God, indivisibles, and logic in the later middle ages: Adam Wodeham's response to Henry of Harclay

Medieval Philosophy and Theology

Volumn 7, Issue 1, 1998, Pages 69-87

  Sylla, Edith Dudley ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

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EID: 64149097819     PISSN: 10570608     EISSN: None     Source Type: Journal    
DOI: 10.5840/medievalpt1998715     Document Type: Article

References (33)

1. Adam de Wodeham, Tractatus de indivisibilibus. A Critical Edition with Translation, and Textual Notes Introduction, Translation, and Textual Notes, ed. Rega Wood (Dordrecht: Kluwer Academic Publishers, 1988)
2. Wodeham, Tractatus de indivisibilibus, p. 33
3. Averroes had pointed out this difference between mathematical and Alteration physical entities. ed. Norman Kretzmann Ithaca: Cornell University Press physical entities. See Edith Sylla, "Infinite Indivisibles and Continuity in Fourteenth Century Theories of Alteration," in Infinity Continuity in Antiquity and the Middle Ages, ed. Norman Kretzmann (Ithaca: Cornell University Press, 1982), pp. 233-34
4. See Edith Sylla, "The A Posteriori Foundations of Natural Science; Commentaries on Aristotle's Physics, Book I Some Medieval Commentaries on Aristotle's Physics, Book I, chapters 1 and 2," Synthese 40 (1979): 147-87
5. For Chatton, see John Murdoch and Edward Synan, "Two Questions on Continuum: Walter Chatton (?), O.F.M. and Adam Wodeham, O.F.M., Franciscan Studies 26 (1966): 212-88. the Continuum: Walter Chatton (?), O.F.M. and Adam Wodeham, O.F.M.," Franciscan Studies 26 (1966): 212-88
6. See John Murdoch, Geometry and the Continuum in the Fourteenth Century: A Analysis of Thomas Bradwardine's Tractatus de continuo Philosophical Analysis of Thomas Bradwardine's Tractatus de continuo (unpub. Ph.D. diss., University of Wisconsin, 1957)
7. The definitions, suppositions, and conclusions are published in John Grant and John E. Murdoch (Cambridge: Cambridge University Press,. In what follows, I rely on John Murdoch's unpublished edition and translation of the Tractatus de continuo (versions subsequent to his Ph.D. dissertation). Murdoch, "Thomas Bradwardine: Mathematics and Continuity in the Fourteenth Century," in Mathematics and its Applications to Science and Natural Philosophy in the Middle Ages, ed. Edward Grant and John E. Murdoch (Cambridge: Cambridge University Press, 1987), pp. 119-30. In what follows, I rely on John Murdoch's unpublished edition and translation of the Tractatus de continuo (versions subsequent to his Ph.D. dissertation)
8. See Edith Sylla, "Thomas Bradwardine's De continuo and the Structure Learning Occasion of John E. Murdoch's Seventieth Birthday of Fourteenth-Century Learning," in Texts and Contexts in Ancient and Medieval Science. Studies on the Occasion of John E. Murdoch's Seventieth Birthday, ed. Edith Sylla and Michael McVaugh, (Leiden: E. J. Brill, 1997), pp. 158-59
9. My translation from Murdoch's text
10. "Therefore by [Conclusion] 30 the same is true for all Conclusion 30 is in turn based on Supposition 3: Where there is no cause of diversity or dissimilarity, the judgment is assumed to be similar continua." Conclusion 30 is in turn based on Supposition 3: "Where there is no cause of diversity or dissimilarity, the judgment is assumed to be similar."
11. Reuben Hirsh, What is Mathematics Really? (New York: Oxford University Press, 1997)
12. See John Murdoch, "Henry of Harclay and the Infinite," in A. Storia e Letteratura Maierù Studi sul XIV secolo in memoria di Anneliese Maier and A. Paravicini-Bagliani, Studi sul XIV secolo in memoria di Anneliese Maier (Rome: Èdizioni di Storia e Letteratura, 1982), pp. 219-61
13. See Sylla, "Thomas Bradwardine's De continuo and the Structure of Learning Fourteenth-Century Learning," pp. 164-66
14. For texts of Harclay, I am relying upon unpublished texts and translations by John Murdoch, except where he has published short excerpts of the text or translation. Although I do not have a microfilm to check, I suggest emending alia to read aliqua, changing the English translation from another to some. translations by John Murdoch, except where he has published short excerpts of the text or translation. Although I do not have a microfilm to check, I suggest emending "alia" to read "aliqua," changing the English translation from "another" to "some."
15. Translation based on the translation of John Murdoch from his edition. Murdoch, Henry of Harclay and the Infinite. The Latin of this passage is in n. 24. See Murdoch, "Henry of Harclay and the Infinite." The Latin of this passage is in n. 24
16. Cf. Latin texts in Murdoch, "Henry of Harclay," p. 230 n.27
17. "To the first - where, in arguing, it is asked whether or not there mean line between the first point of a line and every other point known by God. If not [it is replied, then God perceives this [first] point to be immediate to the other [point, If there is, then since points can be assigned in the [mean] line, these mean points will not be perceived by God, which is false. To this argument, I have replied at length in the question, Whether God knows an infinity of things, while excluding the unsatisfactory replies of others who are ignorant of logic. However, I reply in brief that this is true: 'Between the first point of the line and every other point of the same line known by God (omnem alium punctum eiusdem lineae cognitum a Deo) there is a mean line, For any singular [of this universal] is true, and, moreover, its contradictory is false. And this is so because the term 'mean line' in the predicate mediately following the universal sign has merely confused sup is a mean line between the first point of a line and every other point known by God. If not [it is replied], then God perceives this [first] point to be immediate to the other [point]. If there is, then since points can be assigned in the [mean] line, these mean points will not be perceived by God, which is false. To this argument, I have replied at length in the question, 'Whether God knows an infinity of things,' while excluding the unsatisfactory replies of others who are ignorant of logic. However, I reply in brief that this is true: 'Between the first point of the line and every other point of the same line known by God (omnem alium punctum eiusdem lineae cognitum a Deo) there is a mean line.' For any singular [of this universal] is true, and, moreover, its contradictory is false. And this is so because the term 'mean line' in the predicate mediately following the universal sign has merely confused supposition. On the other hand, this is false: 'There is [some one] mean line between the first point and every other point (omnem alium punctum) of the same line seen by God,' since there is no [one] mean line between the first point and every other point seen by God. For no such mean line can be given (non enim contingit dare aliquam talem lineam), for it would fall between the first point and itself; nor would that line be seen by God. And therefore, when it is inferred: 'If there is [such a mean line], then, as points can be assigned in the line, etc.,' the term 'line' there has particular supposition. And hence an inference is made affirmatively from a superior to an inferior and thus the fallacy [of affirming] the consequent is committed. Similarly, an inference is made from a term having merely confused supposition to the same term having determinate or particular supposition, and quale quid is changed into hoc aliquid, and a fallacy of a Figure of speech occurs. To the proof [of the consequence in Harclay's argument]: When he takes as that assumed 'a line falls between this first point and any other point of the same line seen by God (quodlibet aliud punctum eiusdem lineae visum a Deo), ' it should be said that this is not what is posited or conceded. But this has been conceded if 'mean line' is placed in the predicate, namely [if we assert]: 'between the first point and any other (quodlibet aliud) point seen by God there is a mean line.' The other [proposition above] does not follow from this, as is clear for the reason stipulated. And thus it is clear that this doctor, howsoever subtle, has cozened by [committing] fallacies of the consequent and of a figure of speech." I have made some minor changes in John Murdoch's translation
18. For the Latin text see John Murdoch, "Naissance et l'Atomisme au Bas Moyen Âge Latin, Cahiers d'éludes médiévales II: La science de la nature: théorìes et pratiques (Montreal: Bellarmin; Paris: Vrin, 1974), p. 26 n.41; Développement de l'Atomisme au Bas Moyen Âge Latin," Cahiers d'éludes médiévales II: La science de la nature: théorìes et pratiques (Montreal: Bellarmin; Paris: Vrin, 1974), p. 26 n.41
19. or Adam de Wodeham, Tractatus de indivisibilibus, ed. Rega Wood, p. 292 n.4. n.4
20. Unpublished translation by Murdoch (typescript p. 34). Latin in Adam de Wodeham, Tractatus de indivisibilibus, p. 289 n.2. Wodeham, Tractatus de indivisibilibus, p. 289 n.2
21. Note that here the text says 'point' rather than 'line,' which may be a scribal error scribal error
22. Unpublished translation by Murdoch (typescript pp. 8-9). I have not risked emending the translation to be consistent with my other translations, because I do not have the Latin text handy. Yet a third version of Harclay's argument a shorter question on the continuum by Wodeham. Murdoch and Synan, Two Questions on the Continuum, p. 274. risked emending the translation to be consistent with my other translations, because I do not have the Latin text handy. Yet a third version of Harclay's argument appears in a shorter question on the continuum by Wodeham. See Murdoch and Synan, "Two Questions on the Continuum," p. 274
23. I cannot understand this example unless 'animal' means in some sense a singular thing, as in the recent song with the phrase singular thing, as in the recent song with the phrase, "We are the world."
24. Murdoch and Synan, "Two Questions on the Continuum," p. 282, pro argumento quod ly omnia potest teneri collective vel divisive; si collective, quando dicitur inter omnia puncta huius continui et a est punctus medius, neganda est. "dico, igitur, pro argumento quod ly omnia potest teneri collective vel divisive; si collective, quando dicitur inter omnia puncta huius continui et a est punctus medius, neganda est."
25. Murdoch and Synan, "Two Questions on the Continuum," p. 282: dico quod hoc verum est de qualibet multitudine punctorum incepta ex alio extremo huius linee et terminata secundum aliud extremem citra a punctum [i.e. that there is a point between them and a, si tamen loquamur de punctis inter quorum quodlibet et a est aliquis punctus istorum medius, dicendum est quod inter omnia puncta et a non est medium, et si arguitur ultra: igitur omnia ilia et a sunt immediata, concedunt quidam consequenciam, quia sicud sequitur: omnia illa ani-malia sunt alba, igitur quodlibet istorum est album, ita in proposito. Sed, si predicatum sit terminus inportans multitudinem, non valeret consequencia quia ista conse-quencia non valet: omnia tria sunt ternarius, igitur quilibet istorum est ternarius, et ideo antecedens est falsum "si divisive, dico quod hoc verum est de qualibet multitudine punctorum incepta ex alio extremo huius linee et terminata secundum aliud extremem citra a punctum [i.e. that there is a point between them and a]. si tamen loquamur de punctis inter quorum quodlibet et a est aliquis punctus istorum medius, dicendum est quod inter omnia puncta et a non est medium, et si arguitur ultra: igitur omnia ilia et a sunt immediata, concedunt quidam consequenciam, quia sicud sequitur: omnia illa ani-malia sunt alba, igitur quodlibet istorum est album, ita in proposito. Sed, si predicatum sit terminus inportans multitudinem, non valeret consequencia quia ista conse-quencia non valet: omnia tria sunt ternarius, igitur quilibet istorum est ternarius, et ideo antecedens est falsum."
26. Murdoch and Syrian, "Two Questions on the Continuum," p. 282
27. Wodeham, Tractatus de indixnsibilibus, pp. 106-7. I have modified the translation slightly
28. Wodeham says "indivisible," which makes no sense for those who indivisibles deny indivisibles
29. Wodeham, Tractatus de indivisibilibus, p. 106, "Nec tamen videtur sint immediate ipsi a, cum per casum nulla demonstrentur nisi talia inter quorum quodlibet et a aliquod indivisible mediat. quod sint immediate ipsi a, cum per casum nulla demonstrentur nisi talia inter quorum quodlibet et a aliquod indivisible mediat."
30. Norman Kretzmann, "Adam W'odeham's Anti-Aristotelian of Philosophy Quarterly 1 (1984): 389. This paper, submitted well before Norman Kretzmann's recent death, was written with the expectation that he would be able to consider my suggestions and, if he saw fit, dispute them or offer alternatives. I very much regret that his death has deprived the scholarly community of his continuing insight into the enigmas of fourteenth-century thought. Anti-Atomism," History of Philosophy Quarterly 1 (1984): 389. This paper, submitted well before Norman Kretzmann's recent death, was written with the expectation that he would be able to consider my suggestions and, if he saw fit, dispute them or offer alternatives. I very much regret that his death has deprived the scholarly community of his continuing insight into the enigmas of fourteenth-century thought
31. Kretzmann, "Adam W'odeham's Anti-Aristotelian Anti-Atomism," p. 389
32. Kretzmann, "Adam Wodeham's Anti-Aristotelian Anti-Atomism," p. 398 n.46
33. Kretzmann, "Adam Wodeham's Anti-Aristotelian Anti-Atomism."