The Stars Are Eternal.
We take Aristotle's claims to be not merely wrong but laughably so. The sun, not the earth, is the center of our solar system, the planets do not move in circular orbits, matter is homogeneous, and stars have both weight and a history.
This chapter analyzes Aristotle's arguments on behalf of these claims. Not only that: it defends them.
I.1: There Are Only Three Dimensions.
Aristotle begins his study of the heavenly bodies by asserting that bodies, or physical entities in general, have three dimensions. A âcontinuous magnitude,â or an infinitely divisible measure of quantity, that is divisible in one way only is a line. A magnitude divisible in two ways, namely length and width, is a plane; in three waysâlength, width, depthâa body. âThere is no other magnitude or dimension besides theseâ (On the Heavens 268a9). Three-dimensional bodies are, therefore, the complete magnitude.
Proponents of today's âstring theoryâ would disagree. For them there are as many as twenty-six dimensions. Others would count time as a fourth dimension. Contemporary topologists are free to work (algebraically) with as many dimensions as they like. But for Aristotle, there are only three. Of course, three-dimensionality is the way in which we experience bodies in everyday life. But Aristotle does more than simply rely on this commonsensical fact as support for his position. Instead, he offers the following argument defending it.
There is no dimension other than these [the three dimensions] since three are all and âin three waysâ is the same as âin all ways.â For#1 just as the Pythagoreans say, the all and all things have been determined by the three. For#2 end (teleutĂȘ), middle (meson) and beginning (archĂȘ) hold the number of the all, and their number is three. Thus it is that we have taken this number from nature as one of her laws. Furthermore#3 we use this number in the rituals performed in worship of the gods. And#4 the way we name objects reveals this same point as well. For of two things or two people we say âbothâ and we do not say âall.â We first use this term when it comes to three. As has been said, we follow these practices because nature itself leads us in this way. (268a9â20)
Aristotle summons four reasons, flagged by my underlining and numeration, to demonstrate that âthree are all,â a proposition that in turn is used to support the claim that physical bodies have three dimensions. The first (#1) summons a reputable belief (one that is endoxos) passed down by the Pythagoreans.1 On its own, such a reference would hardly prove that âthree are allâ or even explain what this phrase means. Nonetheless, as discussed in the Introduction, a reputable belief is that which âseems true to everyone or to most people or to the wise, either to all of the wise or to most of the wise or to the best known and most reputable of the wiseâ (Topics, 100b21â22) and by itself carries some evidentiary force. Even if it is neither entirely right nor maximally clear, it will never be all wrong. It can thus be counted as some sort of epistemic clue (>IV).
Aristotle next supplies an independent conceptual argument on behalf of the claim that âthree are all.â He asserts in #2 that a whole must have an end, middle, and beginning, and thus is triadic in structure. This is the key to understanding and appreciating Aristotle's argument and it is discussed in detail shortly (>I.2).
In #3 Aristotle alludes to religious practices in which the triad figures prominently. He may be referring to the pouring of one libation to the gods, a second to the heroes, and a third to Zeus the savior. Whether he is or not cannot be determined because so many Greek religious rituals were triadically structured.2 This prominence of the triad may be derived from a primitive division of the cosmos into sky above, earth below, and some in between that mediates or connects the two. Hesiod, for example, has the god Sky descend upon the goddess Earth in order to begin the process of generating the rest of the cosmos. In this case, nightfall could be construed as a connective tissue (as could rainfall). Many a myth, including one found in Plato's Symposium, treats human being as in between the immortal, found above, and the mortal, found below.3
Reason #4 refers to the fact that ordinary language, both Greek and English at least, testifies to the exceptional status of the three. If there are two apples on the table, and I tell you that I want them, you might ask, âDo you really want both?â You wouldn't ask, âDo you want all of them?â If my eyes hurt, and you ask me, âWhich one hurts?â I will answer, âBoth of themâ rather than âAll of them.â The word âallâ is first used when I have at least three items to count. (That Greek verbs have, in addition to the singular and the plural, the dual further reinforces this point.) For Aristotle, this linguistic observation counts as another piece of evidence for, a reason to believe that, threeness determines allness.4
Differently stated, in a (nontechnical) sense three is the first ârealâ number. If there is but a single item clearly visible on the table, say a book, no one would ask the question, âHow many books are on the table?â Instead, someone might ask, âWhat's that on the table?â One item is not counted, but recognized for what it is. Only when there are at least two items does the question âHow many?â become relevant. This fact is reflected in the Greek word arithmos, which means ânumberâ as well as âa count.â A count requires a plurality, a number of items or units. This is also why, in standard Greek arithmetic, two was taken to be the first number. (See Physics 220a27.) However, in order to determine that there are two books on the table, there must be some way of differentiating them. Either they are not by the same author, or even if they are two virtually identical copies of the same book, they are made from different pieces of paper and located in different places on the table. In short, if there is to be a two there must be a third; a differentiating principle. In this sense, three is the first ârealâ number.
Because reasons #3 and #4 seem to do no more than report bits of anthropological data, it is easy to formulate objections to them. Why, for example, should the fact that many religious rituals and practices are triadically structured play any role whatsoever in an argument about the nature of the nonhuman cosmos? This question resurfaces later in On the Heavens when Aristotle deploys a similar argumentative strategy. After having argued that the âfirst body,â the fifth element of which the stars and planets are made, is eternal and divine, and so more âhonorableâ than any found here on earth, he asserts that âall human beings have a conception of the gods and all, both barbarian and Greek, assign the highest place to the divineâ (270b5â7). He cites this putative fact as a supplementary piece of evidence to confirm his theoretical analysis of the nature of the âfirst body.â Exactly as in #3, Aristotle marshals an anthropological datumânamely, that human beings regularly locate god upstairsâin the service of his scientific claim that the heavenly bodies above us are eternal. (Also see Metaphysics 1074b1â15.)
Aristotle seems to invest these sorts of anthropological data with the same sort of evidentiary value he finds in empirical observations. âBy appealing to perception, this conclusion [that the heavenly bodies are eternal] follows in a manner sufficient in order to generate human conviction. For in all time past, according to the memory that has been passed down, no change has appeared (phainetai) to have taken place either in the whole of the outermost heaven or in any one of its proper partsâ (270b13â15).5
In other words, according to the best record of empirical observations made by astronomers available at the time, nothing has changed in the heavens. Therefore, Aristotle reasons, the heavenly bodies must eternally move in the same orbit.
Aristotle's conjunction of these two strands of evidenceâone citing the phenomena of religious belief and ordinary language and the other empirical observations of the heavensâtells much about how he argues, how he thinks, in general. As discussed in the Introduction, his theory aims to do justice to the phenomena, the way the world shows itself to us in ordinary experience. It is, in other words, âphenomenological.â The âphenomena,â however, must be construed broadly, for they include both empirical observations and the âreputable beliefsâ (ta endoxa). They include, as Owen put it in a famous essay, the legomena, âthe things saidâ or âlinguistic usageâ or âthe conceptual structure revealed by language.â Or to cite Nussbaum, in addition to empirical observations, âAristotle's phainomena must be understood to be our beliefs and interpretations, often as revealed in linguistic usage.â6 The world shows itself to us not only through our senses, but also in the way we talk and how we conduct ourselves in daily life.
Because his theorizing is characterized by this sort of hybrid argumentation, Aristotle seems subject to the charge of anthropocentrismâor, even worse, anthropomorphismâof exactly the sort Bacon and Spinoza criticized so harshly. Regardless of whether this charge is fair or not, Aristotle himself certainly would deny that he is projecting a human perspective onto a nonhuman screen. Instead, he claims quite the opposite: âwe follow these practices because nature itself leads us in this wayâ (268a19â20). So, for example, the number three is privileged in human practices and language not because human beings favor it, but because we âhave taken it from natureâ (268a13). The ways in which we speak and perform our religious rituals are guided by the way things really are. In turn, such phenomena can provide evidence about the world as it really is.
Of course, it is necessary to explain why phenomena like ordinary language and religious practices have epistemic value. To prefigure the discussion whose elaboration constitutes a major chunk of Chapter Four, Aristotle believes that human beings by nature tend to get things right. As he puts it, âhuman beings are naturally and sufficiently disposed towards seeking the truth, and in most cases attain the truthâ (Rhetoric 1355a15). We are âtruthingâ animals whose perceptual, cognitive, and linguistic apparatus are well suited to know the world. As such, it is entirely reasonable to pay attention to how we talk and act in order to figure out how things, including things like the planets and stars, really are.7
I.2: Threeness Determines Wholeness.
Back to the argument in On the Heavens: bodies have only three dimensions because âend, middle and beginning hold the number of the all, and their number is three.â To begin elaboration, consider the following definitions Aristotle offers of the âallâ and the âwholeâ:
- ââWholeâ (holon) means âthat from which no part of that which is said to be by nature a whole is missingâ (Metaphysics 1023b26).
- âThat of which nothing is outside is complete (teleion) and whole. For we define a âwholeâ thus: as that from which nothing is absentâ (Physics 207a9â11).
- ââAllâ (pan) means âa quantity that has a beginning, middle and termination point (eschaton) but whose positions make no difference.â If position does make a difference, then it is a wholeâ (Metaphysics 1024a1â3).
A âwholeâ is an ordered unity of parts, whereas an âallâ is an unordered collection or sum of parts. Aristotle's terminology vacillates between these three texts and On the Heavens. In the latter, pan, translated as âall,â actually means âwholeâ in the sense given in the Metaphysics and Physics (and which is the only concern of this section).8
These definitions illuminate what Aristotle means when he says, to paraphrase, that the number of the whole is three; or that threeness determines wholeness; or that wholes are by nature triadic. Because it is an ordered unity of parts, a whole has a beginning and an end, and something in between. So, for example, the word âBATâ is a whole. It is not an âallâ because the position of the elements does matter. The word âBATâ cannot be captured by a simple list of its letters, for the letters B, A, and T can be combined in more than one way. âTABâ is not the same as âBAT.â For âBATâ to be what it is, its three letters must be in their proper order. A whole is more than âallâ of its parts because it has a formal structure, an intelligible ordering of its parts. The spelling of âBATâ begins with the letter B and continues in proper sequence until T. Then the end has been reached, and the word is complete. âBATâ stands available for inspection as a whole.9
To approach this same point from a different angle: in the Physics, Aristotle says, âThe whole and the complete (teleion) are either entirely the same or of kindred nature.â The whole is âcompleteâ because its telos, its end, goal, or purpose, has been achieved and ânothing is complete that does not have a telos.â This implies, as Aristotle next states, that âthe telos is a limit (peras)â (207a13â15). For if something can be completed then it is limited; after beginning and traversing what is in-between, an end is reached. Recall that in On the Heavens Aristotle says that the three-dimensional body is the âcompleteâ (teleion: 268a22) magnitude. With it the counting of the dimensions reaches its end.
Another sense of teleion requires brief mention. In the Metaphysics, Aristotle assigns it two meanings. The first is essentially the same as that of the âwhole:â it is that âoutside of which it is impossible to find one of its partsâ (1021b12â13). The second is âthat which is in accord with excellence and the good cannot be exceeded in its kind. For example, a perfect doctor or a perfect flutist are those who, according to the form of the excellence that belongs to them, lack nothingâ (1021b15â17). Here teleion is translated as âperfect,â which in English has the same ambiguity as the Greek; it means both âcompleteâ or âwithout omissionâ and âmost excellentâ (>II.8). In some sense, then, three-dimensional bodies, as the complete or teleion magnitude, are better than lines or planes.
Aristotle argues that because âthree are all and âin three waysâ is the same as âin all waysâââin other words, because threeness determines the wholenessâthere are only three dimensions. Three, in other words, is privileged, for it is the number of completeness. On the one hand, this is a just silly bit of numerology. Three is not special. It's just another number. To glorify it as Aristotle (following the Pythagoreans) does is to invest it with qualities that belong not to it, but to a prejudice held by (some) human beings. On the other hand, if Aristotelian cosmology is construed as phenomenological and is thus required to remain faithful to ordinary experience, a possible line of defense is opened up. For our experience is indeed constituted by the triadic nature of wholeness. Consider the following examples.
1. The topological whole. When we open our eyes and walk forward, what is in front of us appears as a triangulated whole. There is what is to the left of us, the right of us, and in front of us. When we stop walking and remain in one place, we can look upward to what is above, downward to what is below, and straight ahead to what is level with ourselves. Finally, there is front, back, and center. In sum, our experience of occupying a place in the physical world is triangulated, and is so in three different ways. In Aristotelian terms, there are six âparts and forms,â six âdivisionsâ or âdirections,â of place: up, down, left, right, front, back (Physics 208b12).
It is reasonably easy to explain why we experience the world this way. Like other animals, we are bilaterally symmetrical, and vision is thus bifocal. We have left and right eyes, as well as hands, legs, and so forth, and we divide our visual field directi...