Plato’s pupil Aristotle claimed that the “chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree”. For many, THE chief form of beauty is the golden ratio. Two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. The golden ratio is 1:1.618 (1:1.6180339887…) and Phi is the Greek name for the number 1.618. In the BBC documentary series The Face (the episode on Beauty), Dr. Steven Marguardt argues that faces possessing the golden ratio are perceived, across cultures, to be beautiful. Of course, Marguardt’s thesis is not new: the view that beauty resides in objects that manifest the golden ratio has been popular since the renaissance and was known in ancient Greece. But the methods and results of modern science are opening up the possibility that we have the quantifiable essence of objective beauty within reach. However, this view of beauty as some ratio, pattern, or symmetry was subjected to a powerful critique by the Roman philosopher Plotinus (204-270 C.E.) in his Enneads, book I, chapter 6. Here are four arguments from his critique which I think are worth considering:
(1) Plotinus first shows that if beauty is only a relationship or pattern then it will need to be made up of non-beautiful parts which, in turn, leads to the absurd conclusion that the pattern can’t be beautiful after all. Here is my paraphrase of his argument:
Premise 1: If beauty is a relationship of some sort then simple things, i.e., the parts of the relationship that are not themselves relations, cannot be beautiful. Beauty is only a predicate of the relationship between parts not the parts themselves.
Premise 2: If a relationship of parts is beautiful then the parts out of which the whole relationship is made must be beautiful as well: it is absurd to say that a beautiful system of relationships is made of non-beautiful or even ugly parts.
Premise 3: But parts can’t be beautiful (from premise 1).
Conclusion: Therefore, if one says beauty is only a relationship of parts, then no relationship of parts can ever be beautiful (from premises 2 and 3).
Now a possible criticism of premise 2 is that Plotinus has committed a fallacy of division. The fallacy of division is a mistake in reasoning that occurs when someone immediately infers that what is true of a whole must also be true of all or some of its parts. So let us say we have this argument: This football team as a whole is great. Therefore, each member must be great. This argument is invalid since it could be the case that both the team as a whole is great but individual members aren’t. So can a beautiful whole have non-beautiful parts? Perhaps even an ugly one or two? Why does beauty in the whole necessitate beauty in the parts?
(2) If we think that beauty is only a relationship of parts then we would have to exclude simple things that are not made of parts or, at least, not perceived to be made of parts. Plotinus notes that things like color, lightning, gold, and the stars would be excluded. But aren’t these things beautiful? It seems so. St. Augustine talks about the beauty of the elements and how it is their simplicity that makes them beautiful. Shouldn’t we include them? Shouldn’t a theory of beauty be comprehensive enough to include the beauty of water, earth, air, and fire?
(3) If we maintain that beauty is just symmetry or pattern, then we must exclude things from being beautiful that we don’t want to exclude like noble conduct, excellent laws, rational thought, a just soul, and various non-physical entities like numbers. He asks: Where is the symmetry in these things? None will be found. This argument is quite convincing if one is willing to accept these less obvious candidates for beauty.
(4) Plotinus, following Plato, believes that things that participate in transcendent beauty should be like a magnet: they should pull us toward them. According to Plato, there are certain things in the realm of Becoming that shine in a certain way. These are the beautiful things that give us a glimpse of the eternal Form of beauty in the realm of Being. No other Forms can be glimpsed in this sensual way. The myth Socrates tells in Plato’s dialogue Phaedrus gives us a reason for this exception. We learn that our souls, when previously divorced from our body, had seen the Form of beauty in the realm of Being and this Form was the most radiant. Now that we are embodied once again, we forget all the Forms but that one. We can recollect this Form more easily because of the radiant impression it once made. Of course, some are drawn to beauty in ways that are simply erotic. But Plato sees our attraction to beauty as an occasion to be slowly drawn from the corporeal to the incorporeal. In his masterpiece The Symposium, he argues that can move past the love of a certain beautiful body to an appreciation of beautiful bodies in general. From there, we can move to the beauty of the soul, the beauty of social institutions, and the beauty of knowledge. And, ultimately, we are drawn to have an ecstatic encounter with the Form of beauty itself. Such a process is a profound transformation whereby we have our priorities changed and come to seek Being with a passion. So we see that beauty, although objective, plays a crucial function with a subjective component: it helps us become lovers of wisdom or philosophers. Plotinus, influenced as he is by Plato, agrees.
But clearly we can see symmetrical things that don’t move us this way. People can pick out faces with the golden ratio and not be stirred by them. We have all had the experience of seeing a so-called beautiful face that exhibits symmetry but we are not attracted to it. To be sure, this objection can get us into some difficult territory: the metaphysics associated with this approach can be controversial, the psychological dimensions can be subjective, and the mysteries of attraction are notorious. But I think this objection gets to the heart of our transformative experience of beauty with all its magnetism, pursuit, intrigue, destruction, and liberation. It is just a matter of formulating the point in less controversial ways. I think philosopher Alexander Nehamas, in his book Only a Promise of Happiness (Princeton University Press, 2007), does a good job in providing such a formulation.