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From Platonism to Neoplatonism
The first edition of this book appeared in 1953; the second, revised and enlarged, in 1960. The present, third edition is essentially a reprint of the second, except for the correction of a few misprints and the following remarks, which refer to some recent publications* and replace the brief preface to the second edition. Neither Eudemus nor Theophrastus, so I said (p. 208 . ) knew a branch of theoretical philosophy the object of which would be something called 0'. 1 0'. 1 andwhich branch wouldbedistinct from theology. And there is no sign that they found such a branch (corresponding to what was later called metaphysica generalis) in Aristotle. To the names of Eudemus and Theophrastus we now can add that of Nicholas of Damascus. In 1965 H. J. Drossaart Lulofs published: Nicolaus Damascenus On the Philosophy of Aristotle (Leiden: Brill), Le. fragments of his m: pr. njc; 'ApLO''t'o't'&AOUC; qJLAOO'OqJLiXC; preserved in Syriac together with an English trans lation. In these fragments we find a competent presentation of Aristotle's theoretical philosophy, in systematic form. Nicholas subdivides Aristotle's theoretical philosophy into theology, physics, and mathematics and seems to be completely unaware of any additional branch of philosophy the object of which would be 0'. 1 0'. 1 distinct from theology with its object (the divine)."
- GenresPhilosophy
250 pages, Paperback
First published May 31, 1975
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April 2, 2021
This reviewer was led to the present study by the well-known scholar of the history of ancient philosophy, Philip Merlan, from a notice in Ryszard Stachowski’s work on the antique prototype of the modern mathematization of psychology (reviewed here). From the nature of the citation, one could anticipate finding in Merlan the summit of philological erudition and technical proficiency, and indeed he does deliver the goods. As the title From Platonism to Neoplatonism promises, Merlan is interested more in the careful reconstruction of the stages of development than in assessing, say, the justice of Aristotle’s critique of Plato, where the territory over which he ranges is wider in scope than just the problem upon which Stachowski fixes his attention, that of the doctrine of the soul as mathematical. Accordingly, he [Merlan] chooses to downplay Plato and Plotinus themselves and to focus upon the intermediate figures of Speusippus and Posidonius, whom he sees as mediating between the Academy and the forerunners of the Neoplatonist movement, also referred to as the middle Platonists.
Nevertheless, Merlan’s first chapter is devoted precisely to the question of the mathematical nature of the soul. His tack on the problem is to engage in a close reading of an opusculum by Iamblichus which he feels to have been unjustly neglected, viz., the De communi mathematica scientia, in order to differentiate it from the better-known positions later taken by Proclus. Iamblichus and Proclus are alike in being realists (in the medieval sense) who recognize three levels of subsistence, from the intelligibilia to the mathematicals to the sensibilia or subject matter of physics (in contrast with the usual realist-nominalist divide between the sensory world and non-mathematical universalia). Therefore, to disentangle the two presents a challenge. Here is what Merlan adjudges:
Let us sum up the results of the foregoing discussion. Both Iamblichus and Proclus describe the mathematicals (which they take to subsist) as intermediate. The realms between which they mediate are often described in terms of the divisible and the indivisible. Both are aware of the ‘intermediacy’ of the soul, though Proclus stresses it more than Iamblichus. Both deal with the problem whether mathematicals and the soul are identical – Iamblichus arguing sometimes pro, sometimes contra; Proclus assuming identity. In connection with this question both assert the identity of the soul with all branches of mathematics – three in Iamblichus, four in Proclus. These assertions are closely linked with the motive or nonmotive character of mathematicals. Proclus asserts the former, Iamblichus sometimes the former, sometimes the latter. The solution is closely connected with the problem of a tripartite mathematics without astronomy, or a quadripartite one, including astronomy. (p. 30)
In chapter two, Merlan establishes how Posidonius influenced the Neoplatonists by interpreting Plato’s world-soul as being nothing but the mathematicals. In connection with this move, it is of interest to identify the precise point of difference between Xenocrates and Speusippus, both of whom advanced a definition of the soul as self-moving mathematical. Merlan characterizes the difference thus: Xenocrates thought in terms of arithmetic, Speusippus in terms of geometry. But probably for many readers the most rewarding take-away from this chapter is to be gleaned from a few comments at the end, in which Merlan seeks to motivate why these ancient ideas are not as crazy as a modern man might suppose by highlighting how they, or something resembling them, figure in the idealist schemas of Schelling and Hegel (even to some extent, Kant) and, in fact, play a role in Driesch’s innovative program of developmental biology from the first decade of the twentieth century. So: the hard-nosed reductionist of today who may be inclined to dismiss such views as not belonging to serious science is simply ignorant of his intellectual history.
Let pass over the next two chapters, an extensive and detailed look at the subdivisions of theoretical philosophy and the origin of the quadrivium (which turn upon how one construes the faculty of abstraction), as incidental to Merlan’s argument. More important is chapter five, in which Merlan deploys his philological acumen to establish his thesis that Speusippus was a greater source for Iamblichus than was Plotinus (as usually presumed):
If this interpretation of Speusippis is correct, his system is a highly original, interesting, possibly unique system in the history of Western philosophy. Perhaps it could be compared with that of Schelling, according to whose principle of identity God originally is neither good nor evil, i.e. indifferent. If it indeed introduced the concept of what is above non-being, it anticipated some bold speculations which have their proper place in that branch of Western mysticism which harks back to Platonism and Neoplatonism (Dionysius the Areopagite, Master Eckhart, Nicholaus of Cusa). The best known passage in which this concept occurs is the distichon by Angelus Silesius:
The subtile godhead is a naught and overnaught.
Who sees it? Everyone who can see nought in aught.
[Die zarte Gottheit ist ein Nichts und Uebernichts:
Wer nichts in allem sieht, Mensch, glaube, dieser sichts].
(pp. 127-128)
Chapter six on a newly discovered fragment of Aristotle amounts merely to a detour. All we learn is that Aristotle holds mathematics in higher esteem than was hitherto conventionally thought, although this should not come as much of as surprise. The seventh chapter strikes this reviewer as the most interesting in the book. Here is how Merlan sketches his objective:
But Aristotle changes his mind regarding the status of mathematicals. Is there any comparable change in Aristotle with regard to theologicals and theology (first philosophy)?...In [chapter three] we saw how St. Thomas, when interpreting the tripartition of being and knowledge in Boethius, was led to what amounted to making a marked distinction between metaphysica generalis and metaphysica specialis. With the later Aristotle, St. Thomas rejected the theory of the subsistence of mathematicals – they were only objects of abstraction. But if first philosophy was located above mathematics, the assumption was close at hand that its objects, too, would be only objects of abstraction. Such an interpretation of first philosophy was bound to result in a conception of metaphysics as metaphysica generalis. In other words, with the status of mathematicals as subsistent gone, first philosophy, when referred to in the context of a tripartition of knowledge, seemed to designate metaphysica generalis. To what extent is such an interpretation justified? The same problem can also be stated in shorter terms. Sometimes Aristotle refers to first philosophy as being theology; sometimes he refers to it as being science of being-as-such. The former reference seems to lead to metaphysica specialis; the latter to metaphysica generalis. How are the two related? (pp. 160-161)
A fascinating question! Here is what Merlan determines:
What, then, is the way out of this whole confusion? It is very simple. The Aristotle who wrote Met. Γ and E1, and at the time when he wrote them, was not aware that his being-as-such could be interpreted as abstract or as formal; he was not aware that he was starting a general metaphysics as different from special metaphysics. It can not be denied that it may be legitimate to interpret him this way, if by legitimate we mean what is logically implied or what is implied in other passages dealing with the concept of being; but it can be asserted that he was not aware of it. On the contrary, he thinks of being-as-such as an element, something indwelling in all that is. This assertion is tantamount to saying that Met. Γ and E1 were written in the Academic tradition. According to this tradition there are different spheres of being; there is at least one sphere over and above the sphere of the sensible….With this explanation almost all difficulties of Γ and E1 disappear. (pp. 169-171)
Or, put more succinctly:
Aristotle never intended to start a general metaphysics and therefore his science of being-as-such would be neoplatonic in character. (p. 209)
From this conclusion Merlan draws a startling inference:
The whole chapter ends (1064b11-14) with a summary: the subject matter of metaphysics, the unmoved and incorporeal (χωριστόν), precedes the subject matter of physics and mathematics and is in virtue of that precedence (or, by the same token), a ϰαθόλου….The implications of this interpretation of Γ, E1 and K3-7 are of considerable interest….First as to the ideas. [The relation of eternal changeless being to the realm of the changeable] was supposed to be a real relation, or we would say a causal relation. But according to Aristotle it turned out to be at best a logical relation – implication, not causation. To indicate this, we could say that the ideas turned out to be nonmotive. There was no transition from them to the realm of space and time. No matter what the amount of πρόθεσις, there was still no way to ‘derive’ the sensibilia from the ideas. (pp. 178-179)
The conclusion ties to together the strands of the foregoing exposition. Let us abstract what is of greatest interest to us from the point of view of psychology:
The identification of the soul with some kind of mathematical (which Plato’s Timaeus is on the verge of asserting) was explicitly stated by Xenocrates (soul = a self-moving or motive number) and probably also by Speusippus (soul = form of the all-extended), so that in equating the soul with mathematicals, Posidonius only continued and developed the Academic tradition….This identification is connected with another problem: that of the origin of change (motion) in a universe consisting of the aforesaid spheres. The identification of the soul with mathematicals was connected with the further assumption that the mathematicals were, in some way, the source of change. This was most clearly stated by Xenocrates, but the assumption reappears in Proclus and Iamblichus. (p. 222)
The divine character of Aristotle’s astronomicals is obvious and stressed by him. This is an implicit proof that the mathematicals also, as long as they were considered to be subsistent, were taken to be divine. Mathematics, within this framework, was indeed closely allied with theology….Again, an interpretation of all these speculations is possible only when we are ready to grant that soul does not mean necessarily something like consciousness; further if we are ready to grant that mathematicals are in rerum natura and not only in our thoughts. And once we grant that the universe contains mathematicals, it is only natural to assume that in some way these mathematicals are causes. Furthermore, the equation soul = mathematicals is not at all fantastic if we grant the idea of self-thinking (and, in this sense of the word, self-moving or self-changing) mathematicals is not an absurdity. And is it not true that after all what has been called Aristotle’s νοῦς ποιητιϰός may be interpreted precisely as the system of all immutable truths thinking themselves and, thus, changelessly self-changing? (pp. 222-224)
Conclusion: An exquisitely learned work of scholarship; quite demanding, not at all expository, presupposes the reader will already be in command of a fairly good overview of ancient intellectual history – if so, perusing it will give the reflective reader occasion to consolidate his understanding of the relevant figures, major and minor, and the interconnections among them (at about as fine-grained a level as it gets). For a long time, it has been customary to contrast Plato and Aristotle as poles apart; though Aristotle started out as Plato’s pupil, his temperament was too discordant for him to remain a disciple for very long – Plato a dreamer and a mystic, Aristotle the sober metaphysician and proto-scientist. In view of this widespread stereotype, Merlan’s novel suggestion that this characterization might not be as true to the record as all along has been thought is provocative. Maybe Plotinus is righter than we tend to give him credit for to interpret Aristotle, properly understood, as being in harmony with his coryphaeus, Plato, the philosopher of philosophers!
Nevertheless, Merlan’s first chapter is devoted precisely to the question of the mathematical nature of the soul. His tack on the problem is to engage in a close reading of an opusculum by Iamblichus which he feels to have been unjustly neglected, viz., the De communi mathematica scientia, in order to differentiate it from the better-known positions later taken by Proclus. Iamblichus and Proclus are alike in being realists (in the medieval sense) who recognize three levels of subsistence, from the intelligibilia to the mathematicals to the sensibilia or subject matter of physics (in contrast with the usual realist-nominalist divide between the sensory world and non-mathematical universalia). Therefore, to disentangle the two presents a challenge. Here is what Merlan adjudges:
Let us sum up the results of the foregoing discussion. Both Iamblichus and Proclus describe the mathematicals (which they take to subsist) as intermediate. The realms between which they mediate are often described in terms of the divisible and the indivisible. Both are aware of the ‘intermediacy’ of the soul, though Proclus stresses it more than Iamblichus. Both deal with the problem whether mathematicals and the soul are identical – Iamblichus arguing sometimes pro, sometimes contra; Proclus assuming identity. In connection with this question both assert the identity of the soul with all branches of mathematics – three in Iamblichus, four in Proclus. These assertions are closely linked with the motive or nonmotive character of mathematicals. Proclus asserts the former, Iamblichus sometimes the former, sometimes the latter. The solution is closely connected with the problem of a tripartite mathematics without astronomy, or a quadripartite one, including astronomy. (p. 30)
In chapter two, Merlan establishes how Posidonius influenced the Neoplatonists by interpreting Plato’s world-soul as being nothing but the mathematicals. In connection with this move, it is of interest to identify the precise point of difference between Xenocrates and Speusippus, both of whom advanced a definition of the soul as self-moving mathematical. Merlan characterizes the difference thus: Xenocrates thought in terms of arithmetic, Speusippus in terms of geometry. But probably for many readers the most rewarding take-away from this chapter is to be gleaned from a few comments at the end, in which Merlan seeks to motivate why these ancient ideas are not as crazy as a modern man might suppose by highlighting how they, or something resembling them, figure in the idealist schemas of Schelling and Hegel (even to some extent, Kant) and, in fact, play a role in Driesch’s innovative program of developmental biology from the first decade of the twentieth century. So: the hard-nosed reductionist of today who may be inclined to dismiss such views as not belonging to serious science is simply ignorant of his intellectual history.
Let pass over the next two chapters, an extensive and detailed look at the subdivisions of theoretical philosophy and the origin of the quadrivium (which turn upon how one construes the faculty of abstraction), as incidental to Merlan’s argument. More important is chapter five, in which Merlan deploys his philological acumen to establish his thesis that Speusippus was a greater source for Iamblichus than was Plotinus (as usually presumed):
If this interpretation of Speusippis is correct, his system is a highly original, interesting, possibly unique system in the history of Western philosophy. Perhaps it could be compared with that of Schelling, according to whose principle of identity God originally is neither good nor evil, i.e. indifferent. If it indeed introduced the concept of what is above non-being, it anticipated some bold speculations which have their proper place in that branch of Western mysticism which harks back to Platonism and Neoplatonism (Dionysius the Areopagite, Master Eckhart, Nicholaus of Cusa). The best known passage in which this concept occurs is the distichon by Angelus Silesius:
The subtile godhead is a naught and overnaught.
Who sees it? Everyone who can see nought in aught.
[Die zarte Gottheit ist ein Nichts und Uebernichts:
Wer nichts in allem sieht, Mensch, glaube, dieser sichts].
(pp. 127-128)
Chapter six on a newly discovered fragment of Aristotle amounts merely to a detour. All we learn is that Aristotle holds mathematics in higher esteem than was hitherto conventionally thought, although this should not come as much of as surprise. The seventh chapter strikes this reviewer as the most interesting in the book. Here is how Merlan sketches his objective:
But Aristotle changes his mind regarding the status of mathematicals. Is there any comparable change in Aristotle with regard to theologicals and theology (first philosophy)?...In [chapter three] we saw how St. Thomas, when interpreting the tripartition of being and knowledge in Boethius, was led to what amounted to making a marked distinction between metaphysica generalis and metaphysica specialis. With the later Aristotle, St. Thomas rejected the theory of the subsistence of mathematicals – they were only objects of abstraction. But if first philosophy was located above mathematics, the assumption was close at hand that its objects, too, would be only objects of abstraction. Such an interpretation of first philosophy was bound to result in a conception of metaphysics as metaphysica generalis. In other words, with the status of mathematicals as subsistent gone, first philosophy, when referred to in the context of a tripartition of knowledge, seemed to designate metaphysica generalis. To what extent is such an interpretation justified? The same problem can also be stated in shorter terms. Sometimes Aristotle refers to first philosophy as being theology; sometimes he refers to it as being science of being-as-such. The former reference seems to lead to metaphysica specialis; the latter to metaphysica generalis. How are the two related? (pp. 160-161)
A fascinating question! Here is what Merlan determines:
What, then, is the way out of this whole confusion? It is very simple. The Aristotle who wrote Met. Γ and E1, and at the time when he wrote them, was not aware that his being-as-such could be interpreted as abstract or as formal; he was not aware that he was starting a general metaphysics as different from special metaphysics. It can not be denied that it may be legitimate to interpret him this way, if by legitimate we mean what is logically implied or what is implied in other passages dealing with the concept of being; but it can be asserted that he was not aware of it. On the contrary, he thinks of being-as-such as an element, something indwelling in all that is. This assertion is tantamount to saying that Met. Γ and E1 were written in the Academic tradition. According to this tradition there are different spheres of being; there is at least one sphere over and above the sphere of the sensible….With this explanation almost all difficulties of Γ and E1 disappear. (pp. 169-171)
Or, put more succinctly:
Aristotle never intended to start a general metaphysics and therefore his science of being-as-such would be neoplatonic in character. (p. 209)
From this conclusion Merlan draws a startling inference:
The whole chapter ends (1064b11-14) with a summary: the subject matter of metaphysics, the unmoved and incorporeal (χωριστόν), precedes the subject matter of physics and mathematics and is in virtue of that precedence (or, by the same token), a ϰαθόλου….The implications of this interpretation of Γ, E1 and K3-7 are of considerable interest….First as to the ideas. [The relation of eternal changeless being to the realm of the changeable] was supposed to be a real relation, or we would say a causal relation. But according to Aristotle it turned out to be at best a logical relation – implication, not causation. To indicate this, we could say that the ideas turned out to be nonmotive. There was no transition from them to the realm of space and time. No matter what the amount of πρόθεσις, there was still no way to ‘derive’ the sensibilia from the ideas. (pp. 178-179)
The conclusion ties to together the strands of the foregoing exposition. Let us abstract what is of greatest interest to us from the point of view of psychology:
The identification of the soul with some kind of mathematical (which Plato’s Timaeus is on the verge of asserting) was explicitly stated by Xenocrates (soul = a self-moving or motive number) and probably also by Speusippus (soul = form of the all-extended), so that in equating the soul with mathematicals, Posidonius only continued and developed the Academic tradition….This identification is connected with another problem: that of the origin of change (motion) in a universe consisting of the aforesaid spheres. The identification of the soul with mathematicals was connected with the further assumption that the mathematicals were, in some way, the source of change. This was most clearly stated by Xenocrates, but the assumption reappears in Proclus and Iamblichus. (p. 222)
The divine character of Aristotle’s astronomicals is obvious and stressed by him. This is an implicit proof that the mathematicals also, as long as they were considered to be subsistent, were taken to be divine. Mathematics, within this framework, was indeed closely allied with theology….Again, an interpretation of all these speculations is possible only when we are ready to grant that soul does not mean necessarily something like consciousness; further if we are ready to grant that mathematicals are in rerum natura and not only in our thoughts. And once we grant that the universe contains mathematicals, it is only natural to assume that in some way these mathematicals are causes. Furthermore, the equation soul = mathematicals is not at all fantastic if we grant the idea of self-thinking (and, in this sense of the word, self-moving or self-changing) mathematicals is not an absurdity. And is it not true that after all what has been called Aristotle’s νοῦς ποιητιϰός may be interpreted precisely as the system of all immutable truths thinking themselves and, thus, changelessly self-changing? (pp. 222-224)
Conclusion: An exquisitely learned work of scholarship; quite demanding, not at all expository, presupposes the reader will already be in command of a fairly good overview of ancient intellectual history – if so, perusing it will give the reflective reader occasion to consolidate his understanding of the relevant figures, major and minor, and the interconnections among them (at about as fine-grained a level as it gets). For a long time, it has been customary to contrast Plato and Aristotle as poles apart; though Aristotle started out as Plato’s pupil, his temperament was too discordant for him to remain a disciple for very long – Plato a dreamer and a mystic, Aristotle the sober metaphysician and proto-scientist. In view of this widespread stereotype, Merlan’s novel suggestion that this characterization might not be as true to the record as all along has been thought is provocative. Maybe Plotinus is righter than we tend to give him credit for to interpret Aristotle, properly understood, as being in harmony with his coryphaeus, Plato, the philosopher of philosophers!
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