Parmenides Dialogue
The Parmenides dialogue is known for being one of the most difficult to comprehend. Commonly it is divided into two parts. Knowledge of Parmenides poem is critical to understanding the dialogue, for the same approach to logic used here. The consequences of predicates are explored and everything must be of necessity. In the first part we are introduced to Antiphon meeting Glaucon and Adeimantus, who ask him to retell the meeting of the philosophers Parmenides and Zeno with a young Socrates. Antiphon was not a witness to it in person, but has memorized it from the witness Pythodorus which was present. Zeno has just reiterated his criticism of "many" over "one". If things are many then it would hold opposite properties simultaneously, which is contradictory. To resolve this conflict Socrates brings up the forms. Everything with a property has a share of the form of that property, of which many gets a share of contradicting forms. He argues that reasoning with abstract forms is superior to using concrete things which change. In one act one could reason about a thing as singular and in the next divide it, which is not possible with the forms. It can be likened to making proofs for natural numbers themselves than with 4 and 9 specifically. Parmenides then starts critiqueing the forms and their function, showing that Socrates is still a novice. Are there forms of everything or just higher concepts? There is a form of beauty, but is there also one of mud and hair? Socrates is sure of the former but not the later as those are clearly derived from the senses than reason. How can the forms be partaken of? They cannot be wholly possessed as multiple things would need to possess it. And how can they be divided? How could say the form of smallness be divided if it itself is the smallest? The forms can be possessed neither in whole or parts.
Interestingly during his dialogue with Parmenides, Socrates posits that the forms could reside in thought only. Parmenides refutes it, the thoughts must be of something outside of thought. I find this short segment interesting since it posits a conceptualist position long before Abelard.
Socrates suggests that the forms could be patterns that things merely resemble. But if a thing resembles a form, wouldn't the form also to an extent resemble the thing, necessitating a second form? This has been named the Third Man argument. During the grilling Socrates brings up a nominalist argument for the forms, that they only exist in thought. But how can things things that do not think partake of the forms then?
At this point the conclusions about the forms have caused some confounding consequences. The forms must be unknowable to humans, as they can neither possess them nor anything that resembles them. Foreseeing debates on transcendence and immanence, God must be ignorant of the sensual realm as God would only have perfect knowledge through the forms.
## Deductions The second part picks up with Parmenides congratulating Socrates on his philosophical aptitude but that he still has much to learn. He must be rigorous in his logical technique and explore all the consequences of his hypotheses, both the positive and the negative case. What follows are a series of deductions where Parmenides and Aristoteles (unrelated to Plato's student) rigorously explore the consequences of form of the one being one or many. Unlike previous dialogues this section is very terse and, if mathematical logic had existed in the time of Plato then this section would have employed it.
Each deduction starts with a different premise, but there is a common framework of what properties a thing must have:
Divisibility - Is the thing a unified thing with no parts? Or is it a whole composed of parts?
Shape - The thing must have a geometry and in turn be contained by something, possibly itself.
Motion - The thing must be in motion, at rest, or none.
Similarity - Is the thing similar to itself and to others? Or is it different or simply incomparable?
Time - Does the thing partake in time and age?
Intelegibility - Can the thing be named or even known?
The properties are approached in a manner that reminds me of relations in set-theory. Similarity is two-way but can also be reflexive, where a thing is similar to itself. Or a thing can simply not have that relation at all, neither similar nor different to itself or anything.
The deductions start with "common logic" such that the one must be individisble. But if the deduction reaches the conclusion that the one must be both single and multiple in paradox, then that is accepted in the confines of the deduction and the further consequences are explored. Perfect logic without paradoxes seems difficult to find here. Zeno mentions in the start of the dialogue that monism is simply less paradoxical than multiplicity, but not that its without what appears to be paradoxes and flaws. If we want to avoid paradoxes then we must accept that some axioms must be changed, for example that the monistic one must still have being even if it is one.
What can be said of this process? We are seeing a dialectic where a wise man explores the logical consequences of predicates. Socrates is much younger, by necessity of him being historically distant from the involved people in the dialogue, and his philosophy is also portrayed as starting to sprout. His usual irony and moral inquiries are not present.
## Thinking And Being, Dialectical Process The forms are meant to be entities outside the sensual realm which are the source of all qualities. They can be reached only through reason, not the senses. But thinking and being is not straight forward. We can think of non-sensical things, like dry oceans. But does that mean they they are? Then anything can have being in thought, even paradoxical things. Thinking of things that do not exist is impossible as one dialogue finds, for what that truely does not exist cannot ever be thought of and discussed to begin with!
Parmenides poem instructs one to think as things are. Thought could be divided into that which is how things are and how they are not. The deductions do not work on just any premise but the one, which is presumed to be a fundamental concept. The dialectic can then be seen as finding the correct path of thinking, as things are. Thats why the beginning had Socrates assert that there is a form of beauty, but that he was not sure about if there is a form for mud or hair. The first come from reasoning, the later are clearly derived by the senses. But if we distinguish ideas from reason and from senses, then how do we distinguish the truthful and untruthful ideas from reason?
Each deduction starts with a different premise. Successively the interlocutors exhaust the possible ways of thinking with each deduction. What if one is, and what if it is not? Eventually one premise must be judged more correct than the others and possibly the axioms one started out with have to be revised. But axioms come not from logic but are presupposed by our preconceptions of things ought to be. Can the process really be deeemed rational if built on these irrational axioms? Why must a thing partake in time, be divisible or indivisible, be in motion or at rest, etc? These are presumed to be required of things that are. There is a limit to the fruits of logic.
## The One The one, in form and concept (whats even the difference?) is central to the dialogue. Parmenides and Zeno were philosophical monists. The dialogue appears to have been held in high regard by the neoplatonists and considered to be revealing the nature of the one. The first deduction where the one is simply a unity appears the least flawed compared to the one as a multiplicity. It is also the most similar to the reasoning in Parmenides poem.
From the deductions the one appears to be fundamental reality in enabling many qualities. Many is impossible without the one. Division and distinction depend on the one, and in turn thought and knowledge depend on these. To grasp things intellectualy things must be divided to allow comprehension of the qualities of the parts. Coherence itself is unity. The one is what sets limits on the infinite.
# Deduction 1 Parmenides and Aristotle engage in dialogue for the first deduction about the consequences of the one.
## Division The one is not many. It cannot have parts, and neither is it a whole as that would imply a whole of parts. It cannot have a beginning, a middle or an end. It is truly indivisible.
## Motion Without parts it cannot occupy space or location, It is shapeless and cannot be contained by anything. It cannot be in motion or at rest. For without parts motion cannot be facilitated by parts changing location. If the one is whole and moves by being in one location for one time and another location the next, it would either need to exist in two places at one between movements or cease to be between places. And how can something that has ceased to be become again?
## Comparison Comparison is impossible with the one, it can neither be the same as itself or another, nor can it be different from another or itself. It cannot be the same as itself as that would be the property of the "same", where two things end up one. This is not a property of the one. One is not different from another, because it is one and not with another.
When a thing is the same as another, they do not end up one. Thus the one cannot be the same as it itself, for it would not be one. It cannot be different to others or to itself.
The one is immeasureable, for there are no parts to measure.
## Time The one is outside of time, as it cannot be different from itself from one moment to the next as age is. But time seems to be required for being. If has not been, is not currently, and will not be, then it is not at all?
## Intellegibility The one is unknowable, unnamable and unperceivable.
# Deduction 2 The second deduction, by far the longest, revises the one to be the union of oneness and being. As said by Zeno/Parmenides ealrier, unity proves far less paradoxical than multiplicity. The one comes to possess oppossing qualities simultaneously just as it possesses none of them. The incoherence is not limited merely to this definition of the one, but the deduction implicitly puts doubt of the qualities themselves that we test the one with. For example relative difference seems implausible to explain with the forms. If things are different, they partake in the form of difference, which is a similarity between them.
## Composition One is composed of oneness and being, two parts forming a whole. The one is now a multitude. Sometimes in the deduction it seems that one and oneness are the same and that the one recursively posseses itself. The former should be the whole of being and oneness while the later is merely the quality of oneness, which by itself was deemed insufficient in deduction 1.
If one is composed of oneness and being, then both parts must always be joined by the other. Howver we can think of and say the parts separately, "oneness", "being". Then "oneness" also contains being and "being" also contains oneness, infinite regression. This infinite regression consequence from thinking is only valid if all possible thoughts have to be considered. However just because one is thinking logically does not mean that one is thinking truthfully, as the axioms of the framework must be truthful before logic can be. We must think of things "as they are", and mere possible thought is not an argument. This infinite regression is not just because we can think of it, and we shouldn´t. However this problem from multiplicity and union is one of many in the deduction. Parmenides had good reasons to limit what is to itself.
## Containment Being a multitude, the one must then have parts with a beginning, middle and end. The parts form a whole. The one must then contain all of its parts, and thus contain itself. But it must also not contain itself, as the one contains oneness and being neither of which are one. Thus the one must be "somewhere else".
Unifying a multitude is tricky, is a thing the same as its whole? Just as earlier, we can think of the one and the whole of the one separately. Are they the exact same thing? The one was declared to only have two parts, yet now it must also have three other parts of beginning, middle and end. Its hard to reconcile them to be the same, there is no order to oneness and being that can identify them with starts or ends. Containment is also tricky. Everything must be contained by something and a thing cannot contain itself. Perhaps one of the earlier axioms are actually false and must give. Something can actually contain itself or something can be uncontained. A theme of the dialogue is that paradoxes abound force us to make awkward concessions if we want logical systems.
## Motion Being in itself is argued to make the one to be at rest. But being not in itself or its parts but "somewhere else" supports being in motion, for what else can be described to a thing that is not where it is but motion?
## Similarity All things are either the same or different to the one, or a part or a whole of it. Since the one is not a part or the whole of itself, it must be the same as its not different from itself. As it is somewhere else than itself it must also be different from itself.
## Contact As the one is singular, it cannot be in contact with itself. But as it is somewhere other than itself, it must also be in contact with itself and others. The number of contacts is always one less than the number of objects, for at least one object.
## Magnitude Magnitude also proves paradoxal. Largeness and smallness are opposite forms that can never coexist in the same thing and can never be equal to anything. This proves troublesome for the multidinal one. The small can not be in the whole, for then it would be larger than the parts; neither can it be in the parts without being equal to them. The opposite goes for the large. Therefore the one has no magnitude and must be equal to the others without magnitude. But as the one contains itself it would also be bigger than itself, and also smaller than itself. A similar paradox goes for the measures of the one.
## Time Time is explore more in depth in this deduction. Being and time are highly interlinked. To be in the past, present or future a thing has to be. The pairing is interesting, wouldnt this actually mean that the one is tripartite? Oneness and being was said to be inseparable, shouldnt they also be joined by time? If the logical progression of this dialogue continues would we end up with having every quality and form to be inseparable and joined in the one?
Nothing can be at rest in time, there must be constant movement. As something moves through time it is becoming older than itself, which also makes it younger than itself. But since it passes through time in equal measures of time, it must be the same age as itself. No part goes faster than the other.
The previous deduction deemed movement difficult to conceive of without parts. Would it be that one part of the one moves to the future while the other is stuck in the present? Moving through time itself is tricky. Does a thing exist first in the past and then instantaneously in the present? If this is paradoxically unacceptable then is there a transitory state where a thing posesses none? But that then the thing would be outside of time, what could possibly impel it to then go back to time? What would make a thing then go from past to present and not skip ahead from past to future? The intermediate state is identical!
The principle "least things come to be first", is introduced to argue that the one must be older than the others. But the one only comes to be when its end is, forming the whole of the one, making the one older than the others. However its argued why the end of the one would come later than the ends of the others. The argumentation around the principle is shaky as smallness and largeness mentioned earlier would invariably come to be first and last in either case. And the principle is not justified for why it must be.
The one is argued to also come to be at the same time as its first part and the others, not waiting for the whole to be formed with the last part. This makes the one the same age as the others.
A quirk of time, if two things have a difference in age, that remains unchanged forever as time passes. But the fraction between them shrinks and a shrinking fraction of age difference results in the old becoming younger and the young becoming older.
## Intellegibility The deduction ends with the one hastily being declared to be intelligible, knowable and nameable.
# Deduction 3
The third deduction tackles the problem with the one possessing oppossing qualities. If a thing is deduced to have paradoxical properties, then perhaps time can resolve it by letting the thing have each opposing property at different times? Duology becomes trichotomy, for every two oppossing qualities there is now an intermediate where none are possessed. However, what would compel something outside of time to reenter it one way over the other, or at all?
# Deduction 4
Deduction 4 is concerned with the nature of the others if the one is. In set theory terms the complement to the one is being investigated. Parmenides eliminated others in his poem, but here they supposedly must be since the one is "somewhere else" than its whole and parts.
Things other than the one must have parts, since they are not one. This part of the deduction is a bit confusing as to what definition of the one is being used, for example D2 one itself had parts. Is it D1s definition, or just a conventional idea of what the one ought to be? [[Note, conventional idea of the one is in each deduction, not the previous ones worked in D1 and D2. How the one "ought to be"]]
All parts must be of a whole and not of many, otherwise the many would contain itself which is impossible. This assertion is also confusing given that self-containment was accepted earlier, or is it only accepted when logic says it must be so? The others are a disunitd multitude, multiple wholes. But what are the parts of wholes? If they are not wholes they must be one. Wholes also partake of the one by being singular. Then the one again is different from itself and other from itself.
Time and partaking of quality is brought up again. To partake of a quality a thing must not already parrtake of it.
The limits of the others are discussed but I find it hard to understand. The shape of the other starts where the one begins, but making any further elucidations of it is hard.
# Deduction 5:
Separation between the one and the others is the subject of the fifth deduction. Everything is contained in the one and everything not the one. The one is indivisible and does not have parts that the others can partake of. It become difficult for anything to be without partaking of the one. The others must be many, yet many cannot be without posessing the one in its parts. How could two be partaken of if not the one first?
# Deduction 6: The sixth deduction tackles the issue of non-being with the consequences of the one not being. Discussing things that are not is tricky, since the things clearly exist in thought and the discussion. Thinking is being. The truly non-existant is unknowable and unintellegible, and would never be discussed or thought of.
There is a similarity with the previous dialogue, where the consequences of the others being separate from the one is discussed, versus the one not existing.
"We say things that are" Discusses the difference between the one not being and the not-one being. Inversion of a complement. Through the dialogue the not-being one is found to still possess properties. A non-being is different from others and must then posess qualities to be different, such as likeness. Paradoxically the non-being must have and not have being. Here possessing opposing properties means changing between them, and change implies motion.
Again, Parmenides poem made sure to forbid the things that are not to avoid this. One must only think of things as they are, not as they are not. Nothing is never permitted to be.
# Deduction 7: The seventh deduction does another attempt at the non-being of the one, this time it absolutely does not partake of being. It never loses a share of being or receives it. Non-being posssesses no qualities nor interacts with anything. (No state at all)
(Why did non-being not comee to possess being this time? Just because they were adamant it did not?)
# Deduction 8: Revisit the properties of the others if one is not. The others will be a many composed of many. In an infinite recursion the fractal pattern never resolves into individual units but only furhter many. Measure becomes meaningless or impossible as the parts of many would be unending just like the whole. Limits cease as there can be no termination, thus parts like beginning, middle and end cannot be.
(Oneness is what permits thought to begin with. Without division, limits and distinction we cannot intellectually grasp things.) (Underlying theme, independence is difficult if not impossible, then it might be to conclude that one is all.)
# Final Deduction: Revises again the others if the one is not. The others will be not be one, for it is not, neither will they be many, for many cannot be without one. The others are neither many nor one, so they must be nothing. If one is not, nothing is.
# Notes:
The dialogue alleges that Zeno's book was published without permission.
If you read Parmenides poem and still doubt oneness, then reading this dialogue is like being repetedly hit in the head with the book.
What is the significance of this dialogue being told from someone memorizing the retelling of another witness? Phaedo and Symposium have the same narrative structure.