Every day we encounter beauty. I write this after noticing the silhouettes of geese gliding low in formation over the shimmering Thames river. Their reflections stream over the golden winks of the ripples, lit up by the early morning sun.

What is beauty? It’s not a thing by itself. We’ll never find an actual thing called “beauty”. It’s something that we appreciate in things, sometimes only for a moment.

There are many things that are beautiful, but there is one thing that they all share — beauty. We can see beauty in many varieties — people, paintings, sunsets, buildings or flowers can be beautiful — but it’s difficult to really identify what beauty actually is. This is especially true if we consider that what is beautiful for one person isn’t necessarily beautiful for another.

Philosophers call individual things “particulars”, and the singular things that they share — such as beauty — philosophers call “universals”. Beauty is universal like many other notions such as justice, roundness, courage and redness.

As a general rule, universals are what are predicated of things. The ruby is red, the painting is beautiful, Socrates is good, the dog is black, the judgement was just. In all these cases, the subject of the sentence is a material thing that can only exist in one place at a time, the predicate is timeless and placeless.

So while particulars can come to an end, universals endure through time and space. If the dog died, there would still be black, and billions of things are black, before, during and after the dog’s existence. If the painting were burned there would still be beauty.

While universals don’t seem to depend on things, things depend on universals. If you somehow removed beauty from a work of art, would it be art? What makes a dog a dog? Is there a universal “dogness”, or is a dog a particular collection of many universals?

For thousands of years, philosophers have preoccupied themselves with defining what exactly universals are, and in what cases we are justified in using them — if at all. How do we define beauty or justice objectively, when neither exist outside what we observe? We can agree on what is beautiful or just, but the object of our agreement isn’t necessary intrinsically beautiful or just.

The difficulties around our understanding of universals is often wrapped up in one theme, which philosophers call “the problem of universals”.

Are Universals Real?

The problem of universals is important not just to philosophers but also to scientists. Universals get to the heart of the consistency and commonality of our experience of being. Many scientists believe that nature and our universe obey physical “laws” that are universal. Furthermore, these laws are themselves relations between universals — what makes blue the way it is, for example, is a consistency in the way light behaves.

It’s commonly accepted that Socrates was the first philosopher to systematically attempt to understand universals. In the Symposium, a dialogue written in around 385 BCE by Plato, Socrates sets out the case that particular instances of beauty emanate from a profound universal beauty.

The group at the symposium first discuss bodily beauty — simple instances of beauty in people that inspires love — but Socrates begins to excavate the very nature of beauty. How can so many different things be beautiful? What is the source of it? He relays to his companions what he was told by a woman named Diotima about love and beauty.

“‘Starting from individual beauties, the quest for universal beauty must find him mounting the heavenly ladder, stepping from rung to rung—that is, from one to two, and from two to every lovely body, and from bodily beauty to the beauty of institutions, from institutions to learning, and from learning in general to the special lore that pertains to nothing but the beautiful itself—until at last he comes to know what beauty is. And if, my dear Socrates,’ Diotima went on, ‘man’s life is ever worth living, it is when he has attained this vision of the very soul of beauty.’”

Socrates used Diotima’s testimony to describe a oneness in all particular things that had the common property, “beauty”. Bodies and institutions are particular, but the wise person can come to know beauty itself.

Like the Symposium, many of the dialogues that included Socrates were concerned with defining universals like beauty, knowledge and courage. What Socrates and his followers were looking for was a common element within things that shared a trait applied to them.

Thinking like this led to the idea of “essence”. This idea of essence is something that is invisible but, if you were to take it away from an object, that object would be profoundly changed. The essence of a thing is made up of universals. It is the unchanging — “whatness” — of a given thing.

For Plato, everything has an ideal “form” that transcends space and time. Forms cause matter to be shaped in certain ways — material things “participate” in forms, and so their many properties exhibit forms like “blue” and “good”. As such, universals are real — they exist outside our minds.

This makes Plato a “realist” in his treatment of universals. This is also to the extent that universals exist both outside of our minds and outside of the things that exhibit them. There is a form of “red” more real than any red in the world. The material world is a changing and imperfect copy of the unchanging and eternal realm of forms, which is the ultimate reality.

For Aristotle, who advocated a more modest realism, universals exist only in the material things themselves. The redness of a ruby is real, but it does not exist independently outside of space and time as Plato’s “forms” do. For Aristotle, universals are real in the blueprint of things — the essence of the thing itself.

Wittgenstein the Antiphilosopher

Both Plato and Aristotle’s ideas about universals exemplify “Essentialism”. This is the general idea that things have a set of attributes that make them what they are. It’s a core belief shared by a number of philosophical ideas that take universals to be real and fundamental to reality.

While many in history have disputed the real existence of essences and universals, it wasn’t until the twentieth century that what some philosophers consider to be a knock-down argument emerged.

The origin and scope of this argument is not entirely clear, so even today it remains a matter of debate. Its author, Ludwig Wittgenstein, never suggested that it be taken to be a solution to the problem of universals, but it has been taken to be so.

Wittgenstein was an Austrian philosopher who originally set out to be an engineer. Having become interested in mathematics, he relocated to Cambridge to study philosophy with Bertrand Russell. Russell was famous for having co-written Principa Mathematica (1910), widely regarded as the definitive textbook on foundational mathematics and logic.

The two had a preoccupation with the fundamental utility of language. This put them at the heart of the “linguistic turn” in Western philosophy — a new paradigm which emphasized the study of language as the medium of ideas over ideas themselves.

Wittgenstein excelled as a student and quickly introduced new philosophical innovations in the field of logic. Russell even wrote of the inadequacy he felt in young Wittgenstein’s presence. The younger philosopher began to dominate linguistic philosophy, but the direction he in which took it left Russell frustrated and marginalized.

So while Russell went on to become a public intellectual, activist and great popularizer of philosophy, Wittgenstein went on to establish a reputation that would have him described by many as the twentieth century’s greatest intellectual.

People introduced to Wittgenstein may wonder why. His early writings are austere and mystical, containing ideas that he later abandoned. His later work is often so murky that philosophers argue about what he meant or even where his arguments started or stopped in his texts. Wittgenstein was not a great stylist, and his ideas have not permeated the wider culture as much other modern philosophical figures like Sartre’s and Nietzsche’s have.

But what’s indisputable, and what makes the Austrian philosopher so significant, is the destructive power of his arguments against long-standing philosophical assumptions and preoccupations.

Much of this was borne of Wittgenstein’s contempt for academic conventions — which we will later examine in order to understand some of the claims made for his ideas. Wittgenstein is considered by many commentators to be an “anti-philosopher” since his work became focused on unravelling the problems of philosophy, as opposed to attempting to solve them.

He proudly proclaimed to never have read Aristotle. He wrote, “As little philosophy as I have read, I have certainly not read too little, rather too much. I see that whenever I read a philosophical book: it doesn’t improve my thoughts at all, it makes them worse.”

When philosophers consider problematic concepts such as “free will” and “the mind”, they work on the assumption that there is a solution. For the most part, Wittgenstein believed that these are not real problems. They are pseudo-problems caused by the misuse or misunderstanding of language. The philosopher believed that, by examining language, we can unravel these supposed problems at source, rather than vainly search for a solution that doesn’t exist.

The problem of universals is such a problem. For Wittgenstein, so-called problems like this were a result of muddled or disingenuous thinking.

The Craving for Generality

In the Blue Book, a compilation of Wittgenstein’s lectures from the 1930s and published in 1953, the philosopher remarks on a “craving for generality” that results in a “number of tendencies connected with particular philosophical confusions.”

It’s worth quoting in full a passage from the Blue Book, which elaborates on this “craving”,

“There is-

(a) The tendency to look for something in common to all the entities which we commonly subsume under a general term. We are inclined to think that there must be something in common to all games, say, and that this common property is the justification for applying the general term “game” to the various games; whereas games form a family the members of which have family likenesses. Some of them have the same nose, others the same eyebrows and others again the same way of walking; and these likenesses overlap. The idea of a general concept being a common property of its particular instances connects up with other primitive, too simple, ideas of the structure of language. It is comparable to the idea that properties are ingredients of the things which have the properties; e.g., that beauty is an ingredient of all beautiful things as alcohol is of beer and wine, and that we therefore could have pure beauty, unadulterated by anything that is beautiful.

(b) There is a tendency rooted in our usual forms of expression, to think that a man who has learnt to understand a general term, say, the term “leaf,” has thereby come to possess a kind of general picture of a leaf, as opposed to pictures of particular leaves …. This again is connected with the idea that the meaning of a word is an image, or a thing correlated with the word.” (Blue Book, p. 17-18)

Wittgenstein uses games as an example of how things can be related by resemblance — a pool of identifying features, rather than by intrinsic properties.

All the members of a family don’t all look exactly the same, but rather have overlapping similarities in their build, height, their eye-colour, hair, temperament and so on. So it is with games — ball games, card games, solitaire and football do not have one thing in common but are part of a pool of resemblances that connect them. We can spontaneously identify a new game, by seeing one or more features that other games have.

Wittgenstein was making the point that the idea that language was a unitary whole was false. He saw language as a whole multitude of different acts in a pool of similarities with no one unifying essence — just like games.

We use language through many means beyond speaking and writing — hand gestures, using symbols, making glances, “body language”, and pulling funny faces are just some examples. Furthermore, there’s no strict limit to the uses of words, we invent meaning as we go along — think, for example, of irony used between friends.

Wittgenstein observed that we don’t use language according to strict rules, and neither has it been taught to us according to strict rules. We can make up “language games” spontaneously — we make up and follow loose rules but shape them as we participate in our communication. This fluidity of use makes family resemblance an important tool to understand and define what language is. It’s similar with an idea like beauty and other universals.

This approach to identifying concepts has proven to be influential. When theorists ask questions like “what is beautiful?’ or “what is red?” or “what is art?” the family resemblance theory provides a relatively uncomplicated explanation.

We can also use this approach to problems like the “Sorites Paradox”, which ask us questions like “how many grains make a heap?” or “when you take parts away from a bicycle — such as the wheels, the frame, the pedals and so on — when does it stop being a bicycle?” If a bicycle or a heap is a family resemblance concept, then we have easy answers — a bicycle is a bicycle when it resembles other bicycles and the same could be said of a heap of grains.

From Form to Kind

For Rentford Bambrough, a Cambridge philosopher of the generation following Wittgenstein, the idea of family resemblance concepts points toward a solution of the problem of universals.

Though Wittgenstein made no mention of universals in the Blue Book passages, his thoughts on language games and family resemblances had the backdrop of his wider critique of the “craving for generality”. Bambrough notes that Wittgenstein was “understandably wary of expressing his own conclusions in general terms” — it would be ironic if he did — and so avoided claiming his idea to be a solution to such an enduring problem.

And so it is left to Bambrough to explain how Wittgenstein’s approach both solves the problem and dispels the notion of essentialism as a widely accepted but defective solution.

In his 1961 essay, ‘Universals and Family Resemblances’, he wrote,

“When I claim that Wittgenstein solved the problem of universals I am claiming that his remarks can be paraphrased into a doctrine which can be set out in general terms and can be related to the traditional theories, and which can then be shown to deserve to supersede the traditional theories.”

The remarks that Wittgenstein made are paraphrased by Bambrough into a “doctrine” and put to work as part of the long debate around universals and particulars.

The debate consists of two broad opposing views. The first is realism, which, as we’ve seen, treats universals as real things. Nominalism, and the related notion of conceptualism, oppose the realist view. These positions deny the real existence of universals. They instead insist universals exist only in our minds. We give and agree upon arbitrary labels to the properties of things — such as colours, shapes, behaviours — in our use of language. There’s no redness, beauty, justice and strength, they are just agreed labels or ideas that we apply to things.

The realist retort to nominalism is, of course, where do these ideas come from if they are not referring to something that is real? We can imagine a non-existent creature, like a unicorn, but we cannot imagine a non-existent colour or shape.

Bambrough saw in Wittgenstein’s argument an idea that was neither realist nor nominalist. Wittgenstein’s idea denies what the realist believes — that games have something in common other than that they are games. But his idea also denies what the nominalist asserts — that games have nothing in common except that they are called games.

In both cases, Wittgenstein is denying the idea that games must have something common to them to be games, be it our label “game” or some essence. What the philosopher insists on is our capacity to simply see what an aggregate set of objects have in common by their many properties. To look for one thing among those objects is foolish, we are led astray by the “craving for generality”. Games are real insomuch that a pattern we see in some random dots is real.

The problem with this approach is how the limits of resemblance are set. Let’s take the idea of family resemblance itself. People, generally, look like other people. Sometimes you’ll make the mistake of believing two people that are unrelated to be related, and sometimes you’ll not realise that the two people you are speaking to are siblings. It could be argued that the whole of humanity is related if we used the common parameters of family resemblance, since it requires only that two given people resemble a third person. In such a case, the concept becomes so general as to be meaningless, since nobody is excluded.

Of course there are degrees of resemblance. People look more like people than they do lions or dolphins. But is our recognition of the human or lion or the dolphin prior to our understanding of the categories they fall into? Or is it rather the other way around? That is, we see human beings resembling each other because we already have an understanding of what human beings look like.

There’s therefore a paradox in the family resemblance idea. It’s difficult to understand whether seeing resemblances or knowing likeness comes first. Wittgenstein urged his audience not to think — “don’t think, but look!” — about what things have in common, but we think before we see and vice-versa.

But here is where we return to Wittgenstein’s own intentions. As we’ve noted, the family resemblance idea was never intended to be a theory. It was un-theoretical. The philosopher was uninterested in indulging generalities, as both nominalists and realists are.

The Strength of the Thread

While the family resemblance “theory” — as reconstructed by Bambrough — does not entirely knock down universals, it does allow us to think about essentialism in a new critical light. This is perhaps the real aim of Wittgenstein’s work on language.

Wittgenstein loathed systemic types of thinking — the urge to create theories that explain and categorise everything around us along causal lines. Against the scientism and rationality of the modern world, he develops his own ideas that were more about intuitive reasoning — seeing resemblances and connections.

He was interested in the kind of morphology — the study of the relationships of forms — exhibited by Goethe’s Metamorphosis of Plants (1790). “Goethian Science”, put simply, is about connecting, rather than explaining, natural phenomena. While philosophers and scientists seek mechanistic laws and reductive explanations, Wittgenstein was more sympathetic to Goethe’s “delicate empiricism” that married dynamic human sense with equally dynamic natural forms.

Why is any of this important? The promise of an explainable, stable world is both the allure and the danger of essentialism. The craving for generality manifested in essentialism is evident in some of the worst human traits.

Racism is a form of essentialism. A similar form of dehumanization against “barbarians” was used by Aristotle himself to justify war and slavery. Barbarians were lacking, according to Aristotle, in the essence of human beings — the power to reason, and were therefore suspended somewhere between man and beast. The same reasoning of racists is used even today. Such ideas rest on theories of realism and essences for legitimacy.

In his book Philosophical Investigations (1953), Wittgenstein uses a metaphor for his anti-essentialist approach,

“The strength of the thread does not reside in the fact that some one fibre runs through its whole length, but in the overlapping of many fibres.”

Perhaps a metaphor serves fresh attitude better than any theory can. The point is that there’s no unifying trait or essence that runs through things that we regard as the same. The strength of identity lies in the overlapping traits that we see in things. There’s no deeper, unseen essence inside of things, and therefore no ultimate fixity to how things are. Nothing is determined to be as it is. It’s a thought that is as liberating as it is destructive.