Qualities of bees and other animals

An easy answer to the question of how bees could be seen as divine might appear to lie in the general high esteem that ancient writers seem to have had for bees, but the vast majority of evidence for this regard is either later – and often much later – than Aristotle, or else is rooted in mythological or cultic references to bees and their imagery.Footnote ¹¹ Aristotle is not generally one to use folkloric, mythological or cultic material unreflectively (in fact he is often positively opposed to doing so), and I think it can be shown that something more interesting is afoot in the present case.

In his description of bee generation, Aristotle signals again and again that things are unusual and especially interesting. He repeatedly calls bees and their system of generation ‘unique’, ἴδιος, and ‘extraordinary’, περιττός. But neither of these adjectives rises to the level of ‘divine’ (to take a contrasting example, at HA 536a8–11 we see frogs’ tongues singled out as unique, ἴδιος, without any overtones of divinity implied). When it comes to humans, he only twice calls them divine without qualification, the rest of the time giving humans something like divinity by proxy, which is to say via some divine property or faculty that Aristotle thinks that humans possess.

Depending on how one reads an important passage of Metaphysics Λ, where Aristotle is talking about the ability of thought to contemplate thought itself (something he is working up to as a defining characteristic of god), humans, who clearly are capable of reflexive thinking, may also possess this ‘divine’ ability.Footnote ¹² But note that this is a proxy divinity: a person's access to the divine is via the possession of a faculty – reflexive thought – that is itself divine. Aristotle also tells us that a number of other (often closely related) human faculties are divine: the faculty of reason, the possession of intelligence (νοῦς), and the ability to think and reflect. Similarly, Aristotle calls our capacity for moral excellence and happiness divine.Footnote ¹³ In each of these cases, qualities that humans possess are called divine, but not humans in and of themselves.

There are only two places where Aristotle seems to assign divinity directly to humans, which is to say that he gives humans divinity simply by virtue of their humanity. Both occur in the Parts of Animals. In the first of these passages, he says that it is fitting for humans to be the only animal to walk upright, for this is in keeping with our divine essence or substance (οὐσία). He begins the passage by remarking that in the place where other animals have forelegs and paws, humans instead have arms and what are called hands.Footnote ¹⁴ He continues, ὀρθὸν μὲν γάρ ἐστι μόνον τῶν ζῴων διὰ τὸ τὴν φύσιν αὐτοῦ καὶ τὴν οὐσίαν εἶναι θείαν· ἔργον δὲ τοῦ θειοτάτου τὸ νοεῖν καὶ φρονεῖνFootnote ¹⁵ – humans ‘are the only animal that is upright, because their nature and their essence are divine, and also because to think and to be intelligent is the task of the divine’. The idea here is that thinking and intelligence would be impossible if the weight of the body were distributed on all fours as it is in other animals, because the bulk of the body would press down on the mind and on the perceptual apparatus. Nature and essence, on the one hand, and thinking and intelligence, on the other, are a one–two punch attesting to human divinity. I will deal with each of these distinct parts of the claim in turn.

The initial attribution in this passage (nature and essence) is clearly direct: we have divinity simply because our nature and our ousia (our being or essence) are divine. The second attribution (via thinking and intelligence) may at first look like the proxy versions of divinity that we saw a moment ago, where divinity arrives via specific faculties that we possess, but the situation is in fact quite the opposite. Consider the structure of the argument, which is not in the first instance trying to prove that humans are divine (this is simply stated in the previous clause), but rather that the divinity of humans (and only humans) explains why they alone walk upright:

1. (a) Thinking and intelligence are the tasks of what is divine.

2. (b) Thinking and intelligence are impossible for quadrupeds because of the distribution of body weight.Footnote ¹⁶

3. (c) Therefore humans, qua animals that are divine in both nature and essence, cannot be quadrupedal.

What is being emphasized here is just an add-on to the assertion, already made, that humans are divine. We are divine and therefore intelligent, and therefore must be bipedal because the distribution of weight in quadrupeds prevents the necessary freedoms for the parts associated with intelligence.

This, then, is the first direct attribution of divinity to humans. In the second one, things are a little more nuanced and potentially open-ended. Aristotle puts it this way: ἢ γὰρ μόνον [sc. τὸ τῶν ἀνθρώπων γένος] μετέχει τοῦ θείου τῶν ἡμῖν γνωρίμων ζῴων, ἢ μάλιστα πάντωνFootnote ¹⁷ – ‘of all the animals known to us, either the genus of humans alone partakes of the divine, or [it does so] more than all the others’. The qualification ‘more than all the others’ is a concession meant to capture something he discusses in the Generation of Animals about the qualities of the souls that all animals (and indeed all living things) possess:

So, the generative power of the seed ‘shares in’ something ‘analogous to’ the aether, the element of the stars (which is frequently characterized as divine by Aristotle). And this is true for all animals.Footnote ¹⁹ Therefore insofar as (most) animals are generated from seed, they have pneuma, and so they all participate to some extent in the divine. This is no mere throwaway comment.

There is a second aspect, however, in which all species participate in the divine. The process of reproduction is said in the De anima to allow each species to continue eternally. Even though this individual snail must perish, the species of snails is a continuity from infinite time past (there was no beginning to the Aristotelian cosmos) and it will continue for infinite time going forward (there is no end). And so, given that it participates in this eternal existence of its own proper species, the individual animal, this individual snail, is participating in the eternal and therefore the divine: φυσικώτατον γὰρ τῶν ἔργων τοῖς ζῶσιν … τὸ ποιῆσαι ἕτερον οἷον αὐτό, ζῷον μὲν ζῷον, φυτὸν δὲ φυτόν, ἵνα τοῦ ἀεὶ καὶ τοῦ θείου μετέχωσιν ᾗ δύνανταιFootnote ²⁰ – ‘the most natural activity for animals is the making of another like itself … an animal [making] an animal and a plant a plant, in order that they may, to the extent that they are able, participate in the eternal and the divine’.

But people – and bees – are explicitly said to go beyond this basic level. As we have seen, for humans we can parse out from multiple passages what makes them more divine than other animals and the list is not a long one: our possession of reason and nous (mind), our ability to think and understand, and our capacities for moral excellence and happiness. But if we then try to parse out the virtues that Aristotle finds in bees, we never see them qualified in quite these human ways, although in a couple of passages Aristotle may come close. In a perplexing section at the very outset of the Metaphysics, Aristotle tells us that bees are ‘prudent’ or ‘wise’ (phronimos) but unable to learn or to hear sounds.Footnote ²¹ Phronimos as bees may be, though, we note that Aristotle elsewhere calls the deer, the hare, the weasel and the crane (to whom we shall return in a moment), as well as ‘some quadrupeds’, phronimos, but he never calls any of these other animals divine.Footnote ²² Similarly, bees, but also ‘all animals like them’, are said to be more phronimos in their nature (φρονιμώτερα τὴν φύσιν ἐστίν) than even some blooded animals, but again notice the qualifications: bees and others, more than some blooded animals.Footnote ²³ Likewise bees and ants are said to ‘have a more sagacious soul’ (συνετωτέραν ἔχει τὴν ψυχήν) than some blooded animals.Footnote ²⁴ Again, as with the deer and the hare, the ants and ‘all other animals like bees’ are not called divine. Moreover, when Arsitotle tells us at one point that animals other than people οὔτε τέχνῃ οὔτε ζητήσαντα οὔτε βουλευσάμενα ποιεῖ – ‘do nothing by craft nor do they plan objectives’ – he floats two possible outliers to this rule by name, neither of which are bees. He cites instead the spider and the ant, and then adds ‘and animals such as these’, whatever that may mean.Footnote ²⁵ Finally, he tells us that bees and ants lack phantasia, ‘imagination’ or ‘the faculty of representation’, which might be taken to limit, at least somewhat, the extent to which they are phronimos.Footnote ²⁶

Perhaps the most widely discussed of the human-like characteristics that bees are said to possess is their political nature:

Once again, however, bees are far from alone. If we cast about to see what other traits bees may share with some of their fellow political animals we find an interesting list. Like cranes, not only do bees have leaders, but they also apportion specific jobs to particular individuals, stationing ‘guards’, for example, at the openings of their hives.Footnote ²⁸ Cranes do something similar, stationing them at the outside edges of their flight formations:

Like the bees that guard the hives, the cranes here post guards at the edges of their flight formations as well as when they sleep. Notice, too, that the action of the leader for alerting the flock is one of ‘signalling’, albeit wordlessly: σημαίνει βοῶν, ‘he signals [by] shouting’. Bees do something similar, but rather than alerting the hive to awaken, one of them flies around, buzzing ‘as though to tell’, ὥσπερ σημαίνουσα, the others to go to sleep.Footnote ³⁰ Again like cranes, bees are also said in this same section to predict the weather: προγιγνώσκουσι δὲ καὶ χειμῶνα καὶ ὕδωρ οἱ μέλιτται – ‘bees predict both storms and rain’.Footnote ³¹ Talk of leaders and signalling may play into a larger set of what appear to be military metaphors for the activity of bees in Aristotle: bees are said to be ‘marshalled’ (τεταγμέναι) for different jobs,Footnote ³² they can suffer ‘splitting of the ranks’ (διασπῶσι),Footnote ³³ and at one point Aristotle tells us a story about one hive invading the other, with an extended use of military language.Footnote ³⁴

If we search around for other virtues and vices attributed to bees, we do not see much that seems to be promising with regard to divinity. It is true that bees are said to be especially industrious, ἐργατικώτατον ζῴων, but again, Aristotle includes ants in this class, as well as anthrenae, wasps, and all such animals.Footnote ³⁵ Bees are said to be in general ‘thrifty’, and to store food away for later: φεδόμεναι καὶ ἀποτιθέμεναι τροφῆς χάριν (how this fits with Aristotle's rule that no animals plan for the future, he does not say).Footnote ³⁶ The last of the positive attributes of bees for Aristotle is their cleanliness. They are said to be ‘a most clean’ animal (I suspect he does not mean the most clean, but Greek can be ambiguous with its superlatives in this way), and he mentions elsewhere that unlike other insects they never settle on rotting flesh.Footnote ³⁷ More negatively, like other political animals, bees and cranes can be violent to each other,Footnote ³⁸ and finally, among bees (‘like women’, as he feels the need to add) the showy and beautiful ones are lazy: αἱ δὲ φαναὶ καὶ λαμπραί, ὥσπερ γυναῖκες, ἀργαί [ἐστιν].Footnote ³⁹

The divine in Aristotle

If we can find nothing specific or in combination in the discussion above that can clearly explain what comprises the divinity of bees, we should perhaps grasp the stick from the other end, and have a look at what kinds of things other than bees are said to be divine in Aristotelian natural philosophy.Footnote ⁴⁰ In addition to bees, we have already seen humans and (some of) their highest virtues, the generative capacity of seed, and the eternality of species each called ‘divine’. And on this last count we might note that the eternal, for Aristotle, is often a – if not the – key aspect of divinity. Indeed, for Aristotle it is immortality that in many instances forms the central attribute that defines what (a?) god is: ἕκαστόν ἐστιν, ὧν ἐστὶν ἔργον, ἕνεκα τοῦ ἔργου. θεοῦ δ᾽ ἐνέργεια ἀθανασία· τοῦτο δ᾽ ἐστὶ ζωὴ ἀίδιοςFootnote ⁴¹ – ‘everything for which there is a function, exists for that function. The activity [actuality] of god is immortality, so the function of god is eternal existence’.

So, too, the fact that the planets move in circles is a key part of what makes the planets and the cosmos as a whole divine in Aristotelian cosmology because circular motion, unlike rectilinear movement, has no beginning and no end.Footnote ⁴² Anything eternal, whether material or causal, is to that extent divine.Footnote ⁴³ Eternality, though, is not everything for divinity: primacy also seems to play a role, as we find Aristotle assigning divinity to his prime mover, first cause(s), first philosophy, and the first or motive principles of physics or philosophy.Footnote ⁴⁴ None of this, I am afraid, will help us with bees.

Now, we have already seen that bees, like all animals, touch the divine in that they reproduce and maintain the species in eternity. Insofar as they are (non-spontaneously generated) animals, they must also produce seed to generate young and so they contain pneuma in that seed, through which again they touch the eternal and divine matter of the stars, the aether. But this is true of any animal, and thus far there is nothing in the virtues or character of bees in particular that would seem to make them an especially good link with the kinds of things that Aristotle thinks of as divine, and the problem threatens to be a difficult one. As a solution I want to float the following possibility: perhaps it is just the context in which we found Aristotle attributing divinity to bees that offers the solution. That is to say, there is something specific about their mode of generation that links some aspect of the divine to them.

The worry here is that, if we look back to the assertion about bees and divinity that started us on this question, things may well begin to look a little circular with respect to their divinity. But we could structure it as a syllogism thus:

1. (1) Bees have something divine about them because of how they reproduce.

2. (2) Wasps do not have anything divine about them as bees do.

3. (3) Therefore wasps do not reproduce as bees do.

That would certainly be the most natural reading of the γάρ in the second clause of ἀφῄρηται δὲ τὸ περιττὸν εὐλόγως· οὐ γὰρ ἔχουσιν οὐθὲν θεῖον ὥσπερ τὸ γένος τὸ τῶν μελιττῶνFootnote ⁴⁵ – in wasps ‘the unusual aspects are appropriately absent, for they possess nothing divine like the genus of bees does’. This would seem to suggest that the key to bees’ divinity may inhere in their three-caste system for reproduction, one not shared by wasps or other insects. If we look to how Aristotle explains bee reproduction, we find him marvelling at two aspects of it in particular: (1) the blending of the sexes in one individual (although he also says that this is at least possibly mirrored by two kinds of fish), and (2) the hierarchy of the castes in their reproductive roles, a feature apparently unique to bees. Let us look at each of these in turn.

After canvassing all the various theories that people have about bee reproduction and dismissing them, the answer that Aristotle settles on as most likely (on his current evidence) puts the power of both genders into each individual worker bee. This strikes Aristotle as interesting:

He goes on to explain that the same principle applies to the kings, which generate both workers and more kings. The comparison to the fish known as the erythrinus and channa, though, is imperfect, as we said above, for each of these fish reproduces themselves rather than producing something different in kind (and this is assuming that Aristotle is correct in his speculation about how those fish reproduce – even he is often tentative when it comes to the erythrinus and channa, since he only has a negative observation to go on: that no males have yet been found).Footnote ⁴⁷

Triplicity and proportionality

And so this blend of male and female is interesting, and at least possibly unique. But what is really unique about bees is their threefold caste system, unseen anywhere else in nature. Not only is it unique in being threefold, but there are also – and this, I think, is the key – several mathematical harmonies in how the reproductive mechanism seems to work across the castes. Notice that the kings produce two kinds of animal: kings and workers, and one class of the animals that they produce, the workers, then goes on to produce one other class of animal, the drones, which then goes on to produce nothing at all, giving us a remarkable (and, Aristotle thinks, very beautiful) two–one–zero progression: kings produce two kinds of offspring, workers produce one, drones produce none (see Figure 1).Footnote ⁴⁸

Figure 1.

Aristotle's two–one–zero linear series for bee generation. Aristotle sets the hierarchy up in this order (kings, workers, drones) such that the first member of the series generates itself and the next member, the second member generates the third member, and the third generates nothing. The pattern shows itself not just in terms of descending numbers, but also in terms of a descending fecundity which maintains the ordering of the castes at both levels of the diagram.

Moreover, at the two ends of this continuum, we find that the kings and drones are each large in size whereas members of the class standing between them (the workers) are small; at the same time, the two generative types (kings and workers) each have stingers while the sterile type (drones) does not (see Figure 2). Aristotle immediately sees a double mathematical beauty to this arrangement, and it is here, I think, that divinity begins to gain a substantial foothold:

A kind of mathematical proportion (ἀνάλογόν πως),Footnote ⁵⁰ an orderly arrangement (τάξις), has its completion in the third member of the series (ἐν τῷ τρίτῳ ἀριθμῷ πέρας ἔσχεν) – this is strikingly beautiful (and indeed Aristotle says so explicitly).

Figure 2.

Parallel proportionalities (size versus stingers). Note how this centralizes the kings, who have single characteristics in common with each of the other two members of the series, while each of the other two members (workers and drones) are not situated in such a relation to each other. Rather than reorganizing the earlier hierarchy of kings–workers–drones, we see here a kind of a transcendence of it.

But there is one more factor that I suspect is not trivial. It turns out that Aristotle frequently also finds the number three both significant and sublime. For his part, Aristotle is not generally quick to Pythagorize, but we do find him doing so on a few occasions. One such instance occurs at the opening of the De caelo, where he is reflecting on the number of geometrical dimensions possible in our universe, and remarks that the fact that there are three is no accident. For,

Threeness takes us effortlessly for Aristotle from the inherent structure of the cosmos, via a law of nature, to the ritual structure of divine worship. It is worth noting that this may be the only instance in the entire Aristotelian corpus where he mentions the Pythagoreans in more than a passing manner without criticizing or correcting them.Footnote ⁵²

As his argument develops in Book I of the De caelo, Aristotle again returns to the number three as significant when he finds that the number of simple motions is also three. One has to be an Aristotelian to really buy into this, but on his analysis, there can only exist (1) straight-line motion, (2) circular motion and (3) a combination of the two. Moreover, we see another threeness in the two ‘pure’ forms of motion, where straight-line motion is defined as always (1) toward a centre or (2) away from a centre, and circular motion is (3) around a centre. He seems, in the event, particularly pleased that the number of simple motions should match the number of spatial dimensions: καὶ ἔοικεν ἠκολουθηκέναι κατὰ λόγον τοῦτο τοῖς ἐξ ἀρχῆς· τό τε γὰρ σῶμα ἀπετελέσθη ἐν τρισὶ καὶ ἡ κίνησις αὐτοῦFootnote ⁵³ – ‘and it is fitting that this follows proportionally with what we said at the outset: body is completed in a three, and so is its motion’.

To get a sense of the significance of triplicity for Aristotle, I have combed through the entire corpus of his works to isolate the kinds of things he understands in terms of three explicit parameters, and they turn out to be (a) surprisingly ubiquitous and (b) often quite central to his understanding of the world. What follows is, in spite of its length, necessarily non-exhaustive, partly because he doesn't always flag his triplicities in so many words, and partly because I am bound to have missed a few just by dint of sheer volume. These examples, I should also note, do not count times Aristotle claims that someone else thinks that there are three x’s, nor the frequent instances where he casually offers up triplicities of adjectives or examples as a simple rhetorical figure. What remains, for all that, is truly impressive.Footnote ⁵⁴ There are:

• animal and cosmic parts, three archai of (front/back, above/below, right/left);

• animal reproduction – a great number of animals reproduce or come to sexual maturity in intervals of three (months, years), or give birth to three offspring;

• animals, three parts of (parts for food intake, parts for excrement, part in between);

• appetites, three (will, impulse, desire);

• argument, three elements of (speaker, subject, audience);

• attributes obtain in three ways;

• audience, three kinds of (assemblyman, juror, aficionado);

• bodies, three condensed by cold (water, snow, hail);Footnote ⁵⁵

• causes/archai, three (form, privation, matter);

• change, three aspects of (action/passion, combination, contact);

• change, three kinds of;

• channels, three from eye to brain;

• choice, three objects of (the good, the useful, the pleasant);

• coming-to-be, three archai of (two contraries plus a subject of whom they are predicated);

• commerce, three kinds of (capital, transport, sale);

• ‘composition’ of animal parts, three kinds of;

• constitution, three kinds of;

• contempt, three kinds of;

• courts of law, three determinants for (eligibility, mandate, method of appointment);

• craftsman, three grades of;Footnote ⁵⁶

• deception, three causes of;

• deduction, three terms in;

• demonstration, three divisions of ‘by nature’;

• demonstration, three kinds of;

• dimensions (spatial), three;

• dispositions, three kinds of (or three grades of emotion or action: the mean, excess, defect);

• education, three bases for (the mean, the possible, the proper);

• elements (bodily), three (the heavy, the light, the circular) and three elemental ‘places’;

• emotions, three criteria for understanding;

• excellence (in humans), three sources of (nature, habit, reason);Footnote ⁵⁷

• friendship, three kinds of;

• good, three kinds of;

• government appointments, three considerations for (who appoints, from whom, how);

• government, three branches of;

• government, three forms of;

• government, three grounds for equality in;

• governments, three conditions for mixed ones;

• growth, three properties of;Footnote ⁵⁸

• happiness, three means to (excellence, prudence, pleasure);

• harms in a partnership, three kinds of;

• head, three functions for;

• heart, three actions of (palpitation, pulsation, respiration);

• heart, three cavities of;

• ‘heaven’, three senses of the word;

• homonymy, three ambiguities in;

• insect bodies, three parts of;

• insect development, three stages of;

• imitation, three kinds of;

• justice, three forms of (based on three forms of government);Footnote ⁵⁹

• knowing and error, three kinds of;

• life, three kinds of (the hedonistic, the political, the theoretical or philosophical);

• love, three causes of;

• luck, good, three determinants of;

• magistrates, three offices for choosing;

• moral states, three to be avoided (vice, intemperance, brutality);

• movement, three ‘aspects’ to (what, where, when), or differently articulated (from what, to what, what), or differently again (mover, moved, instrument of motion), or again (mover, moved, time of motion), or again (beginning, middle, end);

• movement, three kinds of (quality, quantity, place);

• mover, three kinds of;

• music etc., three benefits of (education, amusement, contemplation);

• non-being, three forms of;

• nutrition, three aspects to;Footnote ⁶⁰

• opposition, three kinds of;

• orator, three bases for confidence in (prudence, virtue, goodwill);

• people, three classes of;

• perceptibility, three meanings of;

• perception, three epistemological grades of;

• persuasion, three forms of (speaker's character, listener's disposition, argument);

• physics, three branches of;

• poetry, three tools of (rhythm, melody, metre);

• political offices, three qualifications for highest;

• power relations in a household, three kinds of (master–slave, husband–wife, father–children);

• presentation, three modes of;

• problems, three kinds of (ethical, natural, logical);

• ‘productive’ (ποιητικός), three senses of;Footnote ⁶¹

• relaxation, three sources of (sleep, drinking, music);

• rhetoric, three ends of;

• rhetoric, three forms of (deliberative, judicial, declamatory);

• rhetoric, three grades of proposition in (proof, likelihood, sign);

• rhetoric, three temporal horizons relevant to (future, past, present);

• sameness, three kinds of;

• speech, three sources of vividness (metaphor, antithesis, vigour);

• speeches, three aspects to (ideas, language, arrangement);Footnote ⁶²

• soul, three characteristics of (movement, sensation, incorporeality);

• soul, three critical faculties of (phantasia, sensation, nous);

• soul, three functions of;

• soul, three parts that control action and truth (perception, mind, appetite);

• soul, three variables in (passions, powers, states);

• stasis and revolution, three causes of;

• substance, three kinds of;

• ‘substance’, three meanings of (form, matter, combination of the two);

• sutures, three in the skulls of male humans (one in females);Footnote ⁶³

• theoretical knowledge, three kinds of (mathematics, physiké, theology);

• tile, three shapes of to cover a two-dimensional surface (triangle, square, hexagon);

• toes, three joints in;

• Topics, three ways it will be useful;

• tyrants, three goals of;

• voice management, three aspects of (volume, pitch modulation, rhythm);

• ‘voluntary’, three senses of (according to appetite, to choice, to thought);

• wrongdoing, three aspects to a determination of.Footnote ⁶⁴

Trifurcation clearly plays a major role in Aristotle's conceptual approach to the world. Even if he does not dwell on the significance of triplicity in the instances listed here, at the very least we can see an inherent bias toward – or at any rate a strong fondness for – trifurcation. Much more rarely than these many simple acts of trifurcation, however, Aristotle also occasionally comments in a little more detail on why triplicity in itself is important to him.

He tells us, for instance, that three is the first number to which the adjective ‘all’ applies (the number two only gives us ‘both’).Footnote ⁶⁵ This is admittedly not much to go on, but the fact that he feels the need to say it explicitly does indicate something. Going further, however, he also adds in another context that threeness as an organizing principle is simply and inherently ubiquitous in the structure of the world. After pointing out that there are ‘three’ colours in a rainbow (as he parses them: purplish red (φοινίκεος), bright green (πράσινος), violet (ἁλουργόν)),Footnote ⁶⁶ he adds as a methodological point, ἐπὶ δὲ τὸ πλεῖον οὐκέτι φαίνεται, ἀλλ᾽ ἐν τοῖς τρισίν, ὥσπερ καὶ τῶν ἄλλων τὰ πλεῖστα – its colour ‘does not manifest any further but comes in threes, as most other things also do’. Here we see an explicit acknowledgement that there is something special about three for ordering concepts, and that Aristotle recognizes the pattern that we identified above as a characteristic of his own thinking (even if he does not see it, perhaps, as idiosyncratic).

Divine order in nature

Three, then, manifests as a significant pattern that emerges from the process of ordering phenomena for Aristotle. And ordering, as it turns out, is a quintessential function of the divine, as he tells us:

Now, one should be careful not to read too much into the last clause of this claim, the idea that what is beautiful or good consists of number and magnitude, since it is unclear how broadly Aristotle really wants to apply such an argument, but the idea that number and order are themselves attributes and proper actions of divinity seems clear.Footnote ⁶⁸ Moreover, the passage picks up language Aristotle happened to use in his discussion of size versus fecundity in king bees, where few are produced, but the ones that are, are large. He phrases this in terms of a ‘repayment’ on the part of nature, where nature takes away from the kings an ability to reproduce many of their kind at once, but repays them with prodigious size. The words he uses for the trade-off are precisely those he uses to describe beauty in the politics passage: it is a balance, a symmetry, between number and magnitude: πλήθος τε καὶ μέγεθος.Footnote ⁶⁹

The ethical point in the initial Politics passage is that good laws and good societies reflect a good order among citizens, non-citizen residents and rulers, and Aristotle parses this order in terms of ‘ordered number’ explicitly. This may appear at first to be a point of relatively narrow scope, but the broader comparison it draws has much larger significance: divinity acts to give order to the otherwise non-self-ordering mass of the cosmos. Part and parcel of this active ordering is a beauty relation of number and magnitude. This matters for two reasons. The first is a potential (but only apparent) conflict involving the idea of the beautiful as number for Aristotle. The specific conflict that is threatened has to do with a Pythagorean–Platonist idea that Aristotle flatly rejects elsewhere (at the end of the Metaphysics): the idea that numbers can have causal force. If numbers cannot have causal force for Aristotle, then one might be tempted to argue that one cannot make sense of his statement that the beautiful (a) consists in number and (b) somehow informs the divinity in ordering the universe. But his argument against the Pythagoreans and Platonists is about how they see particular numbers as final (or even efficient?) causes of unity where Aristotle denies it. Thus, for Aristotle, ‘seven’ may be shared by the number of musical notes and by the number of stars in the Pleiades, but ‘seven’ is not a (Platonic) Form whose essence is being instantiated by things both musical and stellar. This is not to say that it is never significant when particular numbers turn up in different applications, but that in such cases it is not the specific number doing the causal work. The number (in the case of bees, three) may show that two different things share important properties, as we saw with the number of spatial dimensions and the number of simple motions, but the number ‘three’ itself is not causing spatial dimensions and simple motions.

The second reason why the divine act of ordering and its relation to beautiful number and magnitude matter in the present context is because of something Aristotle says about mathematics itself. Mathematics, he says, is beautiful – or more to the point: it exhibits the primary characteristics of beauty, of which, we should not be surprised to learn, there are three:

Order, symmetry and definiteness are the forms of beauty. Here ‘definiteness’, τὸ ὡρισμένον, is a most interesting word choice: this same word – whose root means to limit or to form a boundary – was used by Aristotle in a passage we saw above to say that ‘all things are bound by three’.Footnote ⁷² And, moreover, the language also swings us directly back to Aristotle's discussion of bees once again. Just as we saw a moment ago with number and magnitude, where these qualities are instantiated in the divine order of the cosmos, on the one hand, and simultaneously, on the other, are reflected in the negotiations of nature between size and fecundity in king bees, so too with order, symmetry and beauty: these terms and concepts play central roles in Aristotle's discussion of bees. If we return now to one of the central passages from earlier in the present investigation, we begin to see Aristotle's description in a much richer light:

It is not just that Aristotle uses general language that could be associated with divinity, but that the passage is rich in very specific references to words and concepts that he elsewhere explicitly parses as markers of the divine: proportion (symmetry), magnitude, the number three, order, completion (limit, definiteness) – the parallels are really remarkable with the passages on divinity and ordering that we have just seen. And to top it all off? An explicit admission that all of this strikes Aristotle as a very beautiful arrangement for nature to have employed with bees – another of his key words for the divine.

Bees, it would seem, are infested with divinity, even when Aristotle is not yet saying it in so many words. Given the recent attention that historians of science have paid to the roles of theology in guiding how naturalists approach the structure of the world, perhaps this should not be surprising. But at the same time, ever since the Middle Ages, discussions of Aristotle's theology have centred almost exclusively on contexts involving his Prime Mover. What bees show is that broad considerations of divinity inform his thinking on considerably more mundane subjects as well.