Notes on Parmenides, Zeno, and Melissus
Parmenides of Elea was probably born about 515 BCE and died in the
century. Zeno of Elea was apparently a student of Parmenides (those who attest this
include Plato, who has been found to be generally reliable regarding people's birthdates,
death dates, and associations). Zeno was probably born about 490 and died in the mid-
to late fifth century. Melissus of Samos was probably born in the first quarter of the
century, and died late in the century. There is no evidence that Melissus ever met
Parmenides or Zeno; he is called an "Eleatic" because he evidently tried in his writings
to support what he thought Parmenides intended. ('Eleatic' means 'associated with Elea';
Melissus' association with Elea was not with the town itself but with the philosophical
work that the town had produced, namely that of Parmenides and Zeno.)
The works of the three "Eleatic" philosophers have much in common, but that is not to
say that all three were trying to do the exact same thing, or that all three can be found to
be in agreement on all points.
In Parmenides' poem, a goddess declares that it is necessary to say and to
(think, take it) that what is is (fr. 6). (Most likely she means that this is necessary in or
for inquiry, given what she says in fr. 8, and given the reference to roads of inquiry at
6.3.) She also says that on the only road of inquiry that she considers to be at all viable
or possible, we must say and take it that what is is one, whole, ungenerated,
indestructible, complete, unmoving, unique, continuous, and limited.
Zeno tried to show that the assumption that multiple things are or exist has
contradictory implications. That is, he tried to show that on the analysis of things that
was (and to some extent still is) offered, there cannot coherently or consistently be
taken to be multiple things. He also tried to show that contradictions result from
assuming that there is motion and accepting the standard analysis of motion; and that
contradictions result from assuming that there are things that have extension in space
and accepting the standard analysis of that.
Melissus wrote in support of the claim that what is is one. His understanding
this claim involved and of what it implied led him to argue for some conclusions that
were very different from key statements made by the goddess in Parmenides' poem.
Perhaps most notably, Melissus argues that what is must be spatially and temporally
unlimited, whereas Parmenides' goddess holds that what is must (in or for inquiry) be
said and taken to be limited - and she is not clear, or not explicit, about its relationships
to existence in space or time.
It is important to note the form in which each of these philosophers writes. In
Parmenides, the narrator of the poem recounts a journey to the realm of a goddess, and
this goddess discusses roads of inquiry and the opinions of mortals. In her discussion of
roads of inquiry, she talks of how that which is must be said and taken to be, in or for
inquiry at very least. All of the remarks in Parmenides' fragments that concern the way
what is must be are in fact remarks about the way what is must be (or the way it must be
said and taken to be) on or for roads of inquiry; and they all seem to be part of a speech
by a goddess character.
Zeno, in contrast, discusses how what is cannot be, or how it cannot coherently be
taken to be. He does not make use of characters or narrative, as far as we know. He
also does not in the surviving fragments talk of what that which is could be like, or
characteristics it could or must have (or be taken to have); he only mentions what that
which is could not be like (or characteristics, e.g. multiplicity, that it could not
coherently be taken to have). That is, Zeno only says that what is could not be (or could
not coherently be taken to be) multiple, that there could not be (or could not coherently
be taken to be) multiple things; there is no evidence that he said that what is is one.
Perhaps he thought that our customary ways of looking at that which we say exists (or
at that which we say is, or at that which we say is the case) are so flawed that we will
run into contradictions if we say that what is is one, and that we will run into
contradictions if we say that multiple things exist.
Melissus, on the other hand, does say that what is is one. He also says that what is must
be spatially and temporally unlimited. He says this in his own voice, i.e. not through a
character in a poem.
These differences in the forms of their remarks have significant ramifications for the
interpretation of these philosophers' works, as will be seen below.
- Parmenides. Parmenides wrote a poem in which a young man, the
narrator of the
transported to the realm of a thea, a female divinity. This goddess promises to have
"everything, both the...heart of...[T]ruth; and the opinions of mortals, in which there is no true
assurance" (fragment 1, lines 28-30).
- However, there is no evidence that this goddess presents the young man with a direct
statement or description of the "heart of [T]ruth". Instead, she discusses "roads of
inquiry" that she takes to be conceivable (first mentioned in fr. 2). Then, after she has
talked about the last one (8.1-49), the one that she seems to take to be the most viable
(see e.g. 8.34-38) and the one that has something to do with truth (8.50-52), she
abruptly changes the subject and talks about the opinions of mortals. Thus it may be
helpful to look at the surviving fragments as falling into two main sections: the story of
the journey (1.1-23) and the speech of the goddess (the rest of the fragments, with the
possible exception of frr. 3,5, and 20, for which we have no clearly decisive indications
as to placement). The goddess's speech itself can also be seen to have two parts (though
perhaps there once were more): a section on the roads of inquiry that can be conceived,
and a section on the opinions of mortals.
- Fragment 1: The journey to the goddess.
- Ancient sources report that Parmenides' poem began with these lines. In fragment 1, the
poem's narrator (who may or may not be intended to be Parmenides himself) recounts
an unusual chariot ride. Drawn by mares and led by the daughters of the Sun
the narrator's chariot goes beyond the beaten paths of humans to the gates of the roads
of Night and Day. The gates are guarded by Dike (Justice, Right), but the
persuade Dike to open the doors, and the chariot is able to proceed to the home of
unnamed goddess. This goddess welcomes the narrator and makes the speech that takes
up the rest of the fragments (again, frr. 3,5, and 20 may be exceptions).
- The wording of the first line suggests that the mares continue to conduct the
in the chariot, even after the goddess's speech is done. That is, his quest or journey may
not be complete; it may be an ongoing process or way of living.
- We know that the narrator is male, because the goddess refers to him as "young man"
(koûros). All but one of the other figures in the fragments are female: the
daughters of the Sun, Dike, Ananke (Necessity or Constraint),
Moîra (Fate or Portion),
the goddess who speaks, Truth, Persuasion, Themis (Custom, Right), and the
divinity in frr. 12 and 13. The only other male figure in the fragments is Eros, god of
love or desire, in fr. 13.
- A number of the figures and items mentioned in fr. 1 appear in other contexts in other
fragments; in interpreting their meanings it is important to be aware of the differences
and the parallels among contexts. For example, Dike, Themis, and
Moîra show up again
in fr. 8. Night and Day in fr. 1 would seem to have some connection with night and light
(or fiery stuff) at 8.56-61, and frr. 9 and 12. Ananke appears in frr. 8 and 10. The
mentioned in frr. 1,10,11, and 15. Roads appear in frr. 1,2,6,7, and 8.
- Some authors have suggested that the fact that Parmenides has a goddess make
pronouncements is a sign that he intends a sort of "argument from authority": a sign that
he wants his readers to accept these pronouncements unquestioningly, and that he
himself accepts them unquestioningly.
- But there are reasons to suspect that such an interpretation may not be correct. For one
thing, the goddess argues for the things she says; she provides support and
for her claims. She does not insist that the young man accept her statements as true just
because she is a goddess (or because she could kill him if he refused to accept them);
rather, she gives reasons for her assertions, and asks him to think about them.
- It is noteworthy that the goddess argues at all. The poem of Parmenides provides the
first known example of written deductive arguments in Greek philosophy. The level of
abstraction (e.g. the fact that the goddess talks about being as a whole or in general, or
about that-which-is as a whole or in general; and the fact that she takes as her subject
what it is we'd need to say and to think about what is, in order for inquiry to be
possible) seems to be an innovation as well.
- In fragment 2 the goddess announces that she will discuss "the only roads of inquiry
conceivable". What might be meant by 'road of inquiry'? It may be helpful to note here
that the expressions 'avenue of inquiry' and 'avenue of exploration' are sometimes used
today, and these could well be the sort of thing the goddess intends. A road of inquiry
would seem to be a path that one follows, or makes, in seeking something. (The word
Parmenides uses, 'dizesis', can be translated either as 'inquiry' or as 'seeking'.) It
be a path in though or conceptions; the steps one takes on the road would be the
questions one asks, the ways one looks for answers, and so on. What defines the path or
road would then be the ways of looking at the world that are involved in the steps one
takes. For example, a person who believes that everything that exists in the world is
matter and energy (and that everything that does not immediately appear to be matter or
energy must be explainable in terms of the effects of matter and energy) would look at
the world quite differently, might ask different questions, and would accept different
kinds of answers, from a person who believed that matter and energy do not exist; and
from a person who believed that matter, energy, and some other kinds of entities exist.
- In fragments 6 and 7 she seems to rule out, or to bar the human from following, certain
roads; from the way she describes them, she seems to see them as unviable (presumably,
unviable for inquiry, since they were supposed to be roads of inquiry). There and in fr. 8
she tries to get the young man to reason away from assumptions based on ordinary
experience to some indications about the character of to eon, "that
is" or "what
is" or "being" (or "Being", in Freeman; Parmenides did not use capital letters, so we
don't know if he would want us to capitalize the initial 'b')(1).
It's important to note that
she is talking about how "what is" would have to be (or have to be said and taken to be)
on an apparently viable road of inquiry. That is, she does not say anything about how
"what is" must be (or how we must say and take it to be) independent of contexts of
inquiry. Perhaps even outside contexts of inquiry we must take it that "what is" is as the
goddess says it is (or must be) in fr. 8; or perhaps not. To ask whether outside of
contexts of inquiry "what is" must be a certain way, would itself be an inquiry, and thus
subject to the restrictions the goddess mentions.
- On the road of inquiry discussed at the beginning of fr. 8, "signs" indicate how "what is"
must be one, continuous, ungenerated, indestructible, etc. Why must it be that way? I
would suggest that we must take it to be that way in order for inquiry to be possible
and coherent; and that it must be that way if inquiry is to be able to get valid results
(whether it does is another question). "What is" would have to be taken to be
continuous, for example, because if it were not, what would separate its "parts" or
"members"? The separator could not be something nonexistent, or "non-being", because
then it could not be said to be what separates the parts or members of "being" or
is". The separator could not be said to be something existent other than "what is",
because "what is" is all that is. So "what is" would seem to have to be continuous, or to
have to be taken to be so.
- "What is" would have to be taken to be ungenerated, if inquiry is to be possible, for the
following reasons. To say that it was generated, that it came to be, would seem to imply
first that there was a time at which it did not exist. Then we would have to say either
that "what is" came from nothing, from non-existence; or that it came from something
else. If we suppose that it came into being from nothing, then it would seem that things
can pop into being at random, or without an existent source. Then we could not have
any way of seeking anything, since we would not be able to tell when and where it could
be found. Nothing would be known to be stable enough to allow the "process of
elimination" to be used as a search tool. But perhaps it was only "what is" as a whole
that came into being from nothing. Still, we would not be able to take steps that would
be efficacious (or known to be efficacious) in seeking anything. Why not? The problem
would be that if "what is" came to be from nothing, then we could not trace anything to
its source; we could not know whether the relationships we might think things have with
each other really do obtain. The same problem would arise if we said that "what is"
came to be from something else: if that something else was not "what is", or was utterly
unlike "what is" (because if there was any continuity or commonality between the "two"
then that would be the ultimate nature of "what is", and we'd have to ask whether
thatcame into being), then the relationships that obtain within "what is" would not
any analogue in the "source" of "what is". And we'd have to ask where that source came
from, etc. If we could not answer these questions, inquiry could not be known to be
- According to the goddess, "what is" must be this way, in or for inquiry, because it is
bound by Dike (Justice), Ananke (Necessity), and
Moîra (Fate or Portion). The standard
Greek understandings of these forces would give them powers or implications that can
be seen to correspond (with respect to to eon) to the effects the goddess
them. The standard Greek understandings of these forces, and indeed the language of
the whole poem, invoke multiplicity, change, non-existence, and lots of other things that
the goddess says are incompatible with the way "what is" must be on the road of inquiry
of fr. 8. We could not reach the conclusion that "what is" must be continuous, on that
road, without invoking distinctions (discontinuities), etc. In other words, the goddess
shows that there are contradictions and incoherences in the basic conceptions that make
inquiry possible and that we use in everyday life (and that she uses to point these out to
us). It's paradoxical, but that's why we're mortals: we're mortals insofar as we have lacks
that prevent us from being able to resolve these.
- At 8.50, the goddess abruptly changes the subject, and describes what she
human opinions about cosmology, biology, and the naming or classification of things in
general. She says that mortals lay down two forms or opinions to specify (name)
appearances; these two are light (a high-up, lightweight, fiery thing) and night (a dark,
heavy thing). While these two are fundamental aspects of many cultures' ways of
looking at what exists, no person or culture in Parmenides' area and time is known to
have held that light and night are the onlyfundamental components or aspects of
allthings. Thus the goddess may be saying that mortals' opinions about what exists
implythat mortals believe that light and night (or something equivalent) are at the
foundation of all things. This is not to say that the goddess or Parmenides thinks that
mortals are justified or accurate in holding these opinions; perhaps the goddess or
Parmenides thinks that this is about as good as mortals can do when it comes to
describing their world. (Perhaps Parmenides thinks that this is the best that mortals can
do if they are using the kind of language and conceptions that enable them to understand
his poem.) If light and night name the most basic distinctions that mortals make, it is
perhaps fitting that the young man in the chariot passes beyond the gates from which
they are supposed to issue -- especially since this is the last landmark mentioned
he enters the realm of the goddess.
1. It is not entirely clear what Parmenides means by 'to
eon'. The term
be translated as 'what is',
'being', 'what is real', 'what is the case', 'what occurs', 'what obtains', 'being actual', and so on. If
you think that a thing exists or that a situation obtains or that something is the case, you would
considering it as belonging to to eon. If you think that something can
exist, be the case, etc., you
would seem to be considering it to belong at least potentially to to eon.
situations, colors, sounds, material objects--anything that you say exists or obtains, you are
considering as belonging to "what is", to to eon.
- It seems as though the goddess is talking about "what is" as a whole or in general; or
about whatever all things said to exist are supposed to have in common. She does not
state directly what she thinks this is, nor does she say anything about what specifically
should count as "what is", what qualifies as "being", and so on. She does suggest that it
is incoherent and/or inconsistent for us to suppose, in or for inquiry, that "what is" is not
one, that it came to be or could perish, that it changes, and so on.
- Some commentators (e.g. Owen, Coxon) claim that Parmenides or the goddess thinks
that only what is thought (ideas, perhaps) exists or can exist. But they base this claim on
a combination of a mistranslation of fr. 6, a dubious translation of 8.34-36, and on one
of many possible translations of fr. 3. Fragment 3 is half a hexameter line in length and is
not a complete sentence, however, so its reference is not at all clear and there is no
obvious basis for choosing a translation. Without further evidence, then, these
commentators' interpretation cannot be found to be valid.
- Zeno. Zeno was concerned to show that our understandings of time, motion,
magnitude, unity, singleness, and plurality are incoherent; or that they result in
- Many writers have supposed that Zeno tried to prove (or thought he did prove) that
there is no motion, that there are not multiple things, and so on. In fact, that is how
Aristotle presents Zeno's work, and Aristotle and his school are our main sources on
Zeno. Some of these writers then criticize Zeno, saying that he failed to prove those
- But a careful look at what Aristotle presents of Zeno suggests that Zeno may not have
intended to prove that there is no motion, etc. Instead, Zeno may have been trying to
show that what people in his time (and perhaps even now) mean by "motion" does not
make sense, i.e. that whatever is going on when we say that a thing is moving could not
possibly be what we think we mean when we say that a thing is moving, etc. That is,
Zeno may not have been trying to show that your eyes are not doing anything when you
read this, nor that the keys of the keyboard on which this was typed were not doing
anything different during the typing from what they were doing when no typing was
going on. Instead, he may have been trying to show that the account of movement that
was (and perhaps still is) given is incoherent; that the claims that were (or are) usually
made about what movement involves lead to contradictions. Similarly, he may have
been trying to show not that only one thing exists or is, but that the assumptions
involved in the claim that multiple things exist or are lead to contradictions. (This does
not rule out that he might have thought that the assumptions behind the claim that there
is only one [thing] result in contradictions as well.)
- If in fact Zeno meant only to show that our accounts of motion, multiplicity, and so on
are incoherent and inconsistent (result in contradictions), then his arguments can be seen
to make more sense, and to be more effective, than they would if he meant to show that
there is no motion or multiplicity, etc. (An interesting discussion of whether or to what
extent anyone has ever refuted Zeno's arguments can be found in Thomas Heath, A
History of Greek Mathematics, Chapter VIII.)
- At very least, then, Zeno felt that our analysis or understanding of what is going on
when we say there is motion (or multiple things, or different positions in space, etc.)
leads to inconsistencies no matter which way we turn.
- Zeno's method was to try to show that accepting motion or multiplicity
etc. as an
of what exists leads to two possible alternatives. These alternatives would each lead to
a contradiction or impossible consequence, and would also contradict one another.
- Let us take the first paradox(2) given in
Freeman (Zeno fragments 1 and 2) as
example. It can be applied to time or change as well as to space or magnitude, as we
will see, but let us start with magnitude. It is probably easier to understand the paradox
if you read fr. 2 before fr. 1.(3)
- Consider the things that are supposed to exist in space. We, like people in
generally say that there are spatial things, things that "take up space" or "exist in space".
Maybe not all things that we say exist "take up space", but we generally say that at least
some things do. We suppose that these things have sizes, or spatial magnitudes, or
dimensions; each such thing is supposed to take up a certain amount of space, i.e. to
have a certain size or magnitude.
- An unspoken assumption that the Greeks held (and that we generally do too(4)) is
that each thing that exists in space has a definite size or magnitude, a definite
and end. After all, if we are going to claim that multiple things exist in space, we must
have some idea of where one thing "A" ends and where the next thing "B" starts -
otherwise, we would not be justified in claiming that there are these two distinct things
A and B. (And if they're not distinct from each other, how are they two?) Zeno will
argue that if we can't tell where anyone thing A ends and the next thing B begins, we
would seem to lack justification (certainly we would lack the traditional justification) for
asserting that there are multiple things at all.
- If we consider the things that we suppose to have spatial magnitude, we note that
such thing can be divided into parts, at least conceptually. Even when we can't actually
break a particular thing, we may speak of the right and left sides of it, or the top five
inches of it, etc. We tend to agree, that is, that each thing has parts or units: a
six-inch-long piece of wood is longer than a five-inch piece by a "unit" of one inch.
- Consider, then, the parts or units of the things that we say have size or spatial
- Either the smallest units or parts of which those things are composed have no (that
zero) magnitude, or they have some (positive) magnitude. Or, so goes the common
Greek and modern conception of these matters. Let us see what the consequences of
each of these possibilities are.
- Suppose that the smallest units or parts of spatial things have zero
if you add one of these units to a thing "C", then that thing would not get any larger -
that is, the sum of the two would be no larger than C alone. Then it would be impossible
for there to be anything that had positive magnitude, since all magnitudes would be
multiples of the smallest magnitude. Thus all magnitudes would be consituted of many
units of the smallest magnitude.
- But we just saw that on supposition (a), adding the smallest magnitude to something
will not make that thing larger. So adding up lots of smallest-magnitude units gives you
a sum or aggregate that is no larger than one smallest-magnitude unit - which is zero
magnitude. Put another way, if all magnitudes are multiples of that smallest unit, they
are all zero. Yet we say that there are things with positive magnitude, things that have
size greater than zero. We even claim to see such things. So the smallest parts of
things should have some positive magnitude -- which contradicts premise (a).
- So, let's suppose instead the other possibility given above: Suppose that the
units or parts of spatial things have some positive magnitude. In that case, says Zeno,
let's look harder at those things that we say have definite (limited, finite) sizes. If you
examined a very small end piece of one of those things, you'd notice that that end piece
had an end piece with a magnitude. Then you'd notice that that end piece had an
outermost piece (or area or section) with a magnitude. Every time you would come to
what you thought was the end of what you thought was the smallest piece, you would
notice that this end itself was an even smaller piece with magnitude.
- Or, to look at it another way, imagine that you are trying to get an exact measurement
of something that is supposed to exist in space. You hold the thing up against a ruler,
and you notice that the end of the thing falls in between two of the smallest markings on
the ruler. So you get a ruler with even smaller divisions, and it happens again: the end of
the object falls in between two of the smallest markings on the new ruler. You now have
a somewhat more accurate measurement than you originally had, but it's still not an
exact measurement. So you get rulers with smaller and smaller divisions, and finally the
end of the object does come out right on a ruler marking. But then you look at the
object and the ruler under a magnifier, and you notice that the ruler marking line has
some thickness. You can see that the end of the object falls somewhere in the middle of
the thickness of one of the ruler marking lines. Where exactly does it fall? You need
even a more finely-divided ruler in order to find out, it seems. Since all ruler markings
must have a thickness and since any two ruler markings must have a distance between
them, the end of the object will always fall in something that can be divided further.(5) No
smallest positive magnitude will be found. Further, there will not be determinable
endpoints to things. These conclusions undermine hypothesis (b).
- So now we are stuck: either we can't find the smallest piece of a thing or the smallest
magnitude with which we can measure; or there must be things or units that have zero
magnitude. If we choose the first, we can't find exactly where a thing ends, so
things are unlimited or indefinite(6) in size; there are always
more divisions of the
measuring device or of the thing.Each thing could be seen as indefinitely large (if we
tried to measure it outward from its center or other internal point); and each thing could
be seen as indefinitely small (if we tried to measure the outermost extents of the things
that were supposed to surround it). The exact number of spatial objects might be
indeterminate too, for we might not be able to tell where one supposed spatial object
left off and the next began, so we could not with support the claim that there were in
fact two distinct spatial objects. Moreover, if we cannot find the smallest piece of a
spatial thing, we cannot express spatial magnitudes as multiples of some smallest
unit. That conflicts with our usual belief that there are things that have definite
magnitudes. (Again, to be sure that there are multiple spatial things, it seems we would
have to be able to distinguish them clearly from one another, i.e. find clear distinctions
between them -- exactly what we have seen we cannot do if we assume that there is a
smallest positive magnitude.)
- So it would seem that we would have to choose the second alternative from the
preceding paragraph, that is, choose to say that there is a smallest magnitude, and that
this smallest magnitude is equal to zero. But we have seen in our examination of
hypothesis (a) above that we cannot coherently (i.e. without contradiction)
suppose that there is a unit of zero magnitude.
- Thus it seems that if we suppose that there are distinct things with finite magnitudes
then we must suppose that there is a smallest magnitude; and we must also suppose that
there cannot be a smallest magnitude. If we suppose that there are distinct things of
finite magnitude, we must also hold either that there are no things of positive
magnitude, or that there are no things of finite or determinate positive magnitude. Thus
it would seem to be impossible to hold (without contradicting oneself) that there are
multiple distinct things in space. (Again, in order for us to say with justification that
there are multiple things, we must be able to find clear distinctions between those things;
but if the limits of spatial things are unclear we could not with certainty tell one from
another, nor tell with certainty that there were indeed multiple different things.)
- Similarly, according to Zeno we cannot identify exactly when a process starts because
we could not find a smallest interval of time, an interval that is not made up of smaller
(non-zero) ones -- for if an interval is made up of smaller ones, during which smaller
one did the process start; and during which division of the smaller one, etc.?--. So we
cannot according to Zeno have a coherent account of change.
2. The word 'paradox' comes from a Greek word meaning 'contrary to
opinion'. In the sense in
which it is used to describe Zeno's work, it refers to an argument that derives self-contradictory
mutually contradictory conclusions by valid deduction from accepted or apparently acceptable
3. The fragments are not numbered according to their order in Zeno's
book; we don't know in
what order they occurred in Zeno's book. They are numbered according to the order in which
are quoted in later writers who discuss Zeno. The earliest source in which we find quotations (or
something close to quotations) of the passages in Zeno that are now designated as fragments 1
and 2 is Simplicius' commentary on Aristotle's Physics. (Simplicius lived
years after Zeno.) Simplicius says, and Freeman notes, that what he is presenting first is the
second part of a certain section of Zeno's work, and that what he is presenting second is the first
part of the section.
4. In modern physics, we may try not to hold this assumption, but
problems arise then when it
comes to specifying what an "object" is, and what the relationships are between "middle-sized
objects" - roughly, anything bigger than a molecule and smaller than a galaxy - and the
not-always-particle-like submolecular entities that are supposed to compose the "middle-sized
5. It may be objected that an ideal ruler, one we could not physically
construct but which would
conceivable in pure geometry, could have "markings" or that are line segments. Line segments
have no width (they are one geometrical point "wide", and points have no dimension).
- One response to that would be to point out that the increments of measure
two of these "markings" would still have some width, and so would the tip of the object
being measured, so we would still have the problem of having to look seemingly forever
for finer and finer divisions of distance.
- Another response would be to note that the idea of a "ruler" or measuring line that is
composed of dimensionless (sizeless) geometrical points was already shown to be
incoherent on some level in part (a) above: a thing that is supposed to have positive
magnitude cannot be coherently taken to be made up of pieces that have zero
6. Freeman uses the term 'infinite' in her translation of fragments 1 and 3;
the Greek word is
'apeiron', which can mean "infinite", "indefinite", "indeterminate", "unlimited".
- Melissus. We have seen that it is often said that all three "Eleatics" claimed that
(to eon) is
one; or that all three wrote in support of the claim that what is is one. We have also seen
that Parmenides and Zeno may not have held or supported the claim that what is is one.
- But the third "Eleatic", Melissus, did write in support of the claim that what is is one.
His understanding of what was involved in or implied by this claim led him to argue for
some conclusions that are very different from key statements made by the goddess in
Parmenides' poem. Most notably, Parmenides' goddess holds that on or for a certain
road of inquiry at least, what is (to eon) must be taken to be
limited; whereas Melissus
argues that what is must be spatially and temporally unlimited
goddess is discussing a certain road of inquiry, and is not necessarily at this point saying
anything about space and time; Melissus is not discussing roads of inquiry (i.e. he seems
to be making unconditional claims about what exists), and he does specifically mention
space and time.
- One thing that might account in part for this difference is that Melissus seems
to have a
different focus from those of Parmenides or Zeno. Parmenides' goddess is concerned
about what must be said and conceived, in the most general way, regarding what is.
Zeno examines the consequences of supposing that there are multiple things (especially
in space and time, but conceivably also in general). He draws conclusions about what
cannot exist or take place or be thought without contradiction, but does not as far as we
know make any claims about what kind of entity he might think does exist or the kind of
situation he thinks does obtain. Melissus, however, thinks that at least some terms of the
kind we use to describe the things we usually (if perhaps erroneously) think exist or are,
can in fact be used to describe the unity of "being" ("what is") that Melissus thinks exists
or obtains (see e.g. his use of 'arrangement', 'healthy', and perhaps 'full', in fr. 7).
- Melissus suggests that the ways in which we describe the multiple things we
say "are" lead us
to unavoidable contradictions; what is cannot be as we say it is, he thinks. His response
seems to be to try to look at the implications of the notion of existence, or of the notion
that anything at all exists. When he does this, he concludes that what is must be one,
infinite, eternal, continuous, unchanging, and so on; and that change, multiplicity,
division, creation, destruction, etc. must be illusion. The question may arise as to what
in M.'s unity could account for this change and multiplicity even if the change and
multiplicity are illusory. How could what must be one and undivided produce the
illusion of division? For even if it is an illusion, we really have the illusion, and
supposed to be a distinction or division between the illusion and the truth (or the truth
behind the illusion), so would that not mean that some division or distinction is
- We do not know whether M. ever responded to this sort of question. But he was not
alone in trying to take P.'s and Z.'s observations into account when trying to formulate
an understanding of what exists (including appearances). Empedocles, Anaxagoras, and
Philolaus, among others, tried to meet the same challenge, but did so in very different