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I've had the hardest time grasping the bite of Parmenides argument against change. His argument is summarized in ch. 5 "Article One: Potency Really Distinct From Act" of Reality: A Synthesis of Thomistic Thought by Réginald Garrigou-Lagrange:

  1. If a thing arrives at existence it comes either from being or from nothing.

  2. Now it cannot come from being (statue from existing statue). Still less can it come from nothing.

  3. Therefore all becoming is impossible.

Now, can this be better understood as an application of Zeno's paradox, but instead of physical distance to be covered, a distance of time to be covered? For example, suppose I go from being short to being tall. Attach a device to my arm that continuously registers a "No" if I am short, and a "Yes" if I am tall. Then start the clock. Now, presumably, the device goes from registering a "No" at some point in time, to registering a "Yes" at another. However, we have an infinite number of half time distances to cover before we can go from "No" to "Yes", and hence eventually getting there is logically impossible.

What do you think?

  • I wonder if you would get more response if you put Aquinas in parentheses after your question? It would be easier than inserting Lagrange’s full name. – Gordon Nov 8 at 5:10
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    Already Plato remarked in Parmenides that Zeno says the same thing as Parmenides, "his book states the same position as your own... You assert in your poem that the all is one... Zeno, for his part, asserts that it is not a plurality". But Parmenides's argument does not involve distance or time specifically, it cuts deeper. Parmenides's theses are, first: only that identical with itself is thinkable by us. We cannot think two distinct things at once, and, hence, can not think the transition from one to the other, the change. And second, to be is to be thinkable. Thus, change is not. – Conifold Nov 8 at 5:22
  • No, this cannot be understood as an application of Zeno's paradox. Zeno provided additional support for Parmenides' position. But Parmenides' reasoning and argumentation has nothing to do with the Zeno-style reasoning you mention here. – transitionsynthesis Nov 8 at 7:59
  • See Parmenides for introduction and reference to the (very few) extant texts and e.g. Michael Wedin, Parmenides' Grand Deduction : A Logical Reconstruction of the Way of Truth (Oxford University Press, 2014) for a detailed abalysis. – Mauro ALLEGRANZA Nov 8 at 8:50
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All of this class of paradoxes (including Zeno's) hinge on the conceptual problem of the transition between discrete and continuous measurements, and that conceptual problem is rooted in a problematic of language. Language — and the language of logic in particular — is geared towards species (categories of things or events), and does not have useful structures or simple modes for discussing how things evolve between such species.

  • Something is or it isn't; we don't have words for any state in-between.
  • Something is here or it's there or it's someplace else; we don't have logical structures for expressing that something is 'between' or 'transitioning'.

Notice that Parmenides does not say that 'being' is impossible; he says that 'becoming' is impossible. 'Being' is a category (species), because something either is or it isn't. 'Becoming' is an evolution from one category to another, and Parmenides is pointing out that we cannot capture that evolution in language as a species in its own right, except (perhaps) in the most abstract sense. In some cases we can rest on Newton's trick — representing a continuous transition as as infinite number of infinitely small discrete steps — but that is a practical trick more than a real solution.

Honestly, you might want to read the first few chapters of the Daodejing, which gets at the heart of this problem. I'm not sure that will be less of a head-bender, though...

  • Thank you for your insightful comment. It seems that Parmenides wants to limit us in our ability to refer to things that "are not", and that's where the drive of his argument comes from. To me, it sounds like a questionable move and an direct attempt to wrap us up in a language game. But I do wonder if his argument could be strengthened by a modified version of what I described above: (Continued below) – Mark Nov 8 at 15:32
  • If I transition from A to B, then you should be able to give me an exact moment (time t=0) past which I am B, but before which I am A and not B. That is, for t<0, I am A, and for t=0 and beyond, I am B. But at this exact t=0 moment, there is not even a fraction of a millisecond before this in which I am B. Hence, I seem to have instantaneously gone from "not B" to "is B", and this does seem contradictory indeed. Do you think this gets at the heart of his argument, or am I still off the mark here? – Mark Nov 8 at 15:35
  • You are making an unfounded assumption, namely that we must have a strict dichotomy. You make that assumption because of the way our minds organize information, not because of anything in the physical world. Why can't something be both A and B, overlapping in time, or go through a stage where it is neither A nor B, but something else entirely? – Ted Wrigley Nov 8 at 15:51
  • Let me be clear: I don't think Parmenides or my argument above proves that change cannot occur. I am just trying to understand exactly where the confusion about the matter is coming from, and where the apparent contradiction is coming in. Thus, if somebody were to make the claim that I was A, and am now B, so that we are working under the assumption of such a dichotomy, then I could present the above argument to show that changing from A to B actually cannot occur. – Mark Nov 8 at 15:53
  • I'm not exactly certain what you're missing. That is pretty much what I explained in my post (or so I thought), but you don't seem to see it. The confusion comes because we (natively) impose a concrete universal object schema on the world, but the world is not composed of concrete universal objects. – Ted Wrigley Nov 9 at 15:00

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