opera 4]. 146a24-27) that "is" in "Socrates is" is a predicate term; he may thus have been the first to have contradicted Kant's claim that existence is not a predicate. Alexander's notice of this is phrased in a way that makes to appear to contradict Aristotle (at least under Alexander's interpretation of Aristotle: 15.14-22).
All we know of On the Angle is that Eudemus argued in it that the angle is in the category of quality on the ground that straightness is a quality, fractures are qualities, and an angle is a fractured straightness (Proclus In Eucl. 125.6-13).
The most substantial remains of Eudemus' work are from the Physics; this seems to have been a paraphrase of or commentary on Aris?totle's Physics. Simplicius, in the introduction to his commentary on Physics 7, says (In Phys. 1036.13-15): "Eudemus, having followed the main points in the entire treatise up to this point, passes by this book as superfluous, and proceeds to what is in the last book."
Eudemus' historical works were of very great importance; much of what we know about the early history of mathematics, including as?tronomy, is traceable to Eudemus. Proclus three times quotes him by name for historical points (In Eucl. 299.3, 333.6, 352.14), and Proclus' re?port of the history of geometry before Euclid (64.16-68.6) seems to be taken from Eudemus. Simplicius quotes long extracts from Eudemus de?scribing Hippocrates of Chios' quadrature of the lune (In Phys. 60.22?68.32). Eutocius quotes him for Archytas' solution to the problem of the duplication of the cube (commentary on Archimedes On the Sphere and the Cylinder 2, in Archimedis Opera Omnia ed. Heiber/Stamatis 3.84.12?88.2). The extracts preserved from Eudemus' histories of arithmetic and astronomy (see Wehrli, frs. 143-149) are less extensive, but illustrate his importance for the transmission of what knowledge we have.
Seven passages in Aelian's On the Nature of Animals name a Eudemus as the source for wild stories about animals, but, although *Apuleius (Apologia 36) credits Eudemus along with Aristotle, Theophrastus, and Lyco with books on the genera?tion of animals, these passages seem unlikely to have come from our Eu?demus.
The treatise entitled Eudemian Ethics in the corpus Aristotelicum was taken in the 19th century to be Eudemus'; it is now thought to be Aristotle's
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