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Adam de Wodeham: Tractatus de Indivisibilibus
A Critical Edition with Introduction, Translation, and Textual Notes
Synthese Historical Library
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The English Franciscan philosopher and theologian, Adam of Wodeham (d. 1358), was a disciple and friend of William of Ockham; he was also a student of Walther Chatton. Nevertheless, he was an independent thinker who did not hesitate to criticize his former teachers - Ockham sporadically and benevolently, Chatton, frequently and aggressively. Since W odeham developed his own doctrinal position by a thorough critical examination of current opinions, the first part of this introduc tion briefly outlines the positions of the chief figures in the English controversy over indivisibles. The second part of the introduction pre sents a summary of Wodeham's views in the Tractatus de indivisibilibus, lists the contents of the treatise, and considers the question of its date and its chronological position in the context of Wodeham's other works. In the third part, the editorial procedures used here are set forth. 1. THE INDIVISIBILIST CONTROVERSY In the literature of the 13th and 14th centuries, the term 'indivisible' refers to a simple, un extended entity. Consequently, these indivisibles are not physical atoms but either mathematical points, temporal instants or indivisibles of motion, usually called mutata esse. I THOMAS BRADWARDINE (d. 1349), roughly contemporary with Wodeham, classified the positions it was possible to take regarding indivisibles. He described his own view as the common view, that of "Aristotle, A verroes, and most of the moderns," according to which a "continuum was not composed of atoms (athomis) but of parts divisible without end.
1 / Introduction.- 1. The Indivisibilist Controversy.- Indivisibilists: 1.1. Henry of Harclay.- 1.2. Robert Grosseteste.- 1.3. Walter Chatton.- 1.4. William Crathorn.- Divisibilists: 1.5. William of Ockham.- 1.6. John Duns Scotus.- 1.7. William of Alnwick.- 1.8. Walter Burley.- 2. Tractatus de indivisibilibus.- 2.1. The Author.- 2.2. The Contents.- 2.3. Date Written.- 2.4. Quaestio de divisione et compositione continui.- 2.5. The Date of the Quaestio.- 3. Editorial Principles.- 4. Notes to the Introduction.- II / Text and Translation.- Question 1: Whether forms or extended continua are composed of indivisibles.- Article 1: Twelve arguments proving that continua are not composed of indivisibles.- Article 2: Twelve arguments by Harclay and Chatton purporting to show that continua are composed of indivisibles.- Article 3: Refutation of Harclay’s and Chatton’s arguments.- Question 2: Whether among continua there is any indivisible extensive quantum, or among augmentable forms any intensive indivisible.- Article 1: A proof that neither points nor lines nor surfaces exist.- Article 2: Arguments purporting to show that there must be indivisibles in continua.- Article 3: Replies to the arguments in article 2.- Question 3: Doubts about whether a continuum is infinitely divisible or composed of indivisibles.- Doubts based on Zeno’s arguments.- Doubt 1.- Doubt 2.- Doubt 3.- Doubt 4.- Doubt 5: Whether there are actually infinitely many parts in a continuum.- Doubt 6: Whether there is a natural minimum or least indivisible part.- Doubt 7: Whether a continuum can be divided into infinitely many parts of the same size.- Arguments purporting to show that if it is composed of infinitely many such parts, then it is actually infinite.- Proof that a continuum may be divided into infinitely many completely distinct parts.- Reply to the first arguments.- Question 4: Whether the infinite divisibility of a continuum can be reduced to actuality.- Article 1: A continuum cannot be divided into its parts.- Article 2: The parts of a continuum can be divided.- Doubts.- Question 5: Whether there are more parts of the same proportion in a larger continuum than in a smaller.- Article 1: Proof that there are more parts of the same proportion in a larger continuum.- Article 2: Objections against this proof.- Article 3: Replies to the objections.- III / Notes to the Text.- Notes to Question 1.- Notes to Question 2.- Notes to Question 3.- Notes to Question 4.- Notes to Question 5.- IV / Appendix.- William Crathorn, “De continuo”.- Indices.
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Metaphysik & Ontologie