内容

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The present tendency to bridge the gap between Platonism and Neoplatonism and the main factors of that tendency..- The purpose of the present book: to strengthen this tendency. The way of achieving that purpose..- The intention of interpreting even Aristotle’s metaphysics as essentially neoplatonic (3-4) - The importance of Iamblichus, De communi mathematica scientia for the present investigation (4-5). - A note on excessive realism (4). - A note on the use of later philosophic and scientific theories in interpreting Greek philosophy..- Appendix..- Bibliographical note..- Appendix..- I. Soul and Mathematicals.- The excessively realistic, anti-abstractionist (intuitionist) interpretation of mathematicals in Iamblichus and Proclus and the intermediacy of mathematicals (the mathematical sphere of being) between intelligibles and physicals..- How is this intermediacy of the mathematicals related to the intermediacy of the soul between ideas and physicals according to Plato’s Timaeus?.- The problem of the “motive” character of mathematicals in De communi mathematica scientia ch. III and its solution ibid. ch. IV mathematicals not “motive” and therefore different from the soul..- Resumption of the problem concerning the identity of mathematicals with the soul in De communi mathematica scientia ch. IX; this time the solution favors such an identification, stressing particularly the necessity of identifying the soul with all branches of mathematicals, viz. arithmeticals, geometricals, and harmonicals, the mathematicals, thus, assumed to be tripartite..- This doctrine illustrated also from Iamblichus, On the Soul (19-21) and from Proclus, in whom, however, the identification is with quadripartite mathematicals, including astronomicals, i.e. “motive” mathematicals..- Further discussion of the identification of the soul with (tripartite) mathematicals in De communi mathematica scientia ch. X..- This identification incompatible with the results of De communi mathematica scientia ch.s III and IV, this incompatibility revealing the presence of different sources from which De communi mathematica scientia derived..- Analysis of ch. X resumed; the identification of the soul with mathematicals explained by Iamblichus..- Explanation of the inconsistency of De communi mathematica scientia by its peculiar literary character neither an original, nor plagiarism, nor a florilegium..- Discussion concerning the difference between tripartite and quadripartite mathematicals and the importance of this difference for the problem of the identification of the soul and mathematicals : only if the soul is identified with quadriparted mathematicals (including astronomicals, i.e. “motive” mathematicals), the “motive” character of the soul (fundamental tenet of Plato) can be maintained..- Concluding proofs of the plurality and inconsistency of the sources of De communi mathematica scientia..- Appendix..- II. Posidonius and Neoplatonism.- The problem concerning the identification of the soul with mathematicals traced to Speusippus, Xenocrates, and, particularly, Posidonius, who seems to have combined the tripartition of being into ideas, mathematicals, and sensibles, ascribed to Plato by Aristotle, with the tripartion of being into ideas, soul, and sensibles, as found in Plato’s Timaeus..- This identification, as found in Iamblichus and Proclus, ultimately derived from Posidonius..- Polemic with Cherniss concerning the beginnings of this identification in Speusippus; Iamblichus' report on this identification defended, despite iti apparent discrepancy with Aristotle..- Polemic with Cherniss concerning the beginnings of this identification by Xenocrates; the assumption that Xenocrates assigned to mathematicals an intermediate position not incompatible with his denial of ideas..- Comparison of Cherniss' own interpretation of Plato with the interpretation by Aristotle: the two differ essentially in Cherniss' unwillingness to identify soul and mathematicals mainly because of the “motive” character of the former..- The similarity of Cherniss' position to that of the source of Iamblichus, De communi mathematica scientia ch. III..- The Platonic character of the thesis of the “motive” character of mathematicals..- Thus, the reports concerning Speusippus' identification of the soul with a mathematical (i.e. a geometrical) and Xenocrates' identification of the soul with a mathematical (i.e. an arithmetical) reliable and these identifications, including the assumption of the “motive” character of some or all mathematicals, not entirely unPlatonic; the two identifications of Speusippus and Xenocrates closely related to each other..- Traces of this identification in Aristotle; possibility that the giving up of the doctrine of the subsistence of mathematicals by Aristole closely connected with his giving up of the doctrine of the subsistence of the soul..- Preliminary note on the problem of derivation of singulars from universals and the concept of aedafacg..- Some other examples of the identification of the soul with a mathematical..- Attempt to justify the identification of the soul with mathematicals..- Appendix..- Bibliographical note..- III. The Subdivisions of Theoretical Philosophy.- Aristotle’s tripartition of theoretical knowledge into metaphysics (theology, first philosophy), mathematics, and physics rooted in what he reported to have been Plato’s division of being into ideas, mathematicals, and sensibles (with ideas and mathematicals interpreted as subsistent). The incompatibility of Aristotle’s tripartition of knowledge with his rejection of the subsistence of mathematicals..- Discussion of the two main passages exhibiting this inconsistency. First passage (in Met. E) : the tripartition of knowledge faulty, because based on two different principles, viz. ratio essendi and ratio cognoscendi ; physicals erroneously designated as dx&esara..- Defense of the assertion that Aristotle’s tripartition of knowledge Platonic in its origin..- Attempts to defend Aristotle’s tripartition as consistent, particularly by interpreting it as based on degrees of knowledge (instead of degrees of being), refuted. In connection with the problem of abstraction the problem of a metaphysca generalis in Aristotle emerges..- Attempt to defend the designation of physicals as dxcuema refuted..- Second passage (Met. K) briefly discussed from the point of view of its inconsistency..- Summary: only to the extent to which Aristotle ever accepted the excessively realistic interpretation of ideas (or whatever takes their place in his own philosophy) and mathematicals, could his tripartition of theoretical knowledge be justified..- Historical survey of difficulties resulting whenever a writer who did not accept excessive realism and the attendant tripartition of being, nevertheless professed the tripartition of theoretical knowledge..- The appearance of another tripartition of theoretical knowledge into theology (metaphysics, first philosophy), psychology, and physics and its roots in the identification of the soul with mathematicals..- Conclusion..- Appendix..- IV. The Origin of the Quadrivium.- Survey of the history of the quadrivium (i.e. the quadriparted mathematics) ; ambiguity of the term mathematics in this context (does mathematics mean philosophy of mathematics, deserving an intermediate place between metaphysics and physics, in connection with a tripartition of being and an excessively realistic interpretation of mathematicals, or does it mean elementary grammar school disciplines?) and the treatment of the quadrivium in some representative authors, revealing that ambiguity..- V. Speusippus in Iamblichus.- Ch.s IX and X of De communi mathematica scientia contain references to doctrines of Speusippus. Are there any other traces of him in the same work?.- A comparison of the system of Speusippus as presented by Aristotle (96-98) with the content of De communi mathematica scientia ch. IV (98-90) proves that the latter indeed presents ideas of Speusippus..- But the chapter is not derived from Aristotle (100), nor can the difference between the two presentations be explained by the assumption that Iamblichus “plotinized” Speusippus or read his own neoplatonic doctrines into him..- These points proved..- After having in this way established that Speusippus professed the doctrine of the One which is above being (indeterminate being) as one of his supreme principles, the concept of indeterminate being (and indeterminate non-being) traced to Plato’s Sophist..- Summary: ch. IV of De communi mathematica scientia is an independent source of our knowledge about Speusippus..- Additional arguments, regarding Iamblichus' knowledge of other early philosophers and of Speusippus in particular..- Detailed comparison of Speusippus' supreme formal principle as presented in ch. IV of De communi mathematica scientia with the presentation by Aristotle (103-104), especially the concept of the One-above-being..- Probably even Aristotle himself ascribed this doctrine to Speusippus, although he expressed himself ambiguously, perhaps even on purpose in order to be able to criticize this doctrine better by relating it to his own frame of reference in the form of the Nva uisbEeyEia concept..- How to interpret the term “seed” as applied by Aristotle to the One of Speusippus..- The plurality of formal principles in Speusippus..- The doctrine that the supreme formal principle (the One, the indeterminate being) is not only above being but also above the good and the beautiful and that the beautiful emerges first in the sphere of mathematicals; the presence of the doctrine that there is beauty in mathematicals professed also by Aristotle, not only in his Metaphysics, but also in a passage in Proclus ; and this passage in Proclus derived from a writing different from Aristotle’s Metaphysics, perhaps from his Protrepticus..- The doctrine that the supreme principle not good itself (although the source of goodness) criticized by Aristotle (109-110) ; perhaps also by Theophrastus..- Discussion of the other supreme principle in Speusippus : the material principle, which is neither ugly nor evil nor even cause of evil (111-114) ; Speusippus' theory of evil (evil not subsistent) compared with that of Aristotle..- The interaction of the supreme formal and the supreme material principles (115-116). - Speusippus no evolutionist..- Was Speusippus a “disj ointer” of being?.- The principle of analogy in Speusippus and Aristotle. Some linguistic observations on De communi mathematica scientia ch. IV..- Comparison of Speusippus with Plotinus, establishing differences and resemblances within a fundamental similarity caused by the neoplatonic quality of the doctrines of Speusippus..- Did Speusippus describe his supreme material principle as above non-being? General characteristic of the system of Speusippus ; the originality of his doctrine that the two supreme principles are (morally and esthetically) neutral..- Appendix..- VI. A New Fragment of Aristotle.- Four reasons for deriving De communi mathematica scientia ch. XXIII from Aristotle, particularly from his Protye pticus..- The general content of this chapter: mathematics praised by Aristotle as a branch of theoretical knowledge and eminently appropriate for a life of contemplation..- Mathematics, in this context, interpreted by Aristotle as knowledge of something subsistent..- Why is not only mathematics but also psychology according to one passage in De anima characterized by Aristotle by the quality of dxel fleta ? Possibility that even in De anima Aristotle is still thinking of the soul as a mathematical entity..- A detailed analysis of De communi mathemat ca scientia ch. XXIII. The doctrine that mathematics has the advantage of making it possible to initiate even a young person to the life of contemplation..- Some linguistic observations on De communi mathematica scientia ch. XXIII..- A comparison of Isocrates' and Aristotle’s attitudes toward mathematics..- Conclusion: the newly discovered fragment considerably elucidates Aristotle’s tripartition of theoretical philosophy and illustrates a phase of his philosophy in which he (obviously in connection with an excessively realistic interpretation of mathematicals) interpreted mathematics as a strictly philosophic discipline (i.e. philosophy of mathematics rather than what we should call mathematics), in complete agreement with the Academy..- Note on the educational ideas of Montaigne and Isocrates..- Appendix..- VII. Metaphysica Generalis in Aristotle?.- The problem: Does the term being-as-such, when used by Aristotle to designate the subject matter of metaphysics (theology, first philosophy) mean that which is most abstract, making, thus, Aristotle’s metaphysics a metaphysca generalis ? If this question is answered in the affirmative, how can we explain that Aristotle described his metaphysics as knowledge of just one (the uppermost) sphere of being and, thus, as metaphysca specialis ? In other words: is the entity described by the term being-as-such comparable to a mathematical interpreted non-realistically (a mere, not subsistent abstraction) or rather to a mathematical interpreted realistically (as subsistent) and not merely an object of abstraction?.- Analysis of the pertinent passages in Met. I'. It becomes obvious that in all relevant passages the complete equivalence of the terms “being-as-such” and “supreme sphere of being” is assumed by Aristotle; it becomes, further, obvious that metaphysics is for Aristotle an inquiry into the opposite elements, ultimately being and non-being, of which the supreme sphere primarily and everything else derivatively consists..- In Met. P the principle of contradiction is treated not as a formal principle but as a metaphysical principle; it applies fully only to the supreme sphere of being..- Analysis of Met. E 1: again the equivalence of the terms being-as-such and supreme sphere of being assumed..- Solution of the apparent contradiction in the definition of metaphysics and explanation why Aristotle speaks of metaphysics in terms of a two-oppositeprinciples doctrine: Being-as-such, in this context, does not mean an abstract obj ect (the most abstract at that) in our sense of the word; it means fullest, i.e. fully indeterminate being; it is therefore together with its opposite, non-being-as-such, equivalent to the concept of the supreme sphere of being..- The Academic (and, in this sense of the word, neoplatonic) character of the concept of being-as-such (169-172) and of the doctrine that all beings are ultimately reducible to two opposite principles..- Further clarification of the formula describing metaphysics as xa06A,ov Sts afcoirj : xaOd ov in this context does not mean “universal” in our sense of the word; it means rather “omnipresent”..- Analysis of Met. K 3-7, particularly with regard to the concepts of dpateeCns and xedofatc. In this context, dg9at,oea&g does not designate the process of abstraction in our sense of the word by which we ascend from the individual (concrete) to the universal (abstract) ; it is rather a concept peculiar to the excessively realistic way of thinking, in which, by xedQOsatg, the individual (concrete, real in the ordinary sense of the word) is derived from the universal (sometimes called ideal), in a manner usually termed neoplatonic..- Further clarification of the Academic character of Aristotle’s metaphysics..- The neoplatonic character of the (equivalent) concepts of being-as-such and indeterminate being and the attendant gnoseologic problems. The peculiar character of indeterminate being demands a peculiar type of knowledge, different from ordinary predicative knowledge. Interpretation of Met. O 10, particularly of the concept of da&Bera..- Survey of passages in which Aristotle, in a different phase of his philosophy, criticized the two-oppositeprinciples doctrine and the system of derivation of particulars from universals; the defense of that system for the purpose of elucidation..- Did Plato himself profess a system of derivation Impossibility of answering in the affirmative with certainty; but difficulties arising from an answer in the negative..- Survey of passages implying that according to Aristotle the Pythagoreans, Plato, and other Academics tried to derive the sensible (individual, concrete