What’s Eleatic about the Eleatic Principle?

Abstract:

According to the Eleatic Principle, only items which have the capacity to affect or be affected are. Recently, there has been a question about what, if anything, is Eleatic about the Eleatic Principle (EP). I examine the purported origins of the EP in Plato’s Sophist and argue that the text presents three ways in which something can affect or be affected: (1) as tangible contact, (2) as Cambridge change, and (3) by being responsible for the way something else is. Next, I look to the historical Eleatics in search of precursors to the EP. Against recent work in this area, I argue that elements of the EP are present in Parmenides, Zeno, and Melissus. The poem of Parmenides is compatible with (1) and (2) through the interaction of Light and Night, and the characterization of what-is as knowable. Zeno’s moving arrow paradox employs elements of (2), while his argument from complete divisibility adds preconditions to (3). Finally, against the traditional view that Melissus denies the existence of the sensible world, I show that for Melissus, the sensible world exists alongside what-is. The causal link between what-is and the sensible world, along with Melissus’ commitment to what-is as the object of knowledge renders Melissus the Eleatic whose Eleaticism is most represented in the Eleatic Principle. Alternatives for the application of the EP in contemporary metaphysics and reasons for the inclusion of an Eleatic visitor as the main interlocutor of a dialogue that is often taken as a criticism of Eleaticism emerge.

Keywords:
Eleaticism; Melissus; Eleatic Principle; Parmenides; Zeno

In contemporary metaphysics, the Eleatic Principle (EP) is a criterion according to which only entities with causal potency exist.¹ Articulating the EP with precision is notoriously difficult, for it raises questions about what counts as having the capacity to causally affect something else.² The principle’s name is explained by its purported origins in the Battle of the Gods and Giants in Plato’s Sophist, where the Eleatic Visitor cross-examines the views of the Gods, who are friends of the forms, and the Giants, who are materialists, and offers modifications of them in light of the principle that only items that have the capacity to affect (poiein) or to be affected (paschein) are. The passage is challenging, and among the interpretive problems faced by the reader is the very fact that Plato includes an Eleatic Visitor as the main interlocutor of a dialogue which is often read as a criticism of Eleaticism.³ One question that arises, then, is whether any of the supposedly Eleatic Visitor’s claims can properly be called “Eleatic”. Accordingly, it has recently been asked whether there are genetic precursors to the EP in the historical Eleatics-Parmenides, Zeno, and Melissus.⁴ In response, it has been argued that while some elements of the EP appear in the poem of Parmenides, Zeno’s arguments and Melissus’ ontology are incompatible with the EP.

In this paper, I explore this question with two central aims. First, I revisit the Battle of the Gods and Giants in Plato’s Sophist in search of whether it can shed light on a more precise articulation of the EP. It will turn out that in this section of the text, there are three ways in which something can have the capacity to affect or be affected: (1) as tangible contact, (2) as a change in the relational properties that hold of an item (i.e. Cambridge change), and (3) as something which is responsible for something else’s being the way it is. Second, I explore how a more textually-informed formulation of the EP fares in comparison with the views of the historical Eleatics. I show that there are precursors to the EP in the poem of Parmenides, since the existence of the sensible world in the Doxa is compatible with (1) and the status of what-is in the Aletheia as a changeless object of knowledge is compatible with (2).⁵ I then show that while Zeno’s Millet Seed argument is aimed at someone who assumes (1), his argument about the moving arrow and the argument from complete divisibility are compatible with (2) and (3). Some version of the EP can therefore be found in Zeno’s arguments. Finally, I argue that all three versions of the EP can be found in the fragments of Melissus. For against the traditional interpretation of Melissus, I show that not only is the existence of the changing, plural sensible world compatible with the existence of what-is, which is a changeless, unlimited, invariant, and numerically singular plenum, but also that there is an avenue for interpreting the two as causally linked.

My discussion implies that despite the dialogue’s repeated references to parricide, these parallels are one reason for Plato’s inclusion of an unspecified Eleatic as a dramatis personae in the Sophist. In addition, the interpretation on offer provides some viable alternatives for articulating the EP, which is valuable not only as an ontological criterion in contemporary metaphysics, but for interpretation of historical schools who are interpreted as having been influenced by the Battle of the Gods and Giants.

1. The Eleatic Principle at Sophist 247d-e

Cherubin (2017) offers the following formulation of the EP:

If something is, then that thing has the power to affect and/or to be affected, AND If something has the power to affect and/or to be affected, then that thing is.⁶

The most salient ambiguity in the formulation of the EP is how to understand the pair of notions, affecting (to poiein) and being affected (to paschein). In order to arrive at a precise formulation of the EP, it is helpful to begin with the context in which the EP is articulated by the Eleatic Visitor. The central problem in this part of the dialogue is that although giving an account of what-is-not seems obviously difficult, some preliminary questions reveal that an account of what-is is just as problematic.⁷ To demonstrate the difficulty of giving an account of what-is, the Visitor proposes considering two sets of views.⁸ This leads to the Battle of the Gods and Giants.⁹ The Gods, who are ‘friends of the forms’ are committed to the reality of separate immaterial forms, while the Giants or the ‘earth people’ are materialists, who maintain that only what offers tangible contact is real.

At 246e-247d, the Visitor raises a problem for the materialists. If the materialists are committed to the view that only bodies exist, then they must concede that items such as the virtues and the soul are not real, since they cannot “squeeze ENT#091;themENT#093; in their hands.”¹⁰ For the materialists agree that an agent S being virtuous is due to the virtue J (an immaterial item) acting on S’s soul (another immaterial item). The problem for the materialists is that if only bodies exist, and if the virtues and the soul are not bodies, then it is not clear how S can be virtuous. The Visitor offers the EP as a suggestion for modifying the materialists’ criterion for reality, so that their ontology can account for these items. He articulates the EP as follows:

(a) …a thing really is if it has any capacity at all, either by nature to do something to something else, or to have even the smallest thing done to it by even the most trivial thing, even if it only happens once. I’ll take it as a definition that those which are amount to nothing other than capacity.¹¹ (247d-e)

Theaetetus is quick to claim that the materialists would accept the EP as a modification of their criterion for reality. Presumably, this is because bodies exemplify the EP by means of a straightforward fulfillment of the condition of having the capacity to affect or be affected, insofar as tangible contact is one way to affect or be affected. Since Theaetetus has the materialists agree that the virtues act on the soul, the added advantage of the EP is that it allows the materialists to modify their thesis so that the virtues can be accommodated by their ontology. But while it is clear that bodies meet the condition set by the EP, it is less clear how the virtues affect or are affected, if, as the Visitor stipulates, the materialists admit that the virtues “do not have body” and that the soul is not material. Hence, affecting and being affected do not apply to bodies and non-bodies in the same way. In other words, the sense in which justice, for example, is capable of affecting the soul is not the same as the sense in which a billiard ball affects another billiard ball. But the interlocutors do not press the issue of how affecting and being affected are to be understood in the case of two items which are incapable of tangible contact because they lack body.

By the end of the discussion of the materialists, then, there is at least one sense of affecting or being affected on the table-tangible contact. But the puzzle about the sense in which a body-less item can affect and be affected is carried over to the application of the EP to the position of the Friends. Here, two further ways in which something can affect or be affected are explicated.

For the Friends, being is limited to that which “always stays the same and in the same state” and which we deal with “by our souls and through reasoning”-i.e. the forms. Becoming, on the other hand, “varies from one time to another” and we deal with it “through our bodies and through perception”.¹² Here, the assumption is that the objects of knowledge are the forms, precisely because they are intelligible and have stable essences that do not admit of change.¹³ The Visitor points out at 248e that if knowing involves the objects of knowledge acting on the soul, and the soul acting on the objects of knowledge, then knowing involves a kind of moving and changing, and the Friends must therefore concede that being, which is always the same, admits of change. In other words, the difficulty is that if S knows J, then J affects and is affected by S’s soul (and vice versa). Otherwise, the Friends must surrender and claim either that there is no knowledge, or that since becoming changes, it (rather than being) is the object of knowledge. Neither of these is a tenable option. Instead, the Visitor claims that the philosopher, who values knowledge, must be “like a child begging for both”-that is, the philosopher must maintain that being is both unchanging and changing:

(b) The philosopher, the one who values these things the most, absolutely must refuse to accept the claim that everything is at rest, either from defenders of the one or from friends of the many forms. In addition, he must refuse to listen to people who make what-is change in every way. He has to be like a child begging for both, and say that the totality of what-is is both unchanging and changing.¹⁴ (249c10-d4)

In (b), the Visitor claims that what was previously characterized as wholly unchanging-the forms-must admit of some change qua being known.¹⁵ The forms must have a stable, unchanging essence in order to be appropriate objects for knowledge. At the same time, in order to save the possibility of knowledge, the forms must be capable of undergoing the kind of affecting and being affected that at 248e takes place when an object is known. Some commentators claim that this latter kind of change is Cambridge change-i.e. a change in the relational properties that hold of the forms over time.¹⁶ Say S is ignorant of J at t1. It is therefore true at t1 that J does not hold the relational property ‘known by S’. However, say S comes to know J at t2. At t2, it is true that J holds the relational property ‘known by S’. So, when S comes to know J at t2, J changes from not having the property ‘known by S’ to having the property ‘known by S’. An advantage of the Cambridge change reading is that it gives the Friends a way to claim that a change in the relational properties that hold of a form when it comes to be known is consistent with the form’s having a stable, unchanging essence, because Cambridge change ends up not being genuine change. At this point, then, there are two different senses of affecting and being affected on the table: (1) tangible contact and (2) Cambridge change-i.e. a change in the relational properties that hold of something.

There is a third sense of affecting and being affected in the text, which is operative in the participation of other things in forms. The form’s affecting the participant (whether the participant is another form, a soul, or a sensible particular) happens by way of the form’s being a cause, or an aition-something that is responsible for the participant’s being the way it is.¹⁷ There are several causal readings of affecting and being affected. Here, I will briefly describe one possibility, which I will revisit at the end of my paper.

It has been argued by Leigh (2012) that the notion of a cause at play in the dialogue is one in which the cause itself does not change. For the forms are non-spatio-temporal, and therefore, they are not susceptible to motion or rest. She explains that one way to understand how the forms can be causes to things that partake in them while not being subject to change, alteration, or movement, is to understand the notion of the form affecting something as manifesting or realizing some particular structure:

A particular complex structure belongs to each form as its nature, and specifies what it is to have the property in question. This structure is what is manifested or realized in those individual cases where something participates in the form.¹⁸

Here, the form is a cause, and has the capacity to affect, without admitting of change, motion, or alteration. Similarly, when one form participates in another form, the participant form will have the property as an attribute by roughly the same mechanism. This does not imply that any forms change.

I will revisit the notion of a changeless cause in my discussion of the Eleatics.¹⁹ For now, I emphasize that the notion of the form as a cause indeed counts a third way to explicate affecting and being affected. For in this discussion, the form affects its participants by being a cause to the participants of having a certain property as an attribute. The participants are affected by this form because the form is a cause to the participants of having a certain property as an attribute.

Based on this section, then, we find in the Battle of the Gods and Giants different ways in which something can have the capacity to affect or be affected. Items that exist can affect or be affected in three ways: (1) through tangible contact (as in the case of bodies), (2) through Cambridge change (as in the case of a form being affected by the soul which knows it), or (3) in a causal sense (as in the case of participants being affected by a form, by instantiating it). The context in which the EP appears, then, allows us to formulate a more precise articulation of the EP, which offers three possibilities for how something can affect or be affected.

2. Parmenides, Zeno, Melissus, and the Eleatic Principle

Cherubin (2017) claims that the EP “does not match anything articulated by Parmenides, Zeno, or Melissus.”²⁰ She is right that strictly speaking, we do not find in the fragments of the historical Eleatics any assertions to the effect that only what has the capacity to affect or be affected exists. She argues that while the views of Zeno and Melissus are incompatible with the EP, there are indeed some affinities between the EP and the views of Parmenides. In light of the different formulations of the EP above, I will show that elements of the EP appear in the ontologies of all of the historical Eleatics.

2.1 Parmenides on What-is and the Sensible World

After the proem in B1, Parmenides’ goddess begins at B2 with the section of the poem known as the Alētheia, with a question about the routes of inquiry that are for knowing (noēsai).²¹ The goddess asserts that she will set the parameters for knowing by telling the kouros what to look for if he wants to have knowledge. The two routes here are 1) the route of “is and is not possible for it not to be” (estin te kai hōs ouk esti mē einai) and 2) the route of “is not and it is right that it not be” (ouk estin te kai hōs chreōn esti mē einai).

I pause to explain some of my interpretive assumptions. I take esti to be predicative, so that the first route in B2 represents inquiry into what-it-is-to-be-F, or predicative unities (i.e. items which are all and only F, where F is a predicate).²² Accordingly, I read Parmenides as a predicational monist, whose monism is compatible with there being a plurality of predicative unities. Hence, what-is is not strictly a numerically single thing. The second route in B2 represents inquiry into what is no way at all. I take this to not be a genuine route, since, by virtue of its objects being “no way” it represents inquiry into something that does not have any features and is therefore nothing at all. Such an item is “unable to be investigated”. I take there to be a third route, to which we are introduced at B6.4-5.²³ The results of third-route inquiry are described in the third part of the poem known as the Doxa, which begins at B8.50. This third route does not yield knowledge, but does yield doxa. These are described by the goddess as the untrustworthy opinions of mortals. Importantly, since I take the third route to be distinct from the second route, its objects are not nothing. Rather, the third route yields an account of items that have intertwined natures-i.e. items which are such that they would force us into saying that to be F and not to be F are and are not the same. At B9, the third route of inquiry compels mortals down a path according to which the world is constituted by Light, Night, and composites of Light and Night. This explanation falls short of first-route knowledge, precisely because it attributes fundamentality to items that do not fulfill the metaphysical requirements outlined in B8. This is the sense in which the results of third-route inquiry are deceptive. Importantly, it is not specified that these items do not exist at all. Rather, their natures prevent them from being objects of knowledge-yielding first-route inquiry. As objects of third-route inquiry, I maintain that they must exist in some capacity.²⁴

With these assumptions in place, I consider now whether the poem of Parmenides is compatible with the EP. I begin with the goddess’ characterization of what-is in B8, where we find the metaphysical requirements for what-is. Among the qualities of what-is are that it is ungenerated, imperishable (B8.3), indivisible (B8.23), unchanging, fixed, and “remaining the same and in the same” (B8.29-30). The goddess also says of what-is that “Nor was it ever, nor will it be, since it is now, all together one, holding together” (B8.5-6).²⁵ Importantly, Parmenides does not suggest that what-is has or is a body. These features together in fact imply that what-is is a non-spacio-temporal item-i.e. that it is without body, and located outside of space and time. From this characterization of what-is, it is already clear enough that Parmenides’ what-is does not conform to the EP on the understanding of affecting or being affected as having the capacity for tangible contact. For if what-is is without body, and it is a non-spacio-temporal item, then it cannot make tangible contact with anything.

The emphasis in the poem on the metaphysical requirements that something must fulfill in order to count as the object of knowledge is, however, an interesting parallel to the Eleatic Visitor’s insistence that the objects of knowledge must be both changing and unchanging. In §1, I suggested that in the background of the Visitor’s discussion of the Friends is the view that the forms are objects of knowledge owing to their stability and changelessness. Part of the Visitor’s challenge to the Friends is to explain how knowledge is possible if these items are changeless, for being known is a kind of being affected. I argued that the form’s changelessness is compatible with its being known, because being known can be interpreted as Cambridge change, which is not genuine change. With the poem of Parmenides in the background, it is not surprising that the Eleatic Visitor’s reaction to the Friends is to ask how the knowability of the forms is compatible with their changelessness. For the poem of Parmenides begins with a concern about the route of inquiry that will yield knowledge. B8’s list of metaphysical requirements that an object must fulfill in order to be an object of knowledge describes an item that is not unlike the forms of the Friends. This similarity is not unexpected. For the Eleatic Visitor expresses his anxiety about committing parricide specifically in reference to Parmenides.²⁶ He also includes the “defenders of the one” in his discussion of the Friends in the Battle of the Gods and Giants, which presumably includes not just Parmenides but all of the Eleatics.²⁷ The revisions that he suggests for the ontology of the Friends therefore are meant to apply just as well to the metaphysics of the Eleatics, including Parmenides. I suggested above that owing to its nature, like the forms of the Friends, Parmenides’ what-is cannot affect or be affected in the sense of tangible contact. But if Parmenides’ what-is is the proper object of knowledge by virtue of having these qualities, then like the forms of the Friends, it is plausible that it too satisfies the EP on the Cambridge change interpretation. This would retain the changeless, fixed nature of what-is, while explaining how what-is counts as a proper object of knowledge, as the goddess dictates in B2. This is not to say that there is an explicit acknowledgement of Cambridge change in Parmenides’ poem. Rather, the EP is compatible with Parmenides’ characterization of what-is on the interpretation of affecting and being affected as Cambridge change.

What about the items described in the Doxa? It seems clear enough, given Parmenides’ extensive focus on the kinds of accounts that belong to the third route in the Doxa, that the purpose of the poem isn’t, point blank, that the items described in the Doxa do not exist. Indeed, although the Doxa comprises roughly a third of the extant poem, this is thought to be only about a tenth of the Doxa which comprised the original poem, while the Alētheia survives in near entirety.²⁸ One question that arises is why Parmenides would dedicate a substantial part of his poem to entities that he thinks make no valuable contribution to any epistemic program, and which purportedly do not exist. Responding to this question is made more difficult when we consider not only the contents of the Doxa, but also the testimonia which credit Parmenides with serious scientific innovations. For instance, commentators credit Parmenides with the discovery of the source of the moon’s light on the basis of B14-15.²⁹ Theophrastus also credits Parmenides with the discovery that the earth is spherical, while Aëtius credits Parmenides with the discovery that the Morning Star and the Evening star refer to the same celestial body.³⁰ In addition, the goddess’ language in the Doxa suggests that inquiry into the objects of sense experience indeed does result in some cognitive contribution. For example, at B8.51, the goddess commands us to “learn (manthane) mortal opinions”. At B10.1, she asserts, “You shall know (eise) the nature of the aither and all the signs in the aither.” At B10.3, she says, “you shall learn (peuse) the wandering deeds of the round-faced moon and its nature, and you shall know (eideseis) also the surrounding heaven...”³¹ What is crucial to notice about the goddess’ language in these passages is that the objects of the sensible world do in fact make some sort of epistemic contribution. Empirical investigation has some role to play in learning and cognition.³² It is epistemically interesting, even if it cannot yield an account of what-is, and therefore does not result in knowledge.

One plausible interpretation is that Parmenides indeed believes that the items described in the Doxa exist, but that they do not meet the metaphysical requirements for being objects of knowledge-i.e. for being what-is, or being a fundamental entity. Hence, even the best explanation we can give of the sensible world will only count as opinion. For in order to count as knowledge, it must be of what-is. Importantly, this is not to disparage opinion or the sensible world. For opinions about the sensible world help us, as ourselves objects of sense, get by in our daily lives. The danger lies in believing that the sensible world is all there is-that by engaging in an investigation into the objects of sense experience, one might apprehend what-is.

On this interpretation, Parmenides’ Doxa aligns with the interpretation of the EP according to which the capacity to affect or be affected is understood as tangible contact. This is not only because the items described in the Doxa are extended in time and space, but because at B9, it is the interaction of Light and Night which produces the world we perceive. At B8.56-59, Light is characterized as fiery, mild, and lightweight, while Night is characterized as a dark, dense, and heavy body. They are, in Curd’s (2004) language, enantiomorphic forms which together produce the observable characteristics of things. Cherubin (2017) correctly points out that in the interaction between Light and Night, the characteristics of Light and Night do not change. That they are described at B8.56 as choris allelon-separate from each other-suggests that their arrangement relative to each other is spatial, insofar as when they interact, one pushes the other out of a space. Hence, these interactions are responsible for the changes, motions, and characteristics of the sensible world. So, the sensible world not only satisfies the tangible contact interpretation of the EP because the sensible world is extended, but because the enantiomorphic forms responsible for observable phenomena also interact with each other through tangible contact.

One final possibility to consider is whether anything in the poem of Parmenides is compatible with the causal interpretation of the EP. The question about how the causal interpretation of the EP applies to Parmenides is a question about whether what-is is causally linked to the sensible world. Nothing in the Aletheia explicitly suggests that what-is is causally involved in the sensible world. For as I explained, it is, at least from the perspective of the mortals, who have “gone astray”, the interaction between Light and Night which explains the characteristics of the sensible world, including change and motion. An open question is whether Light and Night are in any way reducible to what-is, such that what-is is causally linked to the sensible world. On some interpretations, such as Curd (2004), this is precisely one way in which the post-Parmenidean Presocratics reconcile Parmenidean ontology with pluralism-i.e. through Empedoclean mixture, or through the combination and separation of atoms.³³ These are mechanisms by which fundamental entities produce and are therefore causally linked to the objects of the sensible world. But there is no explicit evidence to suggest that such a connection is endorsed in the poem of Parmenides. It is therefore an open question whether the causal interpretation of the EP is compatible with Parmenides.³⁴

2.2 Zeno’s Paradoxes

It is difficult to determine how Zeno’s arguments fit with those of Parmenides and Melissus.³⁵ Despite the lack of clarity concerning the aim of Zeno’s arguments, I treat him as an Eleatic. It will turn out that only one of Zeno’s arguments (the Millet Seed argument) explicitly involves the notion of affecting and being affected as tangible contact. In the Millet Seed argument, as Cherubin (2017) argues, the tangible contact interpretation of the EP is assumed and shown to be absurd. However, I will show that the EP is compatible with Zeno’s arguments against motion and divisibility on the Cambridge change and causal interpretations of affecting and being affected.

Cherubin (2017) isolates Zeno’s Millet Seed argument as the one most directly relevant to the EP. She reconstructs the argument as follows:

…if a small portion of one millet seed does not make a sound when it falls to the ground, then a whole millet seed, or even a bushel of seeds, should not make a sound on hitting the ground; and if a whole seed or bushel of seeds makes a sound on hitting the ground, then so too must a tiny portion of seed.³⁶

Cherubin points out that Aristotle and Simplicius’ reports of the argument use ‘psophei’, in the sense of producing a sound, or affecting the ears. If this is the language Zeno used, then one of the themes in the Millet Seed argument is the phenomenon of something affecting or being affected. According to the schema I explicated in §1, the kind of affecting or being affected in the Millet Seed argument must be tangible contact. Cherubin maintains that the Millet Seed argument can be interpreted as Zeno’s challenge to the EP. The target of the Millet Seed argument, she contends, is someone who would start by assuming a version of the EP in which something that makes a sound exists (and in turn, that only things that exist have effects such as sounds). The argument shows that our analysis of auditory effects is incoherent. On this interpretation, auditory effects are aggregates of absences of auditory effect, and can be divided into non-existent components. This is incoherent, she maintains, because it entails that any number of seeds both makes and does not make a sound when it hits the same ground.³⁷ The Millet Seed argument therefore shows, in part, that the tangible contact version of the EP is incoherent.

Do elements of the other formulations of the EP appear in Zeno’s other arguments? The notion of Cambridge change shows up in Zeno’s Arrow paradox. According to the paradox, if we assume that time is composed of instants, that everything that occupies an equal space is at rest, and that everything that moves is always in an instant, then the flying arrow is motionless.³⁸ One response to the paradox grants that motion only happens over finite periods of time. If time is composed of instants, as the paradox stipulates, then there is no instant at which any distance is travelled by the arrow. The only way for the arrow to get from point A to point C, for example, is by virtue of the arrow occupying different successive points or positions at different successive times. This way, the arrow only changes position over intervals that are composed of instants.³⁹ This response involves the arrow undergoing Cambridge change. Say the arrow is at point A at t1. At t1, the property ‘located at point A’ is true of the arrow. When the arrow is at point B at t2, then at t2 it is no longer true of the arrow that it is ‘located at point A’ and it becomes true of the arrow that it is ‘located at point B’. If Zeno grants that the arrow goes from being at point A to being at point B, then this response to the paradox employs Cambridge change, so that the relational properties that hold of the arrow indeed do change.

But the fact that the notion of Cambridge change is compatible with a response to Zeno’s Arrow paradox is not sufficient for claiming that the Cambridge change reading of the EP is compatible with the paradox. This is because what’s at stake in the paradox is not whether the arrow exists (so that the fact that it undergoes Cambridge change entails that the arrow exists). Rather, what’s at stake is whether there is motion. Based on the little surviving evidence of Zeno’s arguments, it’s not clear whether Zeno would deny that the arrow exists on the grounds that it is not moving.

How does the causal version of the EP fare against Zeno’s arguments? Zeno’s arguments against plurality are indeed compatible with the causal version of the EP. Take, for example, the argument from complete divisibility.⁴⁰ The argument begins with the supposition that something is divisible. If one divides it, and continues to divide each part, either one reaches parts that cannot be divided (which will be infinite in number), or one reaches a point where the thing being divided disappears. If these parts are constitutive of the whole, then the whole is either constituted by an infinite number of parts, or by an aggregate of nothings. The latter is problematic for obvious reasons. The former is a problem because the aggregate of an infinity of parts should be infinite in magnitude, which would mean that the aggregate is bigger than the whole that was divided.

The key to seeing why the causal formulation of the EP is compatible with this argument is to consider the target of the argument. The aim of the argument from complete divisibility is to expose the absurdity of the view that the fundamental principles are indefinitely divisible.⁴¹ This view belongs to the Pluralists, Anaxagoras and Empedocles, who argue that separation and mixture take place between the fundamental principles. Separation and mixture are responsible for the characteristics of the sensible world. Such a view requires that the fundamental principles be extended and indefinitely divisible. The causal formulation of the EP maintains that only those things exist which have the capacity to be responsible for something else’s being the way it is. In keeping with the Parmenidean characteristics of what-is, the Pluralists stipulate that the fundamental principles must each have a single nature. Indeed, this is what enables the fundamental principles to act as causes of the relevant sort. But the Pluralists add that in order for the fundamental principles to have this kind of causal potency, they must be extended and indefinitely divisible. Through the paradoxes of plurality, Zeno exposes the absurd consequences that follow from claiming that something that has a single nature is also extended and physically divisible. The argument therefore adds preconditions to the causal formulation of the EP. If the Pluralists want their fundamental principles to be responsible for how the sensible world is, then their fundamental principles cannot be extended or indefinitely divisible. Lurking in the background of Zeno’s arguments from plurality, then, is the causal formulation of the EP. The argument from complete divisibility shows that there are preconditions for something’s being responsible for the way another thing is. These preconditions are not only that the item must have a single nature, but against the Pluralists, it cannot be extended or physically indefinitely divisible.

While the EP is not compatible with anything we find in Zeno’s arguments on the tangible contact interpretation, Zeno’s argument about the moving arrow indeed has a genetic connection to the EP on the Cambridge change reading, and his argument from complete divisibility is compatible with the causal interpretation of the EP, insofar as it adds preconditions for something’s being causally responsible for the way another thing is.

2.3 The Sensible World in Melissus?

In the fragments of Melissus, what-is differs from Parmenides’ what-is in several ways. First, at 30B5-B9 and 30A5, what-is is both numerically and predicationally one, whereas a plurality of beings is not explicitly ruled out in the fragments of Parmenides. Second, while Parmenidean what-is is limited, for Melissus, the rejection of coming-to-be entails that what-is is unlimited (30B2). In addition, while Parmenides states that what-is is fixed and changeless without qualifying the kind of change he has in mind, Melissus explicitly adds that what-is cannot partake of rearrangement (30B7). Importantly, while Parmenides, on my reading, does not link the world of sense experience to what-is, I argue that accounting for this link in the fragments of Melissus is the only way that the sensible world can exist in the system he describes, given his constraints on what-is.⁴² These differences result in important divergences in the ways Parmenides’ poem and the fragments of Melissus can be read as compatible with the EP. In particular, once we can interpret the fragments of Melissus as consistent with the existence of the sensible world, it turns out that they are compatible with the EP on all three versions. My discussion of Melissus will, then, focus on how the fragments do not necessarily rule out the existence of the sensible world.

In my discussion of Parmenides, I argued that the entities described in the Doxa are compatible with the EP because they have the capacity to affect and be affected by virtue of having the capacity for tangible contact. The view of the sensible world in the fragments of Melissus rests partially on our interpretation of 30B8, in which we find the following account:

(c) For if there is (einai) earth, water, air, fire, iron, and gold, and the living and the dead, and black and white, and all the things people say are real (einai alethe)-if these things really are (esti) and we see and hear correctly (orthos), then each of these must be just as it first seemed to us, and they cannot change or become different, but each must always be just as it is.⁴³

In (c), Melissus targets the view that the objects of sense experience are real.⁴⁴ One ambiguity in (c) is whether the view Melissus rejects is that the objects of sense experience exist, or that sensible items are real in the way that what-is is real. I take the latter of these two to be the target view; like Parmenides, Melissus is not worried about whether sensible objects exist, but about whether sensible objects really are.⁴⁵ For although Melissus appears to use both the existential and the predicative einai here, it is the explicitly predicative use-einai alethe, or is real-which qualifies the main description of sensible objects in the view under consideration. Accordingly, I propose supplying alēthē to complete einai as a predicative expression where it is missing throughout (c).

That the view under consideration is whether sensible objects really are (as opposed to whether they merely exist) is also supported by the reductio in (c), which begins with a hypothetical. Melissus asks us to assume that sensible objects meet the criteria for really being, and to assume that the information relayed by our sense experience is correct. The correctness of sense experience here cannot merely indicate that the information provided by our senses matches the sensible qualities actually exhibited by a sensible item. In other words, by asking us to assume that we see or hear correctly, Melissus is not asking us to assume that when we see a green leaf, for example, we ought to believe, for the sake of the argument, that we are in fact seeing a green leaf. Rather, the relevant sense of seeing or hearing correctly is that when we see or hear something, we are sensing the nature of that thing-i.e. we are sensing what-is. If we take up the assumptions outlined in (c), what follows, Melissus claims, is that what we initially perceive must in fact be the fixed nature of the sensible item. Hence, it follows that when I perceive the green leaf, my senses convey to me the nature of that leaf as a green thing with a certain texture. Because I have perceived it correctly-i.e. I have perceived these qualities as what-is, or the nature of the leaf-then it must be the case that these qualities constitute the nature of the leaf. But in fact, if I were to return to that same leaf in a few weeks, I might find that it has become a different colour and that its texture has become rough and papery. My senses would then be reporting conflicting information about what-is, or about the nature of the leaf.⁴⁶

Something has gone wrong with our assumptions, then, since what we perceive is a changing world. Therefore, either the sensible world exists to the senses but is not real, or our sense experience is an inadequate tool for apprehending what really is, or both. The very fact that we can point to the sensible world tells us that it must exist in some capacity. That we perceive a sensible world that changes suggests that although it exists, it is not real, for it does not meet the criterion of changelessness. It also suggests that while our senses are, for the most part, reliable enough to convey the existence of a sensible world with all of its changing qualities, sense experience is not, as Melissus explains at the end of B8, adequate to the task of conveying the true nature of anything in it; our senses cannot be used to apprehend what-is.⁴⁷

Crucially, the argument in B8 alone does not show that sensible objects do not exist. This is because the argument in B8 turns on the fact that change in the sensible world is incompatible with the changelessness of what-is.⁴⁸ What follows is not that the sensible world does not exist at all (indeed, such a conclusion would be too strong given the argument) but that the sensible world is not the same as what-is. The question, then, is whether there is evidence in the other fragments to suggest that the sensible world does not exist.

For Harriman (2019), the argument in B8 does not only emphasize that change in the sensible world is incompatible with the changelessness of what-is. Rather, the argument also aims to emphasize the numerical oneness of what-is, and to thereby eradicate plural entities, which are denizens of the sensible world. But again, even if we consider the changelessness of what-is alongside its numerical oneness, the conclusion that sensible items do not exist on the grounds that they are plural and changing is too strong. A more convincing case for the non-existence of the sensible world is made by Palmer (2009), who argues that it is the numerical oneness of what-is, along with the rejection of void or emptiness via the characterization of what-is as a spatially unlimited, motionless plenum with no variation in density which suggests that nothing can exist outside of what-is-its existence precludes the existence of anything else.⁴⁹ That only what-is exists therefore results not solely from the reductio in B8, but from Melissus’ characterization of what-is.

At this point, we might ask two questions. First, is it true that, strictly speaking, the existence of what-is-a spatially unlimited, indivisible, invariant plenum-precludes the existence of anything else? Second, is there the conceptual possibility for anything other than what-is to exist in Melissus’ world, in the spirit of Parmenides’ modal distinctions?

Adherents of strict monism in the history of philosophy have accounted for a plurality of sensible items in different ways. These accounts might serve as models for understanding how the sensible world can exist alongside what-is. Spinoza, for example, maintains that the only substance that exists is one infinite Nature.⁵⁰ The differentiations we perceive are modes or properties of Nature. For instance, when we perceive iron or stone, we are in fact perceiving Nature that is iron-like in one place, and stone-like in another place. For Spinoza, this is possible because Nature has all possible attributes. Therefore, the existence of one infinite substance for Spinoza is compatible with there being a plurality of sensible objects, as differentiations of it.

We might initially think that such a picture conflicts with the one in Melissus. For the notion of a single substance containing all possible attributes is prima facie incompatible with the claim at A5 that what-is is all alike (i.e. a predicational unity) and the claim at B9 that what-is has an invariant density. This is because we might interpret the fact that what-is is a predicational unity as we did Parmenidean being(s)-i.e. that what-is is all and only F, for example. In addition, we might think that the variations we perceive in sensible bodies are changes in the density of what-is. But this needn’t be the case. Take the claim at A5 that what-is is all alike. We can interpret this as amounting to the claim that what-is is all F, G, H, and so on, because what it is to be F, G, or H, is really the same thing. What we perceive as predicational differentiations-for example, what it is to be blue, what it is to be a triangle, what it is to be wise-are merely illusory differentiations of what-is, which contains all of F, G, and H, without being different from itself, and by still being a unity that is all alike, because all of these are really the same thing. They are what-is. On this interpretation of what-is as containing all possible predicates while still being a unity that is all-alike, the differentiations we perceive as the sensible world are manifestations of what-is. Emptiness or void is therefore not required for the existence of the sensible world because the sensible world is not external to what-is. The existence of the sensible world also does not threaten the invariant density of what-is, because we needn’t interpret the plurality and variation of the sensible world either as variations in the density of what-is, or as real in order for it to exist. For the sensible world is a differentiated manifestation of what-is, which is a unity in every sense.⁵¹

This might be a lot to impose on the fragments of Melissus. But it is nevertheless one way to make sense of how his characterization of what-is is compatible with his discussion of the objects of sense experience as items that exist but are not real in B8, without simply defaulting to a wholesale rejection of the existence of the sensible world. Part of the difficulty of giving an account of the status of the sensible world for Melissus is the absence of the clear logical space for such entities by way of the absence of the Parmenidean modal distinctions that mark off what-is (and cannot not be) from both what-is-not (and it is right that it not be) and what-is-and-is-not. While the sensible world can be located in the Parmenidean schema as what-is-and-is-not, which yields opinions or doxa and not knowledge, the modal schema is entirely missing from Melissus. While Palmer (2009) is more pessimistic about the prospect of the objects of sense experience having a place in Melissus’ ontology, he nevertheless correctly diagnoses the difficulty of accounting for it as resulting from Melissus’ “disastrous mistake of ignoring Parmenides’ modal distinctions.”⁵² For Palmer, the mistake is attributed to the novelty of both Parmenides’ modal distinctions and the restrictive use of the verb ‘to be’ in the poem of Parmenides. I add to this the possibility that Melissus is wholly engrossed in constructing a picture of what-is that will successfully block the possibility that plural entities can conform to the Parmenidean restrictions on what-is. He is in fact so engrossed in this that he ends up not only missing other important pieces of the puzzle, but constructing an account that is initially incompatible with most of those pieces. One such puzzle piece is the existence of the sensible world. As I hope I have shown, it is not clear from his language or from the argument in 30B8 that he intended for it to turn out that the sensible world is nothing at all. The interpretation I have suggested here is one way to account for the sensible world as co-existing with Melissus’ what-is.

This interpretation also provides an avenue for exploring the sense in which the fragments of Melissus might be compatible with the EP. Given the nature of the sensible world as constituted by items that change and interact with each other, the tangible contact reading of the EP is compatible with the fragments of Melissus.

Two additional features of (c) are relevant for considering the compatibility of the EP with the views of Melissus. First, the main argument of (c) is that our senses are not adequate tools for apprehending what-is. This suggests that if what-is is knowable, the source of our knowledge of what-is will not be sense experience. One striking contrast between the fragments of Melissus and the poem of Parmenides is that while the emphasis in Parmenides is squarely on knowledge and its objects, we do not find an explicit discussion of knowledge or of how to apprehend what-is in Melissus. Instead of telling us, Melissus shows us. At B1, he begins from the hypotheses that something is and that it is not possible for something to come to be ex nihilo. Next, taking these two hypotheses as a starting point, Melissus guides us through a set of deductions and infers the nature of what-is by relying only on reason.⁵³ While Melissus does not attach the changelessness of what-is to the fact that it is an object of knowledge (and that the objects of knowledge must have fixed natures), if what-is can be known, as Melissus shows us through the deductions, and if what-is is changeless, as he claims in B7, then the notion of Cambridge change can explain how what-is can be changeless and an object of knowledge. In particular, when what-is goes from not being known to being known, nothing in the fragments prohibits the possibility that what-is undergoes Cambridge change. In the fragments of Melissus, the reality of what-is is therefore in addition compatible with the EP on the interpretation of affecting or being affected as Cambridge change.

Second, distinguishing between things that merely exist and that which really is according to the interpretation I have offered here leaves open the possibility that what-is indeed has some connection to the sensible world. At the end of my discussion of Parmenides, I left open the possibility that what-is is connected in some way to the sensible world, for the poem itself does not explicitly suggest such a connection. Curd (2004) claims that a connection between what-is and the objects of sense experience is not possible for Melissus, since such a link would not allow what-is to remain unchanged while the sensible world changes.⁵⁴ For Curd, Melissus’ claim in B8 that “if there were a many, it would have to be as the One is” blocks any link between the world of the senses and what-is. Presumably, this relies on an interpretation of the claim according to which the many would need to have the same features as what-is. However, I have suggested that one way to understand the sensible world as co-existing with what-is is to understand the sensible world as a manifestation of what-is which exhibits differentiation and change where what-is is wholly unified and unchanging. Here, what-is is responsible for the sensible world insofar as the differentiations we perceive with our senses are merely deceptive manifestations of what-is, which is a unity containing all of the differentiations as numerically one thing which is all-alike and of the same nature. Hence, what we perceive as what it is to be spherical or what it is to be green are differentiations of what-is that are manifested only in our sensory experience. These differentiations, however, are not real. For what it is to be spherical and what it is to be green really are, for Melissus, one and the same thing-they are what-is. It is by virtue of the fact that they are contained in what-is as an undifferentiated unity that they are differentiated in our sense experience. So, in the end, there isn’t such a thing as being what it is to be F, which is different from being what it is to be G. Both of these are the same thing; being what it is to be F and being what it is to G amounts to being what-is. Nevertheless, there would be no sensible manifestation of being F or being G were F and G not contained in what-is as an undifferentiated unity. This is the sense in which the many is like what-is-not in respect of having all of the same features as it, but in respect of the fact that the many are sensible manifestations of all that is contained in what-is as a unity. Hence, it seems that what-is can indeed be understood as causally linked to the sensible world. This characterization of the link between what-is and the objects of sense experience therefore is compatible with the causal articulation of the EP.

Does the causal link between what-is and the sensible world threaten the changelessness of what-is? At the end of §1, I briefly explicated an interpretation of Plato’s Sophist which offers a reading of the causal link between the forms and their participants on which the forms do not change by causally affecting the participants. There, the participant is causally affected by the form in the sense that the structure encoded in the form is manifested by the participant. Forms are therefore changeless causes. Although the evidence does not point one way or another, a similar story is possible for Melissus as well, which is to say that there is a plausible account of causation that is available, on which what-is causally affects the sensible world while remaining changeless.

I have offered, then, one way to interpret Melissus’ what-is and the sensible world as co-existing. This interpretation, against Cherubin (2017), renders the fragments of Melissus most compatible with the EP, as all three versions of the EP are consistent with the fragments.

3. Final Remarks

My aim in this paper was to explore whether the Battle of the Gods and Giants in Plato’s Sophist, where the EP first emerges in a form we recognize, can shed light on how to articulate the EP with more precision and in turn, whether it can illuminate what (if anything) is Eleatic about the EP. I showed that three ways to explicate the notion of affecting and being affected become operative in the Eleatic Visitor’s cross-examination of the Friends and the materialists. First, something can have the capacity to affect or to be affected when it has the capacity to engage in tangible contact with something else. This is the version of the EP that is active in the ontology of the materialists. Second, something can have the capacity to affect or to be affected if the relational properties that hold of it can change over time. This is the sense in which the changeless forms are affected by being known-i.e. they undergo Cambridge change. Finally, something can have the capacity to affect or to be affected when it has the capacity to be responsible for something else’s being the way it is. This is the version of the EP that applies to how the forms affect their participants. With these three ways in which something can satisfy the EP, I showed that on certain readings of the historical Eleatics, elements of the EP show up in Parmenides, Zeno, and Melissus.

Parmenides’ goddess shows that the phenomena described in the Doxa exist, but are not objects of knowledge. The tangible contact version of the EP is therefore compatible with the description of the sensible world as constituted not just by changing items, but fundamentally by the spatial interaction of Light and Night. In addition, the poem’s central focus on setting the parameters for knowing, and describing the metaphysical requirements for something’s counting as an object of knowledge-as what-is-evokes the Visitor’s claim that changeless items undergo Cambridge change when they are known, illuminating a clear parallel between the Cambridge change version of the EP and the poem of Parmenides.

Next, I showed that while the tangible contact version of the EP is not explicitly compatible with Zeno’s arguments (and that the Millet Seed argument in fact seems to show that it entails absurd consequences), the notion of Cambridge change appears in Zeno’s moving arrow paradox, and his argument from complete divisibility assumes the causal version of the EP and sets preconditions on when something can be responsible for the features of something else.

Finally, I showed, against the traditional interpretation of Melissus, that there is in fact room for interpreting the ontology of Melissus as including the existence of both what-is and the sensible world. This requires understanding what-is as containing all of the differentiations of the sensible world as an undifferentiated unity. The tangible contact version of the EP is compatible with this reading of Melissus, since the sensible world admits of tangible contact. The Cambridge change version of the EP is also compatible with the fragments of Melissus, because he shows in B8 that the senses are not a reliable means for apprehending what-is, and that coming to know what-is is a thoroughly rational exercise. Therefore, what-is is the object of knowledge. It remains changeless because in being known, it undergoes Cambridge change. Finally, because the existence of the sensible world can be reconciled with the existence of what-is as a manifestation of differentiations that are a unified whole of a single character in what-is, what-is is responsible for how the sensible world is, rendering the fragments of Melissus consistent with the causal version of the EP. Melissus turns out to be the Eleatic whose Eleaticism is most represented by all versions of the EP.

It is clear, then, why Plato would include an unnamed Eleatic as the main interlocutor of the Sophist. The EP is the central criterion that drives forward the middle section of the dialogue, and as we have seen, despite the Visitor’s anxieties about committing parricide, its roots are firmly planted in the views of the historical Eleatics, albeit in different forms. These different versions of the EP are useful not only as more precise starting points for the ontological criterion in contemporary metaphysics, but also open up avenues for interpreting the Stoics, for example, who are widely interpreted as adopting the EP as a criterion for existence in their metaphysics.⁵⁵ The status of the Eleatic Principle as Eleatic, then, is not merely an artifact of its articulation by an otherwise anonymous character who is deemed Eleatic by Plato, but by virtue of the principle representing various aspects of the views of the historical Eleatics. There is, then, much that is Eleatic about the Eleatic Principle.

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• 1
  This criterion most famously appears in Armstrong (1978), where it is used as a premise to argue against the reality of abstract entities. The name ‘Eleatic Principle’ is coined in Oddie’s (1982) discussion of Armstrong.
• 2
  Some formulations of the EP that have been offered include: Only those things which are causally active are real; Nothing is real unless it plays some role in the causal structure of the world; Nothing is real unless it is at least conceivable or intelligible that it should play some role in the causal structure of the world. See Oddie (1982).
• 3
  See Bossi (2013) for a discussion of the different interpretations of parricide in the Sophist.
• 4
  In grouping these figures together as “Eleatics”, I do not imply that Eleaticism is a monolithic philosophical view, or that there are no doctrinal differences between the three figures. Rather, I conceive of Eleaticism as a family of positions, in which Zeno and Melissus can be interpreted as developing or clarifying the views of Parmenides, sometimes by diverging from them.
• 5
  Throughout this paper, I use ‘what-is’ and ‘being(s)’ interchangeably.
• 6
  Cherubin, 2017, p. 26. Given the context, I agree with Cherubin that ‘is’ is existential here.
• 7
  Soph. 243b7-9
• 8
  Soph. 245e-246a
• 9
  Soph. 246e-249d
• 10
  Soph. 247c
• 11
  Λέγω δὴ τὸ καὶ ὁποιανοῦν τινα κεκτημένον δύναμιν εἴτ᾽ εἰς τὸ ποιεῖν ἕτερον ὁτιοῦν πεφυκὸς εἴτ᾽ εἰς τὸ παθεῖν καὶ σμικρότατον ὑπὸ τοῦ φαυλοτάτου, κἄν εἰ μόνον εἰς ἅπαξ, πᾶν τοῦτο ὄντως εἶναι· τίθεμαι γάρ ὅρον ὁριζειν <δεῖν>, τὰ ὄντα ὡς ἔστιν οὐκ ἄλλο τι πλὴν δύναμις. The Visitor repeats the EP at 248c: “We took it as a sufficient condition of beings that the capacity be present in a thing to do something or have something done to it, to or by even the smallest thing or degree?” (ἱκανὸν ἔθεμεν ὅρον που τῶν ὄντων, ὅταν τῳ παρῇ ἡ ποῦ πάσχειν ἤ δρᾶν καὶ πρὸς τὸ σμικρότατον δύναμις;)
• 12
  Soph. 248a
• 13
  This is a position that is repeated for example, at Rep. 476a-480a, where knowledge and opinion are distinguished by their objects—knowledge is set over what-is (i.e. the forms), while opinion is set over the intermediate between what-is and what-is-not (i.e. what participates in both opposites). Cf. Leigh, 2012, p. 254, n. 22, where in the Sophist, “Plato… no longer requires an argument that turns on a notion of…the compresence of opposites…in order to distinguish Forms from non-Forms.” For Leigh, the discussion that follows the Battle of the Gods and Giants establishes that the forms are external to change and changelessness. For others, including Fine (2003) and Irani (forthcoming), the subsequent discussion shows that every form suffers a compresence of opposite properties. It seems that in this part of the discussion, the Visitor indeed assumes that the stability or changelessness of the forms is what makes the forms proper objects of knowledge. The evidence for this is his characterization of what-is as that which is changeless at Soph. 248c. I do not take a stance on whether Plato changes his view about the objects of knowledge or about the compresence of opposites. I am only focussed on this assumption about the stable natures of the objects of knowledge as it advances the Visitor’s argument in this narrow section of the text.
• 14
  Τῷ δὴ φιλοσόφῳ καὶ ταῦτα μάλιστα τιμῶντι πᾶσα, ὡς ἔοικεν, ἀνάγκη διὰ ταῦτα μήτε τῶν ἕν ἤ καὶ τὰ πολλὰ εἴδη λεγόντων τὸ πᾶν ἑστηκὸς ἀποδέχεσθαι, τῶν τε αὖ πανταχῇ τὸ ὄν κινούντων μηδὲ τὸ παράπαν ἀκούειν, ἀλλὰ κατὰ τὴν τῶν παίδων εὐχήν, ὅσα ἀκίνητα καὶ κεκινημένα, τὸ ὄν τε καὶ τὸ πᾶν σθναμφότερα λέγειν.
• 15
  I have set aside the difficult passage directly before (c) at 248e6-249b6, which with Owen (1966), I take to reinforce the conclusion in (c) that being must be both changing and unchanging. According to another interpretation, the final line of (c) is rendered “what-is is as many things as are both unmoved and moved” and shows that both being and becoming are real. For defenses of this interpretation, see Cornford (1935), Keyt (1969), Seligman (1974), Ketchum (1978), Teloh (1981), and Miller (2004). Against this reading, see Wiitala (2018) pp. 195-197. That the Visitor speaks as if there is a distinction between being and becoming at 262d, and that an ontology encompassing both being and becoming is attributed to the Friends at 248c undermines this reading.
• 16
  See Moravcsik (1962), Runciman (1962), Owen (1966), Reeve (1985), McPherran (1986), Silverman (2002), Thomas (2008), Gill (2012), Leigh (2012), and Buckels (2015). For objections to the Cambridge change reading, see Brown (1998) and Wiitala (2018) pp. 175-177. See Leigh (2012) pp. 245-249 for a response to Brown’s objections. With respect to Wiitala’s objection that the Cambridge change reading does not fit in with the Visitor’s wider project of showing that non-being is, I maintain that this discussion need not be in direct service of the Visitor’s wider project. For it fits in with the narrower project of showing how saying what being is is not easier than saying what non-being is.
• 17
  In line with the view of the form as aition at Phaedo 100c, for example.
• 18
  Leigh (2012) p. 257
• 19
  I do not take a stance on this interpretation, because whether Plato thinks the forms can change in the discussion subsequent to the Battle of the Gods and Giants is not directly relevant for the question about whether this text tells us about a third sense of affecting or being affected.
• 20
  Cherubin, 2017, p. 26
• 21
  Noein (to think, to know) is one of the verbs whose meaning changes depending on the tense and aspect. The perfective aspect of the aorist infinitive, noēsai implies that it is a kind of cognitive activity that was completed or successful. Accordingly, I take the infinitive to mean “knowing”. See Mourelatos (2008). See Kahn, 1969, p. 704-6 for a discussion of how the theme of knowledge and inquiry is also woven into the proem.
• 22
  The predicative reading of esti and the language of ‘predicative unity’ for what-is is most forcefully defended in Curd (2004). A version of the predicative reading can also be found in Mourelatos (1970), though the interpretations in (1973), (1976), and (2008) are less straightforwardly predicative. Other possibilities for interpreting esti include the existential reading, according to which the first route involves inquiry into what exists, while the second route involves inquiry into what does not exist, and the veridical reading, according to which the first route involves inquiry into what is true or what is the case, while the second route involves inquiry into what is not true or what is not the case. The existential reading is historically the most popular. See Owen (1960), Guthrie (1965), Kirk, Raven, and Schofield (1983), Brown (1994), and Wedin (2014). For the veridical reading, see Kahn (1969).
• 23
  The goddess’ claim that there are two routes at B2 is then a reference to there being two genuine routes—i.e. the one which yields knowledge, and the other “on which mortals, knowing nothing, wander, two-headed…” (B6.4-5). This route is distinct from B2’s route of what-is-not. I also reject Diels’ suggestion to supply eirgo (I hold ENT#091;youENT#093; back) for the lacuna at B6.3 and instead supply a form of archein, so that the line reads “I begin for you from this first route of inquiry, and then from that, on which mortals, knowing nothing, wander, two-headed…” (i.e. a third “de facto” route, but second genuine route). See Nehamas (2002) for a criticism of the Diels supplement and a defense of supplying a form of archein instead. See also Cordero (1979), where the lacuna is supplemented by archein in the second-person form. For three-route readings, see for example Cornford (1933) and Palmer (2009).
• 24
  I agree with Nehamas (2002) and Curd (2004) that Parmenides is not engaged in the project of asking how many things there are, and take him to be interested in what the essence or the nature of a thing is. This is important, because the EP is fundamentally a criterion for existence—it is a test that must be passed by an item if it exists. My earlier emphasis on the goddess’ aim to elucidate the different routes of inquiry and the epistemic states that result from them is some evidence for the view that Parmenides’ project is not to provide a list of what exists. Accordingly, what is at stake is not the existence of the objects of knowledge or the objects of opinion. Rather, Parmenides is concerned about the fundamentality of a certain class of items, in relation to the status of these items as the objects of knowledge. Nevertheless, he is often read as a strict numerical monist who advances a system on which sensible items (i.e. the objects of opinion) do not exist. As such, the Doxa is often treated disparagingly by some commentators. For example in Owen (1960) and Gurthrie (1965). I reject this view, since I do not take Parmenides to be a strict numerical monist. I maintain that if Parmenides is a monist, he is a ‘kind’ monist who argues that the basic entity or entities are each of a single kind. I also maintain that the account in the Doxa ought to be taken as the result of a rigorous inquiry and that the phenomena discussed in the Doxa (i.e. the objects of sense experience, which yield opinion) do in fact exist. I do not give a substantial argument in favour of this view, but I do suggest some reasons to take the Doxa seriously below.
• 25
  Translation from Curd & McKirahan (2011)
• 26
  For example, at Soph. 241d-242a
• 27
  Soph. 249c-d
• 28
  See Palmer (2009) pp. 138-139.
• 29
  See Finkelberg (1986), Popper (1992), Mourelatos (2012), and Graham (2013) p. 179.
• 30
  Thphr., Physicorum Opiniones Fr. 6a and D.L. 447, 18, Aët. ii, 15 7 (On the order of the stars). See also xxxix-xlii in Mourelatos (2008).
• 31
  The translations in this paragraph are modified from Curd & McKirahan (2011).
• 32
  Cf. Interpretations of Parmenides which identify what I am calling the third route with the route of non-being in B8, such as defenders of the strict monist reading in fn. 24. The occurrence of these verbs in the Doxa is evidence against this reading, for the route of non-being cannot be known or declared at B2.6ff.
• 33
  See Curd (2004) pp. 233-234.
• 34
  Cherubin (2017) points out another parallel between the EP and the poem of Parmenides—i.e. that Parmenides seems committed to the inverse of the first conjunct of the EP (articulated at the beginning of §1). She maintains that Parmenides’ goddess argues that if something is not, then it does not have the power to affect or to be affected. She also correctly points out, however, that “the truth of the inverse of a proposition does not imply the truth of the original proposition” but nevertheless claims that “the fact that Parmenides articulated this inverse part of the Eleatic Principle could be part of the reason why the Eleatic Visitor articulates the principle.” (p. 32) In other words, the Visitor proposes the EP as a development of the views of the historical Parmenides.
• 35
  It is difficult to determine what Zeno’s intentions are. He is linked with Parmenides by Plato at Soph. 216a, and Aristotle at Soph. Elench. 182b and Met. 1001b. He is portrayed by Plato at Prm. 128b-e as a loyal defender of Parmenides’ views, using his paradoxes to show how objections to Parmenides entail absurd consequences. Some have raised doubts about whether defending Parmenides was in fact one of Zeno’s aims, or if he was simply a dialectician equally opposing both the One and the Many. See Solmsen (1971), Barnes (1982) pp. 234-7, and Barnes (2011). See also the discussions of the links between Parmenides and Zeno at Curd (2004) pp. 171-172 and Cordero (1983).
• 36
  Cherubin, 2017, p. 29, based on Aristotle, Physics 250a19ff and Simplicius, In Phys. 1108.18-28.
• 37
  Cherubin, 2017, p. 30
• 38
  Aristotle, Physics 239b30; D.L. 9.72
• 39
  See Arntzenius (2000) and Salmon (2001) pp. 23-24.
• 40
  From Aristotle, GC 316a and Simplicius, In Phys. 139.2.
• 41
  See for example Curd, 2004, p. 173-177.
• 42
  It is not clear whether Melissus preceded or post-dated the Presocratic Pluralists and Atomists. Therefore, it is not clear whether his arguments are inspiration for or criticisms of these views, though he is often read as modifying Parmenidean views to block Pluralism and Atomism, for example by Guthrie, 1965, p. 117-8 and Furley, 1967, p. 79-103. See also the discussion at Curd, 2004, p. 206-216 and Harriman, 2019, p. 1-23 for a discussion of the chronology of Melissus’ treatise.
• 43
  Εἰ γὰρ πολλά, τοιαῦτα χρὴ αὐτὰ εἲναι οἷόν περ ἐγώ φημι τὸ ἓν εἶναι. Εἰ γὰρ ἔστι γῆ καὶ ὕδωρ καὶ ἀὴρ καὶ πῦρ καὶ σίδρος καὶ χρυσός, καὶ τὸ μὲν ζῶν τὸ δὲ τεθνηκός, καὶ μέλαν καὶ λευκὸν καὶ τὰ ἄλλα, ὅσα φασὶν οἱ ἄνθρωποι εἶναι ἀληθῆ, εἰ δὴ ταῦτα ἔστι, καὶ ἡμεῖς ὀρθῶς ὁρῶμεν καὶ ἀκούομεν, εἶναι χρὴ ἕκαστον τοιοῦτον οἷόν περ τὸ πρῶτον ἔδοξεν ἡμῖν, καὶ μὴ μεταπίπτειν μηδέ γίνεσθαι ἑτεροῖον, ἀλλά ἀεὶ εἶναι ἕκαστον οἷόν πέρ ἐστιν. (ed. Harriman)
• 44
  With Loenen, 1959, p. 169-70, Reale, 1970, pp. 243-4, Palmer ,2009, p. 212-3, and Harriman, 2019, p. 199, I take these opinions to belong to a broad category of people (i.e. not just philosophers, but anyone who believes that the objects of sense experience are real).
• 45
  As summarized by Palmer, 2009, p. 212: “The passage is not concerned with the mere existence of earth, water, air, and the rest, but with the question of whether any of these things can properly be said to ‘be’, that is, whether any of these things really are…” See also Mourelatos, 1965, p. 362-3. For Palmer, the argument does end up entailing that these objects do not exist (in the first sense), because it turns out that in order for something to exist at all, it must really be. Cf. Barnes, 1982, p. 299, fn. 4 and Harriman, 2019, p. 200-202, where Melissus does not distinguish between ontologically or modally distinct states of being, but is concerned in B8 with whether the information relayed by sense experience is reliable.
• 46
  Harriman, 2019, p. 205-6 correctly points out that the results of sense experience do not merely conflict in that the leaf ends up being both F and G, but that given Melissus’ examples in the middle of B8, the results of sense experience suggest that the natures of these objects are opposites in that the same thing ends up being both F and not-F. This makes a stronger case for why sense experience is unreliable.
• 47
  Cf. Harriman, 2019, p. 199-207, where (c) is taken to eliminate sense experience, since it is responsible for the postulation of plural entities. Since I am taking einai in (c) to be predicative, I do not take Melissus to deny any being whatsoever to sensible entities. Therefore, on my interpretation, sense experience is not being eliminated tout court—rather, it is rendered an insufficient means for apprehending what-is.
• 48
  See Mourelatos, 1965, p. 363, fn. 52, where the argument “is intended to complement the thesis ‘only the One is’ by showing that the many of perceptual experience are not… It is important to note that the only feature of ‘the One’ which matters for the argument in this fragment is its permanence.”
• 49
  Palmer, 2009, p. 214-216
• 50
  Spinoza, Ethics, 1d4-p14
• 51
  Robbiano (2016) makes an interesting case for interpreting what-is in Melissus as the reality of experience, on the grounds that we do not experience non-being, nor do we experience boundaries between being and anything else. She claims, “If you drink tea while listening to music, the tea and the music cannot be real, since they change and seem to vanish either in our stomach or in the air. However, being might be visualized as the truth of this very experience of drinking and listening… There is only experiencing or being: in Melissus’ words, there are not two things… that set boundaries to each other” (p. 172). While I do not endorse the reading of what-is as experience, I agree with the spirit of her interpretation, that the world we sense or experience is not totally distinct from what-is.
• 52
  Palmer, 2009, p. 215-216
• 53
  For a discussion of Melissus’ deductive strategy, see Harriman (2019).
• 54
  Curd, 2004, p. 213
• 55
  See, for example, Brunschwig (1994) and Marmodoro (2017).

Publication Dates

• Publication in this collection
  17 Dec 2021
• Date of issue
  2021

History

• Received
  01 May 2021
• Accepted
  01 Aug 2021