For a long time I've been interested in Zeno and Parmenides. Their arguments are integral to this notion I have about how conceptual thought introduces discrete divisions into a reality that is basically contiguous. It seems to me that the bottom line of Zeno's paradox of motion is that space itself is not divisble; only our metric of space bears division.
That's a pretty core belief of mine, and fundamental to my metaphysics. So I was taken aback when I recently looked at Plato's Parmenides. Socrates takes Zeno's argument and replies that there is no paradox in a thing being both singular and multiple at the same time. Things partake equally of the idea of singularity and the idea of multiplicity.
Now my thinking has been thrown into chaos. I submit to you philosophers, does it make sense to say that the same object is both singular and multiple at the same time?
That's a pretty core belief of mine, and fundamental to my metaphysics. So I was taken aback when I recently looked at Plato's Parmenides. Socrates takes Zeno's argument and replies that there is no paradox in a thing being both singular and multiple at the same time. Things partake equally of the idea of singularity and the idea of multiplicity.
Now my thinking has been thrown into chaos. I submit to you philosophers, does it make sense to say that the same object is both singular and multiple at the same time?
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Re: Parmenides
Thu, April 7, 2005 - 5:14 PMBarnaby:
I suggest you go look up the name "Georg Cantor" before disposing with the continuum.
I realize that "digital" space time is a popular modern day paradigm, but it seems to be popular for the same reasons that fluid mechanical descriptions of electromagnetism were popular in the 1800s: philosophers see the universe through the high technology of the day. There certainly seems to be no physical reason to suppose the universe is discretized at any length scale. Quantum mechanics certainly doesn't imply this, as is so often asserted.
I don't know anything about Plato's Permedides, however. I'm not real fond of Aristocles as a rule; he reminds me of the type of self-hating upper class college professor who fetishized the Soviet Union when it still existed. I suspect much of the folly of western philosophy originates with Plato.
-Lupo
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Re: Parmenides
Thu, April 7, 2005 - 5:15 PMI'm not a philosopher, so my two cents probably won't buy me much, but...
It seems that there are often seemingly conflicting models of phenomena that are equally valid. For instance, light can be modelled as either a particle or a wave, depending on context. Perhaps singularity and multiplicity depend more on context than on the innate qualities of a thing?
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Re: Parmenides
Tue, February 14, 2006 - 7:29 PMHmmm... Interesting. I have a completely different take on Parmenides and Zeno. Zeno's paradox is the confoundment of logic. Parmenides laid out a very elaborate logical argument of why your senses cannot be trusted, and why logic is the only way to reveal the truth about the way things are. Then Zeno comes along and shows that logic cannot be trusted either.
The problem (I think) with your interpretation of Zeno is that you are using his paradox to negate the idea of divisible space, when his examples require space to be infinitely divisible.
The result that I see of Parmenides and Zeno is to become an agnostic. If you cannot trust logic or the senses to be accurate, then the best we can do at any moment is guess.
Now, regarding the question of simultaneous singularity and multiplicity I think there are different ways to come at it. Depending on how you look at it, almost everything is singular and multiple simultaneously. You are a singular entity. But, you are made up of multiple parts. Likewise the universe is singular, though it is made of many (connected) parts. This is one level of thinking. Another would be to say that if the mind has trouble with the notion of simultaneous singularity and multiplicity it is because most minds are so bogged down in duality that they cannot see anything but separation, and perhaps once you can overcome that tendency towards unconsciously applying duality onto the world then you can see that what seems mutually exclusive is in fact not. And yet another way to deal with this issue would be to dissolve the whole problem altogether and say that Plato is wrong. There is no such thing as singularity or multiplicity. This would be the way of Zen and Taoism. We like to think of the cosmos as a unity, as a singularity, as one. Whereas this perspective would say not only "not two" (non-duality), but "not one, not two". -
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Re: Parmenides
Sat, April 8, 2006 - 3:21 AMHi,
I am new to this site and english is not my native language so please bare with my grammar and spelling misstakes. I believe it is a point of view. The problem is that we look upon existance and reality, whatever that means, as objects and events. But where does and object start and an event end? For example. When does the event birth of the object animal cat begin? Does it begin at the partuition? Or does it begin when the mother or the father of the cat came into being? There is not beginning to an event and there is no end, there is a flow of one event which we have divided into parts to make sense of the world. A cat would could then be seen as an event and we might call it the cating. That event would then flow into a cats corpse and we might call it corpsing. So when did the event cating begin? We can go as far back as to the ancestors to the cat which have their own ancestors which came from the ameba which arrived from the sun and the world coming into being, which came to being as the event universe had its course. So when did the event universing begin? And when does it end? Objects, events can be seperate and one. Depends how we look the question, which is missleading anyways.
Martin
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Re: Parmenides
Thu, June 29, 2006 - 10:31 PM>> Now my thinking has been thrown into chaos. I submit to you philosophers, does it make sense to say that the same object is both singular and multiple at the same time?
Ask Heraclitus. The majority of his philosophy revolves around this very idea. He answers your question by describing The Logos. -
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Re: Parmenides
Fri, June 30, 2006 - 12:12 AMWhat do you see in Heraclitus that illuminates this question? It's obviously something he's interested in, but I don't get a very sense of his answer from the fragments we have. Saying the river both changes and doesn't change doesn't really illuminate this question - it just asks it. -
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Re: Parmenides
Fri, June 30, 2006 - 4:12 PMUpon hearing an explanation of the Logos, people do not understand. We are no better off after hearing this Logos, yet it is through hearing this Logos that one becomes wise.
To illuminate means to bring what was dark into the light, thereby exposing what cannot be seen. What can be seen is seen only in relation to what cannot be seen. Sound is exposed silence, silence is hidden sound.
When I say "lemon" you experience a lemon. It isn't just a word in the mind, but an experience. It's a memory. When a person thinks about their favorite food, the mouth waters as if the food is really there. We experience what we hear.
When we see logos on products, we experience various images -- rugged, innovative, durable, clean, crisp, etc. Logos are like hosts for images. Logos are impregnated with experience. When we see, we experience.
Through seeing and hearing, one experiences and learns, but what one learns is ignorance, just as one hears a secret.
A circle is composed of an infinite number of points, each a simultaneous beginning and ending, but it is only one circle. It has an infinite number of tangents, but it is only one circle.
It is because of infinite change that the circle is at rest in its form. It stays true to itself because its nature is perpetual change.
A physical body is composed of many parts, yet it is singular. This web page you are looking at is composed of many parts, yet it is singular.
Content is the label applied to the current Context, but apart from that label, it does not exist. Content is one, Context many. Content is not, Context is. Where does context arise if not from content? What am I saying?
Heraclitus said it is wise to listen, not to me, but to my Word, and to confess that all things are one.
There is a rule in animation that says individual frames must be presented to the viewer at least 12 times a second, otherwise animated objects will appear to "pop" from place to place, thus destroying the illusion of continuity.
An animation is composed of many different frames, yet it appears to be one continuous thing. It is because the many are presented rapidly that it appears to be one, but it is not. It is, but it isn't.
A hot fire poker doesn't cool in a continuous fashion, but in discrete bursts of energy. Although it appears to cool in a smooth succession from fiery red to black, it actually takes little hops. It's not one "cooling" state as it appears to be, but many "less cool" states presented one after another.
In the microscopic world, events appear to be acausal and measurements are uncertain. In the macroscopic world, there is a cause and effect, events are predictable, and measurements are certain.
We can say there is a 1 in 1 million chance that a subatomic particle will strike a probe, but we can't say which one it will be, just as we can say 1 in 100 students will score 100 on the exam, but not which student it will be.
If a group is composed of individuals, and individuals are naturally chaotic, why is a group more predictable than an individual? The chaos should increase with each new individual. Why is the opposite true?
Where there are many individuals, chaos is supreme. Where there is a government, there is a body. The body exists because of Law, the Creator Logos, but the body itself is composed of chaos, as a sculpture is composed of clay.
A wet soul is like mud -- formless and chaotic, it cannot accept the gift of self-government. The dry soul is like stone -- firm and malleable, able to retain any given shape.
Individual is Chaos. Law is Context. Group is Content. Content is Illusion. Group is a fictional reality -- One and Many.
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Re: Parmenides
Mon, July 3, 2006 - 2:50 AMI don't have that dialogue at hand to read again unfortunately, however, Plato is doing something with this dialogue that he did not do with the earlier dialogues. He is making a break with Socrates and using Zeno's paradox to do so. It is unlikely that this dialogue ever took place, but is instead a construct to propel Plato into the world of philosophers in his own right.
The paradox of the arrow in motion is to a degree simply sophistry. The arrow obviously completes the "assigned" distance. The problem is a "rational" conflict between language and experience, whereby mathematical language contradicts with perceived reality.
The discussion about the forms is far more interesting to me. . .the form of an apple with one bite, the form of an apple with two bites.
Plato uses this example to ridicule Socrates' notion of the forms, that there is a form for everything that exists. Unfortunately, in a "post classical" examination of the doctrine of the forms, Plato can be seen to have only a naive understanding of where the forms actually originate, and how they resolve into the form of the forms.
But still it is an amusing little episode. -
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Re: Parmenides
Mon, July 3, 2006 - 2:59 AMThis is an interesting comment. . .
"There is no such thing as singularity or multiplicity. This would be the way of Zen and Taoism. We like to think of the cosmos as a unity, as a singularity, as one. Whereas this perspective would say not only "not two" (non-duality), but "not one, not two".
I think that Empedocles, Shankara and Spinoza come the closest to coming to grips with the one and the many.
Empedocles doesn't offer a lot but gives us a nice metaphor. Shankara offers us the mystery, while Spinoza tries to create a science out of describing the nature of substance and modes of substance.
Ultimately, this is all unknowable, but it's a useful exercise and the best we can do through the exercise is to achieve an ever closer approximation of the truth. . .and we will get closer and closer, just as zeno's arrow does. -
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Re: Parmenides
Mon, July 3, 2006 - 6:35 AMThe way I learned/studied Plato was that the doctrine of forms was his contribution. My reading and studies have held that the early dialogs represent Socrates' own position, which was mostly apophatic and existential. The middle and late dialogs, becoming increasingly metaphysical, represented Plato's view (e.g. Parmenides, the Republic). Intersting to get another perspective!
You were quite right that my own thinking is strongly shaped by non-dual traditions like Zen and Advaita Vedanta.
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Re: Parmenides
Sun, February 18, 2007 - 10:57 AMParmenides would NOT affirm that conceptual thought introduces divisions into a reality that is continuous.
Actually in the poem he wrote (if I remember rightly) is was titled 'On Nature' he presents the apparent statement ,
'being neighbors being' ---
Thus if we take what he wrote at face value , he doesn't object to the idea of a plenum of extended and, hence, differentiatible space. What he objects to is the notion of change and temporal becoming .
I doubt that Parmenides--- given a less contemporary exegesis of what he wrote would have---faulted conceptual thought with making division in reality . Rather he seems to posit that there is some sort of illusion that many have fallen into. He details the scope of the so-called illusion (i.e.change and becoming being the so-called illusion) but NOT what its ultimate cosmological origin is .
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Beyond what Parmenides puts forth , here is a postulate I would like to present .
Space is potentially divisible---inasmuch as the potentially infinite components within compoents exists in potentia as perhaps vector spaces within the topography of space.( If we ever split the quark then we'd probably find yet smaller components ) Yet, such *potential* components would NOT have much of an active role in terms of efficient or material causation UNTIL AFTER *each succesive splice* of space is done . -
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Re: Parmenides
Sun, February 18, 2007 - 1:37 PM> Parmenides would NOT affirm that conceptual thought introduces divisions into a reality that is continuous.
Parmenides wrote: "For they made up their minds to name two forms, of which it is not right to name one - in this they have gone astray - and they distinguished things opposite in body, and established signs apart from one another...." DK 28B, 53-56
Given this, and your assertion that mortals somehow fall into ignorance, what would you say is the source of the illusion? -
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Re: Parmenides
Tue, February 20, 2007 - 1:29 AMRe: Parmenides
> Parmenides would NOT affirm that conceptual thought introduces divisions into a reality that is continuous.
Parmenides wrote: "For they made up their minds to name two forms, of which it is not right to name one - in this they have gone astray - and they distinguished things opposite in body, and established signs apart from one another...." DK 28B, 53-56
Given this, and your assertion that mortals somehow fall into ignorance, what would you say is the source of the illusion?
THE RESPONSE : Parmenides does NOT directly say what the source is--unless one interprets the established signs he writes about in that quote as the source ....
That quote is quite interesting . But i would wonder how Parmenides would reconcile that statement with the statement he wrote in the poem on nature where he apparently wrote ,
-----'Being neighbors being '.
The use of the verb 'neighbors' in reference to the word 'being' would suggest a differentiatible plenum of plural spaces ....
That is a good question you ask . -
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Re: Parmenides
Tue, February 20, 2007 - 9:15 AMHmm, I can see what you're saying, though I think that anything Parmenides says is going to be a problem, because language is premised on our sense of the universe as composed by discrete entities that undergo modification through time. The very idea of conjugation is at odds with his final theory.
So we are left with the question, "what is he getting at?" My reading of Parmenides is influenced, it is true, but my sense of what I think he must mean, but I can't argue that the paucity of textual evidence precludes a definitive answer.
Incidentally, the quote I exerpted is from the same fragment, though my translation gives: "Therefore, it is all continuuous, for what is draws near to what is." I am certain that "what is draws near to what is" is the same as "being neighbors being".
The precise formulation of the translation you mentioned leads me to wonder if you're looking at the pre-socratics through the eyes of Heidegger? He is an important and interesting philosopher, but not much of a philologist. -
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Re: Parmenides
Wed, February 21, 2007 - 5:12 PMHello Barnaby ,
It was a library book wherein I read the poem by Parmenides 'on Nature' so i don't recall if the translator was Heidegger or not . The matter you raise about alternate translations is quite well taken . Perhaps the tranlation you cited may be a better rendering of the Greek syntax . However, even with that translation there remains the question of how Parmenides could have conceptualized that there could be any 'drawing near' (as a verb) of what is to what (also) is --without some sort of spatial differentiation .? After all if there is NO differentiation then one wonders why Parmenides wouldn't have thought that any Action of drawing near would be any other than superfluous ?
Who knows ---maybe a long lost commentary or supplementary book by Parmenides will be found one day and offer a glimpse as to whether Parmenides intended some terms to be hyperbolic ----and IF so---in what sense such possible figurative expressions are to be conceptually unpacked ....Parmenides is damn fascinating . -
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Re: Parmenides
Wed, February 21, 2007 - 8:07 PMWell, let's start with the premise that Parmenides is saying that change is impossible. If that's the case, we've already got a major language problem, because the basic structure of language assumes a time-dimension, more or less as it appears to us before we enter into any kind of philosophical reflection. The idea of verb tense, for example, implies time.
Even with a conservative reading of Parmenides, we already know that there has to be sharp disconnect between how he sees the universe and what is implied by language, because language implies time.
We could call this a species of a "language falsification problem", which is a common problem in philosophy and theology. Essentially, we're saying that there are ontological implications built into the structure of language that are at odds with how things actually are, and that in using language to describe the world, we simultaneously obscure important features of existence.
I think we can take it for granted that Parmenides is facing a language faslification problem with time. He has to use language to point to something ineffable so I'm not too worried about subtle implications of language. I think we have to be a little more bold in plunging into what he's getting at.
If time is an illusion and change is impossible, how could there be things? For all things arise out of the causal interaction of other things. Our whole fundamental sense of how things are cannot be real. Without change, the whole universe has to be completely re-thought.
Once temporal distinctions are out the window, spatial distinctions go right with them, because space and time are inextricably bound. I'm willing to grant that this is going beyond the letter on the page, but I think it's consistent with what he MUST mean, unless he's raving.
$.02
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Re: Parmenides
Thu, March 1, 2007 - 1:35 PMHello Barnaby ,
But are space in time inextricably bound ?It is possibly to conceptualize space without time (where objects and spaces are differentiated as a kind of pre-given) state without any visualized change. Yet the reverse is NOT possible---time cannot be conceptualized without a template of space . -
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Re: Parmenides
Thu, March 1, 2007 - 3:21 PMMaybe it's inappropriate to frame a reading of Parmenides in terms of contemporary physics, but as a point of fact space and time ARE inextricably bound in a four-dimensional space-time. In fact, every object in the universe is moving at precisely the same speed, C, through space-time. As you speed up in space, you slow down in time, and the product of those velocities is always exactly equal to the speed of light.
But sticking with the Greeks, Parmenides' student Zeno can get us to the bound relationship between space and time quickly enough. And I would argue from first principles that our perception of space is contingent on our ability to move, which is time-dependent.
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Re: Parmenides
Thu, March 1, 2007 - 4:14 PMI like to think of Zeno's paradoxes as a satire of philosophy. I can't think about his paradoxes without suspecting the man had a sense of humor and a desire to lampoon his fellow philosophers. This is not to say they don't have philosophical value.
So far as I can tell, his paradoxes lie in the fuzzy area between the observer, what is observed, and how the observer creates a semantic model of the observation, and I think the solutions lie in this area as well.
Barnaby asks "does it make sense to say that the same object is both singular and multiple at the same time?" I think the "isness" in this question might work as a semantic trap, subliminally encouraging us to respond as though we were talking of how something "is" apart from our perceptions of it.
From a modern naturalistic perspective, we have embodied nervous systems that make models of our experience, which generally fall short of containing *all* information about any given thing. Our understanding lies not purely in objects, or in our brains, but in the synergetic interaction between them.
"Is" the grass really green? Well, according to one useful set of models, the grass gives off a wavelength of about 510 nm, and our visual systems (when functioning "normally" during daylight) experience this as "greenness," but a dog or a bat would have a very different experience of the grass -- not what we would call "greenness".
With this in mind, we might rephrase the question something like "do we find it useful to speak of things as singular in some instances and multiple in others?" It seems that we do. And it seems that attempts to get at the "real reality" apart from us always short-circuit on the fact that our understanding manifests within the milieu created by our experience, our instruments, and our semantic maps. From the perspective of phenomenology and operationalism, metaphysical descriptions of how something "is" break down into descriptions of how it appears to us, how our instruments measure it, and/or how we model it.
Anyone curious about whether "isness" can create problems in thought and communication might find this article interesting (or insufferably pedantic): nobeliefs.com/eprime.htm
