21 Theol. Plat. II 66, 1-9.
From this truth Parmenides demonstrates, according to Proclus, the derivation, in order and according to strict syllogistic procedure, of subsequent metaphysical truths, expressing thereby in scientific form the derivation of all levels of the divine from an ultimate principle. Proclus summarizes the procedure thus:
For the first conclusions are made evident immediately from the smallest number and the most simple and most knowable , common concepts so-to-speak; and the conclusions subsequent to these through more numerous and complex ; and the last are the most composite. For Parmenides always uses the first conclusions for demonstrations of the subsequent and offers, as an intellectual paradigm of the order in geometry and in the other mathematical sciences, this chain of conclusions fitted to each other. If then discourse brings an image of the things it interprets (Tim. 29 b), and as are the demonstrative unfoldings so must what are demonstrated be in order, it is necessary, I believe, that the first conclusions demonstrated from the simplest premises must be absolutely primary and joined closely to the One, those that are multiplied continuously and depend on complex demonstrations being products at a greater distance, in 'alienation', one might say, 'from the One'. 22
22 Theol. Plat. I 45, 20-46, 9; Saffrey and Westerink indicate that at the end Proclus is quoting Plotinus, VI 6, 1.
I have suggested elsewhere (1986) that Proclus' conception of dialectic represents a theory of metaphysics whose originality and coherence has hitherto been scarcely noticed, a result no doubt of the fact that it regards itself as no more than an exegesis, and an improbable one at that, of Plato. In view of the lack of evidence concerning Syrianus it is difficult to determine the extent of Proclus' debt here to Syrianus, although we may suppose that a certain amount derives
end p.202
from Syrianus. 23
23 Cf. above nn. 13, 16.
Even less is known of how Iamblichus conceived dialectic or the science of the divine. But one can reasonably suppose that Iamblichus did not, as does Proclus, discount the scientific claims of Pythagorean theory, reserving for Plato alone the title of true dialectician. This probably means that Proclus did not find in Iamblichus' accounts of Pythagorean theology an approach corresponding to his conception of dialectic. In other words there is some likelihood that in clarifying and systematizing the distinction between theologizing mathematics and theology or dialectic proper, Proclus came to conceive of the latter science in a way that no longer corresponded to Iamblichus' treatment of the subject.
Be that as it may, it might be noted that in his attempt to formulate the nature of dialectic as a science independent of, superior to, and paradigmatic for mathematics, Proclus is largely guided by his understanding of the structure of mathematical science, in particular geometry. Thus dialectic, like geometry, 'projects' or 'unfolds' innate a priori concepts, demonstrating them by means of rigorous syllogistic arguments. The concepts are of course of a higher order, nearer the intelligible principles of soul and of a broader application than the concepts explicated by the geometer. But it remains that mathematics, and in particular geometry, provides Proclus with the model (he would say the image) of scientific discourse whereby the distinctiveness and superiority of dialectic vis-à-vis other sciences can be determined. The same phenomenon will be observed in the following section with respect, not to form, but to the content of dialectic. In general one might say that in imposing limits on Iamblichus' Pythagoreanizing of Platonic philosophy, in subordinating Pythagorean mathematics and theologizing mathematics to Platonic dialectic, Proclus adopted for this a principle, namely the image-status of mathematics that he found in Iamblichus' Pythagoreanizing programme itself.
We may conclude finally that Proclus' description of Platonic dialectic in his Commentary on the Parmenides and in his Platonic Theology corresponds in many respects to the structure of the Elements of Theology. The chain of syllogisms described in the passage quoted immediately above is a distinctive feature of the Elements of Theology. The propositions that precede and are supported by the syllogisms can be regarded as the metaphysical concepts which the dialectician
end p.203
seeks to unfold. Indeed the fourth proposition, 'All that is unified is other than the One itself', turns out to be what Proclus considers as the very first metaphysical concept, the first hypothesis of the Parmenides ('The One, if it is one, may not be many') if, applying the first proposition, we describe all multitude as unified. The first three propositions and their demonstrations prepare the way and lead up to the first metaphysical truth, after which Proclus proceeds to unfold truths concerning divine causes in general and concerning each level of the divine treated in particular and in descending order. Thus the Elements of Theology shows the motion upwards and downwards that Plato attributes to dialectic in the Republic. However it is especially in the Parmenides that Proclus finds dialectical exposition, and the correspondence between the fourth proposition of the Elements of Theology and the first hypothesis of the Parmenides suggests that the major source of inspiration of Proclus' work is the Parmenides, as he interpreted that dialogue. 24
24 Dodds indicates in his edition (e.g., 188, 189, 190) connections with the Parmenides; such parallels could be multiplied.
Thus another striking originality of the Elements of Theology, besides its rigorous syllogistic form—namely the fact that, contrary to Proclus' normal practice, no authorities are cited—can be clarified, if the work is seen as an exposé of dialectic: an authority is in fact present in the work, namely Plato, for the work unfolds the science of the divine that Plato alone communicated to mankind.
3. Mathematical Theology and Dialectic
In the preceding section I have attempted to indicate how Proclus, emphasizing a point already made by Iamblichus, drew a clear distinction between theologizing mathematics and theology or dialectic proper, and how, in order to bring out the distinctiveness and superiority of the latter science, he gave it a form derived from his own understanding of the structure of geometry. In this section I shall suggest that a similar situation arises with regard to the content of theology: in his account of this content, i.e. the divine, Proclus seeks to proceed independently of theologizing mathematics, but this account can nevertheless be seen to be inspired to a considerable degree by theologizing mathematics.
A first example of this may be found in the presentation of the gods that Proclus calls 'henads' in the Elements of Theology. Having dealt
end p.204
with the supreme principle, the One, and its relations to its products in the first part of the Elements of Theology, Proclus turns in propositions 113-65 to the gods that are subordinate to the One and that transcend the level of intelligible being, the henads. Iamblichus had also treated of an order of gods corresponding to these henads in On Pythagoreanism VII, 25
25 Saffrey and Westerink argue, in Theol. Plat. III ix-lxxvii, against there having been a theory of henads in Iamblichus, on the basis of a study of later reports in Proclus and Damascius and before the first-hand evidence provided by Psellus' excerpts could be considered.
and what remains of this treatment in Psellus' excerpts shows some similarities with Proclus' approach. In both Iamblichus and Proclus this order of gods is considered as unified both in itself and in each of its members. 26
26 Proclus, El. theol. props. 113-14; cf. above, p.84.
Both treat first of the general properties of the order as a whole before discussing specific properties. For both each god is distinct, forms part of a serial ordering, and is reflected in its effects in corresponding features found on the successive lower levels of reality. 27
27 Proclus, props. 133, 135; 126, 136; 129, 131, 145; cf. above, pp. 83-4.
Yet one notices also in Proclus' account of the henads aspects that differentiate it from the theologizing arithmetic of On Pythagoreanism VII. It appears first that in referring to the henads as 'divine number' Proclus gives to the term 'number' a broad, non-mathematical sense, i.e. that of group or class. 28
28
Dodds's translation of
ιθμ
ζ
(a possible exception may be 104, 9-10); Merlan argues against this
(1965),
I believe unconvincingly.
Furthermore, in discussing the specific properties of the henads, Proclus does not take in turn each of the distinct members of the order as does Iamblichus when he deals with the monad, dyad, triad of the order. Rather each property is presented without reference to particular henads. Finally the properties that are named by Proclus—the 'paternal', the 'generative', the 'perfective', the 'protective', etc. (props. 151 ff.)—are not especially mathematical in character. It is true that their analogues can be found in mathematical objects: Proclus elsewhere relates the 'paternal' to the monad and the 'generative' to the dyad, 29
29 Cf. Theol. Plat. I 122, 3-10.
whereas the triad is traditionally regarded as perfective. But it is surely significant that Proclus, in introducing these different properties of the henads, does not attribute them to particular members of a numerical series, as does Iamblichus. It is as if Proclus wishes to avoid an identification of each of the henads with each number in a decadic series. 30
30 Merlan (1965), 175-6, argues that Proclus thought of the henads as constituting a decad, but the evidence is not that clear.
In this we may regard Proclus
end p.205
as applying with rigour the distinction he finds between theologizing mathematics and theology proper. In consequence however Proclus' treatment of the henads in the Elements is somewhat general and vague. If the henads are not to be seen simply as the monad, dyad, triad of a decad, it is not clear what individually they are supposed to be.
If Proclus' account of the henads in the Elements of Theology seeks to establish itself independently of the account of the same matter yielded by theologizing mathematics, it must be admitted, however, that the source of inspiration of much of what Proclus says of the henads is mathematics and theologizing mathematics. I have indicated above the broad similarities of treatment between the section on henads in the Elements and On Pythagoreanism VII. To these one might add Proclus' frequent recourse to mathematical principles and laws. For example the law of mean terms serves to link not only the members of the order of henads but also almost everything else in Proclus' theological universe. 31
31 Prop. 132; cf. prop. 148; Dodds, in his edn., xxii.
The principles of 'limit' and the 'unlimited', principles that occur in Plato's Philebus and that Syrianus and Proclus identify with the Pythagorean monad and dyad, 32
32 Cf. above, p. 146; Sheppard (1982); Beierwaltes (1972), 179 ff.
are responsible for the constitution of the order of henads. Indeed the concept of the monad and its relation to the series it generates is of great importance to the ordering of reality as Proclus conceives it in the Elements. 33
33 Cf. e.g. props. 21-2 (with Dodds's comment, 208), 204 (178, 28-31).
One might reasonably say then that despite his effort to separate (Platonic) dialectic or theology from (Pythagorean) theologizing mathematics, Proclus in effect produces a theological account that cannot but strike us, in certain respects, as heavily indebted to mathematics.
The same can be observed, I believe, in Proclus' other theological works, his Commentary on the Parmenides and his Platonic Theology. In the Commentary on the Parmenides, for example, Proclus treats of the henads in the same very general way that characterizes the account in the Elements of Theology: the henads are described collectively in terms of a number of metaphysical properties. 34
34 Cf. In Parm. 1048, 14-1049, 3.
In his interpretation of the Parmenides Proclus indicates that mathematical terms occurring in Plato's (theological) text are to be understood, not in a mathematical, but in a higher sense. 35
35 In Parm. 1129, 22-6; 1204, 19-41.
And when he analyses the orders of the gods in terms of the relations between monad and dyad, he notes that he is
end p.206
using a mathematical image. 36
36 In Parm. 662, 4-12.
And yet the use of mathematical relationships to describe meta-mathematical realities is such that it is not clear sometimes how such realities could otherwise be presented. 37
37 Cf. e.g. In Parm. 703, 12-704, 10; 706, 27-33.
In the Platonic Theology Proclus also treats of the gods in a fashion that is in part inspired by mathematics while at the same time separating itself from theologizing mathematics. On the subject of the henads he claims that:
There must be an order among the henads such as we see among numbers, some being nearer the principle, others being further away, some being simpler, others more composite, greater in quantity, but lesser in power. And we have rightly recalled the numbers. For if we must contemplate the order of the very first monads among themselves and the production of beings, using numbers as images, it is necessary that in these monads those that are nearer the One be shared in by those that are simpler in being, those that are further being shared in by those that are more composite. (III 17, 18-18, 3)
If emphasis is placed here on the function of numbers as images of higher realities, in other contexts it looks as if mathematical principles are what governs the orders of the gods: the monad and its relation to a number series, the interplay between monad and dyad in the production of the decad are the structural principles that constitute Proclus' world of gods. 38
38 Cf. e.g. Theol. Plat. II 38, 3-8; 71, 5-8; III 8, 1-9, 11; 30, 19-34, 19.
Of course Proclus made use of other sources in his theology such as the general metaphysical truths he found stated in the hypotheses of Plato's Parmenides as well as in the utterances of the 'Chaldaean Oracles'. However, we might plausibly claim, given the examples cited, that his 'Platonic' theology, although asserting its independence of and superiority to 'Pythagorean' theologizing mathematics, is still marked by this theologizing mathematics. The somewhat ambivalent character of his theology—both mathematical and not mathematical in form and content—is testimony to its origins as, in part at least, a critical reaction to the theologizing mathematics of Iamblichus' Pythagoreanizing programme.
end p.207
4. Concluding Comment
In the first chapters devoted to Proclus above I have suggested that Proclus, far from simply adopting Iamblichus' Pythagoreanizing programme, changed that programme in various significant ways. He altered the relations between the figures of Pythagoras and Plato in such a way that Plato and his dialogues took over the pre-eminence given by Iamblichus to Pythagoras and Pythagorean works. For Proclus Plato was the first scientific philosopher and it is only in Plato's writings that the scientific exposition of truth is to be found. This shift in focus is accompanied by a shift in the attitude taken to mathematics in its relations to the other parts of philosophy. While acknowledging the mediatory and pivotal role of mathematics, Proclus insisted on the limitations of mathematics, in particular as regards a distinct and higher science, Platonic dialectic. In reducing Pythagorean theology to the status of theologizing mathematics and in claiming to find in Plato alone the science of the divine, Proclus was able to distinguish much more clearly than could Iamblichus between these two approaches to the divine.
In presenting the latter point in this chapter I have not tried to survey the full breadth of Proclus' metaphysics. I have sought rather to give some indications of how Proclus attempted to separate Pythagoreanizing theologizing mathematics from Platonic dialectic. For this purpose Proclus had to elaborate an interpretation of what precisely Platonic dialectic is: Plato himself gives only some obscure hints, in particular in the Republic. Elaborating an approach inspired, it appears, in some respects by his teacher Syrianus, Proclus conceived of dialectic very much after the pattern of the structure of geometry as he understood it: dialectic is a demonstrative science, explicating certain a priori metaphysical truths given in the soul. These truths are more profound and general than geometrical axioms, concerning as they do the first principles of all reality, the gods. This characterization of dialectic, if effective in permitting of a sharp discrimination between the science of the divine and theologizing mathematics, is nevertheless based on an assimilation of mathematical method to scientific method in general. And although in his theology Proclus attempts to describe the gods independently of mathematical assimilations, he often introduces what are in effect mathematical concepts and laws. Theology thus establishes itself in Proclus in large part in
end p.208
relation to mathematics and theologizing mathematics. The Elements of Theology may be regarded as a worthy expression of the originality and vigour Proclus brought to bear on the effort to go beyond the Pythagoreanizing theology of Iamblichus in the direction of the formulation of a truly Platonic metaphysics. And it is precisely this Iamblichean background that provides a means of grasping and measuring the extent of Proclus' achievement.
end p.209
Conclusion
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