Views of Anaximander and the ἄπειρον

by existential Calvinist on 2007年09月28日 03:07 AM

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It is both a blessing and a curse for pre-Socratic scholarship that for certain figures the textual resources available to us are insufficient to determine with any precision what views were held by the figure in question. Unfortunately, we know only the names and terminology important to these figures, but not the exact signification given by those figures to their terms. On the positive side, this gives modern scholars great flexibility in their own interpretations, allowing us to creatively reconstruct the past in a way that is most useful to our situation. One such figure for which we face these hermeneutic difficulties is Anaximander. The fragment attributed to him is not enough to describe with certainty what views he held, and the commentary around his philosophy paints a sometimes conflicting picture. What we do know is that he held the ἄπειρον to be the ἀρχή or fundamental principle of the cosmos. What we do not know is what Anaximander meant in using these terms. This paper will paint plausible portraits of Anaximander’s beliefs on the basis of his own remarks and reconstruction of his motivating theoretical outlook as well as commentary by Aristotle and Simplicius in order to explore the tenability of each portrait, both as a representation of Anaximander’s original views and as a viable theory of cosmology today.

1. Preliminary remarks about the ἄπειρον and ἀρχή

Before examining any presentation of Anaximander’s cosmological claims, more needs to be explained about the ἄπειρον, the central material principle in Anaximander’s thought, and about ἀρχή, “principle” itself.

1.1 About the ἄπειρον

Ἄπειρον can be translated several ways. Its literal meaning is “without limit” or “unbounded,” and it has frequently been translated as the “infinite,” as it was for example by St. Augustine (Kirk, Raven, and Schofield 114). However, a strong case can also be made for translating it as the “indefinite.” These two main translations of ἄπειρον—infinite and indefinite—suggest two main means of thinking of the ἄπειρον: the positive interpretation and the negative interpretation. Although the word infinite means etymologically the “not finished,” nevertheless modern American English speakers tend to interpret the infinite in a ‘positive’ sense for two reasons. First, linguistically, infinite is pronounced in a way that is distinct from the pronunciation of finite (infənit versus ‘fīnīt), which conceals the link between the two and makes it seem that the infinite is its own entity and not the privation of limitedness. Second and more importantly, the concept of the infinite has in our society become bound up with ideas about the powerfulness of God, the interminability of numbers, and so on. For these reasons we tend to think of the infinite as the greatest of the great and largest of the large. The indefinite on the other hand is often seen negatively as that which is without form or shape, like an amoeba or a blob. The indefinite is linguistically seen to be a privative version of the defined. Properly speaking, neither view of the ἄπειρον completely encompasses what seems to have been meant by Anaximander. In order to more completely capture his meaning, we must turn briefly to Anaximander’s predecessor Thales and provide context for his theory.

While it should be noted that we have no definitive proof of a connection between the two thinkers, since references to Anaximander’s having been a pupil of Thales’ seem to have been included only in later commentaries, perhaps as the result of inference by later authors rather than as the transmission of historical fact, nevertheless, it is reasonable to presume that Anaximander’s cosmological speculations were informed by those of Thales in at least some ways. Thales’ theory that water is the hidden principle of the world appears to have been motivated by the observation of the transformation of water from one form to the next. Thus, we can speculate that the genius of Anaximander was in questioning in what sense water can continue to be called “the same thing” even after its transformation from one material form to another. The ἄπειρον seems to be his formulation of a response to the question, if water can become anything, then why should we refer to it as the primordial substance rather than any other? For example, if water can become through time fire, and fire can become through time water, then neither water nor fire should be spoken of as the “primary” stuff in the world. Instead, we should understand the two as complimentary expressions of an underlying sameness. While a Thalesian cosmology might be defended on the grounds that all things are equal in being water, but “water” is to be preferred as our way of referring to the primordial stuff because ordinary water pedagogically demonstrates the fluidity of properties secretly possessed by all matter or because ordinary water is the most pure form of what everything else is, we are not in a position to know if Thales offered either (or any) defense of his cosmology against this question. Nevertheless, since in Anaximander we seem to see the implications of the question firmly grasped, it is fitting to take this hypothetical rebuttal to Thales as our starting point for answering our own questions about the nature of the ἄπειρον.

With this question about the nature of the monistic material of the world in mind and under the presumption that Anaximander was working within a Thalesian framework then, we can say that the ἄπειρον should be seen as meaning something closer to our understanding of the “indefinite” rather than the “infinite.” Of course, we should also not rule out the possibility that Anaximander took the ἄπειρον to be infinite in the extent of its existence or in its permeation of the cosmos. Nevertheless, when considering the ἄπειρον we must see it primarily as an answer to the question, “What sort of stuff could be common to all things?” In that context, it is clear that the only way that some substance could be common to all substances would be for the primordial substance to be a plenum out of which all other possible substances can freely arise. Thus, epistemically, we gain access to the existence of the ἄπειρον by positing the properties of a substance of the sort which would be able to underlie all substances and we do so in the absence of empirical access to the substance itself, since if the ἄπειρον were empirically accessible, then (like water) its existence as an empirically observable substance would undermine its claim to primordiality. As Simplicius explains, Anaximander’s theories arose because,

seeing the changing of the four elements into each other, [he] thought it right to make none of these the substratum, but something else besides these (KRS 119, emphasis mine)

In other words, what accounts for the unity of substances must be completely other than the substances themselves lest it be subject to the limitations that come for definite existence. For this reason, our method for describing the ἄπειρον must be primarily a via negativa in which we specify the properties of the underlying by removing from it those properties which are not common to all things in the cosmos. Therefore, we can say that the underlying is not like water, is not like fire, and so forth. Furthermore, we can specify that the underlying, whatever it is, cannot have any determinate size, shape, weight, &c., lest it be unable to take on the myriad of sizes, shapes, and weights of various object in this world. Accordingly, in our understanding of Anaximander’s cosmology we should first think of the ἄπειρον as “indefinite” and only secondarily consider it as being “infinite” in its extent.

1.2 About the ἀρχή

If then we take the ἄπειρον to be an answer, we must also reconsider the question to which it is the answer. So far, we have called the ἄπειρον a “thing,” a “primordial substance,” the “stuff” of the cosmos. However, the exact question to which ἄπειρον is intended to be the answer is, “What is the ἀρχή?” In Greek, ἀρχή means literally the beginning or starting point (Peters 23). In the context of Anaximander’s thought, however, it is more helpful to think of the ἀρχή as the “principle” of the world. Where Hesiod’s Theogony had the world arising because of the interplay of the gods, according to Aristotle the pre-Socratic philosophers,

thought that principles in the form of matter were the only principles of all things; for the original source of all existing things, that from which a thing first comes-into-being and into which it is finally destroyed… (KRS 90)

These principles are thus both the substance of the world and the motive force behind the transformation of the elements. Indeed, the one surviving quote that is attributed to Anaximander attests precisely to this later property of the ἀρχή, when he claims that the various forms of matter will return to the ἄπειρον,

according to necessity; for they pay penalty and retribution to each other for their injustice according to the assessment of time. (KRS 101 & 110)

As Kirk, Raven, and Schofield explain the phrase “the assessment of time” should be interpreted as a poetic flourish meaning that the counter-transformation of elements is an inevitability (120). The ἄπειρον as ἀρχή must then be seen as both the cause of change and the object of change. Thus, unlike more contemporary systems of physical principles, such as early modern physics, no distinction is made between the material which undergoes changes and the rules which govern these changes. Where the Newtonian would carefully make a distinction between impelled substances (the Earth and the apple) and the source of their mutual attraction (gravity), Anaximander seems to be making no clear distinction between the ἄπειρον as the material which makes up of the world and the justice-like system of rules that applies to things in this world.

2. The problem of differentiation

We have thus far pictured the ἄπειρον of Anaximander as being an indefinite “stuff” which pervades the universe and is responsible for the regularity of the transformations within it. However, in order for these transformations to occur, it cannot be the case that the universe is composed of the self-same ἄπειρον alone without qualification. For if the ἄπειρον is the only sort of thing in the world, then we must question how it is possible that we experience at different times different sorts of material within the world. Returning to Thales, if all things were merely liquid water, then there would be none of the diversity that we experience in the world, merely an endless ocean. Instead, Thales’ claim that everything is water must be understood to mean that everything is water as it expresses itself in various forms. In the same way, Anaximander’s claim that everything is ἄπειρον cannot mean that everything is undistinguished ἄπειρον. Rather, it means that the ἄπειρον is that out which things arise, but it is distinct from being itself any particular form of matter even while it is at the same time covertly every form of matter. For reasons similar to those for which we insisted that the ἄπειρον be understood by a via negativa, so too are we compelled to say that nothing we experience in the world is itself a full expression of what the ἄπειρον is. Hence we are faced with the problem of explaining differentiation in a monistic cosmos. There are two interpretations we may initially use in this explanatory process, that of Aristotle and that of Simplicius.

2.1 Aristotelian portrait

These different qualities of elements in the world can be understood in different terms, but for Aristotle the key was to see how they were related by means of “opposite” properties. “Dry” is the opposite of “wet,” and “hot” is the opposite “cold.” Thus in his own interpretation of Anaximander (and remember that Aristotle himself was separated from Anaximander by more than two centuries), Aristotle claims that, “the opposites are separated out from the One, being present in it” (KRS 118). Under this interpretation, the differentiating of unique elements from the monistic ἄπειρον comes about primarily as a result of the process in which what is already latent within the indefinite unity of ἄπειρον becomes manifest in the world. There are various opposites already contained in the one, and it is only later that they become known. As Kirk, Raven, and Schofield explain Aristotle’s view, the ἄπειρον is like “a compound, either a mechanical mixture or a fusion” (130) and out of it the various elements are manifested in turn according to the dictates of the “justice” of the ἄπειρον.

2.2 Simplicius’ portrait

Against this portrait, Simplicius instead reports that according to Anaximander the ἄπειρον,

produces coming-to-be not through the alteration of the element, but by the separation off of the opposites through eternal motion. (KRS 119)

The difference between these two descriptions is slight but telling. Instead of separating “out” of the ἄπειρον, the variety in our world separates “off” of the ἄπειρον. The word “out” in Aristotle’s report implies that the opposites in one sense already existed inchoate within the ἄπειρον. In contrast, the word “off” in Simplicius implies that the opposites only come into being through the process of being differentiated from the metaphysical one. The image Simplicius’ description seems to be resonating off of is that of Aristotle’s prime mover. Like the primer mover, the ἄπειρον is in an eternal motion which induces the spontaneous generation of the elements without itself being affected by its progeny. The elements are caused by the ἄπειρον, but at the same time, their existence is distinctly separate from it.

2.3 Comparison of the portraits in relation to Anaximander

Looking at these two portraits, it seems that both leave something to be desired. Aristotle’s description of the opposites being separated out of the one seems more like a portrait of Anaxagoras’ views than Anaximander’s. Simplicius captures the aloofness of the ἄπειρον, but at the cost of making it something external to the universe, rather than immanently omnipresent. At times it may seem that he considers the ἄπειρον to be merely an undetected fifth element, rather than a truly universal ground of substance.

In judging these interpretations, we must again return to our own projection of the thought process of Anaximander. When considering his thought process, there are two pitfalls that must be avoided. The first is presuming that since Anaximander lived before other philosophers, his conception of the world must be accordingly less sophisticated. This view sees philosophy as a linear progression from the irrational (Hesiod) to the rational (Aristotle), with intervening figures each one degree closer to the culmination of thought. Seeing Anaximander in such a light neglects the fact that he was as intelligent as his successors and had his own lifetime to contemplate the details of his cosmology. While later thinkers may have had a more complex vocabulary ready-to-hand when they began their philosophical endeavors, their own contributions and theories should not therefore be considered to have content that is of a complexity proportionate to their vocabulary. Philosophic vocabulary is able to be accreted through time, but it also needs to be reintroduced to every generation lest it become meaningless jargon. For this reason, every generation is equal to every other in that the world which they uncover will be new to the individuals within it, even if it is described according to a terminology that is no longer new to their culture.

The second pitfall is the opposite of the first, and it is the denial of the possibility of progress and its attendant misstep, the anachronistic attribution of concerns. Though Anaximander was no less a thinker than any of his successors, he nevertheless had a more limited range of concerns. Indeed, progress in philosophy, where it is made, is made most often by changing the field of our concerns rather than producing new critiques of long established fields. For that reason, we should be very careful about imputing an opinion to Anaximander about a field that he may have never considered. Anaximander, like Thales, was clearly interested in pursuing the ἀρχή of all things, but that does not mean he necessarily had carefully considered kinds of causes in the way that Aristotle did. Anaximander may never have systemically considered the “relationship” of elements and opposites that was endorsed by Aristotle, and not because he was any less intelligent, but merely because it had not occurred to him and the terms were not yet a part of the background of Greek thought.

If we reexamine the descriptions of Aristotle and Simplicius in light of these hermeneutic pitfalls, we are led to wonder if we cannot see elements of both failings in the work of these otherwise eminent scholars. While we must of course acknowledge them as invaluable sources for our pursuit of the true Anaximander, at the same time, we must be aware of how they conceal with the left hand even as they reveal with the right. Aristotle confines his predecessors to the unenlightened past, and Simplicius introduces vocabulary (“eternal motion”) that may be more reflective of later thought than his subject’s true opinions. Of course, these true opinions are now lost to the ages and underdetermined by the materials we are given, but nevertheless, by making some charitable assumptions, we might reconstruct the appearance of difference in the monistic world of Anaximander as follows.

The ἄπειρον for reasons previously given must be completely different from any material that we experience in order for it to be more basic or more primordial than other sorts of material. For this reason, it should not be thought of as merely a fifth element alongside the others nor should it be thought of as a simple compound of them as Anaxagoras taught. Instead, the ἄπειρον must be seen as unifying potential for substance that once allows for the generation of matter as a form of itself and at the same time regulates their expression. It is not proper to speak of opposites emerge either “out of” or “off of” the ἄπειρον. Rather, opposites are merely different expressions of the same material, just as the same material in water can be experienced whether it is a liquid or gas. It is by taking one of the various forms of matter that the ἄπειρον become definite in size, shape, weight, &c. and thus able to be experienced by the senses, but the ἄπειρον is always what allows form to become experience-able. A form without the ἄπειρον to give it matter would be an empty thought and lack any true reality other than as thought. Though the nature of forms was apparently not explored extensively by Anaximander, we can nevertheless say that their expression is totally regulated by the ἄπειρον and the blooming of one form at a particular time will lead to ἄπειρον to give reality to the arising of its opposite later in time in order to preserve its sense of cosmic justice.

3. Anaximander and the modern age

With this conception of the ἄπειρον fixed in our minds, we are still left with questions about the practicality of this exercise. Is there any use for Anaximander in the modern age? We have given an interpretation of Anaximander’s thought that we believe reflects his own thoughts about the nature of the ἄπειρον, but it still remains to be shown that his theory (or something like it) possesses value for our own time. In judging whether this is the case, there are two areas to consider. The first is the usefulness of an ἄπειρον-like ἀρχή in the context of modern physics, and the second is an examination of the ἄπειρον as an embodiment of the difficulties of foundationalism.

In early modern physics, the rules of nature and the objects that were believed to be governed by those rules were kept perfectly distinct. With the advent of Maxwell’s laws of electromagnetism, however, there came to be a shift whereby it was unclear whether the objects of scientific examination were themselves anything other than the embodied principles in question. That is, because the electron and its effects are too small for direct observation, our interactions with them are always mediated by scientific equipment, the interpretive operation of which depends on certain presuppositions about the way the machine works. Unlike the apple and the Earth in Newton’s physics, we cannot point to the electron itself except by means of some apparatus. Thus, not only do we impute the existence of a force (gravity in the case of Newtonian physics, electromagnetism following Maxwell’s equations), but we also merely impute the existence of the objects of our studies. The relationship this has to Anaximander is that as was the case with the ἀρχή, we no longer have a clear way of distinguishing the principle which regulates motion and transformation and the material which is moved and transformed. Like Anaximander’s conception of ἄπειρον as ἀρχή, it is not clear that there is any meaningful difference between speaking of Maxwell’s laws (or its successors in quantum theory) as “real” outside of the reality of unobservable substance (sub-atomic particles/ἄπειρον), which is imputed to exist because of its explanatory power at the macroscopic realm. In both cases, the clear separation between principles as causal and principles as material that was so sharply stated in Aristotle has fallen away.

The other application that we can draw from Anaximander’s theories (though again, this is one that he himself would not have drawn since his concerns were not the same as our own) is that since ordinary matter can only be experienced to the extent that it has determinate empirical properties, the ἄπειρον or whatever we call that which is most fundamentally real must be seen as a paradoxical entity which possesses at once both all properties and none. The ἄπειρον is both the immaterial potential for materiality and the material actuality that gives force to immaterial principles. In this sense then the ἄπειρον is a transcendent thing-as-such that is inferred by the human mind but necessarily cannot be experienced. This hints therefore that all theories containing some foundational element or substance must imbue that substance with properties that are seemingly contradictory, because the deepest principles must, if they are truly the deepest principles, be unlike other principles in that they are as deep as a principle can be. When principles becomes so secluded, they can no longer be the sorts of properties common to ordinary things. Based on our inclinations then we can either turn to non-foundationalism in our fundamental ontology or embrace the paradoxical nature of the ultimate.

Thus, we have seen that though Anaximander was one of the earliest Greek philosophers and left behind him only one quotation and a few fragments, nevertheless, his theories can be used as a springboard into new depths of thoughts for us about the ultimate nature of our world that are no less useful than those inspired by more modern thought.

4. Bibliography

• Kirk, G.S., J.E. Raven, and M. Schofield. The Presocratic Philosophers. Second edition. Cambridge University Press, 1983. (Please distinguish bold numbers, which refer to their system of internal numbering for quotations within the book, and plain numbers, which refer to specific pages.)
• Peters, F.E. Greek Philosophical Terms: A Historical Lexicon. New York University, 1967.

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