Sorglose Nacht

Overview

Critical interpretation of this dialogue varies more widely than with any other. The general structure works like this:

1. Introduction / Socrates’ Speech
2. Problems with the Theory of the Forms (4, generally understood to be scathing)
3. How to Save the Forms: The (8) Deductions.

There are a lot of notes internally here. The gist of it is that Socrates is reliant on a middle period Platonic conception of the forms. Parmenides tries to save it. Critical assessment of his success and what this meant to Plato is noted in overview at the end of this outline.

The Setup

CEPHALUS arrives at Athens from Clazomenae with some of his countrymen. ADEIMANTUS welcomes him. They ask Adeimantus to take them to his half-brother, ANTIPHON, who they wish to recall a conversation which took place between a young SOCRATES, ZENO (40ish), and PARMENIDES (old, 65) many years ago.

Introduction

1. Zeno is giving a lecture in Athens. At the end of the lecture, Socrates asks Zeno to clarify, and Zeno maintains each division of his treatise is an argument to (negatively) prove the unity of Being: “if being is many, it must be both like and unlike, and that this is impossible.”
   1. Socrates notes that Parmenides (present) affirmed that “the All is one” positively, and Zeno echos his sentiment here negatively. “You affirm unity, he denies plurality.” Zeno affirms that he is defending Parmenidean monism to its many opponents.

Background

1. Socrates now, under the guise of asking a question, begins to articulate the distinction between the sensible (particular) things, and the Forms (universals).
   1. “Participate-things” (particulars) participate in both likeness and unlikeness. They (things) are both (like and unlike) by degree.
   2. This does not imply, though, that “…the absolute one [is] many, or the absolute many one…” - “if a person shows that such things as wood, stones, and the like, being many are also one, we admit that he shows the coexistence the one and many, but he does not show that the many are one or the one many; he is uttering not a paradox but a truism.”
   3. Parmenides now asks Socrates if he believes that there are particulars and also universals (ideas and things that partake in them).

Socrates’ objection is based on the theory of the Forms based on Plato’s Middle Dialogues.

The Arguments

1. ARGUMENT 1: The Paradox of the Singular Plural

   Overview: If particular things come to partake of the Form of Beauty or Likeness or Largeness they thereby become beautiful or like or large. Now each particular thing must receive either the whole of the Form of which it partakes, or a part of that Form. Either way, however, the Form becomes many - in the first case by multiplication, in the second by division - and thus will not still be one.

   1. Socrates affirms that there are absolute ideas of things like the Good, the Beautiful, etc. but not of things like hair, mud, and dirt. On the question of whether there is one for “man”, Socrates is undecided. He even wavers about dirt, etc.
   2. Parminedes confirms that Socrates is suggesting that particulars participate in universals (”partake of them”). Further, Socrates must admit, he thinks that each Idea is one, and is simultaneously apparently in each one of the many. Parminedes suggests that this is a paradox.
      1. (a)&(b) may also constitute a separate argument: “The extent of forms”.
   3. Socrates suggets that Ideas are more like the day, “is one and the same in many places at once, and yet continuous with itself.” They thus continue to discuss the potential for an Idea to be both whole and divided into pieces (as it’s found in particulars).
   4. Argument 1: The Paradox of the Singular Plural
      1. They confirm to themselves that these Ideas must be divisible, because it would be impossible for each particular to possess a whole Idea. This would imply that the Idea was multiple (multiply-instantiated). [Sail]
      2. They deny the possibility that things are (e.g.) great in virtue of possessing a framgment of the whole of the Idea. This would imply that the whole was multiple (divided and distributed). [Greatness, etc.]
      3. Socrates concedes that this is indeed a paradox.

2. ARGUMENT 2: The Third Man Argument

   Overview: Socrates’ reason for believing in the existence of a single Form in each case is that when he views a number of large (for example) things, there appears to be a single character which they all share, viz. the character of Largeness. But consider the series of large things: x,y,z, Largeness Itself. If all members of this series partake of a single Form, it must be the Form Largeness Two. Similarly, x,y,z, Largeness and Largeness Two must all partake of a further Form, Largeness Three, and so on ad infinitum. Hence, instead of there being one Form in every case, we are confronted with an indefinite number.

   1. Parmenides begins by apparently introducing a dialectic in which:
      1. He suggests that inductive reasoning leads Socrates to his conclusions about Ideas. Socrates sees great things, and their common greatness helps him to reason that they participate in one absolute Greatness.
      2. However, Parmenides suggests, when you combine the Absolute Greatness above with the particulars which participate in it, it seems that their unity constitutes a greatness even greater than Absolute Greatness.
      3. This seems to introduce an infinite regress.
   2. Socrates responds that “the ideas are, as it were, patterns fixed in nature”. That is, they aren’t thoughts, per se. Things “assimilate” to them.
   3. Parmenides then says that if Ideas are discernable in things via some “assimilation”, then Ideas must at least resemble the things that assimilate to them. This is what would provide the condition of recognizability.
   4. But this co-likeness between Ideas and things assimilating them again suggests a “higher” likeness, which again leads to an infinite regress.
      1. Assuming non-contradiction of Forms, this infinity contradicts Oneness.
      2. (c)&(d) may also constitute a separate argument: “The likeness regress”.

3. ARGUMENT 3: Animism versus the Empty Thought

   Overview: To the suggestion that each Form is a thought existing in a soul, thus maintaining the unity of the Form, Parmenides replies that a thought must be a thought of something that is a Form. Thus we still have to explain the participation relation. Further, if things share in Forms which are no more than thoughts, then either things consist of thoughts and think, or else they are thoughts, yet do not think.

   NOTE: Chronologically, This argument takes place between (3a) and (3b) above.

   1. Socrates tries to suggest that Ideas are simply mental states (not things - they are without “proper existence”).
   2. Parmenides tells him that all thoughts are thoughts of something (which is a singular form or nature, and thus apprehended as one).
   3. And this would entail that everything was thinking, or that there were thoughts with no object. Both of which seem wrong to Socrates.

4. ARGUMENT 4: The Separate Domains Argument

   Overview: The gravest difficulty with the theory of Forms arises as a consequence of the assertion of the separate existence of the Forms. Forms do not exist in our world but have their being with reference to one another in their own world. Similarly, things of our world are related among themselves, but not to Forms.

   All our knowledge is such with respect to our world, not to the world of the Forms, while ideal Knowledge is knowledge of the things not of our world but of the world of the Forms. Hence, we cannot know the Forms. What is more, the gods who dwell in the divine world, can have no knowledge of us, and nor can their ideal mastership rule us.

   1. Parmenides now cites his greatest difficulty, “If an opponent argues that these ideas, being such as we say they ought to be, must remain unknown, no one can prove to him that he is wrong…” (note that this seems to mirror the problem of arguing against Kant).
   2. Socrates must agree that in order for Ideas/essences to remain absolute, they cannot exist in us. This would make them finite.
   3. Parmenides’ example: A master and a slave. “Mastery” and “slavery” are only meaningful in relationship to one another - as abstract ideas. They have nothing to do with the two men, at least not absolutely.
   4. Which is to say that:
      1. We can’t have access to the absolute Ideas. We can’t know “the nature of the beautiful in itself, and of the good in itself, and all other ideas which we suppose to exist absolutely.”
      2. Parmenides also suggests that since the converse is true: “the ideas are not valid in relation to human things; nor human things in relation to them; the relations of either are limited to their respective spheres.”
         1. No terrestrial master is master of Slave itself, and no terrestrial master-slave relation has any relationship to the ideal Master-Slave relation. And so it is with knowledge.

         Thus, the idea that their is a relationship of exclusivity between the two denies God knowledge.

   5. Further, the inaccessibility of Formal knowledge eradicates the possibility of any real success in philosophy. (I think this is actually Hegel’s critique of Kant’s moral philosophy as well - “all formalisms are empty.”)

The Exercise

5. Parmenides now recommends that Socrates try an exercise. Here, it seems clear that although
   Socrates has failed to prove his doctrine to Parmenides’s satisfaction, Parmenides buys it
   anyway, and thinks that Socrates is just too young to argue it correctly.
   1. He suggests that Socrates attempt to disprove Zeno’s argument negatively (as opposed
      to positively - see [2] above) - that is, to extrapolate the consequences to the one
      and the many in relation to themselves and each other on the opposite of “the
      hypothesis of the being of the many”. [Presumably here, the hypothesis of the being
      of the one.]
   2. Socrates demurs, and reciprocates the request. Parmenides says he’s too old, then
      Socrates asks Zeno, who asks Parmenides again, who now agrees. Parmenides will
      demonstrate this technique based on his own hypothesis - the being of the one. He
      will extrapolate the consequences of affirming and denying this hypothesis.
      Parmenides will dialogue now with Aristoteles.

The Deductions

These all run similarly, and they’re all dry, so after the first deduction, we’re just going
to paste the conclusions in from the SEP.

6. THE FIRST DEDUCTION

   (D1) If the G is, then the G is not F and not con-F (in relation to itself and in relation to the others).

   1. The if the One exists, it can’t be a part or a whole (wholes necessitating parts and vice versa) - which means also that it would be infinite in time (beginning, end, etc. being parts).
   2. The One is thus unlimited by time, and for similar reasons unlimited by space (reminiscent of Kant’s ‘container’ hypothesis in the trancendental deduction of space).
   3. Further, then, the One cannot “move”, which is to say, it cannot come into being (this being a process constrained by space and time). It is immovable, and it is nowhere. Since it is nowhere, it is not “in the same”, since it can’t be anywhere, and hence it is likewise never in the same place. This implies that it is never at rest. One “is neither rest nor in motion.”
   4. Neither will it be the same (with itself, another) nor other (than itself, another). The second part of this gets handled first, and then the first: “Neither will it be other than other, while it remains one; for not one, but only other, can be other than other, and nothing else.” Which is to say, I guess, that its oneness would be divided by the relationship to any other. Further since anything that becomes the “same” with the many, becomes many. Hence, if there were no difference between oneness and sameness, this would violate the Purity of Forms hypothesis. (Oneness would be both oneness and sameness.)
   5. Thus we have determined that: the the one is not different from itself, the one is not the same as another, the one is not different from another, the one is not the same as itself, the one is not like another or itself, and the one is not unlike itself or another.
   6. Continuing, we find that the one cannot be equal or unequal to itself or others, nor can it be greater or less than itself or others, nor can it be older, younger, or the same age as itself or others.
   7. Finally, the one - since it cannot partake of being (be the subject of predication) cannot be in time. Thus it neither comes to be nor ceases to be, and hence does not partake of being. Thus the one is not, and it is not one. Hence, the one is not named, expressed, opined, known, or perceived. However, this cannot be.

7. THE SECOND DEDUCTION

   (D2) If the G is, then the G is F and con-F (in relation to itself and in relation to the others).

   1. If the one is, then the one partakes of being, the one is not the same as being, the one is a whole, being and the one are parts of the one, the one is infinitely many.
   2. The argument from one admitting all numbers: the different is not the same as the one, the different is not the same as being, the one has parts, the one is a whole, the one is limited, the one is unlimited.
   3. Then (”can anything be a whole without these three?”) the one has a beginning, a middle, and an end. Which implies that it has a shape. And, in containing its parts, it is thus in itself (and thus not nowhere) and thus in another [the whole is not in the parts]. Since in itself and in another, the one is always both at rest and in motion.
   4. And by these relations, the one is the same as itself, the one is different from itself, the one is different from the others, the one is the same as the others, the one is like the others, the one is unlike the others, the one is like itself, and the one is unlike itself.
   5. Further, being in itself it cannot touch others, but being in others, it can. Since the one cannot be next to itself (be two), however, it cannot touch itself. And since its other cannot be it (one), consequently, they cannot have number, which means that the one is alone, and cannot touch an other
   6. Now, by Purity-F, greatness and smallness cannot be in oneness, but also, everything must either be in the one or the others (one of these must contains them). In consequence, the one is equal to itself, the one is equal to the others, the one is both greater than and less than itself, the one is unequal to itself, the one is both greater than and less than the others, the one is unequal to the others, the one is more than, less than, and equal to itself in number, the one is more than, less than, and equal to the others in number.
   7. Further, the one must partake of time (being must be predicated of it), and from that: 1) The one comes to be older than itself, the one comes to be younger than itself, the one always is older than itself, the one always is younger than itself, the one is the same age as itself, the one is neither older nor younger than itself, the one neither comes to be older nor comes to be younger than itself. 2) The one is older than the others (as their condition), the one is younger than the others (them being its condition), the one is the same age as the others (being contained in each one), the one is neither older nor younger than the others, the one neither comes to be older nor comes to be younger than the others (materially), the one comes to be younger than the others (relatively), the one comes to be older than the others.
   8. Finally, since the one partakes of time past, future, and present, the one is and comes to be, was and was coming to be, and will be and will be coming to be. And thus it could be named and spoken of, as well as be the object of an account, knowledge, perception, and opinion.

8. THE APPENDIX TO THE FIRST AND SECOND DEDUCTIONS

   “The function of the Appendix is to show that the Conclusions of D1 and D2 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.”

   1. If the one is, then there are 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.
   2. There is a definite time at which the one comes to be, and there is a definite time at which the one ceases to be, there is a time at which the one ceases to be many, there is a time at which the one ceases to be one, there is a time at which the one is combined, there is a time at which the one is separated, there is a time at which the one is made like, there is a time at which the one is made unlike, there is a time at which the one is increased, there is a time at which the one is decreased, and there is a time at which the one is made equal.
   3. There is something (call it “the instant”) that is in no time at all and
      1. at which the one changes both from being in motion to being at rest and vice versa, and at which the one is neither at rest nor in motion
      2. at which the one changes both from not-being to being and vice versa at which the one neither is nor is not
      3. at which the one changes both from being one to being many and vice versa and at which the one is neither one nor many
      4. at which the one changes both from being like to being unlike and vice versa and at which the one is neither like nor unlike
      5. at which the one changes both from being small to being large and vice versa and at which the one is neither large nor small.

9. THE THIRD DEDUCTION

   (D3) If the G is, then the others are F and con-F (in relation to themselves and in relation to the G).

   1. If the one is, then the others are not the one, the others have parts, the others are a whole, the others are one, the whole and the part of the others are many, the whole and the part of the others are unlimited in multitude, the whole and the part of the others are unlimited, the whole and the part of the others are limited, each of the others is like itself, each of the others is like each of the others other than itself, each of the others is unlike itself, and each of the others is unlike each of the others other than itself.

10. THE FOURTH DEDUCTION

    (D4) If the G is, then the others are not F and not con-F (in relation to themselves and in relation to the G).

    1. If the one is, then the others are not one, the others are not many, the others are not a whole, the others do not have parts, the others are not like, the others are not unlike, the others are not both like and unlike, the others are not the same, the others are not different, the others are not in motion, the others are not at rest, the others are not coming to be, the others are not ceasing to be, the others are not greater, the others are not equal, and the others are not less.

11. THE FIFTH DEDUCTION

    (D5) If the G is not, then the G is F and con-F (in relation to itself and in relation to the others).

    1. If the one is not, then the one is different from the others, we have knowledge of the one, the one is different in kind from the others, the one partakes of something, that, and this, the one is unlike the others, the others are unlike the one, the one partakes of the unlike (i.e., has unlikeness) in relation to the others, the one partakes of the like in relation to itself, the one is like itself, the one is unequal to the others, the others are unequal to the one, the one partakes of the unequal in relation to the others, the one partakes of the large, the one partakes of the small, the one partakes of the equal, the one partakes of being, the one partakes of not-being, the one is in motion, the one is not in motion, the one is at rest, the one is altered, the one is not altered, the one comes to be, the one ceases to be, the one does not come to be, and the one does not cease to be.

12. THE SIXTH DEDUCTION

    (D6) If the G is not, then the G is not F and not con-F (in relation to itself and in relation to the others).

    1. If the one is not, then the one in no way is, the one in no way partakes of being, the one in no way comes to be, the one in no way ceases to be, the one is not altered in any way, the one is not in motion, the one is not at rest, the one does not partake of the small, the one does not partake of the large, the one does not partake of the equal, the one does not partake of the like, the one does not partake of the different, the others are not like the one, the others are not unlike the one, the others are not the same as the one, the others are not different from the one, none of the following (namely, of that, to that, something, this, of this, of another, to another, time past, time future, time present, knowledge, perception, opinion, account, and name) is applicable to the one, and the one is in no state at all.

13. THE SEVENTH DEDUCTION

    (D7) If the G is not, then the others are F and con-F (in relation to themselves and in relation to the G).

    1. If the one is not, then the others are, the others are other, the others are different, the others are other than each other, the others are infinitely many, each of the others appears to be one, each of the others is not one, the others appear to be infinitely many, some of the others appear to be even, others odd, none of the others is either even or odd, among the others there appears to be a smallest, each of the others (even the other that appears smallest) appears large in relation to its parts, each of the others appears to come to the equal, each of the others appears to have no beginning, middle, or end in relation to itself, each of the others appears unlimited in relation to itself, each of the others appears limited in relation to another, each of the others appears to be like itself and each of the others, and each of the others appears to be unlike itself and each of the others.

14. THE EIGHTH DEDUCTION

    (D8) If the G is not, then the others are not F and not con-F (in relation to themselves and in relation to the G).

    1. If the one is not, then none of the others is one, the others are not many, the others cannot be conceived to be either one or many.

Potential Interpretations

1. Parmenides’ criticisms are no more than a “record of honest perplexity”.
2. Plato means us to understand that Parmenides’ criticims are false in this way:
   1. The form of the deductions is always “in relation to G and in relation to F”)
   2. 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).
   3. This entails that Plato meant us to understand that self-predicational sentences (”The F is F”) are ambiguous. If this is the case, the Third Man Argument and the Greatest Difficulty are equivocal. However, it is provably false that even given a-c, the TMA always comes out fallacious.
3. Plato puts the reader in the position to recognize that Parmenides’ criticisms are effective only on the wrong-headed supposition that forms are fundamentally similar to the sensible, material things that partake of them. The point of the dialogue, on this view, 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. [Problem: There’s no textual evidence to support this.]
4. What Parmenides’ criticisms reveal is that, whether combined with the Pie Model conception of partaking or with Paradigmatism, Plato’s middle period theory of forms is internally inconsistent. It turns out that there are three principles the abandonment of which would eliminate all inconsistencies apart from the Greatest Difficulty: Purity-F, Uniqueness, and No Causation by Contraries. Careful logical analysis of the second part of the dialogue then reveals that the Deductions establish not only that the forms posited by the middle period theory exist, but also that Purity-F, Uniqueness, and No Causation by Contraries are all false. It is then reasonable to suppose that Plato meant the reader to recognize that the proper way to save the forms is by abandoning these three basic assumptions. And, importantly, this can be done without abandoning the most important principles at the heart of the middle period theory, namely One-over-Many and Separation. The aptly-named Greatest Difficulty is then left as a challenge for future work.