Monday, September 1, 2008

Parmenides refutation of change

Parmenides was a pre-Socratic philosopher from Elea. He is notorious for denying that there can be any change. He believed that everything is part of a single unified and unchanging whole. All apparent change is merely illusion. His follower, Zeno, extended this idea by providing further logical paradoxes which attempted to show that motion leads to essential contradictions that are logically irreconcilable. For example, he showed that motion isn't possible because in order to travel from A to B we have to travel half the distance, and then half that distance and then half that distance, and an infinite number of halves. But if we have to cross an infinite number of halves, how can we even get started? Aristotle, simply rejected this argument on the grounds that we can observe things in motion, but this isn't very effective because Parmenides already argument that motion is an illusion. The difficuly in this paradox is that of the infinite, which Greek mathematics couldn't handle, and it would require a far more sophisticated relationship with infinity in mathematics for this problem ultimately to be solved.

Parmenides' argument for lack of motion was twofold. First, he argued that for change to occur it must progress from being to non-being, since something which was not before now is. For example, if I grow tall, I have to start from not-tall and then change to tall. But how could something possible come from nothing? How could being come from nothing, since nothing is completely nothing? After Parmenides, thinkers would recognize that this absolute change, (something from nothing) is not possible, but change is possible because things don't need to change completely. There is something that persists through the change. For example, if I grow tall, it is I who persists through the change. Tall to non-tall is not absolute change, because the I is the unchanging ground upon which the ball of change can roll.

Parmenides other argument is about the incomprehensibility of non-being. A world in which there is change requires a combination of being and non-being, but we can't possibly comprehend non-being since it is absolutely nothing. Thus, the comprehensibility of the world would be undermined by change. Parmenides here was again mistaken since the presence of change only undermines the complete comprehensibility of the world, which is an unfortunate fact which all we people who would like to know more about the world have to deal with.

I think the essential lesson to learn from Parmenides is the danger of thinking only with absolutes. Parmenides assumed that all change must be absolute change and so rejected change altogether. He assumed that for the world to be comprehensible it must be completely comprehensible. He will not be the last philosopher to make this error. For example, if one were to say, since we can't have complete access to truth, then we can't know anything.

13 comments:

Stephen Paul King said...

Excellent essay! One does not often see such a skilled refutation of Parmenides in literature.

David Jimenez said...

Great work! This is very helpful. I hope your a professor now.

Stephen Paul King said...

Parmenides' argument can be refuted the same way we refute Zeno, the calculus of variation. So long as we allow infinities and measures to exist, we can show how we can go from arbitrarily close to Zero to arbitrarily close to One, thus the transition from non-being to being is accomplished smoothly.

Apex said...

Nice post! As a notion to Stephen's last comment is that one could claim that arbitrarily close to something is equally much infinitely far from it, and so nothing has been proven or disproven by not reaching the end. It's really a rather big problem in both maths and physics - e.g. we might know what happened at the smallest fraction of a second after the big bang, but the time before that fraction of a second might be infinite when there's no other point of reference.
On the notion of change, I interpret it as a matter of thinking of causality that we must abide to in order to feel as free agents. What is changing is not seldom something of a different density than something else, e.g. an Arrow soaring through the air (or an arm for that matter). The question is really if the two subjects are coherent or not (i.e. part of a unity)? If we think that the air around the arrow has as little effect on the Arrow as the Arrow has on it, then movement is possible. But if the atoms in the air are indeed predictively interacting with the atoms of the arrow, then movement (or change) 'per se' is not possible, for when the Arrow moves the air moves in relation to it and their relative movement was as predictable as if they were one. The Parmenidan One and the block universe theory comes as the logical extention of those latter thoughts.

Roy IV said...

I know you posted this a long time ago, but I came across it when Googling Parmenides' argument against change. I read this: "Aristotle, simply rejected this argument on the grounds that we can observe things in motion."

In fact, Aristotle provided a much more substantial refutation of Parmenides' argument. It involves act, potency, and other Aristotelian metaphysical concepts that- it being seven years later- I assume you know at this point.

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William McEnaney said...

Remember the Aristotelian-Thomistic between potentiality and actuality. I'm actually wearing a beard. But I'm potentially clean-shaven. Boiling water is actually hot and potentially cold. Cold water is potentially hot. In general, change is actualization of a potential. For someone or something to undergo a change, the change's cause must already exist. In fact, you contradict yourself when you say that something can make itself begin to exist. In that case, the cause would need to exists because the cause and its effect would be exactly the same thing. So for anything to cause itself to begin to exist, it would need to both exist and not exist at the same time. And that implies a self-contradiction.

Stephen Paul King said...

@Wiliam McEnaney The contradiction to me implies that Existence is passive with respect to properties. Properties are those aspects that can be measured, and thus determined to be or not to me.

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David Martin-Lee said...

Here's a thought - perhaps parmenides was correct if we were to view time under Mctaggart's B-theory. Even further, Hugh Everett's Many-Worlds interpretation of quantum mechanics tells us that every possible outcome for every particle interaction actually exists in infinitely diverging realities. Putting these two theories together and you have an unchanging (un-'becoming') reality where every potentiality is actualized. At least that was what I wrote in my Ancient Greek philosophy class. Curious on what others think about that.

David Martin-Lee said...

Here's a thought - perhaps parmenides was correct if we were to view time under Mctaggart's B-theory. Even further, Hugh Everett's Many-Worlds interpretation of quantum mechanics tells us that every possible outcome for every particle interaction actually exists in infinitely diverging realities. Putting these two theories together and you have an unchanging (un-'becoming') reality where every potentiality is actualized. At least that was what I wrote in my Ancient Greek philosophy class. Curious on what others think about that.

Stephen Paul King said...

David Martin-Lee, work has been done that looks at this from a different perspective that balances the timelessness of the infinite total Universe with the temporality of subuniverses, such as ours. For example: http://arxiv.org/abs/1606.04759