Abstract
We found the tripartition of theoretical knowledge to correspond with a tripartition of being into physicals, mathematicals (= world-soul), and theologicals. In this context, mathematics was a study of things subsisting and was considered to be such even by the early Aristotle. What is true for mathematics should be true a fortiori for first philosophy. We may expect its objects to subsist in an even higher degree than do mathematicals. And indeed, first philosophy is frequently designated by Aristotle as theology. Who could doubt that theologicals subsist?
According to R. Eisler, Woerterbuch der philosophischen Begriffe 4 (1928), for the terms metaphysica generalis and specialis, together with their precise definition, we are indebted to Micraelius, a person otherwise little known in the history of philosophy. The terms are convenient indeed and will be used to indicate the difference between metaphysics as the knowledge of the transcendental (God, disembodied souls, angels) and metaphysics as science of being as what is common to everything (so with particular clarity Petrus Fonseca: the subject matter of metaphysics is ens quatenus est commune Deo et creaturis, Commentarii in libros Metaphysicorum, 2 vv. [Lyon, 1591], v. 1490–504).
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And probably never became aware of it: cf. E. v. Ivánka, “Die Behandlung der Metaphysik in Jaegers “Aristoteles’”, Scholastik 7 (1932) 1–29, quoting Met. Zl, 1028b13-15; 11,1037a10-16; 17,1041a6-9 — all passages assumed by Jaeger to be much later than Τ, E, K, and yet all describing metaphysics as knowledge of the suprasensible, i. e. just one sphere of being.
The theories deriving knowledge from sensation by abstraction have been criticized most incisively by Hegel in his Phenomenology (section: Die sinnliche Gewiszheit oder das Dieses und das Meinen, SW ed. Glockner, v. II [1927] 81-92). From a different, unmetaphysical point of view the ordinary concept of abstraction was destroyed by one single sentence of Husserl: in some respect everything is similar to everything and it would be in vain to describe concepts in terms of “abstracting” the similarities (E. Husserl, Logische Untersuchungen II/13 [1922] 106–224, esp. 115-121).
The problem of the authenticity of EE cannot here be discussed. See on it J. Geffcken, Griechische Literaturgeschichte, v. II (1934), Anmerkungen, pp. 220–222.
See F. M. Cornford, Plato and Parmenides (1939) 13 f. Cf. C. Mugler, Platon (1948) 120-122 for a discussion of this problem in terms of contemporary physics. See also A. Goerland, Aristoteles und die Mathematik (1899) 22-25; 207. It should also be noted that the doctrine of mathematical atomism is another shock to our ways of thinking, perhaps not much more lenient than the derivation of body from geometrical figures. See S. Luria, “Die Infinitesimaltheorie der antiken Atomisten”, Quellen und Studien zur Geschichte der Mathematik... Abt. B: Studien 2 (1933) 106–185, esp. 120-160.
A. Schmekel, Die positive Philosophie in ihrer geschichtlichen Entwicklung, v. I (1938) 15–17; 59; for a modern defense cf. P. Bernays, “Die Erneuerung der rationalen Aufgabe”, Proceedings of the Tenth International Congress of Philosophy (1949) 42-50, esp. 47. The whole problem of deriving existence from essence is treated in a very stimulating way in A. Lautman, Essai sur les notions de structure et d’existence en mathématique, 2 vv. (1938), esp. 126 and 150-156; and Nouvelles recherches sur la Structure dialectique des mathématiques (1939), esp. 31.
This is the interpretation of F. M. Cornford, Plato and Parmenides (1939) 1-27, and 76-80. Cf., however, e. g. S. Marck, Die Platonische Ideenlehre in ihren Motiven (1912) 57. The problem of the efficient causality by the demiurge is beyond the scope of the present inquiry; there is certainly not the slightest trace of him in the Phaedo. The almost complete absence of any efficient causality in Plato has recently been asserted e. g. by M. D. Philippe, “La Participation dans la philosophie d’Aristote”, Revue Thomiste 49 (1949) 254–277, esp. 254-257. He even considers it possible that Plato’s incipient admission of some kind of causality different from the causality of ideas is the result of Aristotle’s influence on Plato.
Just as does the famous report of Alexander Polyhistor (Diog. Laert., VIII 24-33), on which cf. A.-J. Festugière, “Les ‘Mémoires Pythagoriques’ cités par Alexandre Polyhistor”, Revue des Etudes grecques 58 (1945) 1–65.
A. Schmekel, Die positive Philosophie, v. I (1938) 84–86 traces parts of the Sextus passage to Eratosthenes, who, however, according to Schmekel admitted the (generic?) difference between mathematical solids and physical bodies.
Cf. E. Gilson, “Avicenne et le point de départ de Duns Scot”, Archives d’histoire doctrinale et littéraire du Moyen Age 2 (1927), pp. 89–149, esp. 93 f.
But cf. E. v. Ivánka, “Die Behandlung der Metaphysik in Jaegers ‘Aristoteles’”, Scholastik 7 (1932) 1–29, esp. 17 and 20.
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Merlan, P. (1953). Metaphysica Generalis in Aristotle?. In: From Platonism to Neoplatonism. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-6205-2_8
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