The Parmenides

1

• The Parmenides
• Philosophy 190 Plato
• Fall, 2014
• Prof. Peter Hadreas
• Course website
• http//www.sjsu.edu/people/peter.hadreas/courses/P
  lato

2

• Overview of main differences of the Parmenides
  as compared with other dialogues1
• Socrates is very young (127C5) in the
  Parmenides, somewhere between fifteen and
  nineteen years old.
• Unlike other dialogues of question and answer
  form, in which Socrates typically questions
  others who contradict themselves, Parmenides
  questions Socrates and Socrates contradicts
  himself.
• Parmenides argues with Socrates and wins the
  arguments regarding the forms. Forms such as
  justice itself and good itself are mentioned. The
  older Socrates of the other dialogues presents
  Forms as central to his philosophy.
• The question arises as to whether this dialogue
  signals Platos revision of the Theory of Forms.
• The Parmenides is the only dialogue in which
  forms are the main topic.
• The dialogues second part, 137C-166C, is the
  longest passage of unrelenting argument in
  Platos writings and its arguments are his most
  puzzling.
• 1. adapted from Peterson, Sandra, The
  Parmenides, The Oxford Handbook of Plato, edited
  by Gail Fine, (Oxford/New York Oxford University
  Press, 2011), p. 383.

3
Parmenides flourished late sixth or early fifth
century BCE He was from Elea in Magna Graecia and
he was the founder of the Eleatic school of
philosophy.
4

• Zeno (c. 490 c. 430 BCE)
• Part of Eleatic School and principal student of
  Parmenides.
• According to the ancient historian of philosophy,
  Diogenes Laertius, Aristotle said that Zeno
  invented the dialectic.1
• All the extant works we have Zeno are the result
  of discussions or quotes from other writers. The
  paradoxes of which he is best known are related
  by Aristotle in Physics, 233a and 239b.
• Proclus in his commentary on Plato's Parmenides
  states that Zeno produced "not less than forty
  arguments revealing contradictions2. Nine of his
  arguments have survived.
• Zenos arguments are the first examples we have
  of indirect proofs or proofs by reductio ad
  absurdum.
• Plutarch, who usually is a fairly careful
  historian, says that Zeno tried to kill the
  tyrant Demylus. He couldnt do so, so "with his
  own teeth bit off the tyrants tongue and spit it
  in the tyrants face.3
• 1. Diogenes Laërtius, 8.57, 9.25
• 2. Proclus, Commentary on Plato's Parmenides,
  p. 293.
• 3. Plutarch, Against Colotes.

5
Zeno shows the Doors to Truth and Falsity
(Veritas et Falsitas). Fresco in the Library of
El Escorial, Madrid.
6
(No Transcript)
7

• Proposed interpretation of the frame of the
  Parmenides
• The Republic begins with a character named
  Cephalus and the main characters are Socrates and
  Platos full brothers Adeimantus and Glaucus.
  Adeimantus and Glaucus retain a sincere interest
  in the conversations as they arise in the
  Republic.
• The Parmenides begins also with a character named
  Cephalus, but its a different Cephalus from the
  Republic. In the Parmenides he is from
  Clazomenae, the home of Anaxagoras. In the
  Republic he is presumably from Piraeus.
• Platos half brother, Antiphon, is sought in the
  Parmenides. Hes given up philosophy, now he
  devotes most of his time to horses. (p. 361,
  126C) But before he gave up philosophy, he
  memorized, after much practice, the conversation
  that took place between Socrates, Zeno,
  Parmenides and others that make up the dialogue.
• Proposal In the Parmenides Plato is suggesting
  that the results of the Parmenides are more
  distantly related to his own teaching and, if
  taken at their face value, dissuade people from
  applying philosophy to their lives.
•  
•  

8

• Is the Aristotle of Platos Parmenides an
  allusion to Aristotle the philosopher?
• There would seem to be no connection.
• It is probable that the Parmenides was written
  before Aristotle joined the Academy in 367 or 366
  BCE at about the age of seventeen.
• Aristotles early writings indicate that for
  years afterwards Aristotle was, as we should
  expect, a faithful adherent of the theory of
  Forms under the overwhelming influence of his
  master.
• The objections to the theory in the Parmenides
  are advanced by Parmenides, not by Aristoteles,
  who has nothing to say of himself.  
• Argument adapted from Cornford, Francis
  MacDonald, Plato and Parmenides, (Bobbs-Merrill,
  Indianapolis) p. 109, n. 1.

9
The character of the teenage Socrates at the
beginning of the Parmenides Socrates treats Zeno
rather condescendingly. Hes brash, maybe rude.1
Perhaps what wed expect from a very bright
teenager. Consider the way he sums up the
combination of Parmenides and Zenos cooperative
work, 128B, p. 362 Parmenides, Socrates said,
I understand that Zeno wants to be on intimate
terms with you not only in friendship, but also
in his book. He has in a way written the same
thing as you, but by changing it round he tries
to fool us into thinking he is saying something
different. You say in your poem that all is one,
and you give splendid and excellent proofs for
that he, for his part, says it is not many and
gives a vast array of very grand proofs of his
own. So with one of you saying one, and the
other not many, and with each of you speaking
in a way that suggests youve said nothing the
same although you mean practically the same
thing what youve said you appear to have said
over the heads of us. 1. Sandra Peterson makes a
similar point in The Parmenides, The Oxford
Handbook of Plato, edited by Gail Fine,
(Oxford/New York Oxford University Press, 2011),
p. 383-4.
10
In the initial conversation with Parmenides and
Zeno, Socrates summarizes a typical argument of
Zeno at 127E, p. 362-31 Zeno, what do you mean
by this If things are many, they must be both
like and unlike, But that is impossible, because
unlike things cant be like like and unlike
things likes? That what you say, isnt it? It
is, said Zeno. But as Socrates will later say,
obviously things can be unlike and unlike or many
and one, 129D, p. 363 He will say, when he
wants to show that I am many, that my right side
is different from my left, and my front from my
back, and likewise my upper and lower parts
since I take it I do partake in multitude. But
when he wants to show that Im one, he will say
that I am one person among the seven of us,
because I also partake of oneness. Thus he shows
both are true.
11
The teenage Socrates already has an interest in
and admires a philosophy that takes seriously a
theory of forms. p. 363, 129B E SOCRATES
If some showed that the likes themselves come to
be unlike or the unlike like that I think would
be marvel but if he shows that things that
partake of both of these have properties, there
seems to be nothing strange about this, Zeno
But if someone first distinguishes as
separate the forms, themselves by themselves, of
the things I was talking about a moment ago for
example, likeness and unlikeness, multitude and
oneness, rest and motion, and everything of that
sort and then shows that in themselves they can
mix together and separate, I for my part he
said, would be utterly amazed, Zeno.
12
Six Properties of the Forms as collected from
Parmenides 129B-130Di 1. Causality. Things take
on a property by virtue of participating or
partaking in a Form. .. things that partake of
both of these likeness and unlikessness have
both properties. 129B, p. 363. 2. Separation. A
form is itself by not being identical with the
things that partake in it. But if some first
distinguishes as separate the form, themselves by
themselves, 129D, p. 363 3. Purity Forms
cannot have contrary properties. And its the
same with all the others Forms if he could
show that the kinds and forms themselves have in
themselves these opposite properties, that would
call for astonishment. 129C, p. 363 4.
Uniqueness There is only one Form with a
perfection of a certain property. And what about
these? asked Parmenides. Is there a form,
itself by itself, of just, and beautiful, and
good, and everything of that sort? Yes, he
Socrates said. 130B, p. 364. i. This list
follows Ricklesss analysis Rickless, Samuel,
"Plato's Parmenides", The Stanford Encyclopedia
of Philosophy (Winter 2012 Edition), Edward N.
Zalta (ed.), URL lthttp//plato.stanford.edu/arch
ives/win2012/entries/plato-parmenides/gt.
13
Properties of the Forms1 continued 5.
Self-Predication Any Form has the property which
itself is. If someone showed that the likes of
themselves come to be unlike or the unlikes like
that, I think, would be a marvel but if he
shows that things that partake of both of these
have both properties, there seems to be nothing
strange about that Zeno 129C, p. 363. 6.
Oneness Something that can be counted as a
necessarily homogenous. But if someone first
distinguishes as separate the forms, themselves
by themselves . . . and then shows that in
themselves they can mix together and separate, I
Socrates for my part, he said would be
utterly amazed Zeno. 129E, p. 363. NOTE
Oneness is different from Uniqueness. 1. Ibid.  
14
130A-E Parmenides Criticism of the Theory of the
Forms The Extent of the Forms1 And what about
these Socrates? Things that might seem absurd,
like hair and mud and dirt or anything else
totally undignified and worthless? Are you
doubtful whether you should say that a form is
separate for each of these too, which in turn is
other than anything we touch with our hands. p.
130D. p. 364.   1. Rickless, S. Platos Forms
in Transition, (Cambridge Cambridge University
Press, 2007) pp. 54-55 and Miller, M., Platos
Parmenides (Princeton, NJ Princeton University
Press, 1986) counter-argue. Both justice and mud
have self-predication. Justice is just, mud is
muddy. But its difficult to see how those things
that self-predicate materially, could also be
separate from sensible things. So then if there
is a Form of mud or hair, it would not be the
material self-predicating hairiness and that
seems to be what is objectionable. Or perhaps
there could not be Forms of such things.
15
Parmenides Criticism of the Theory of the Forms
Objections to Participation. I (130E-131E) A
thing cannot contain either Form as a whole or as
a part of it. Samuel Rickless in the Stanford
Encyclopedia of Philosophy article p. 7ff. says
this presumes what he calls the Pie Model of the
forms. According to the Pie Model, if the whole
is extended to discrete parts the whole will be
made into parts. (The whole Form is in
things.) NOTE The Greek terms for the
connection of Forms to ordinary things are
metalambabein (129A3) which Peterson fairly
translates here as together or jointly get
instead of the traditional participate and
metechein, 129A8, which she also fairly
translates here as together have instead of the
usual, share, participate, or partake.1 1.
Peterson, Sandra, The Parmenides, in The Oxford
Handbook of Plato, edited by Gail Fine,
(Oxford/New York Oxford University Press,
2011).  
16
Parmenides Criticism of the Theory of the Forms
Objections to Participation. I (130E-131E)
  Socrates responds to the application of the
Pie Model of the Forms p. 365, 131B. No it
wouldnt Socrates said. Not if its like one and
the same day. That is in many places at the same
time and is none the less not separate from
itself. If its like that, each of the forms
might be, at the same time one and in all.
Notice how day satisfies the six properties of
Forms.
17
Parmenides Criticism of the Theory of the Forms
Objections to Participation. II (130E-131E)
Parmenides shift from the daylight to the sail
model. A sail can cover things perhaps
something like daylight does. But a sail can be a
whole and a part. Taking a sail as a model of the
relation of a Form to material things, leads to
the sort of contradictions we find in the Pie
Model of the forms.  
18

• Parmenides Criticism of the Theory of the Forms
  Objections to Participation. III The Third Man
  Argument 132A-B
•  
• Note Plato never refers to the Third Man
  argument as such. The designation arises with
  Aristotles criticism of the Theory of Forms.
•  
• Colin Strang in Plato and the Third Man1 sees
  that the conflict enters in between the
• Unique Thesis (U)
• The One over Many thesis (OM) and the
• Non Identity Assumption (NI)
• Strang, C. Plato in the Third Man, in Vlastos
  (ed.), Plato I, 184-200.

19
  Strangs concluding paragraph The more you
become aware of and enthralled by the peculiar
anatomy of the individual Forms, the fewer and
less important become the thing that can be said
about Form in general. They remain unchanging if
only to be the subject matter of timeless truths.
(Parmenides 135C1) They remain single (Philebus
14E5ff.) but what they do not remain is
paradigms. (OM)  
20
Parmenides Criticism of the Theory of the Forms
Objections to Participation. IV Making a Form
into a thought in a Mind does not provide
connection to the Form in Itself p. 366. 132B-C
If inanimate objects have forms, then
presumably we require thought for us to be aware
of them. Thus thoughts seem to have a share in
forms and thus again a problem arises as to how
thoughts can be connected to Forms which are
supposed to be in themselves.  
21
Can the objections be met by making the forms
patterns or paradeigmata of which there are
likeness in things? (132C-133A) Again Parmenides
introduces a version of what is later referred to
as the Third Man Argument. This time
Parmenides formulation is closer Aristotles.
If something resembles the form, he
Parmenides said, can that form not be what has
ben modeled on it, to the extent that the thing
has been made like it? Or is there any way for
something like to be like what is not like
it? There is not. And isnt there a compelling
necessity for that which is to partake of the
same one form of that which is like it?  
22
Further development of Third Man Argument.
continued (132C-133A) There is not. But if
like things are like by partaking of something,
wont that be the form itself? Undoubtedly Ther
efore nothing can be like the form, nor can the
form like anything else. Otherwise, alongside the
form another form will always make its
appearance, and if that form is like anything,
yet another and if the form proves to be like
what partakes of it, a fresh form will never
cease emerging. Thats very true.
23

•  
• Parmenides Criticism of the Theory of the Forms
  Objections to Participation. V We cannot know
  the Forms and the gods cannot apply them to us
• 133A-134E
•  
• If Forms are just in themselves, they are not in
  real world.
• 2. They may have reference to each other, but
  they will be unknowable to us and, further, gods
  cannot apply them to us.

24
  Parmenides reintroduces the Forms (135A-5, p.
369)  And yet, Socrates, said Parmenides, the
forms inevitably involve these objections and a
host of others besides if there are those
characters for things and a person is to mark off
each form as something itself. As a result,
whoever hears about them is doubtful and objects
that they do not exist, and that, even if they
do, they must by strict necessity be unknowable
to human nature and in saying this he seems to
have a point and, as we said, he is
extraordinarily hard to win over. Only a very
gifted man can come to know that for each thing
there is some kind, a being itself by itself but
only a prodigy more remarkable still will
discover that and be able to teach someone else
who has sifted all these difficulties thoroughly
and critically for himself. empasis added
25
  Parmenides reintroduces the Forms (135A-5, p.
369) continued   I agree with you
Parmenides, Socrates said. Thats very much
what I think too. Yet on the other hand,
Socrates, said Parmenides, if someone, having
an eye on all the difficulties we have just
brought up and others of the same sort, wont
allow that there are forms of things and wont
mark off a form for each one, he wont have
anywhere to turn his thought, since he doesnt
allow that for each thing there is a character
that is always the same. In this way he will
destroy the power of dialectic entirely. But I
think you are only too well aware of that.      
26
A REVIEW OF MAIN ARGUMENTS OF PARMENIDES AND ZENO
OUTSIDE OF PLATOS DIALOGUE, PARMENIDES
27
From Parmenides Poem1 Fragment 2 Come now, I
shall telland convey home the tale once you have
heard/just which ways of inquiry alone there are
for understanding/ the one, that it is and
that it is not not to be,/ is the path of
conviction, for it attends upon true reality,/
but the other, that it is not and that it
must not be,/ this, I tell you, is a path wholly
without report/ for neither could you apprehend
what is not, for it is not to be accomplished,/
nor could you indicate it. . . . .
. . but not ever was it, nor yet will it be,
since it is now together entire,/ single,
continuous for what birth will you seek of it?/
How, whence increased? From not being I shall not
allow/ you to say or to think for not to be said
and not to be thought/ is it that it is not. And
indeed what need could have aroused it/ later
rather than before, beginning from nothing, to
grow?/ Thus it must either be altogether or not
at all./ 1. Translations are from Coxon, A. H.
2009. The Fragments of Parmenides A critical
text with introduction, translation, the ancient
testimonia and a commentary. Revised and expanded
edition with new translations by Richard
McKirahan. Las Vegas/Zurich/Athens Parmenides
Publishing.
28
From Parmenides Poem continued Nor ever from
not being will the force of conviction allow/
something to come to be beyond it on account of
this neither to be born/ nor to die has Justice
allowed it, having loosed its bonds,/ but she
holds it fast. And the decision about these
matter lies in this/ it is or it is not but it
has in fact been decided, just as is necessary,/
to leave the one unthought and nameless (for no
true/ way is it), and ltit has been decidedgt that
the one that it is indeed is genuine./ And how
could What Is be hereafter? And how might it have
been?/ For if it was, it is not, nor if ever it
is going to be/ thus generation is extinguished
and destruction unheard of.
29
Zenos Four Paradoxes of Motion Two based on
Space Achilles and the Tortoise In a race, the
quickest runner can never overtake the slowest,
since the pursuer must first reach the point
whence the pursued started, so that the slower
must always hold a lead. Aristotle, Physics,
VI9, 239b15 Dichotomy paradox That which is in
locomotion must arrive at the half-way stage
before it arrives at the goal.Physics, VI9,
239b10. The result is that locomotion can never
begin. Note Both these paradoxes presume that
the points referred to are part of the whole
space to be traversed. If we assume they have no
extension in space nor duration in time the
paradoxes dissolve.
30
Zenos Four Paradoxes of Motion One based
onTime The Arrow If everything when it occupies
an equal space is at rest, and if that which is
in locomotion is always occupying such a space at
any moment, the flying arrow is therefore
motionless. Aristotle, Physics VI9,
239b5 Note This paradox presumes that a whole
expanse of time may be divided into parts which
are moments during which an object is in a
position. If we assume, a position in time has no
duration, the paradoxes dissolve. Zeno paradoxes
rely upon types of whole/part relations. 2.
Parmenides, in his poem, derives the
consequences regarding whole/part, single/many,
continuous/discrete, generated, increased, etc.
from it is. and from it is not being
unthinkable. The logic of his poem is analogous
to the method of inquiry he proposes in the
Parmenides consequences that befall various
fundamental opposites given A and not-A.
31
Parmenides Proposes How To Investigate Whether
and How There Are Forms p. 370, 136-C PARMENIDES
If you like, said Parmenides, take as an
example this hypothesis that Zeno entertained if
many are, what must the consequences be both for
the many themselves in relation to themselves and
in relations to the one, and for the one in
relation to itself and in relation to the many?
And, in turn, on the hypothesis, if many are not,
you must again examine what the consequences will
be both for the one and for the many in relation
to themselves and in relation to each other. And
again, in turn, if you hypothesize, if likeness
is or it is not, you must examine what the
consequences will be on each hypothesis, both for
the things hypothesized themselves and for the
others, both in relation to themselves and in
relation to each other. . . .
32
Problem with Parmenides Plan of
Investigation The plan of the Deductions is such
that they rely on a condition where the
consequence is a denial of a feature and its
contrary. If the one is, for example, then it is
not the case that it is at rest and it is not the
case that it is in motion, etc. But this involves
a methodical fallacy of deriving a contradiction
by denying contraries. You can get a
contradiction by affirming two contraries but not
by denying them. Suppose I say that If the
number 4 exists, then it is not at rest and it is
not in motion. From that I cannot conclude that
the number 4 does not exist. 1. Quoted very
closely but not verbatim from Rickless, Samuel,
"Plato's Parmenides", The Stanford Encyclopedia
of Philosophy (Winter 2012 Edition), Edward N.
Zalta (ed.), URL lthttp//plato.stanford.edu/arch
ives/win2012/entries/plato-parmenides/gt.
33
Problem with Parmenides Plan of Investigation
continued Thus there is an error in supposing
that the contraries are such that one or the
other must be true of the subject. Thus some
large part of the features that are used to argue
against that the One is, or is not, will not
apply to the Forms, because, as for example, with
rest and motion, rest and motion do not apply to
intellectual objects, but rather only material
objects. There are in fact two ways that the
denial of contraries does not apply 1) if there
is a middle, Note Plato worries about such in
Symposium 202B about state in between gods and
mortals, or pleasure and pain in Philebus --
pleasure and pain might have, as Plato but not
Aristotle thought, a middle state which is
neither pleasurable not painful. 2) the
contraries no longer apply to the subject, e. g.
odd/even no longer applies to irrational numbers,
or rest/motion to intellectual objects.
34
Parmenides, Second Part (137C-166C) Survey of
the Deductions Hypothesis 1 (137C-142A). General
logical form If the One is, but is not a whole
with parts, then it is not F and not the contrary
of F. F stands for many features and their
contraries, such as being many (contrary, being
one) whole (contrary, part)1 limited (contrary,
unlimited) shape (contrary, opposite shape)
motion (contrary, rest) sameness (contrary,
difference) being older (contrary, being
younger) knowable (contrary, being unknowable),
etc.   NOTE 1 This hypothesis was appropriated
in Neo-Platonic interpretations. NOTE 2 Platos
introduction of the notion of the whole/part
dichotomy plays a central role the reductiones ad
absurdum in Parmenides II. But Plato would
likely deny that the Forms are subject to the
whole/part distinction. Even so, Hypothesis I
presumes that (i) anything that has parts is
many (ii) a whole is a thing with parts from
which no part is missing.
35
Parmenides, Second Part (137C-166C) The Plan of
the Deductions continued   Hypothesis 2
(142B-155D) In this hypothesis the One is said
to be able to partake of Being. Parmenides
immediately then derives that the One allows for
the part/whole distinction. Even though this
contrary would not be allowed in the description
of Forms in the Middle dialogues, this
hypothesis, where the One would count for
concept, types, universals of some sort let
alone Forms -- would have to be supported to
allow for rational discourse in general. Again,
it is assumed that the one has parts and that the
one is a whole. PARMENIDES 142D, p. 376 . .
. If we state the is of the one that is, and
the one of that which is one, and if being and
oneness are not the same, but both belong to the
same thing that we hypothesized, namely, the one
that is, must it not itself, since it is one
being, be a whole, and the parts of this whole be
oneness and being?  NOTE In The Republic the
Form of the Good is beyond Being 509B p.
1130 Therefore, you should also say that not
only do the objects of knowledge owe their being
known to the good, but their being is also due to
it, although the good is not being, but superior
to it in rank and power.
36
The Greater Mysteries in the Symposium 210A-212C,
p. 492-4
210E3- 211B6 Original 210E3-211B6 (almost) literal translation
??d? p??? µ?? t? ?a???, p??? d? t? a?s????, ??d ???a µ?? ?a???, ???a d? a?s????, ?? t?s? µ?? ?? ?a???, t?s? d? a?s???? ??d a? fa?tas??seta? (5) a?t? t? ?a??? ???? p??s?p?? t? ??d? ?e??e? ??d? ???? ??d?? ?? s?µa µet??e?, ??d? t?? ????? ??d? t?? ?p?st?µ?, ??d? p?? ?? ?? ?t??? t???, ???? ?? ??? ? ?? ?? ? ?? ???a?? (b.) ? ?? t? ????, ??? a?t? ?a? a?t? µe? a?t?? µ???e?d?? ?e? ??, t? d? ???a p??ta ?a?? ??e???? µet????ta t??p?? t??? t????t??, ???? ?????µ???? te t?? ????? ?a? ?p????µ???? µ?d?? ??e??? µ?te t? p???? µ?te ??att?? ????es?a? µ?d? p?s?e?? µ?d??. neither in relation to the beautiful/good, nor in relation to the ugly/base, neither only at its core the beautiful/good, nor at its core the ugly/base, and not for some people beautiful/good nor for others ugly/base nor yet will it appear to him beautiful/good such as in a face, nor hands, nor anything else belonging to the body, nor yet some word, nor some knowledge, nor as being in some other thing, such as in an animal, or on the earth, or in the heavens, but itself, according to itself, with itself, always being of one kind, and the other beautiful/good things partake of it in such a manner, that although they come to be and perish, never does it become more nor less, nor yet is ever changed.
37
 Parmenides, Second Part (137C-166C) The Plan of
the Deductions Hypothesis 2A, (155E-157B),
Appendix to Hypotheses 1 2 Consideration of
Becoming in Time Becoming is not a feature F and
not the contrary of a feature F. Arguments rely
on impossibility of change between motion and
rest and vice versa. The Appendix purports to
show that the Conclusions of Hypothesis 1 2
together entail that, for a range of properties
F, if the one is, then there is a moment outside
of time (the so-called instant) at which the
one changes from being F to being con-F.
Rickless observes that all of the Arguments of
the Appendix depend for their soundness on there
being times T1 and T2 such that T1 is distinct
from T2 and the one partakes of being at T1 and
the one does not partake of being at T2. But this
premise depends for its soundness of Hypothesis 1
that the one does not partake of being. And the
soundness of the One not partaking in Being
depends the Purity condition. So if the Purity
condition holds, then all the Arguments of the
Appendix become unsound.1 1. Rickless, Samuel,
"Plato's Parmenides", The Stanford Encyclopedia
of Philosophy (Winter 2012 Edition), Edward N.
Zalta (ed.), URL lthttp//plato.stanford.edu/arch
ives/win2012/entries/plato-parmenides/gt.
38
 Parmenides, Second Part (137C-166C) The Plan of
the Deductions   Hypothesis 3 (157B-159B) This
hypothesis and the next addresses the majority of
arguments that Parmenides has brought to the
Socrates early working on the Theory of Forms
the relation possibly their participation --
of other things to the Forms PARMENIDES (157B,
p. 389) Must we not examine what would be proper
for the others to undergo if one is? We
must. Are we to say, then, what properties
things other than the one must have, if one is?
Lets do. Well then since they are other
than the one, the others are not the one. For if
they were they would not be other than the one.
Thats right. And yet the others are not
absolutely deprived on the one, but somehow
partake of it. In what way? In that things
other than the one are surely other because they
have parts for if they didnt have parts, they
would be altogether one. Note Assume that to
be other is to have parts, otherwise they would
be altogether one. Thus Hypothesis 3 assumes
Hypothesis 1.  
39
 Parmenides, Second Part (137C-166C) The Plan of
the Deductions   Hypothesis 4 (159B-160B)
PARMENIDES159B, p. 390, Well, then, suppose
we now concede those results as evident and
examine again, if one is Are things other than
the also not so or only so? Of course.
Lets say from the beginning what properties
things other than the one must have, if one is.
Yes. Lets do. Must not the one be separate
from the others and the others separate from the
one? Why? Because surely there is not
something else in addition to them that is both
other than the one and other than the others for
all things have been mentioned, since the one and
the others are mentioned. -- Yes, all
things. Note Assumes that the one others
the totality of all things. Seems reasonable
unless there are things that are both one and
other. Such a consideration would seem to suggest
that the elements of Parmenides arguments do not
involve entities that may be transcendent.
40
Parmenides, Second Part (137C-166C) The Plan of
the Deductions (continued) Hypothesis 5
(160B-163B) Note The alleged contradiction
depends upon conceiving non-Being as dependent on
becoming, as in Hypothesis 2a. Conclusion 163C,
p. 394 PARMENIDES Therefore also the one, if it
is one, comes to be and ceases to be, if it is
altered, and does not come to be or cease to come
to be, if it is not altered. And thus the one, if
it is not, both comes to be and ceases to come to
be, and does not come to be be or cease to come
to be. Yes, youre quite right.   Note Of
course we need not assume that the one is not
altered. If we dont, we are left with a cosmos
without Forms and a world of Becoming coming to
be and ceasing to come to be. Hardly an
impossible conclusion. But the problem remains
that if we admit the existence of concepts, types
or universals again let alone Forms this
hypothesis cannot be supported.
41
The Plan of the Deductions (continued) Hypothesis
6 (163B-164B) Given the One is not, and has no
sort of being. This hypothesis is the contrary of
Hypothesis I and results in the consequence that
the One has no character whatsoever. Conclusion
164A-B, p. 395 What about this? Can the others
be related to it, if, necessarily, nothing
belongs to it? They cant. So the others
are neither like nor unlike it, and they are
neither the same nor different from it. No,
they arent. And again will of that, to
that, something, this, of this, of another, to
another, or time past, hereafter, or now, or
knowledge, opinion perception, an account, a
name, or anything else that is be applicable to
what is not? It will not. Thus one, since
it is not, is not in any state at all. At any
rate, it seems to be in no state at all. Note
This argument would seem to lead to the
conclusion, that if there is to be a world at all
some form of oneness, perhaps even as concepts,
universals, types, must exist.
42
Parmenides, Second Part (137C-166C) The Plan of
the Deductions (continued) Hypothesis 7
(164B-165E) Given the One is not, means nothing
that is one thing exists, then the Others can
only be masses or bulks and will only have
appearances of some feature Fs. Note This
would suggest a material cosmos in which, thanks
to unavoidable human misperception, we think we
see and think about things. But those things are
mere appearances. What actually exists are bulks
or masses o perhaps bulks and masses of quanta
might be exemplified by a current scientistic
metaphysical view. But of course however this
scientistic view might be supported, it is
inconsistent because, quanta, or photons, are
understood as a type which would return us to
Hypothesis 2.  
43
Parmenides, Second Part (137C-166C) The Plan of
the Deductions (continued)   Hypothesis 8
(165E-160B) If the One is not, means no one
entity exists, even an entity which is a bulk or
a mass, then the Others cannot even appear as
having one or many, or any character. So nothing
will have any being whatsoever. Therefore, once
again one may say this hypothesis leads to not
some feature F and the contrary of some feature
F, just because there is nothing to have either F
or the contrary of F. Rickless notes that
Taken together, Hypothesis 7 and Hypothesis 8
establish that the one is. Its argued that if
the one is not, then the others are many. Its
also shown that if the one is not, then the
others are not many. Thus Hypotheses 7 8 show
that if the one is not, then the others have
contradictory properties. Given that nothing can
have contradictory properties, it follows
directly that the one is. This reinforces the
result previously established in Hypothesis
6.1 1. Rickless, Samuel, "Plato's Parmenides",
The Stanford Encyclopedia of Philosophy (Winter
2012 Edition), Edward N. Zalta (ed.), URL
lthttp//plato.stanford.edu/archives/win2012/entrie
s/plato-parmenides/gt.
44
Interpretations of the Parmenides  I A Record of
Socrates Perplexities about How to Understand
the Relation of What Will Later Be Called
Universals, Types or Essences to the Multitude of
Things.1 Plato's set out to put forward
difficulties for the theory of forms that he
himself did not, at least at the time he wrote
the dialogue, see a way to resolve. But
Parmenides does say as he is proposing his method
that a very gifted man should be able defend
the existence of the forms, and thereby explain
the possibility of dialectic, through the very
method Parmenides applies in the second part of
the dialogue. 1. see Vlastos (1954, 343) Gill
(1996) Allen (1997).
45
Interpretations of the Parmenides  II Theory of
Forms Comes Out in Tact If a Distinction Is Made
Between Platos Writing a Phrase Meaning
Definitionally True and his Writing a Phrase
Meaning Displays a Feature of Being --- The
most influential version of this view belongs to
Meinwald (1991 1992) and Peterson (1996 2000
2003). According to Meinwald, Plato meant us to
recognize the invalidity of Parmenides'
criticisms of the theory of forms by having us
focus on the in-relation-to qualifications that
are supposed to serve as one of the principles of
division that explain the fact that the second
part takes the shape of eight separate
Deductions.
46
Interpretations of the Parmenides  II These
qualifications, properly understood, reveal that
subject-predicate sentences (of the form X is
F) are ambiguous to say that X is F is to say
either that X is F in relation to itself (i.e.,
pros heauto) or that X is F in relation to the
others (i.e., pros ta alla), where to say that X
is F pros heauto is to say that the F is
definitionally true of X, and to say that X is F
pros ta alla is to say that X displays the
feature of being F. As Meinwald argues, if Plato
meant us to recognize the existence of such an
ambiguity, then he probably meant us to recognize
that self-predicational sentences (of the form
The F is F) are also ambiguous, and that the
ambiguity of such sentences reveals that the
Third Man argument and the Greatest Difficulty
commit the fallacy of equivocation.
47
Interpretations of the Parmenides  III The
Discerning Reader Would Understand that
Parmenides Criticisms are Effective Only on the
Mistaken Assumption that Forms are Fundamentally
Similar to the Material, Sensible Things that
Participate in Them.  Miller (1986), for
example, argues that the point of the dialogue is
to help the discerning reader see the forms for
what they really are, transcendent beings that
should be accessed by reason rather than with the
help of categories drawn from sense experience.
48
IV Parmenides II Reveals That Many Features of
the Forms Hold Up To the Scrutiny of Parmenides
Eightfold Analysis. But Certain Features of Forms
Must Be Dismissed. Ricklesss View1 Whether
combined with the Pie Model conception of
partaking or with Paradigmatism, Plato's middle
period theory of forms is internally inconsistent
if taken at face value. However, if three
principles are abandoned inconsistencies are
eliminated. Causality, Separation,
Self-Predication, and Oneness hold up under the
test of the analyses in the Parmenides. But
Purity, Uniqueness, and No Causation by
Contraries must be abandoned. 1. Rickless,
Samuel, "Plato's Parmenides", The Stanford
Encyclopedia of Philosophy (Winter 2012 Edition),
Edward N. Zalta (ed.), URL lthttp//plato.stanfor
d.edu/archives/win2012/entries/plato-parmenides/gt.

49
Platos Timaeus on Fire Itself 51D So heres
how I cast my vote If understanding and true
opinion are distinct, then these by themselves
things definitely exist-these Forms, the objects
not of our sense perception, but of our
understanding only. But if as some people
think-- true opinion does not differ in any way
from understanding, then all the things we
perceive through our bodily senses must be
assumed to be the most stable things there are.
But we do have to speak of understanding and true
opinion as distinct, of course, because we can
come to have one without the other and the one is
not like the other. It is through instruction
that we come to have understanding, and through
persuasion that we come to have true belief.
Understanding always involves a true account
while true belief lacks any account. And while
understanding remains unmoved by persuasion, true
belief gives into persuasion. And of true belief,
it must be said, all men have a share, but of
understanding, only the gods and a small group of
people do.
50
Platos Timaeus on Fire Itself 51D Is there
such a thing as a Fire by itself? Do all these
things of which we always say that each of them
is something by itself really exist? Or are the
things we see, and whatever else we perceive
through the body, the only things that possess
this kind of actuality, so that there is
absolutely nothing else besides them all? Is our
perpetual claim that there exists an intelligible
Form for each thing a vacuous gesture, in the end
nothing but mere talk? Now we certainly do not do
justice to the question before us if we dismiss
it, leaving it undecided and unadjudicated, and
just insist that such things exist, but neither
must we append a further lengthy digression to a
discourse already quite long. If, however, a
significant distinction formulated in a few words
were to present itself, that would suit our
present needs best of all.
51
References for slides used in this powerpoint
Slide3, bust of Parmenides http//www.volker-do
ormann.org/parmenides.htmhttp//platosymposium.fil
es.wordpress.com/2009/04/framing-narrative41.jpg S
lide 4, portrait, Zeno shows the doors to
Truth http//en.wikipedia.org/wiki/Zeno_of_Elea
mediaviewer/FileZeno_of_Elea_Tibaldi_or_Carducci_
Escorial.jpghttp//de.wikipedia.org/wiki/Aristopha
nesmediaviewer/FileAristofanes.jpg