Jaap Mansfeld et al. Ja ap m a n sf

Melissus between Miletus and Elea I

 

 

79

 

ἄπαυστον) in the Alētheia section.

29

 As an interpretation of Parmenides’ state-

ments about coming to be and passing away Melissus’ new formula concerned 

with all time is entirely legitimate, although, as we have seen, it is not the only 

possible one. Typically, Melissus again argues from a to b and then counterfac-

tually back from b to a. We shall encounter further examples of this chiastic type 

of reasoning with its roots in the traditions of oral performance, for instance in 

fr. 30 B7. The present instance irritated Aristotle, as we shall see in Part II below. 

According to Melissus the absence of both beginning and end has to mean 

that Being is ‘unlimited’ (ἄπειρόν, fr. 30 B3).

30

 As we know this is not a Par-

menidean thought at all, for Parmenides’ Being ‘is situated in the limits (πείρασι) 

of great chains’, and ‘since there is a final limit (πεῖρας πύματον), it is like the 

mass of a concentric ball’.

31

 Melissus revises this notion. Parmenides’ descrip-

tion of Being as having a sphere-like form and as being located inside limits, or 

‘as remaining in the same state it lies by itself, and so remains fixed there’ (‘on 

the spot’, αὖθι) suggests that it is somewhere specific, that is, that it occupies a 

definite place or space (in fact, all available space if the limit is ultimate). It has 

generally been seen as a problem that Melissus’ Being is not only unlimited as 

to time, but is also ‘always unlimited in size’ (μέγεθος)

32

 as stated in fr. 30 B3, 

for how did he manage to prove this?

33

 It seems that he believed that one way of 

being unlimited entails being unlimited in another way as well, which is a bit 

hard to gauge. I assume (but do not insist) that the spatial aura of Parmenides’ 

Being-within-limits is one of the factors that prompted Melissus to move from 

unlimited being in unlimited time to unlimited being in unlimited space, his re-

vision of the temporal aspect helping to bring along the spatial aspect. This too 

is an issue I shall return to. 

It anyhow seems that arguing in favour of spatial infinity was of special in-

terest to him. The point is driven home in fr. 30 B4, a back-to-front version of 

the argument of fr. 30 B2: ‘nothing that has a beginning and end is either eternal 

(ἀίδιον) or unlimited’. 

                                                            

29

 Fr. 28 B8.27. 

30

 The term ἄπειρος in relation to size occurs also in Zeno’s dialectical arguments: fr. B1 infinite size 

(μεγάλα δὲ ὥστε ἄπειρα εἶναι), fr. 29 B3 infinite division. Anaxagoras used the concept of infinity in 

several ways, see below, III.1, text to n. 4. 

31

 Fr. 28 B8.26, B8.43–44. 

32

 The word μέγεθος is not found in Parmenides, but occurs several times in Zeno: frr. 29 B1 and Β2; 

for his use of the idea of infinite size see above, n. 30. 

33

 Cherniss (1935), 69–73 attempts to construct an argument for Melissus and ibid., 70 argues that ‘time 

and space are two complementary dimensions in which all process occurs’; see also Verdenius (1948), 

8–10. Vlastos (1953) plus additional note in the repr. unsuccessfully argues that only temporal infinity is 

meant. Owen (1960), 67, at some cost to the interpretation of Parmenides, argues that Melissus follows 

Parmenides ‘without reservation’. Barnes (1979), 181 speaks of ‘an analogous argument’ but does not 

spell this out. Rapp (1997), 166 wonders whether we only have an analogy. Sedley (1999), 127 argues 

that ‘a process of generation, …, being temporally bounded, could only have generated a spatially finite 

being’. 

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80

 

Jaap Mansfeld

 

 

From Being’s unlimitedness it next follows that it is ‘one’ in the sense of 

one in number, or single, or alone: ‘as it is unlimited, it must be one (ἕν); for if 

there were two  (δύο) they could not be unlimited, but would have limits 

(πείρατα) against each other’ (fr. 30 B6).

34

 Or, as fr. 30 B5 has it, with the argu-

ment reversed in the typically chiastic way characteristic of literature with an 

oral background: ‘if it were not one, it would be limited against something 

else’.

35

 It is true that ‘one’ (ἕν, 28 B8.6) is also one of the attributes (σήματα) of 

Parmenides’ Being, but in Melissus the emphasis is stronger and different, as 

has been generally appreciated.

35a

 Parmenides’ Being moreover is also charac-

terized as the ‘only member of its kind’ (μουνογενές),

36

 which leaves room for 

the possibility that there are other entities, of a different kind. And in fact such 

entities do appear in Parmenides’ poem: the physical elements, posited by erring 

humans, of which there are ‘two, … one of which is not necessarily’ (μορφὰς … 

δύο / τῶν μίαν οὐ χρεών ἐστιν).

37

 The relations of these two ‘Forms’ to the one 

Being and the precise meaning or nature of the mistake made by humans are 

difficult if not impossible to fathom, as the various efforts by modern scholars 

demonstrate. Fortunately I do not have to enter into this issue here, and may limit 

myself to the observation that Melissus simply avoids the problem by declaring, 

in a phrase that anticipates a variation of George Orwell’s famous formula: one 

is good and two is wrong – and thus by adhering to ‘one’. 

What causes a surprise is not that Eudemus could easily maintain that an 

entity can still be unlimited even when bordering on another one, as does the 

past when abutting on the present.

38

 What may really surprise is that Melissus 

failed to take Xenophanes’ doctrine into account that the earth is limited at its 

upper side, but unlimited in the other direction.

39

 But presumably this did not 

count for him, because it is about the world of experience he rejected. 

The deduction of the next attribute, ‘wholly homogenous’ (ὅμοιον πᾶν), has 

                                                            

34

 The fourth of the five reasons for the assumption of infinity summarized by Aristotle at Phys. 

3.4.203b15–30 is that what is limited is always limited against another thing, ἔτι τῷ τὸ πεπερασμένον ἀεὶ 

πρός τι περαίνειν, ὥστε ἀνάγκη μηδὲν εἶναι πέρας, εἰ ἀεὶ περαίνειν ἀνάγκη ἕτερον πρὸς ἕτερον. 

35

 This inversion is in favour of reversing the order of these two fragments. 

35a

 Rapp (2013a) is very clear about the difficulty of relating Zeno’s paradoxes about plurality to the 

ontological argument of Parmenides, whose monism according to Plato was defended by Zeno, while the 

term ἕν, occurring once only and only as an adjective, merely plays a subordinate part in the poem. His 

elegant solution (2.555) is that Parmenides may well have been ‘wahrgenommen’ (perceived, interpreted) 

as a numerical monist. He does not, however, mention this point in his interpretation of Melissus, for 

whom this is perhaps even more relevant. Rapp’s suggestion is supported by the fact that according to 

Parmenides 28 B8.12-3 DK there can be no other Being next to Being, while according to B8.42–9 there 

is only a single sphere of Being. 

36

 Fr. 28 B8.4. This is the reading of the majority of our sources, over against Plutarch’s (and DK’s) 

οὐλομελές, and has come to be preferred. 

37

 Fr. 28 B8.53–54. 

38

 Fr. 41 Wehrli ap. Simp. in Phys. 110.5–11 (see at Melissus fr. 30 B5), criticizing this fragment of 

Melissus. Cf., e.g., also Chrysippus on time, SVF 2.509 (Arius Didymus fr. 26 Diels). 

39

 Fr. 21 B28. 

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