The Problem of Universals

I. The argument against empiricism as found in the work of Plato and the 'problem' of universals

Empiricism is the doctrine that all our knowledge is gained through sense-experience. Therefore, if there is any knowledge that cannot be accounted for by means of sense-experience, empiricism will be false.

Hume, as an example of an empiricist, asserts that all ideas are copies of impressions — by this he means that any concept we find in or before our minds must either be a sense-experience or copied from a sense-experience. He challenges opponents of empiricism to demonstrate such knowledge in the following extract from The Enquiries.

Or, to express myself in philosophical language, all our ideas or more feeble perceptions are copies of our impressions or more lively ones.

To prove this, the two following arguments will, I hope, be sufficient. First, when we analyse our thoughts or ideas, however compounded or sublime, we always find, that they resolve themselves into such simple ideas as were copied from a precedent feeling or sentiment. Even those ideas, which, at first view, seem the most wide of this origin, are found, upon a nearer scrutiny, to be derived from it. The idea of God, as meaning an infinitely intelligent, wise, and good Being, arises from reflecting on the operations of our own mind, and augmenting, without limit, those qualities of goodness and wisdom. We may prosecute this enquiry to what length we please; where we shall always find, that every idea which we examine is copied from a similar impression. Those who would assert, that this position is not universally true not without exception, have only one, and that an easy method of refuting it; by producing that idea, which, in their opinion, is not derived from this source. It will then be incumbent on us, if we would maintain our doctrine, to produce the impression or lively perception, which corresponds to it. [My italics] [Hume: Enquiries Concerning Human Understanding, Section II: Of the Origin of Ideas.]

The importance to empricism of being able to demonstrate that every meaningful idea is derived from experience is also illustrated by this extract from A.J. Ayer's Language, Truth and Logic.

For the admission that there were some facts about the world which could be known independently of experience would be incompatible with our fundamental contention that a sentence says nothing unless it is empirically verifiable.

However, an earlier reply to the challenge proclaimed by Hume was presented by Plato. He maintained that the knowledge of the meaning of every general term of our language could not be derived from sense-experience.

Let us explore this point. Take, for example, a general term of our language such as the term “red”. This word has a meaning, and as such that meaning is grasped by the minds of people who use it. [This point could in fact be denied. Wittgenstein's theory of meaning, that meaning is use, seems to deny that minds do grasp concepts when they use words. According to Wittgenstein, the understanding of a word is encompassed by the ability of a person to use it correctly. This approach to meaning should be explored in a different context. Here we will assume that people do grasp ideas (or concepts or meanings) when they use words..] In this context we will use the terms meaning, idea and concept synonymously — to stand for what it is that people grasp when they understand a word.

Empiricism is the doctrine that all knowledge is gained through sense-experience. Since the idea of red is knowledge, it must be derived from sense-experience. If empiricism is true, what, then, is the relationship between the idea of red and sense-experiences? Hume makes an explicit suggestion

Or, to express myself in philosophical language, all our ideas or more feeble perceptions are copies of our impressions or more lively ones.

In this case the idea of red should be red. This means that it would be a faint after-image in our minds of a red object. This would entail that when we are thinking about red things, then faint images of red things should pass through our minds.

A number of difficulties immediately come to mind — what is the image that corresponds to, say, “solubility”? Or, when dealing with more abstract ideas — what is the image that corresponds to the idea of “the law”? Already, these examples suggest that the mind's capacity to grasp meaning extends far and beyond its capacity to retain faint impressions.

However, even the colour term red poses problems. For when we have an image of a red thing, then that image must be of a particular shade of red, but the concept of red (the idea of red) encompasses every shade of red. Thus the idea of red embraces a generality that no particular shade could embrace.

Similarly, suppose two red objects are laid before me, and I utter the sentence, “Both of these objects are red”. Now my judgement embraces both objects. If I have a faint image of a red blob in my head then my judgement will embrace that also. With my mind I have been able to encompass all three objects in a single judgement. So the idea of red embraces all of them; since it embraces all of them, the idea of red cannot be equal to the faint copy of a red object that I might have in my mind at the time I make the judgement. The faint image of a red object seems to be irrelevant to the meaning of red.

Wittgenstein makes a similar point in his work, The Blue Book

Our problem is analogous to the following:

If I give someone the order “fetch me a red flower from that meadow, how is he to know what sort of flower to bring, as I have only given him a word?

Now the answer one might suggest first is that he went to look for a red flower carrying a red image in his mind, and comparing it with the flowers to see which of them had the colour of the image. Now there is such a way of searching, and it is not at all essential that the image we use should be a mental one. In fact the process may be this: I carry a chart co-ordinating names and coloured squares. When I hear the order “fetch me etc.” I draw my finger across the chart from the word “red” to a certain square, and I go and look for a flower which has the same colour as the square. But this is not the only way of searching and it isn't the usual way. We go, look about us, walk up to a flower and pick it, without comparing it to anything. To see that the process of obeying the order can be of this kind, consider the order “imagine a red patch”. You are not tempted in this case to think that before obeying you must have imagined a red patch to serve you as a pattern for the red patch which you were ordered to imagine.

[Wittgenstein does not believe that there is any mental process or meaning involved in grasping an idea; however, in this passage he is explicitly attacking Hume, so it serves to illustrate the problem of saying that ideas (meanings) are copies of impressions.]

This seems to demonstrate that ideas (meanings) cannot be copies of impressions.

The point that Plato would make, however, is that all meanings embrace a generality that applies to a potentially infinite number of cases, whereas all experiences are experiences of particular, unique objects in space and time. Hence it is not possible to derive the knowledge of meanings from particular sense-experiences.

If this is true then every general term of our language has a content that could not be derived from experience; hence empiricism must be false.

Naturally, empiricists do not agree to this proposition, and we must explore their replies further. However, let us first examine Plato's doctrine further.

Since meanings cannot be copied from experience, then there must be some other source of our knowledge of them. Plato calls meanings, Ideas or Forms (translations of the Greek, logos) and he claims that Forms are abstract entities not located in space and time, and our experience of them explains how we can have knowledge of the general terms of our language.

He does not believe that our knowledge of Forms could be derived from our experience during our lifetime. He is, therefore, led to conclude that we must have be born with this knowledge. If we are born with the knowledge, then we must have pre-existed our birth. Here is an indicator of the kind of conclusions that Plato is prepared to draw regarding the existence and nature of the soul as a consequence of this argument.

Plato: The Meno

Men's souls are immortal. Souls pass through death and are reborn, but they are never really annihilated.

The soul, since it is immortal, has been born many times, and has seen all things both here and in the other world. It has already learnt everything that is. So we should not be surprised if we discover that the soul can recall the knowledge of virtue or any other matter that it formerly possessed. Nature forms one whole, and the soul has already learned everything, so when a man has recalled a single part of knowledge — that is, what we commonly call learnt it — there is no reason why he should not go on to discover everything else, especially if he is courageous and does not tire in his researches; for discovery and learning are in fact both forms of recollection.

This is called the doctrine of recollection.

Plato was primarily led to the belief that there exists a realm of Forms through his examination of abstract general terms. Bertrand Russell in The Problems of Philosophy explains this as follows.

The way the problem arose for Plato was more or less as follows. Let us consider, say, such a notion as justice. If we ask ourselves what justice is, it is natural to proceed by considering this, that, and the other just act, with a view to discovering what they have in common. They must all, in some sense, partake of a common nature, which will be found in whatever is just and in nothing else. This common nature, in virtue of which they are all just, will be justice itself, the pure essence the admixture of which with facts of ordinary life produces the multiplicity of just acts. Similarly with any other word which may be applicable to common facts, such as “whiteness” for example. The word will be applicable to a number of particular things because they all participate in a common nature or essence. This pure essence is what Plato calls an 'idea' or 'form'. (It must not be supposed that 'ideas', in his sense, exist in minds, though they may be apprehended by minds.) The 'idea' justice is not 'identical' with anything that is just: it is something other than particular things, which particular things partake of. Not being particular, it cannot itself exist in the world of sense. Moreover, it is not fleeting or changeable like the things of sense: it is eternally itself, immutable and indestructible. [Bertrand Russell: The Problems of Philosophy, Chapter 9: The World of Universals.]

Russell rejects Plato's further arguments; he also rejects Plato's use of terms like “ideas” and “forms” and proposes the term “universal” instead.

We speak of whatever is given in sensation, or is of the same nature as things given in sensation, as a particular; by opposition to this, a universal will be anything which may be shared by many particulars, and has those characteristics which, as we saw, distinguish justice and whiteness from just acts and white things.

It may also be helpful to think of universals as structures. We experience the world largely unconsciously. When, for instance, we look at red flowers, we may, but often do not, form conscious judgements about what we see. We may say to ourselves, or our friends, “What lovely red flowers!” but usually we don't. We just look at the flowers. Therefore, we are not generally conscious of anything other than the particular flowers. However, the argument that we are examining here asks us to consider that there are two components to the experience of particular flowers. These can only be separated in thought. The first component is the unique content of the experience — these flowers and no others. The second component is the element that they share with other experiences — the structure of the experience — that they are flowers and that they are red — properties that they share with other particulars. So what is being suggested is that the structure of experience is universal and cannot be derived form particular experience. Russell, who is very friendly to empiricism, nonetheless agrees. In this passage he is discussing the attempt of Berkeley and Hume to deny the existence of abstract properties.

But a difficulty emerges as soon as we ask ourselves how we know that a thing is white or a triangle. If we wish to avoid the universals whiteness and triangularity, we shall choose some particular patch or a triangle if it has the right sort of resemblance to a universal. Since there are many white things, the resemblance must hold between many pairs of particular white things; and this is the characteristic of a universal. It will be useless to say that there is a different resemblance for each pair, for then we shall have to say that these resemblances resemble each other, and thus at last we shall be forced to admit a resemblance as a universal. The relation of resemblance, therefore, must be a true universal. And having been forced to admit this universal, we find that it is no longer worth while to invent difficult and implausible theories to avoid the admission of such universals as whiteness and triangularity.

This, then, is the problem of universals.

The expression problem of universals also needs some consideration. The problem is a problem primarily for empiricism; for rationalists, universals are the cornerstone of their logical argument that there is knowledge not derivable from experience. However, once they acknowledge that universals do exist, there may be the problem of explaining how such knowledge is possible, and how such knowledge combines with particular experiences. If experience has two elements to it — the particular and the universal, how do the two elements combine?

The belief that there are universals (or Forms, to use Plato's term) is sometimes called realism. This is potentially confusing, because the term realism is also used to denote the belief that there exists a real world that corresponds to our perceptions. The term realism is used in many different contexts. For example, Kant, who believes that there are universals also adopts a form of idealism when it comes to material reality. [He calls his form of idealism, critical idealism or transcendental idealism. He does not deny that there is a material reality existing independently of the mind, but he says that we know nothing about it. However, the point here is to illustrate that not all forms of realism are equivalent..] He is a realist with respect to forms, but an idealist with respect to matter.

Empiricists do not agree that there are universals. The doctrine that there are no universals and that the only things common to general terms of our language are the terms themselves is called nominalism. (Thus, in the question of universals, forms and abstract objects, realism is opposed to nominalism.) This is how Hobbes defends his view.

Of Names, some are Proper, and singular to one onely thing; as Peter, John, this Man, this Tree: and some are Common to many things; as Man, Hore, Tree; every of which though but one Name, is nevertheless the name of divers particular things; in respect of all which together, it is called an Universall; there being nothing in the world Universall but Names; for the things named are every one of them Individuall and Singular.

One Universall name is imposed on many things, for their similitude in some quality, or other accident: And whereas a Proper Name bringeth to mind one thing only; Universals recall any one of those many. [Hobbes: Leviathan]

He affirms his doctrine of nominalism when he writes, “there being nothing in the world Universall but Names; for the things named are every one of them Individuall and Singular”; however, he appears to contradict himself when he writes “One Universall name is imposed on many things, for their similitude in some quality..” [my italics]. This seems to be exactly the point Russell is making, and Hobbes has stated his doctrine of nominalism here, but has not effectively defended it.

We saw that empiricism affirms that all knowledge is derived from experience. But what does the term “derived” mean? Hume offers a specific interpretation of the relationship between knowledge and experience when he says that ideas are copies of impressions. However, this interpretation of how meanings are derived from sense-experience seems inadequate — if we follow the arguments already cited. On the other hand, perhaps empiricists can counter the argument by offering a different interpretation of the relationship between ideas and sense-impressions. Generally, when an idea is derived from sense-experience we say that it is abstracted from sense-experience. Could empiricists say, “all ideas are abstracted from experience”?

The problem with this reply is that it is vague. It simply asserts that ideas are abstracted from experience but does not show how they are abstracted. When Hume proposes that ideas are copied from experience we have a clear understanding of what that relationship might be, but the relationship of abstraction needs further clarification.

II. The problem of participation and the third man argument

Plato, who proposed the existence of universals also considered a counter-argument against their existence. In his dialogue The Parmenides he has his hero, Socrates, facing difficult and challenging questions from an older philosopher, Parmenides.

In this extract the young Socrates and the elder Parmenides are discussing the precise nature of the relationship between a Form and a concrete instance of a Form. For example, they are trying to discover the precise nature of the relationship that may or may or may not exist between the universal man ( which is the Form that makes it possible for all men to be alike — the property of being a Man), and a particular instance of that universal — a concrete man such as Plato. This is a relationship that Plato describes as one of “participation”, but the question remains, what exactly is participation?

Socrates replied. “Well, Parmenides, the best answer I can provide is as follows: I suggest that these Forms are patterns imbued in the nature of things. All other things are made in their image and resemble them, and for the instance to participate in the Form is nothing more than their being made in their likeness.”

Parmenides: “But if a concrete instance is made in the image of a Form, then must it not follow that the Form resembles the image, for the image of the Form was made in the likeness of the Form? If A resembles B then B must resemble A. [If the image resembles the Form, then the form must resemble the image.]

Socrates: “It must!”

Parmenides: “Furthermore, whenever two things resemble each other, so that they can be alike, there must be a Form to account for this, just as you showed earlier.”

Socrates: “Certainly!”

Parmenides: “In that case, it follows that nothing can resemble a Form, nor can a Form be like anything else. For if that was the case, then it would always be necessary to posit a second Form in addition to the first Form [to account for the resemblance between the Form and the particular], and since that second Form will be like the first, we will have to posit a third Form, and so on ad infinitum, on the assumption that Form is like the thing that partakes of it.”

Socrates: “I agree!”

Parmenides: “It follows that particulars cannot partake of Forms by resembling them. We must seek some other understanding of the relationship of participation.”

Socrates: “So it seems.”

Parmenides: “You should appreciate the great difficulties that arise from the assertion that Forms independently [of their particulars, in a separate realm].

Socrates: “Certainly!”

The question considered here is how a form and a particular combine. The discussion starts when the young Socrates suggests that the relationship must be one of resemblance. This is similar to Hume's suggestion that an idea is a copy of a particular, and leads to related problems.

An infinite regress occurs when a solution to a problem simply regenerates that problem, so the problem repeats itself over and over again, ad infinitum. In this extract Parmenides argues that the supposition that forms (universals) resemble particulars leads to a regeneration of exactly the same problem.

The difficulty is explained as follows. We posit the existence of a Form in order to account for the resemblance between particulars. All men resemble each other in being men, so there must be a Form of Man. However, if the Form of Man resembles particular men, then we will have to posit the existence of a another Form (the Form of the Form of Man — or the “third man”) in order to account for this resemblance. Now we have the Form of the Form of Man and also the Form of Man, so we will need a fourth Form, the Form of the Form of the Form of Man and so on ad infinitum.

The question is — does this show that the notion of a Form or universal is useless as a means of explaining why objects resemble each other?

Clearly, Plato did not intend this conclusion. Plato sought to defend the doctrine of Forms not to expose it. Hence, in this dialogue he makes Socrates a young man, in order to indicate that his responses are not mature. The conclusion to be drawn from the problem, which is what Parmenides does draw from it, is that one or both of the following premises of the problem must be false.

1		That Forms resemble particulars
2		That Forms exist independently of particulars.

However, if Forms do not resemble particulars there is the question of how forms and particulars relate to each other. The particular is said to participate in the form, but what exactly is the relationship of participation? This is analogous to the problem of abstraction that we saw at the end of the last section. If ideas are abstracted from impressions, what exactly is the relationship of abstraction?

There is, however, one solution to the problem of participation offered by Kant. This solution is consistent only with some form of idealism — namely that the whole world of experience (of phenomena) is, in some sense, in the mind. Kant denies both premises above. He maintains that the mind (or a faculty of the mind, which he calls Imagination) unconsciously structures experience and makes experience intelligible to consciousness. The structure exists because we ourselves put it there. This is possible because both the Forms (that is the structures) and the particulars are mental in origin. No doubt this solution is high debatable.

III. Wittgenstein's attack on universals

In modern times Wittgenstein has sought to solve the problem of universals in a manner that would be consistent with empiricism.

His attack is linked to his theory of meaning — namely, that meaning is use — and that is considered on another occasion.

The tenor of his attack can be seen from the following extract from The Blue Book

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.

However, it is not clear from this passage that Wittgenstein has sufficiently defended his brand of nominalism from Russell's point, quoted earlier, that relations of similarity and dissimilarity are the real basis of the need to posit universals. To recap on Russell's point

We could replace the terms whiteness and triangularity in the above passage by gameness, and so forth. The Platonist would argue that there are relationships of resemblance between games, and these resemblances are (a) real and (b) not to be found in particular instances of games. Hence, there is at least one universal — the relationship of resemblance.

Nonetheless, Wittgenstein's attack on universals should not be read separately from his theory of meaning as a whole.