Bedeutung der Vielheit von Pythagoras bis Plato

angelegt 31.06.2021

Significance of Multiplicity from Pythagoras to Plato

From the early Presocratics through Pythagoras and Plato, Plotinus inherits the central function of the philosophy of number in explaining both the multiplicity of beings and the relation of this multiplicity to the One.¹⁷ Slaveva-Griffin distinguishes three central philosophical functions fulfilled by number in ancient philosophy:

• a cosmogonic function that “searches for the origin of multiplicity from some physical or metaphysical source”;
• a cosmological function that “searches for a way to explain the innumerable diversity of material world in an orderly fashion” and;
• an epistemological function that “attempts to comprehend the visible and invisible constituents of the universe in a rational form” (Slaveva-Griffin 2009: 4).

Number is the crucial concept that mediates both between the move from the One to the many (cosmology) and from the many to the One (cosmogony). It allows these two to be held together in their irreducible tension. An epistemological investigation into the properties of numbers is thus not an enquiry undertaken for its own sake, but an attempt to understand the structure of reality in its outward pull away from the One and its inward pull towards the One.¹⁸ Besides the problem of the relation of the cosmogonical and the cosmological properties of number, however, there is a further problem that arises in relation the One: this is the problem of the polysemy of the term “one,” which Plato discusses in the Parmenides.

Pythagorean elements are interspersed throughout Plato’s dialogues, especially the Timaeus and Philebus, which Slaveva-Griffin discusses, and the Laws, Theaetetus and the Republic, which Rist (1967) analyses. However, I will focus here primarily on Plato’s dialogue Parmenides. While the Timaeus and Philebus focus on cosmogonic and cosmological themes, and the latter three texts on the challenges to monism arising out of the problem of evil, the Parmenides is explicitly and technically ontological, setting for itself an investigation into the one, unity and multiplicity. The dialogue lists eight hypotheses, of which only the first two are of relevance to us here in the Plotinian framework. The first hypothesis, which speaks of the unity of the one as absolute, is most closely related to Parmenides’ Peri Physeōs (Anmerk. On Nature). This conception of the One insists on its absolute, pure and simple unity and excludes any predicates – including the predicate that it is one! Plato felt this last deduction of the first hypothesis to be self-contradictory, and thus introduces the second hypothesis, which is of most relevance to our discussion. This second hypothesis introduces sophistication or qualification (one can hardly call it difference) into the One.¹⁹ The One, according to the deductions of this hypothesis, consists of both unity and being: to hen and ousia, to einai or to on. Slaveva-Griffin convincingly shows how this qualification of the One, “as unity and multiplicity interact at an ontological level, especially as represented in Plotinus’ concepts of the Indefinite Dyad and Intellect” (Slaveva-Griffin 2009: 6). In support, she cites Simplicius, Metaphysics 187a: “Alexander says that ‘according to Plato the One and the Indefinite Dyad, which he spoke of as Great and Small, are the Principles of all things and even the Forms themselves.’... It is very likely that Plato made the One and the Indefinite Dyad the Principles of all things, since this was the doctrine of the Pythagoreans whom Plato followed at many points.”²⁰ Note, however, that Plato does not elaborate on the Indefinite Dyad as such, but the unwritten doctrines of Plato, the agrapha dogmata, attest to this notion.²¹ Whatever the actual relationship between Plato’s written and unwritten doctrines may be, we can accept with reliable confidence that the concept of the Indefinite Dyad played a role in Plato’s conception of the “many” (Krämer 1990; Dillon 2003; Guthrie 1978: 418–42; Slaveva-Griffin 2009).

After Plato, the next thinker to consider is Speusippus, who renames Plato’s One and the Indefinite Dyad as One and Multiplicity (plēthos). He constructs a conceptual system in de Communi Mathematica Scientia.²² Slaveva-Griffin writes:

According to this system, the first level of reality that derives from the union of a One and Multiplicity is the first principle of number, which in turn unites with multiplicity once again to produce the sequence of numbers and geometrical figures .... the One imposes limit and quality into Multiplicity, being infinite divisibility .... Aristotle interprets multiplicity quantitatively as multiplicity of units and number as a composition of units, while Speusippus and, in retrospect, Plato view them as ontologically primal.

(2009: 7)

Rist (1965: 330–31) approaches the same issue from an ethical rather than an ontological point of view, relying heavily on Aristotle. Rist’s ethical approach clarifies some of the background behind the issues of One, multiplicity and the Dyad, and how Aristotle’s materialistic interpretations of number were stirring debate, but Rist makes the same error as Aristotle of confusing one as a simple, undifferentiated one with one as the first of a series.²³ To add to the problem of rescuing Parmenidean (or Platonic) monism, intellectual debates did not fail to exploit the analytic avenues opened. Thus, Rist takes Theophrastus’ comment on this Pythagorean structure seriously, and asserts that unlike the later Milesians, Pythagoras was a dualist. Here it is important for us that Rist’s interpretation explicitly hinges on the fact that “they [i.e. Plato and Pythagoras] ... make a kind of opposition (ἀντίθεσιν τινα ποιοῦσιν) between the One and the Indefinite Dyad” (Anmerkg. Rist statement is wrong) (ibid.: 332).

In contrast to Rist’s views, I would like to suggest that there is an alternative way to think of the Indefinite Dyad in Plato, namely, through holding apart the different sense of “one”, as is the case in the Nārāyanīya.²⁴ As we have seen, the text distinguishes between two main senses of one: the One Being, which is without a second and yet somehow engenders a procession through doubling, is different from the one of the series eka, dvi and tri. Retaining this distinction between two senses of one, we can now better address the problem as defined by Rist. First, we should note that in the Nārāyan ̣īya, the One does not become the many; it remains distinct from the numeric series identified with cosmology: Ekata, Dvita and Trita are the sons of the Creator; yet, when sage Nārada arrives at Śvetadvīpa, wishing to behold the One, he sees the entire cosmos of becoming contained within the One. The Creator’s sons are less fortunate and are told that the One is seen through the dyadic beings of Śvetadvīpa being seen. Curiously, when Nārada returns to the Bādarī hermitage of Nara-Nārāyana, the sages, who were formerly a pair, now appear exactly as the dyadic beings of Śvetadvīpa. Distinguishing between the simple One and one as the first in a series would thus allow us to posit the Dyad without necessarily reverting to a dualistic ontology.²⁵

With Xenocrates, we find a new way to conceive the relation of unity to multiplicity: Xenocrates genders the first two principles of the Monad and the Dyad: the Monad is considered masculine, and described as the Intellect. The Dyad is female, properly conceived of as the Indefinite Dyad owing to it containing multiplicity and unlimitedness.²⁶ The “World Soul” is created through the union of these male and female first principles.²⁷

With these comments on the significance of number in Greek philosophers, I would now like to turn to the Nārāyanīya.