Generic Science, 3

Zeno, Melissus, Empedocles

To this point, our discussion of a generic science, itself a continuation of our discussion of the Milesian intuition of an originary dual, has been mostly concerned with the sketching of a diagram, the drawing of a line of continuity, between Anaximander’s distinctly Milesian abstraction and Heraclitus’s apparent mandate of an empirical methodology. This sketchwork has allowed for a rereading of Parmenides, and his inheritor Anaxagoras, outside of, and properly prior to, the opposition of Parmenides and Heraclitus in the Platonic duel.

Having spent a significant amount of time on this outline, I would now like to apply it to three distinct thinkers: Zeno of Elea, Melissus of Samos, and Empedocles of Acragas. To avoid making our model into a monolith, I will not attempt to expand our continuity, but rather will treat of each of these thinkers in a direct and radical way, each responding to the Parmenidean fortress of being in a distinct fashion.

In this context, Zeno is the easiest to deal with. Zeno’s philosophy is, quite simply, a failure with respect to the generic program elaborated by Heraclitus.1 Having contended previously that Parmenides shares in Heraclitus’s generic program, maintaining that the “point from which [he] start[s] is common,” Zeno’s doubling down on the speculative aspect of Parmenides thought is misguided.2 Zeno’s paradoxes “respond[] to those who argue in favour of a plurality, paying them back what is due to them and then more besides,” unlike Anaxagoras who, through reason and observation, mounts a direct and radical response to Parmenides, supporting some of his conclusions while either nuancing or refuting others.3 Anaxagoras treats Parmenides’s philosophy as statements about what is common that can be verified or falsified; Zeno treats Parmenides’s philosophy as a revelation to be defended at all costs.

Melissus, on the other hand, continues in the generic mode that we saw put into practice by Anaxagoras. In the previous essay, we cited the eighth fragment of Parmenides at length, in order to capture each of his statements made with respect to what is. Melissus, reflecting upon these statements, is not led to defend their truth, but is rather led to refute and replace one of them. If what is is one, and it “always was and always will be”—in Parmenides’s terms, “unborn and imperishable”—then what is can certainly not be held within “the bonds of a limit which restrains it all about,” but rather must be “without limits.”4 Parmenides’s perfect sphere, complete and therefore finite—of which Archytas of Tarentum rightly quipped, “If I were to reach the edge … could I stretch my hand or my stick outside or not?”—is an empirically testable, rationally considerable statement.5 Indeed, it is a statement with which physicists are still concerned today: whether the universe does in fact have an edge, and if it does, how that edge works. On Melissus’s part, the edge, given Parmenides’s other premises, must be denied.

Parmenides asserts that for what is, the common, to be one, it must, by definition, be “alone of its kind.”6 For Melissus, the fact that what is has neither beginning nor end entails its unlimitedness, which in turn entails its aloneness: “for if there were two things, they could not be unlimited, but would have limits in relation to each other.”7 The question of the edge always remains a real question. So, looking at being, reflecting on being, Melissus comes to the same conclusion of oneness as his predecessors, but this conclusion allows him to identify a flaw in Parmenides’s framework and provide a correction to it without discounting the subtlety or rigour of Parmenides’s thought in general.

Melissus’s revision of Parmenides’s also leads to the fascinating conclusion that if being “exists, its must be one; and being one it must be incorporeal,” because if it had “solidity, it would have parts, and then it would no longer be one.”8 This is in no way frivolous speculation, but a legitimate conclusion based on a critically considered set of principles. Having already exerted much effort examining the real abstraction at work in Anaximander and Pythagoras, Melissus’s incorporeal real is not a problematic mystification, but a useful means for approaching a singular universe in a non-subtantialist way. Thus, in the same way that Anaxagoras is able to open Eleatic being to the possibilities of Milesian becoming, we might say by way of parallel that Melissus opens Eleatic being to the possibilities of a kind of Pythagorean abstraction. In both cases, these possibilities are possibilities afforded by Parmenides’s philosophy. Though he asserts the closure of being, his philosophical method and the conclusions it produces remain open to extension and critique.

Turning now to Empedocles, we see that although he is known for his system of the four classical elements, he is not detached from his intellectual milieu. Empedocles asserts that “there is no way for what-is-not to be born, and for what-is to perish is impossible and inconceivable.”9 He also asserts: “Nor in the totality is there anything empty or overfull.”10 In these two fragments, we see a distinctly Parmenidean framework undergirding Empedocles’s philosophy. Being remains, for Empedocles, unborn and imperishable, complete and all together. But unlike Parmenides, who argues that what is “stays in the same state and in the same place” and is “everywhere of equal intensity,” Empedocles allows for “a mixing and then a separating of what was mixed.”11 Parmenides cannot account for structure, but we have already seen how Anaxagoras introduces structure through dispersion. Empedocles’s earth, water, aither, and fire obey most of the Parmenidean rules, but are subject to organization by the “two initiatory forces, love and strife.”12 Like Anaxagoras, he allows for structure without denying the oneness of being.

Empedocles goes on to argue that “[n]othing comes into existence or ceases to exist; there is only them … they are just themselves, and by running through one another they become now this and now that, and remain for ever the same.”13 In the age of love, everything comes together in a “rounded sphere,” “equal to itself from every direction, and entirely boundless … delighting in its encircling solitude.”14 This sphere Empedocles also names “mind,” “sacred and inexpressibly vast.”15 So, like Anaximander, wherein there is a sort of phase transition whereby by the opposites are separated out from the boundless, like Pythagoras, wherein the unlimited is determined by limit, and like Anaxagoras, wherein small, compact, and indeterminate being undergoes dispersion, Empedocles presents another argument for the mechanism whereby being becomes that does not deny the oneness of being, the fact that everything is.

Indeed, just like the Milesians, Empedocles positions a sort of dual at the origin of things—the “principles” that are the four elements and the “forces” that “set [them] in motion.”16 Love and strife, as the coupled, tensional forces of becoming, are not subsidiary to being, but equiprimordial with it. Coming after Parmenides, we also see Empedocles responding to the powerful challenge that Parmenides mounts, using both reason and the senses to affirm some of Parmenides’s conclusions and deny others.

We conclude with Empedocles because of a rather startling testimonial that comes late in the collection. Theophrastus reports that Empedocles assumes “that thinking is either identical to or very similar to sense-perception.”17 As we have seen in the Pythagorean unit-point and the Heraclitean intelligence-common, Empedocles operates in the same Presocratic tradition wherein thought is unilaterally determined by the real because thought is real.18 This is a remarkable externalist psychology that we lose with the scission of the real and its syntax by Plato’s bar, a psychology that this series on generic science has hoped to recover. It is this identification of thought with its object that, in part, makes possible the direct and radical approach to (meta)physics that we have been pursuing here.

In taking this approach, we can assess the thought of the likes of Zeno, Melissus, and Empedocles by identifying their claims with respect to the real, empirically assessing their veracity (is this statement in fact correct?), and rationally assessing their consistency (is this abstraction in fact coherent?). By refusing an ontological divide between the empirical and rational standpoints, we also open ourselves to pragmatic rereadings of these Presocratic thinkers. Where an intuition might have led to an ultimately false set of empirical conclusions, it may yet prove instructive as an abstraction. Such abstractions can be useful for us today insofar as they furnish us with problems to pursue in our own experimental and theoretical pursuits—many of which, indeed, bring us to the cutting edge of research in the natural sciences.


  1. Heraclitus “rate[s] highly … those which are accessible to sight, hearing, apprehension,” and directs his listeners to listen not to him “but to the principle,” the common logos. See Heraclitus, F28 and F12, in The First Philosophers: The Presocratics and the Sophists, trans. Robin Waterfield (Oxford, UK: Oxford World Classics, 2000), 41 and 39. 

  2. Parmenides, F2, in Waterfield, The First Philosophers, 57. 

  3. Zeno in Plato, Parmenides, 127d6-128d6, in Waterfield, The First Philosophers, 75. 

  4. Melissus, F2, in Waterfield, The First Philosophers, 84, and Parmenides, F8, in Waterfield, The First Philosophers, 59 and 60. 

  5. Archytas, in Waterfield, The First Philosophers, 54, footnote 9. 

  6. Parmenides, F8, in Waterfield, The First Philosophers, 59. 

  7. Melissus, F5, in Waterfield, The First Philosophers, 84. 

  8. Melissus, F7, in Waterfield, The First Philosophers, 85. 

  9. Empedocles, F11, in Waterfield, The First Philosophers, 145. 

  10. Empedocles, F12, in Waterfield, The First Philosophers, 145. 

  11. Parmenides, F8, in Waterfield, The First Philosophers, 60, and Empedocles, F13, in Waterfield, The First Philosophers, 145. 

  12. Empedocles, F10, in Waterfield, The First Philosophers, 144. 

  13. Empedocles, F20, in Waterfield, The First Philosophers, 148. 

  14. Empedocles, F25, in Waterfield, The First Philosophers, 151. 

  15. Empedocles, F26, in Waterfield, The First Philosophers, 151. 

  16. Simplicius, Commentary on Aristotle’s Physics, in Waterfield, The First Philosophers, 147. 

  17. Theophrastus, On the Senses, in Waterfield, The First Philosophers, 157. 

  18. To signify this determination, we should perhaps flip “unit-point” and “intelligence-common” to “point-unit” and “common-intelligence”—the real determines thought. 

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