Plenitude, possibility, and the limits of reason: A medieval Arabic debate on the metaphysics of nature

Journal of the History of Ideas

Volumn 61, Issue 4, 2000, Pages 539-560

  Kukkonen, Taneli ^a  

^a NONE

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EID: 0041723460     PISSN: 00225037     EISSN: None     Source Type: Journal    
DOI: 10.2307/3654068     Document Type: Article

References (125)

1. S. Knuuttila, "Plenitude, Reason and Value: Old and New in the Metaphysics of Nature," Nature and Lifeworld: Theoretical and Practical Metaphysics, ed. C. Bengt-Pedersen and N. Thomassen (Odense, 1998), 139-51. On Theories of Everything, see J. D. Barrow's work of that name (Oxford, 1991).
2. S. Knuuttila, "Plenitude, Reason and Value: Old and New in the Metaphysics of Nature," Nature and Lifeworld: Theoretical and Practical Metaphysics, ed. C. Bengt-Pedersen and N. Thomassen (Odense, 1998), 139-51. On Theories of Everything, see J. D. Barrow's work of that name (Oxford, 1991).
3. Al-Ghazâlî's work is available in The Incoherence of the Philosophers: A Parallel English-Arabic Text, ed. and tr. M. E. Marmura (Provo, Utah, 1997; henceforth TF). The standard edition for the Tahâfut al-tahâfut is by M. Bouyges (Beirut, 1930; henceforth TT). Translations for al-Ghazâlî are from Marmura and for Averroës, from Averroes' Tahâfut al-Tahâfut, tr. and annot. S. Van Den Bergh (2 vols., with pagination to the Arabic indicated; London, 1954).
4. Knuuttila, "Plenitude," 144-47; see S. Knuuttila, Modalities in Medieval Philosophy (London, 1993). Although the expression is a distinctly modern one and refers to the so-called possible-worlds semantics employed in modern modal theory, I use the term here in a rather concrete fashion. The loose definition of "possible worlds" as causally independent universes fairly accurately describes the sense in which the term is used in the two Tahâfut works: it also corresponds to the way the idea is handled in contemporary cosmological discussions (Knuuttila, "Plenitude," 144).
5. Knuuttila, "Plenitude," 144-47; see S. Knuuttila, Modalities in Medieval Philosophy (London, 1993). Although the expression is a distinctly modern one and refers to the so-called possible-worlds semantics employed in modern modal theory, I use the term here in a rather concrete fashion. The loose definition of "possible worlds" as causally independent universes fairly accurately describes the sense in which the term is used in the two Tahâfut works: it also corresponds to the way the idea is handled in contemporary cosmological discussions (Knuuttila, "Plenitude," 144).
6. Knuuttila, "Plenitude," 144-47; see S. Knuuttila, Modalities in Medieval Philosophy (London, 1993). Although the expression is a distinctly modern one and refers to the so-called possible-worlds semantics employed in modern modal theory, I use the term here in a rather concrete fashion. The loose definition of "possible worlds" as causally independent universes fairly accurately describes the sense in which the term is used in the two Tahâfut works: it also corresponds to the way the idea is handled in contemporary cosmological discussions (Knuuttila, "Plenitude," 144).
7. About the background to this temporal interpretation in Aristotle, see J. Hintikka, Time and Necessity: Studies in Aristotle's Theory of Modality (Oxford, 1973), 93-113. See also Knuuttila, Modalities, 1-38 with references to recent scholarship.
8. About the background to this temporal interpretation in Aristotle, see J. Hintikka, Time and Necessity: Studies in Aristotle's Theory of Modality (Oxford, 1973), 93-113. See also Knuuttila, Modalities, 1-38 with references to recent scholarship.
9. Cf. TT, 97.14-98.5. Averroës's argument is taken from Aristotle's De Caelo, I.12.
10. In Aristotelian terms, matter, form, and privation must all have been pre-existent for any given change to take place: cf. TT, 100-102, 104-7 (for Aristotle, Physics I.7-9). Similarly by definition there can be no beginning to either motion or time (Aristotle, Physics VII. 1; TT, 64-65, 74-80).
11. In Aristotelian terms, matter, form, and privation must all have been pre-existent for any given change to take place: cf. TT, 100-102, 104-7 (for Aristotle, Physics I.7-9). Similarly by definition there can be no beginning to either motion or time (Aristotle, Physics VII. 1; TT, 64-65, 74-80).
12. On the proofs and their modal content see the author's "Possible Worlds in the Tahâfut altahâfut: Averroes on Plenitude and Possibility," Journal of the History of Philosophy, 38/3 (2000); see also H. A. Davidson, Proofs for Eternity, Creation and the Existence of God in Medieval Islamic and Jewish Philosophy (Oxford, 1987).
13. On the proofs and their modal content see the author's "Possible Worlds in the Tahâfut altahâfut: Averroes on Plenitude and Possibility," Journal of the History of Philosophy, 38/3 (2000); see also H. A. Davidson, Proofs for Eternity, Creation and the Existence of God in Medieval Islamic and Jewish Philosophy (Oxford, 1987).
14. TT, 98.14-99.2.
15. There are several ways to do this. See G. Gale, "Cosmological Fecundity: Theories of Multiple Universes," Physical Cosmology and Philosophy, ed. J. Leslie (London, 1990); J. Leslie, Universes (London, 1989), 66-103.
16. There are several ways to do this. See G. Gale, "Cosmological Fecundity: Theories of Multiple Universes," Physical Cosmology and Philosophy, ed. J. Leslie (London, 1990); J. Leslie, Universes (London, 1989), 66-103.
17. See Leslie, Universes, 10ff. The theory has therefore been said to grossly violate the principle of "Ockham's Razor."
18. See TF, 82.14-83.12 (TT, 277-78); TF, 125.2-12 (TT, 414); and TF, 57ff (TT, 147ff.).
19. For materials on the Islamic discussions see E. L. Ormsby, Theodicy in Islamic Thought (Princeton, 1984); for the Christian background, Knuuttila, Modalities, 62-98.
20. For materials on the Islamic discussions see E. L. Ormsby, Theodicy in Islamic Thought (Princeton, 1984); for the Christian background, Knuuttila, Modalities, 62-98.
21. TF, 40.14-15, with minor alterations to Marmura's translation (TT, 98; Van Den Bergh translates the passage altogether differently). For the point that it is the actual infinity of the past which precludes its pre-eternity, TF, 47.10-48.3 (TT, 119).
22. Cf. TF, 40.9-14 (TT, 98). Marmura correctly points out that al-Ghazâlî's views regarding the contingency of the earth's two poles' positions (cf. §2 of this article) suffices to bring about an infinity of unrealized possibilia ("Ghazâlian Causes and Intermediaries," Journal of the American Oriental Society, 115/1 [1995], 89-100, at 99). To these can be added infinities upon infinities of unrealized combinations of atoms and accidents.
23. Al-Ghazâlî's full occasionalist refutation of the workings of secondary causality and natural necessity can be found in the famous Seventeenth Discussion, or the first "On the Natural Sciences": cf. e.g., the graphic examples given in TF, 173.17-174.14 (TT, 529-30).
24. TF, 42.2-5 (TT, 102-3); TF, 44.8-14 (TT, 109-10); TF, 178.10-11 (TT, 535); 179.5-6 (TT, 536).
25. See M. E. Marmura, "Ghazâlî and Demonstrative Science," Journal of the History of Philosophy, 3 (1965), 183-204; by the same author, "Ghazâlî's Attitude to the Secular Sciences and Logic," Essays in Islamic Philosophy and Science, ed. G. F. Hourani (Albany, N.Y., 1975), 100-111.
26. See M. E. Marmura, "Ghazâlî and Demonstrative Science," Journal of the History of Philosophy, 3 (1965), 183-204; by the same author, "Ghazâlî's Attitude to the Secular Sciences and Logic," Essays in Islamic Philosophy and Science, ed. G. F. Hourani (Albany, N.Y., 1975), 100-111.
27. See the author's "Possible Worlds in the Tahâfut al-falâsifa: Al-Ghazâlî on Creation and Contingency," Journal of the History of Philosophy, 38 (2001); and Ormsby, Theodicy and R. M. Frank, Creation and the Cosmic System: Avicenna and al-Ghazâlî (Heidelberg, 1992).
28. See the author's "Possible Worlds in the Tahâfut al-falâsifa: Al-Ghazâlî on Creation and Contingency," Journal of the History of Philosophy, 38 (2001); and Ormsby, Theodicy and R. M. Frank, Creation and the Cosmic System: Avicenna and al-Ghazâlî (Heidelberg, 1992).
29. See the author's "Possible Worlds in the Tahâfut al-falâsifa: Al-Ghazâlî on Creation and Contingency," Journal of the History of Philosophy, 38 (2001); and Ormsby, Theodicy and R. M. Frank, Creation and the Cosmic System: Avicenna and al-Ghazâlî (Heidelberg, 1992).
30. See the author's "Possible Worlds in the Tahâfut al-falâsifa: Al-Ghazâlî on Creation and Contingency," Journal of the History of Philosophy, 38 (2001); and Ormsby, Theodicy and R. M. Frank, Creation and the Cosmic System: Avicenna and al-Ghazâlî (Heidelberg, 1992).
31. The claim of the philosophers' "first proof for the eternity of the world was that an immutable God cannot have limited actions (cf. TF, 13.7-14.16; TT, 4): however, according to al-Ghazâlî, God's eternal will can perfectly well take temporal objects without this implying any temporality or change in the willer (TF, 15.1-5 and 17.5-15; TT, 7 and 13).
32. See W. L. Craig, The Cosmological Argument from Plato to Leibniz (London, 1980), 54ff.
33. TF, 25-27 (TT, 41, curtailed; Van Den Bergh supplements the full text); and see D. Parfit, "The Puzzle of Reality," Times Literary Supplement, 3 July 1992.
34. TT, 44.13-14 and 47.3-9 (cf. TT, 129.3-12 and 491.12-492.5).
35. Ca, ed. M. Bouyges (4 vols.; Beirut, 1938-52), III, 1658ff.
36. See J. D. Barrow and F. J. Tipler, The Anthropic Cosmological Principle (Oxford, 1986); The Anthropic Principle, ed. F. Bertola and U. Curi (Cambridge, 1989). On fine-tuning arguments cf. Leslie, Universes, 1-65.
37. See J. D. Barrow and F. J. Tipler, The Anthropic Cosmological Principle (Oxford, 1986); The Anthropic Principle, ed. F. Bertola and U. Curi (Cambridge, 1989). On fine-tuning arguments cf. Leslie, Universes, 1-65.
38. See J. D. Barrow and F. J. Tipler, The Anthropic Cosmological Principle (Oxford, 1986); The Anthropic Principle, ed. F. Bertola and U. Curi (Cambridge, 1989). On fine-tuning arguments cf. Leslie, Universes, 1-65.
39. Câni asmâ' Allâh alhusnâ, ed. F. A. Shehadi (Beirut, 1986), 98-111.
40. Cf. Ormsby, Theodicy; by the same author, "Creation in Time in Islamic Thought with Special Reference to Al-Ghazâlî," God and Creation, ed. D. B. Burrell and B. McGinn (Notre Dame, Ind., 1990), 246-64.
41. Cf. Ormsby, Theodicy; by the same author, "Creation in Time in Islamic Thought with Special Reference to Al-Ghazâlî," God and Creation, ed. D. B. Burrell and B. McGinn (Notre Dame, Ind., 1990), 246-64.
42. TT, 412.2-7.
43. Carite account of knowledge cf. TF, 174.16-175.11 (TT, 324).
44. Ca, II, 1126, 1135).
45. TT, 113.7-9. This aspect of Averroës's philosophy is magisterially handled in B. S. Kogan's Averroes and the Metaphysics of Causation (Albany, N.Y., 1985).
46. TT, 50.9.
47. Cf. E. Booth, Aristotelian Aporetic Ontology in Islamic and Christian Thinkers (Cambridge, 1983), 131ff.
48. Knuuttila, "Plenitude," 147.
49. On the topic see J. D. Barrow, Pi in the Sky: Counting, Thinking, and Being (Oxford, 1992).
50. Quoted from Barrow. Theories of Everything, 89.
51. See D. R. Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid (New York, 1980); R. Rucker, Infinity and the Mind (Boston, 1982); also J. D. Barrow, Impossibility: The Limits of Science and the Science of Limits (Oxford, 1998), 218ff and H. Kirjavainen, "Cosmology, Theology, and the Question of Ultimate Explanation," Infinity, Causality, and Determinism: Cosmological Enterprises and their Preconditions, ed. E. Martikainen (Dordrecht, forthcoming).
52. See D. R. Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid (New York, 1980); R. Rucker, Infinity and the Mind (Boston, 1982); also J. D. Barrow, Impossibility: The Limits of Science and the Science of Limits (Oxford, 1998), 218ff and H. Kirjavainen, "Cosmology, Theology, and the Question of Ultimate Explanation," Infinity, Causality, and Determinism: Cosmological Enterprises and their Preconditions, ed. E. Martikainen (Dordrecht, forthcoming).
53. See D. R. Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid (New York, 1980); R. Rucker, Infinity and the Mind (Boston, 1982); also J. D. Barrow, Impossibility: The Limits of Science and the Science of Limits (Oxford, 1998), 218ff and H. Kirjavainen, "Cosmology, Theology, and the Question of Ultimate Explanation," Infinity, Causality, and Determinism: Cosmological Enterprises and their Preconditions, ed. E. Martikainen (Dordrecht, forthcoming).
54. See D. R. Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid (New York, 1980); R. Rucker, Infinity and the Mind (Boston, 1982); also J. D. Barrow, Impossibility: The Limits of Science and the Science of Limits (Oxford, 1998), 218ff and H. Kirjavainen, "Cosmology, Theology, and the Question of Ultimate Explanation," Infinity, Causality, and Determinism: Cosmological Enterprises and their Preconditions, ed. E. Martikainen (Dordrecht, forthcoming).
55. On different applications of the argument see Craig, The Cosmological Argument.
56. Philoponus's most clear formulation of this is in a fragment preserved by Simplicius: cf. In Aristotelis Physicorum libros quattuor posteriores commentaria, ed. H. Diels (Berlin, 1895), 1178.9-35. See Davidson, Proofs, 86ff and R. Sorabji (ed.), Philoponus and the Rejection of Aristotelian Science (London, 1987).
57. Philoponus's most clear formulation of this is in a fragment preserved by Simplicius: cf. In Aristotelis Physicorum libros quattuor posteriores commentaria, ed. H. Diels (Berlin, 1895), 1178.9-35. See Davidson, Proofs, 86ff and R. Sorabji (ed.), Philoponus and the Rejection of Aristotelian Science (London, 1987).
58. Philoponus's most clear formulation of this is in a fragment preserved by Simplicius: cf. In Aristotelis Physicorum libros quattuor posteriores commentaria, ed. H. Diels (Berlin, 1895), 1178.9-35. See Davidson, Proofs, 86ff and R. Sorabji (ed.), Philoponus and the Rejection of Aristotelian Science (London, 1987).
59. Cf. W. L. Craig, The Kalam Cosmological Argument (London, 1979); also Craig, The Cosmological Argument, 48ff. Craig's proof has last been discussed in Religious Studies in 1996 through 1998.
60. Cf. W. L. Craig, The Kalam Cosmological Argument (London, 1979); also Craig, The Cosmological Argument, 48ff. Craig's proof has last been discussed in Religious Studies in 1996 through 1998.
61. Cf. W. L. Craig, The Kalam Cosmological Argument (London, 1979); also Craig, The Cosmological Argument, 48ff. Craig's proof has last been discussed in Religious Studies in 1996 through 1998.
62. Cf. Philoponus, Against Aristotle, as quoted by Simplicius, In Phys., 1141.11-30; 1150.22-25;
63. Cf. Philoponus, Against Aristotle, as quoted by Simplicius, In Phys., 1141.11-30; 1150.22-25;
64. Cf. Philoponus, Against Aristotle, as quoted by Simplicius, In Phys., 1141.11-30; 1150.22-25;
65. for further applications, Davidson, Proofs, 30-33.
66. Cf. TT, 171-72 and Averroes 'Questions in Physics, ed. and tr. H. T. Goldstein (Dordrecht, 1991), 8-9; for Plato, Timaeus 28a. On the evolution of the doctrine of creatio ex nihilo and on Plato's see G. May, Schöpfung aus dem Nichts (Berlin, 1978).
67. Cf. TT, 171-72 and Averroes 'Questions in Physics, ed. and tr. H. T. Goldstein (Dordrecht, 1991), 8-9; for Plato, Timaeus 28a. On the evolution of the doctrine of creatio ex nihilo and on Plato's see G. May, Schöpfung aus dem Nichts (Berlin, 1978).
68. Cf. TT, 171-72 and Averroes 'Questions in Physics, ed. and tr. H. T. Goldstein (Dordrecht, 1991), 8-9; for Plato, Timaeus 28a. On the evolution of the doctrine of creatio ex nihilo and on Plato's see G. May, Schöpfung aus dem Nichts (Berlin, 1978).
69. Cf. Averroës, Long Commentary on the Physics, VIII, comm. 1, in Aristotelis opera cum Averrois Cordubensis in eius commentaria (9 vols.; Venice, 1562; repr. Frankfurt am Main, 1962; hereafter AOACC), IV, fol. 338F-339F.
70. Cf. Averroës, Long Commentary on the Physics, VIII, comm. 1, in Aristotelis opera cum Averrois Cordubensis in eius commentaria (9 vols.; Venice, 1562; repr. Frankfurt am Main, 1962; hereafter AOACC), IV, fol. 338F-339F.
71. Cf. Averroës, Long Commentary on the Physics, VIII, comm. 1, in Aristotelis opera cum Averrois Cordubensis in eius commentaria (9 vols.; Venice, 1562; repr. Frankfurt am Main, 1962; hereafter AOACC), IV, fol. 338F-339F.
72. TT, 268.12-13 and 269.1-5; cf. also Long Commentary on the Physics, VIII, comm. 47 (AOACC, IV, fol. 388Fff).
73. TT, 268.12-13 and 269.1-5; cf. also Long Commentary on the Physics, VIII, comm. 47 (AOACC, IV, fol. 388Fff).
74. Cf. TT, 56-60; for Aristotle, Physics III.5, V.2 and Averroës's explanations in the Long Commentary on the Physics, VIII, comm. 15 (AOACC, IV, fol. 349Eff.; the idea is present already in Simplicius, In Phys., 843-49). For critical remarks cf. Davidson, Proofs, 130-33.
75. Cf. TT, 56-60; for Aristotle, Physics III.5, V.2 and Averroës's explanations in the Long Commentary on the Physics, VIII, comm. 15 (AOACC, IV, fol. 349Eff.; the idea is present already in Simplicius, In Phys., 843-49). For critical remarks cf. Davidson, Proofs, 130-33.
76. Cf. TT, 56-60; for Aristotle, Physics III.5, V.2 and Averroës's explanations in the Long Commentary on the Physics, VIII, comm. 15 (AOACC, IV, fol. 349Eff.; the idea is present already in Simplicius, In Phys., 843-49). For critical remarks cf. Davidson, Proofs, 130-33.
77. Cf. TT, 56-60; for Aristotle, Physics III.5, V.2 and Averroës's explanations in the Long Commentary on the Physics, VIII, comm. 15 (AOACC, IV, fol. 349Eff.; the idea is present already in Simplicius, In Phys., 843-49). For critical remarks cf. Davidson, Proofs, 130-33.
78. Cf. TT, 56-60; for Aristotle, Physics III.5, V.2 and Averroës's explanations in the Long Commentary on the Physics, VIII, comm. 15 (AOACC, IV, fol. 349Eff.; the idea is present already in Simplicius, In Phys., 843-49). For critical remarks cf. Davidson, Proofs, 130-33.
79. A. O. Lovejoy, The Great Chain of Being (Cambridge, Mass., 1936), 45ff.
80. See V. Boland, Ideas in God According to St. Thomas Aquinas: Sources and Synthesis (Leiden, 1996), 49-65; and Enneads 3.7.4-5, 5.2.1-2.
81. See V. Boland, Ideas in God According to St. Thomas Aquinas: Sources and Synthesis (Leiden, 1996), 49-65; and Enneads 3.7.4-5, 5.2.1-2.
82. Proclus Diadochus, In Platonis Timaeum Commentaria, ed. E. Diehl (3 vols.; Leipzig, 1903-6), III, 92.5-28. Op. cit., II, 290.6-17.
83. Proclus Diadochus, In Platonis Timaeum Commentaria, ed. E. Diehl (3 vols.; Leipzig, 1903-6), III, 92.5-28. Op. cit., II, 290.6-17.
84. Op. cit., I, 266-68 ; trans. in R. Sorabji, Matter, Space and Motion: Theories in Antiquity and their Sequel (London, 1988), at 250-53. For materials see op. cit., 249-85, and my "Infinite Power and Plenitude: Two Traditions on the Necessity of the Eternal," in Medieval Philosophy and the Classical Tradition in Islam, Judaism and Christianity, ed. J. Inglis (Richmond, 2001).
85. Op. cit., I, 266-68 ; trans. in R. Sorabji, Matter, Space and Motion: Theories in Antiquity and their Sequel (London, 1988), at 250-53. For materials see op. cit., 249-85, and my "Infinite Power and Plenitude: Two Traditions on the Necessity of the Eternal," in Medieval Philosophy and the Classical Tradition in Islam, Judaism and Christianity, ed. J. Inglis (Richmond, 2001).
86. Op. cit., I, 266-68 ; trans. in R. Sorabji, Matter, Space and Motion: Theories in Antiquity and their Sequel (London, 1988), at 250-53. For materials see op. cit., 249-85, and my "Infinite Power and Plenitude: Two Traditions on the Necessity of the Eternal," in Medieval Philosophy and the Classical Tradition in Islam, Judaism and Christianity, ed. J. Inglis (Richmond, 2001).
87. Op. cit., I, 266-68 ; trans. in R. Sorabji, Matter, Space and Motion: Theories in Antiquity and their Sequel (London, 1988), at 250-53. For materials see op. cit., 249-85, and my "Infinite Power and Plenitude: Two Traditions on the Necessity of the Eternal," in Medieval Philosophy and the Classical Tradition in Islam, Judaism and Christianity, ed. J. Inglis (Richmond, 2001).
88. Proclus, In Tim., I, 436-38 and II, 130-31.
89. Cf. In Tim., II, 66.1-14; also II, 102-3; cf. L. Siorvanes, Proclus: Neoplatonic Philosophy and Science (Edinburgh, 1996), 175-79; and also my "Proclus on Plenitude," Dionysius, 18 (2000).
90. Cf. In Tim., II, 66.1-14; also II, 102-3; cf. L. Siorvanes, Proclus: Neoplatonic Philosophy and Science (Edinburgh, 1996), 175-79; and also my "Proclus on Plenitude," Dionysius, 18 (2000).
91. Cf. In Tim., II, 66.1-14; also II, 102-3; cf. L. Siorvanes, Proclus: Neoplatonic Philosophy and Science (Edinburgh, 1996), 175-79; and also my "Proclus on Plenitude," Dionysius, 18 (2000).
92. Cf. In Tim., II, 66.1-14; also II, 102-3; cf. L. Siorvanes, Proclus: Neoplatonic Philosophy and Science (Edinburgh, 1996), 175-79; and also my "Proclus on Plenitude," Dionysius, 18 (2000).
93. Cf. TT, 184-94, 226-34. Cf. F. Rosenthal. "Ash-Shaykh al-Yûnânî and the Arabic Plotinus Source," Orientalia New Series, 22 (1953), 370-400, at 397-400; reprinted in Greek Philosophy and the Arab World (Brookfield, Vt., 1990).
94. Cf. TT, 184-94, 226-34. Cf. F. Rosenthal. "Ash-Shaykh al-Yûnânî and the Arabic Plotinus Source," Orientalia New Series, 22 (1953), 370-400, at 397-400; reprinted in Greek Philosophy and the Arab World (Brookfield, Vt., 1990).
95. Cf. e.g., Barrow, Theories of Everything, 18-23.
96. See K. R. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (London, 1963), 75-93; further Á. Szabó, Anfänge der Griechischen Mathematik (Munich, 1969), translated by A. M. Ungar as The Beginnings of Greek Mathematics (Dordrecht, 1978); D. J. O'Meara, Pythagoras Revived: Mathematics and Philosophy in Late Antiquity (Oxford, 1989);
97. See K. R. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (London, 1963), 75-93; further Á. Szabó, Anfänge der Griechischen Mathematik (Munich, 1969), translated by A. M. Ungar as The Beginnings of Greek Mathematics (Dordrecht, 1978); D. J. O'Meara, Pythagoras Revived: Mathematics and Philosophy in Late Antiquity (Oxford, 1989);
98. See K. R. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (London, 1963), 75-93; further Á. Szabó, Anfänge der Griechischen Mathematik (Munich, 1969), translated by A. M. Ungar as The Beginnings of Greek Mathematics (Dordrecht, 1978); D. J. O'Meara, Pythagoras Revived: Mathematics and Philosophy in Late Antiquity (Oxford, 1989);
99. See K. R. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (London, 1963), 75-93; further Á. Szabó, Anfänge der Griechischen Mathematik (Munich, 1969), translated by A. M. Ungar as The Beginnings of Greek Mathematics (Dordrecht, 1978); D. J. O'Meara, Pythagoras Revived: Mathematics and Philosophy in Late Antiquity (Oxford, 1989);
100. L. J. Zhmud', " 'All is number'? 'Basic Doctrine' of Pythagoreanism reconsidered," Phronesis, 34 (1989), 270-92.
101. See A. Koyré, From the Closed World to the Infinite Universe (Baltimore, 1957); and see E. Grant, Planets, Stars, and Orbs: The Medieval Cosmos, 1200-1687 (Cambridge, 1994). See now also W. G. L. Randles, The Unmaking of the Medieval Christian Cosmos 1500-1760: From Solid Heavens to Boundless Aether (Aldershot, 1999).
102. See A. Koyré, From the Closed World to the Infinite Universe (Baltimore, 1957); and see E. Grant, Planets, Stars, and Orbs: The Medieval Cosmos, 1200-1687 (Cambridge, 1994). See now also W. G. L. Randles, The Unmaking of the Medieval Christian Cosmos 1500-1760: From Solid Heavens to Boundless Aether (Aldershot, 1999).
103. See A. Koyré, From the Closed World to the Infinite Universe (Baltimore, 1957); and see E. Grant, Planets, Stars, and Orbs: The Medieval Cosmos, 1200-1687 (Cambridge, 1994). See now also W. G. L. Randles, The Unmaking of the Medieval Christian Cosmos 1500-1760: From Solid Heavens to Boundless Aether (Aldershot, 1999).
104. E. Brient, "Transitions to a Modern Cosmology: Meister Eckhart and Nicholas of Cusa on the Intensive Infinite," Journal of the History of Philosophy, 37 (1999), 575-600.
105. Cf., however, p. 595 and esp. n. 67.
106. Cf. e.g. TF, 47.10-48.5 (TT, 119).
107. TF, 178.2-8 (TT, 535).
108. TT, 476.6-7 (cf. TT, 519-25).
109. Brient, "Transitions," 599.
110. See L. E. Goodman, Avicenna (New York, 1992), 184-211.
111. A. W. Moore, The Infinite (New York, 1990), 223.
112. In W. L. Craig and Q. Smith, Theism, Atheism, and Big Bang Cosmology (Oxford, 1993), 337.
113. Q. Smith, in Theism, Atheism, 217, quoted as reproduced here.
114. Knuuttila, "Plenitude," 147-49.
115. Citations from the Tractatus Logico-Philosophicus: The German Text of Ludwig Wittgensteins's Logisch-Philosophische Abhandlung with a new Translation, tr. D. F. Pears and B. F. McGuinness (London, 1961), 6.432 and 6.45.
116. Cf. Tractatus 6.13;
117. for Moore's comments. The Infinite, 186-200 and ff.
118. Cp. Tractatus 6.44: "It is not how things are in the world that is mystical, but that it exists."
119. See Knuuttila, "Plenitude," 149-50 and Kirjavainen, "Cosmology"; cf. further M. Kusch, Language as Calculus vs. Language as Universal Medium: A Study in Husserl, Heidegger and Gadamer (Dordrecht, 1989).
120. See Knuuttila, "Plenitude," 149-50 and Kirjavainen, "Cosmology"; cf. further M. Kusch, Language as Calculus vs. Language as Universal Medium: A Study in Husserl, Heidegger and Gadamer (Dordrecht, 1989).
121. See Knuuttila, "Plenitude," 149-50 and Kirjavainen, "Cosmology"; cf. further M. Kusch, Language as Calculus vs. Language as Universal Medium: A Study in Husserl, Heidegger and Gadamer (Dordrecht, 1989).
122. CAyyâd (Beirut, s.a.), 132; English translation in The Faith and Practice of Al-Ghazálí, tr. W. M. Watt (Oxford, 1994), 57; similarly Munqidh, 141 (Watt tr., 64).
123. CAyyâd (Beirut, s.a.), 132; English translation in The Faith and Practice of Al-Ghazálí, tr. W. M. Watt (Oxford, 1994), 57; similarly Munqidh, 141 (Watt tr., 64).
124. CAyyâd (Beirut, s.a.), 132; English translation in The Faith and Practice of Al-Ghazálí, tr. W. M. Watt (Oxford, 1994), 57; similarly Munqidh, 141 (Watt tr., 64).
125. Munqidh, 128 (Watt tr., 55).