Parmenides' Principle

by Allan F. Randall

An Interpretation

The following is my interpretation of the philosophy of Parmenides of Elea, the Greek father of metaphysics. His only work, On Nature, is written in rather obscure verse, and so his thesis can be viewed from a variety of perspectives, of which mine is only one (although a fairly standard one). Parmenides' most important principle, hereafter called "Parmenides' Principle", was that anything rationally conceivable must exist. Nonbeing is not a thing and can neither be thought of nor spoken about in any meaningful or coherent way. Parmenides forbade talking as if there are possible things that nonetheless do not exist. He illustrated this principle by showing us three possible methods of inquiry, of which only one is valid. The following chart summarizes them.
The Parmenidean Paths of Inquiry
1. The Way of Truth: Necessarily, all possibilities exist. Consistent,   Coherent
2. The Unthinkable Way: Necessarily, no possibilities exist. Consistent,   Incoherent
3. The Way of Belief: Some possibilities exist, some do not. Inconsistent, Incoherent
These paths are laid out in the first part of the poem on Truth. What is meant here by "being" or "existence" is objective reality: what exists independently of any particular mind or viewpoint. The kind of "existence" that is dependent on a human perspective is considered in the second part of the poem on Belief.

What does it mean, Parmenides asks, "to exist"? He gives three possible alternatives. Only one of these three definitions does he consider both consistent and coherent: Path #1, the Way of Truth. Of the others, Path #2, the Unthinkable Way, is likewise logically consistent, but is incoherent (it lacks any precisely definable meaning). Path #3, the Way of Belief, is even worse, for it suffers from the same incoherence, but is also inconsistent (Parmenides only sees it as inconsistent, however, as a way to objective truth, not as a way to understand oneself and one's immediate environment).

The Unthinkable Way, although not contradictory, is nonetheless not something that can be spoken about or thought of (i.e., it is incoherent). It states that, necessarily, no possibilities at all exist. If no conceivable thing exists, then existence cannot be spoken of at all, and we might as well not continue. If "existence" is to be a meaningful concept, there must be at least some conceivable things that exist. So "existence" under this definition is incoherent. It is an empty concept, although it is perfectly consistent. There is no logical inconsistency in adopting a term without any real meaning. I can declare, for instance, that certain things in the world are "squodimous" and that this means that they "pertain to squodimosity". Now most people would agree that there is a problem with this definition, yet my claim remains completely consistent. There is no inconsistency in my utterance, but there is unfortunately no meaning either. Likewise with the concept of objective existence as necessarily not applying to any conceivable entity.

The Way of Belief holds that indeed some conceivable things do exist, but there are others that do not. Parmenides sees this as contradictory, a view held by those "uncritical tribes...for whom being and not-being are thought the same and yet not the same...for never shall this be proved: that things that are not are" [fragments 6-7]. Those who follow this path believe that there exist perfectly conceivable things (things that are), such as unicorns perhaps, that nonetheless do not exist (they "are not"). This is contradictory. We say they are, in that they are conceivable structures, yet we say that they are "not", since we observe no unicorns in our passage through life. Parmenides warns you not to "let habit, born from much experience, compel you along this path," which is fundamentally against reason [fragment 7]. We say unicorns are "not" only because they are not part of our immediate experience. Insofar as they can be described, they are, in an objective sense, as much as we. There is nothing conceivable that distinguishes a nonexisting conceivable entity from an existing one. There is nothing descriptive that we can say about the one that distinguishes it from the other. We see now that a corollary to Parmenides' Principle is that there is nothing more to an entity than its structure.

With Path #3, instead of simply declaring a term that has no real meaning, as in Path #2, we are actually trying to apply this term to some things and not others: cubes, we declare, are squodimous, while spheres are not. So it would seem that Path #3 suffers from the same incoherence as Path #2. So why does Parmenides say that it is also inconsistent? It is inconsistent only insofar as we agree with Parmenides' Principle that nothingness is incoherent, and we cannot refer to things which cannot be spoken or thought of. For in declaring that some things "are" and some "are not", we are doing just that. Path #2, while incoherent, escapes the inconsistency by not applying existence to anything at all. Path #3 can be made consistent only by rejecting the Principle and simply declaring that there is something underneath an entity apart from its descriptive structure, what some call the "bare particular" (a particular thing bare of all structural properties). According to Parmenides, in his rejection of Path #2, this makes no sense, since the nature of the bare particular is not something describable. It is effectively nothing. And nothing is not something that can be spoken or thought of.

The only path left to follow is Path #1, the Way of Truth: all possible, conceivable things just are. The sum total of what we mean when we say something exists is that it is thinkable, or rationally conceivable:

"Whatever can be spoken or thought of necessarily is, since it is possible for it to be, but it is not possible for nothing to be." [fragment 6]
Note that what-is is defined not just in terms of the thinkable, but equivalently in terms of the speakable. So "thinkable" does not mean sensory experiences or images or the like, but only that which can be logically and precisely thought of, all of which can also be precisely described verbally.

Parmenides admits that, from a human perspective, it appears that some things exist and other things do not. He only forbids the Way of Belief as a means to finding objective truth. In a pragmatic sense, he seems to believe it completely proper to seek a "probable" [fragment 8d], if not absolutely true, explanation for things in terms of a real world in which some possibilities are realized, and some are not. In fact, the second part of his poem on belief was originally far longer than the first part on truth. Although most of the Way of Belief has been lost, it appears to have contained an extensive physical science. But in a strict, absolute sense, the high "probability" of this physical explanation (the World Order, or Cosmos) is just a kind of illusion of perspective. While the Cosmos does exist objectively, it does not exist to the exclusion of all other possible Cosmoi. The objective truth is that all possible cosmoi, or worlds, are equally real. This leads Parmenides to the conclusion that the whole of existence is a single, continuous, undivided and unchanging unity: the "One."

If it seems strange that taking all possibilities as real leads to a single indivisible and undifferentiated substance (a "plenum") consider the following analogy. Assume that we have a block of marble from which a sculptor is about to carve a statue. This block of marble is, for the purposes of this analogy, everything that can clearly and distinctly be thought about or spoken of (i.e., it contains all possible sculptures). To get any particular sculpture, a sculptor need only remove the bits that are not part of what she has in mind. Once some bits are removed, there is no going back; some possible sculptures are now eliminated from the marble forever. But if all possible sculptures are included, no bits can be removed and the block remains continuous, undifferentiated and unchanging. Taking the block of marble to be reality, most of us certainly consider it to be differentiated, but only because we are part of the marble--passing through it, as Parmenides says [end of fragment 1], so we naturally see some of it as outside us and some of it as part of us. But from the viewpoint of the external sculptor, the marble is, in Parmenides' words, "full" everywhere: a plenum of what-is.

As an example of Eleatic reasoning, imagine you are trying to convince Parmenides that, in fact, the immediate world of your experience is the "One True World", to the exclusion of all others. "Over here," you say, "is a tree, and over there is a house, and in between are other things that are neither trees nor houses. That is surely plain for anyone to see." "But," Parmenides objects, "this implies that over here, there is not a house and over there, there is not a tree. You are excluding from objective reality the arrangement in which the house and tree are in reverse positions. Yet is this not a logically possible arrangement of things? Is it not just as rationally plausible a state-of-affairs as what you see? Then, rationally, it must exist, too. But this means, if we are to think of the universe in terms of matter in space, that all space must be uniformly filled up with matter. Otherwise, there will always be some perfectly plausible arrangement of objects that, it is claimed, objectively does not exist. It is true that for you, there is a house over here and a tree over there, but that is your world. Objectively, there is only the plenum, which contains all possible worlds equally."

This "many-worlds-as-one-world" cosmology differs somewhat from an earlier but similar view held by Anaximander, the author of the first known (although not presently surviving) book of Western science and philosophy (he is thus arguably the father of Western science and philosophy). Anaximander, who seems to have had a great influence on Parmenides, thought that the World Order, or Cosmos, originally developed via some kind of separating off process (something like a vortex), from an originating undifferentiated substance, which he called the apeiron, or "indefinite". This, as the ultimate nature and explanation of the world, could not have any of the definite properties of the things in our ordinary world. To count as an explanation, said Anaximander, a theory must be put in terms of something other than what is to be explained. Anaximander held that there were an indefinite number of other worlds (what today we might more likely call universes), which were also separated off from the apeiron. The apeiron fills the space between the worlds. One gets an image of a vast array of worlds bubbling up out of the cauldron that is the apeiron, each completely cut off from the others. It probably seemed only logical to Anaximander that there be an indefinite number of other worlds, since that gave his apeiron more explanatory power. If the apeiron had only produced one world (this world) then its nature would be so closely tied to the specifics of this world, that it would no longer be an explanatory first principle. Anaximander is sometimes thought of as the originator of what we now call the "Principle of Sufficient Reason", of which this kind of reasoning is an example. For instance, he held that the Earth must be at rest, since if it exists in empty space, with nothing pushing it one way or another, there is no sufficient reason for it to move, so it must not. His view of many-worlds was probably similarly motivated. If the apeiron is a first principle, and is to be truly explanatory, there can be no sufficient reason why it should produce only this world to the exclusion of any others.

This view is very similar to that of Parmenides, and it almost certainly greatly influenced him. The plenum is just a more developed version of Anaximander's apeiron. However, Parmenides gave the Principle of Sufficient Reason a logical grounding, and this yielded a cosmology that, while not directly conflicting with Anaximander's system, was quite different in tone. Besides Anaximander and the other Ionians, Parmenides was also highly influenced by the Pythagoreans, who viewed the universe as ultimately mathematical in nature. So it was probably not obvious to Parmenides that he should accept Anaximander's reduction of the world to concepts of space, time and matter, which are then left unquestioned. Instead, he wanted to reduce everything to something mathematical or logical, in the Pythagorean tradition. Parmenides would almost certainly object to the Anaximanderean vision of an array of multiple universes in space or time, since this would seem to indicate a particular arrangement. Over here we have universe A, and over there we have universe B, and in between is this apeiron stuff. But Parmenides would say that this is illogical, because it implies that over here where we have universe A, we do not have universe B. And over there where we have universe B, we do not have universe A. Yet the arrangement where the two are reversed must surely be as logically valid as this one, so what sufficient reason could there possibly be for this particular arrangement of universes to exist and not some other? For Parmenides, there are many worlds in some sense, as there were for Anaximander. But for Parmenides, these many worlds somehow cancel each other out, at least from the point of view of total objectivity. From this radically objective point of view, these "world orderings" or Cosmoi, may not necessarily really be "worlds" any more, since anything thinkable at all is part of the plenum, whether it is a "world" or not (it need only be something that one can fix "firmly" [fragment 4] in one's mind). Parmenides did not literally refer to the plenum as a collection of worlds, and he would probably say (and probably did say) that Anaximander's system loses its explanatory power if we view it as some kind of "superspace" of worlds laid out in a particular arrangement. To be fully explanatory, by Anaximander's own criterion, the apeiron must explain space, and even time, in terms of something else, something that we are justified in not requiring a further explanation for. For Parmenides this something was logic: "whatever can be spoken or thought of".

The Modern Eleatics

This idea of a plenum of all possibility, which is simultaneously the simplest thing and yet that from which all things complex can be generated, plays an important role for all the seventeenth century rationalists. As such, Parmenides was the ancient father of the modern rationalism championed by Descartes, Spinoza and Leibniz. Yet in spite of the similarity, all of these modern thinkers, one way or another, took the Way of Belief. Spinoza believed, like Parmenides, that what-is is simply all possibility. Yet he excluded incompatible possibilities--since they would yield a contradiction. Thus, for Spinoza, our universe is the maximally consistent set of possibilities. There are possibilities excluded from reality, but to include them would be contradictory. It is not clear why Spinoza thought the universe was the maximal set of consistent possibilities, since there is no logical preference given to "larger" sets that would make them exist while smaller sets languish in nonexistence. But for Spinoza, being a modern, the ancient concept of many co-existing worlds was not natural. He simply did not question that in the end there could be only one. Maximal consistency seemed to him the most plausible scenario. But it was his system's fatal flaw. As a rationalist, he was trying to show that objective reality was simply equivalent to logical necessity, and so he tried to argue that his maximal criterion was somehow logically necessary. But Leibniz saw that this cannot be so. For one can still consider the other incompatible possibilities as completely separate, disjoint "possible worlds." So Leibniz held that all possible worlds exist in the mind of God, who chooses one to be the actual "really existing" one: the best of all possible worlds. Do the others exist? Are they, or are they not? Leibniz says they "are" in the mind of God, yet they "are not" in actuality. Yet Leibniz cannot state precisely what it means to "be" in actuality rather than in the mind of God. Leibniz, like Spinoza, is falling for the self-contradictory Path #3; he is trying to say that the other worlds can both be and not be, because he has an unshakeable faith that he is living in the "One True World". Either this is a contradiction, or as we have seen, Leibniz must believe in a property of things that is as unthinkable as Path #2 (in this case, the really-actually-existing property determined by the will of God). So both Leibniz and Spinoza, while arguing much after the style of Parmenides, bail out in the end and find some reason to take the Way of Belief in their search for objective truth.

The closest thinkers to Parmenides in modern times prior to the twentieth century are probably the absolute idealists, such as Fichte, Hegel, Schelling and most especially F.H. Bradley. Bradley, writing in the late nineteenth to early twentieth centuries, believed that all possible worlds exist in what he called Absolute Reality. Our concept of a single, "really existing" finite world around us is due to the fact that we must perceive the Absolute through the perspective of our "finite centre" (our immediate conscious awareness). Our understanding of the immediate world of experience around us is simply the most coherent way we have of describing, from our own human perspective, the Absolute Reality of all possible worlds. Unlike Leibniz, Bradley believed that all possible worlds have equal absolute, objective status. Our particular world is only special to us (naturally enough, since we are "passing through" it). Bradley was ultimately a mentalist, however, in that he saw objective reality (as did the other absolute idealists) as not just "what can be thought of", but "thought itself". Although Parmenides seems to have held a similar view of the plenum as somehow thought-in-general, I would argue he was not ultimately a mentalist, since he viewed the mind as an "emergent property" of lower level nonmental processes:

"According to the union within each person of disparate body parts, thus does mind emerge in humans. For it is the composition of body parts which does the thinking, and Thought (since it defines the plenum) is the same in each and every human." [fragment 16]
The above claim that "the plenum is defined by thought" is more literally translated "the plenum is thought". Some might claim on the strength of such a translation that Parmenides was a mentalist. But that interpretation is really not consistent with the rest of the passage, nor the rest of the poem, which favours glossing "is" here as "is defined by". Parmenides seems to clearly maintain in this passage that mind emerges from the workings of body parts that are not in themselves inherently connected to each other, any more than they are to other objects in the world (all of which, of course, are emergent from, and dependent on, the objective plenum). In the Way of Objectivity, Parmenides repeatedly characterizes the plenum as "what can be thought of" rather than the actual thoughts themselves (this also depends, however, on which translators you trust, but most translate Parmenides as a nonmentalist). Moreover, Parmenides consistently refers to language as an equally valid characterization of what-is, so it would seem that only verbalizable, rationally describable objects of thought are things we can truly and clearly think of. The plenum is Thought-in-general, or Language-in-general (that which is common in the thinking and speaking of all intelligent beings). This for Parmenides must surely have meant that it loses any particular characteristics of mind, just as it loses the usual material characteristics of motion and plurality. The plenum is Thought in the same way that the plenum  is Matter. It is not fundamentally "mental stuff", but is nonetheless all that thought is capable of understanding (likewise, it is not fundamentally "material stuff", but is nonetheless all possible arrangements and movements of matter in space and time). So we can only define it or understand it in terms of its ability to be thought of (any other way of understanding it would presumably not even make it into Parmenides' initial list of possible methods of inquiry). This view of the plenum as Thought-in-general or Language-in-general is very much like the view of Bradley, who had objectified idealism almost to the point of a Parmenidean position. It is unclear to what extent the two philosophers would agree with each other if they could be brought together, and some will probably equate their positions, but I will stop short of placing Bradley as fully in the nonmentalist camp as Parmenides, since he does not unambiguously state an emergent theory of mind, on occasion indicating just the opposite, and does not sufficiently separate the logically definable aspect of thought from its experiential aspect. In other words, Thought-in-general has not been as fully objectified for Bradley as for Parmenides. A result is that Bradley did not believe in the "strong postulate of artificial intelligence", that an appropriately programmed computer would be conscious. Presumably Parmenides would agree with the strong AI postulate (considering his view of mind as an emergent property). And since Parmenides also quite clearly equates "what can be thought of" with "what can be spoken of", and in parts of the poem characterizes it in purely material terms, it is doubtful that he saw reality as "total Feeling or Experience" the way Bradley did. To Parmenides, the plenum is specifically not made up of all possible experiences, rational or otherwise. Rather, it is made up of everything that can rationally or logically be described.

Absolute idealism suffered a serious setback in the early-to-mid twentieth century, when logical positivism and analytic philosophy seemed to almost eradicate metaphysics. One might think the nonmentalism of analytic philosophy would take things even closer to a Parmenidean view, since Parmenides was a nonmentalist who was, for his time, highly analytic in his approach. But this is not what happened. The so-called "analytic" philosophers, in rejecting mentalism, generally opted for material realism as a way of ensuring that their world of experience remained the "One True World" (and materialism is as opposed to the Eleatic worldview as is mentalism). But Parmenidean ideas are now becoming popular once again. David Lewis and others, working within the analytic tradition, advocate a view that is essentially Parmenidean, stating that all possible worlds really do concretely exist just as ours does. Lewis does not call it absolute idealism, though, but rather "modal realism". And most encouraging of all for the longevity of Eleatic philosophy, there has emerged impressive empirical evidence for Parmenides' views in the field of quantum mechanics. Some versions of Everett's "many-worlds" interpretation of quantum mechanics hold that all possible worlds are equally real. Other versions, while agreeing that many worlds are required to explain the empirical evidence, do not take quantum theory to its logical extreme and postulate the real existence of all possible worlds--they maintain that there is some kind of a priori, logically arbitrary "boundary condition" that limits the number of possible worlds that exist, so that some "are", while others "are not". Others, including myself, believe that a Parmenidean solution is the only one that can explain the evidence of quantum physics without introducing unjustified, ad hoc additions to the theory. As physicist Stephen Hawking has suggested, what more natural boundary condition could there be than that there is no boundary condition? In fact, some of the things Hawking and others have suggested are almost quotes from Parmenides (for instance, that globally the universe has zero mass-energy, and that the finite amounts of matter and energy we experience are merely local phenomena). The idea of many worlds co-existing equally, and somehow cancelling each other out on a more objective level, is remarkably consistent with modern quantum cosmology.

To modern cosmologists, "no boundary condition" means no absolute boundary condition. One must still impose a boundary condition based on our human perspective on the Cosmos; in other words, the simple principle that the only worlds one can be conscious of are worlds that are capable of supporting conscious life. Only worlds with certain life-supporting properties are worlds in which it is possible to be "passing through" in the first place, so we can effectively eliminate any others in trying to explain our world of experience. This is the many-worlds version of Carter's "Strong Anthropic Principle", and it gives us something that Parmenides sought but could not explicitly articulate: a well-defined, purely rationalist foundation for connecting the Way of Truth with the Way of Belief. Such a foundation was Parmenides' hope and his challenge to the rest of the scientific community of his day.

Something else we have today that Parmenides lacked is a rigorous and universal conception of language, logic and mathematics (i.e., that which can be spoken or thought of). The modern notion of computability (developed by Gödel, Church, Turing and others) gives a precise definition of the thinkable. There are numerous different languages that are generally assumed to be "maximally expressive", as they seem to be capable of precisely describing anything describable. Such "Turing-equivalent" languages include English, computer programming languages and predicate logic (to name but a few). It has been shown that these languages are all interdefinable and intertranslatable. Anything expressible in one can be translated into any of the others, and any one of them can be defined within any of the others. This provides a precise and mathematical way of characterizing Objective Truth (see my papers on quantum phenomenologymodality, Platonism, and Wittgenstein for a more detailed treatment). The objective component to an expression is just what is preserved when we translate between different Turing-equivalent languages. We cannot, of course, step completely outside of language and see Objective Truth from the point of view of the Goddess, the view of all possible languages, since there are an infinite number of them. But that is exactly how Parmenides would have it, since the Goddess-view is just a fanciful literary device, a useful aid to the human imagination, but a viewpoint that cannot in reality ever be achieved. There is no "outside" to the universe as a whole, from which to view it. Yet through logic, we can indeed take a kind of objective stance, even though it is necessarily incomplete.

Bradley, Everett and Lewis are all making the same, essentially Parmenidean, claim: the particular world we are experiencing is only "more real" than the other possible worlds because we happen to be passing through it. We are looking at that part of the block of marble that is ourselves and saying that it is more real than that which is outside of us. Yet in an objective sense, reality is just the continuous undifferentiated block of marble: a plenum of what-is. (Or, which is objectively just the same, a plenum of what-could-be.) Father Parmenides (as Plato called him) warned us not to falter and take the forbidden Way of Belief in our search for objective truth. Do not believe, he tells us, that appearances are any more real than all the other conceivable things. There is no rational basis on which to distinguish a really objectively existing conceivable thing from a really objectively nonexisting conceivable thing. There is nothing structural to distinguish them, one as existing and the other as not; therefore the distinction is meaningless.

Yet the history of metaphysics is riddled with metaphysicians who reject the Principle. In the twentieth century, logical positivism and "analytic" philosophy have predominated, based on a firm rejection of Parmenides' Principle (although the tide seems to now be turning). Even with the same Eleatic paradoxes cropping up in quantum mechanics, there remains a minority of physicists (although perhaps a majority of cosmologists) who accept any kind of many-worlds view. Most physicists, like Leibniz, reject Parmenides' Principle and assume that they are living in the "One True World", and that hence there are conceivable things that "are" and conceivable things that "are not", but not by virtue of anything about them that is conceivable. The result is a whole slew of "quantum paradoxes" that have driven physicists mad for most of this century. A simple application of Parmenides' Principle, and the paradoxes disappear [Randall 1996, 1997].

There are some, whether they be mentalists or materialists or something else, who may argue that the Parmenidean One is incomplete, as there are things conceivable apart from what can logically and rationally be described; but this is a kind of mysticism that is hard to answer. Until I experience such a direct grasping of nonstructural properties, I will stick to rationality. Parmenides, the true father of rationalism, stands with only a few others in his fight against the "uncritical tribes" swarming down Path #3. Today, at the end of the twentieth century, we might do well to listen to the father of metaphysics. In so doing, we may be better equipped to treat the universe as a rational place, and the most perplexing metaphysical mysteries of the past centuries might just dissolve into sheer Necessity.

Copyright © 1996, 1997 by Allan Randall (
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