Philosopher Gonzago Rodriguez-Pereyra defines the very old and well-known "Problem of Universals" thusly:

But what then is the Problem of Universals? As I said, it is usually taken to be the problem of accounting for how different particulars can have the same properties.

And the Australian metaphysician David Armstrong does it in exactly the same way:

[The Problem of Universals is] the problem of how numerically different particulars can nevertheless be identical in nature, all be of the same "type".

To me, for two particulars a and b to have the same property F, or be of the same type F, simply means that "a is F and b is F*. But I don't see why the fact that "a is F and b is F" is puzzling at all. Why does the fact that "a is F" and "b is F" need to be accounted for?

I really don't see any kind of incompatibility, while for Armstrong the fact that both propositions are true is, prima facie, a good reason to postulate the existence of a rather bizarre kind of entities (namely, Universals). In fact, he writes

I would wish to start by saying that many different particulars can all have what appears to be the same nature and draw the conclusion that, as a result, there is a prima facie case for postulating universals.

Moreover, he calls the belief, held by philosophers like Quine, that the Problem is not really a problem, and that it is a fact that does not require further explanation, 'Ostrich nominalism'. This is because, according to him, dismissing this as a problem means refusing to solve it, like an ostrich would do by sticking its head in the sand.

However, I still can't manage to see why a is F and b is F both being true is problematic at all. Could you perhaps enlighten me? I've tried by reading books and practically all the SEP/IEP articles on the subject, but these mainly address the solutions, which are hard to understand to someone, like me, who hasn't even got what the problem is all about.

  • I think one way to say this is about the problem of participation (so: how does the ideal Form of "triangle" participate with real instances of triangles? This is a classical issue with speculative idealist metaphysics.)
    – Joseph Weissman
    Commented Jul 2, 2015 at 17:01
  • Wait, isn't the problem of participation one of the objections to the theory of Forms (which Armstrong I think would call trascendent realism, as opposed to his scientific realism)? If I'm not wrong, then perhaps I haven't made myself quite clear: I'm not looking for arguments against the existence of universals, but rather why the problems of universals is even a problem.
    – Adrian
    Commented Jul 2, 2015 at 17:07
  • @nicol: Socrates in Parmenides sometimes thinks it is a problem, and at other times like you - doesn't. Commented Jul 2, 2015 at 23:14
  • @Nicol what does it mean in your view to say something is an F? Does F itself exist? If not, then how can something be an F? and then how can two things be the same F? Quine says "to be is to be the value of a bound variable" but does F meet this definition? These are all interrelated questions that create the problem of universals.
    – virmaior
    Commented Jul 3, 2015 at 7:18
  • @virmaior "Does F itself exist? If not, then how can something be an F?" sorry, but the fact that something is an F entails that F exists is not at all obvious to me.
    – Adrian
    Commented Jul 3, 2015 at 21:04

7 Answers 7


Good question. One characterization of "the problem" in the problem of universals, is that it pertains to the very existence, or lack, of a basic correspondence between our thoughts and reality. Our thoughts are saturated with general terms and concepts. Reality, on the other hand, seems everywhere particular and individual. So, how can our thoughts match reality?

Here how it is put in the Catholic Encyclopedia article on universals:

The problem of universals is the problem of the correspondence of our intellectual concepts to things existing outside our intellect. Whereas external objects are determinate, individual, formally exclusive of all multiplicity, our concepts or mental representations offer us the realities independent of all particular determination; they are abstract and universal. The question, therefore, is to discover to what extent the concepts of the mind correspond to the things they represent; how the flower we conceive represents the flower existing in nature; in a word, whether our ideas are faithful and have an objective reality.

"The problem" of universals is considered to be one of the pervasive problems of western philosophy. Bertrand Russell wrote:

The most important matters in Plato's philosophy are . . . second, his theory of ideas, which was a pioneer attempt to deal with the still unsolved problem of universals. (History of Western Philosophy p. 108)


A particular is this bowl of apples before me; when I count them I find that there are seven apples.

  • Arithmetically, the universal is seven

  • in set theory it is the unique finite set with three elements - the elements being indistinguishable ie have no further structure

  • in category theory it is an object of the category/topos FinSet; it is not unique

These are all mathematical solutions to the problem of universals; the description that you use to solve the problem is the type theoretic version of the set theory one - which is in a way why the problem escaped you: you used a conceptual apparatus which solves the problem (or just sidesteps it).

Once this has been posited the question then arises about what do we mean by a universal 7, or a set of 7 elements; are they merely a string of symbols? This cannot be right - the main positions are nominalism, (mathematical) Platonism, and formalism.

Platonism posits an actually existing world of universals that we as rational creatures have access to; it is aspatial atemporal.

There we find the universal 7.

The problem of universals (in the form commented by Weissman above) is the how does this universal 7 participate with the particular, to give seven apples - this was originally a problematic of Platos theory of Forms, and probably goes back to the Pythagorean brotherhood (except that his Forms were not mathematical in nature - involving instead ideas The Good, The Beautiful, The Truth - later in Islamic theology by the mu'takallkmin attributes of the One - identified as Allah).

Aristotle solved this problem of participation by his notion of the hylomorphism: Form and substance are never separate but always together; in a sense he just side-stepped the issue.


I also struggle with a similar question, see here.

Now, why should ostrich nominalism (= predicate nominalism, austere nominalism) not be a respectable position? As you said it was held by Quine. It is difficult to believe that he made an elementary blunder.

Maybe that's the answer: You and Quine are right and the "problem of universals" is a pseudoproblem.

Anyway, I think there is a nice discussion about 'ostrich/austere nominalism' in "Metaphysics: A Contemporary Introduction" by Michael Loux, page 52-62, I'll quote a small part:

So austere nominalists take the fact that concrete particulars agree in being courageous, in being triangular, and in being human to be an ontologically basic fact; and their account of predication follows naturally from their interpretation of attribute agreement. How, then, do they deal with the third phenomenon that played a role in the realists’ case for properties, kinds, and relations – the phenomenon of abstract reference? Recall that the central fact here is that there are true sentences like

  1. Courage is a moral virtue,
  2. Triangularity is a shape,
  3. Hilary prefers red to blue,


  1. Red is a color,

that incorporate what appear to be proper names of universals. These sentences and others like them seem to be vehicles for making claims about the universals named by their constituent abstract singular terms. Since the claims in question are true, we seem to be committed to the existence of things like properties, kinds, and relations.


Let me start by saying this, suppose you go outside and see two red apples. The apples are red. The problem of universals is how to account for this datum. When we admit that two things agree in an attribute the problem opens up.

To me, for two particulars a and b to have the same property F, or be of the same type F, simply means that "a is F and b is F*. But I don't see why the fact that "a is F and b is F" is puzzling at all. Why does the fact that "a is F" and "b is F" need to be accounted for?

I really don't see any kind of incompatibility, while for Armstrong the fact that both propositions are true is, prima facie, a good reason to postulate the existence of a rather bizarre kind of entities (namely, Universals). In fact, he writes

How do you account for an entity which is numerically one that runs through numerically distinct particulars? We can run this problem on any level of reality. Take two electrons that have the same charge and spin. If we admit that there are not two distinct properties, but a numerically one property which is found in both of these electrons, this question naturally presents itself. This is a universal, the problem is how to account for its existence.

There is simply a lot of confusion with regard to this problem so I'd like to be terse here and wait until you can tell me what you're struggling with so that I can expand on them in due time.

Quine was an Ostrich Nominalist, an ostrich nominalist is something like an Austere nominalist, but less kind. The austere nominalist is someone who takes two things agree in attribute to be "primitive" or in other words, a further un-analyzable affair. Ostrich nominalism simply ignores this primitive nature of the sense datum, and says there's no such thing as the problem itself.

I could say a lot about Quine and ontological commitment, but I'd like you to interact in order for us to communicate better. He stacks the ontological deck against universals just by how he formulates what it means to be ontologically committed to something. Don't worry too much about not getting the problem 'first time,' it is a central problem and depending on how you answer it, gives you the lens with which you see the whole world.


Why do different objects resemble each other? Because they have some properties in common. And what are those properties they have in common, are they also objects? If so, objects can be many places at once, if not, what are they, and how are they shared? How do they interact with physical objects and with us? That's the problem of universals in a nutshell. Attempts at its solution go back to Plato's theory of ideal forms, but the name was coined by medieval scholasts who got preoccupied with it. Medieval Problem of Universals focuses on the genesis of the problem rather than its solutions, see also Gould's paper.

Quine's position suffers from the same problems as trope nominalism:"If trope theories are presented as a solution to the Problem of Universals, they should explain how there can be truths to explain the appearance of generality in reality. What we end up with, though, is brute and ungrounded qualitative identity among distinct tropes... What we want is an explanation of qualitative similarity. Accounting for it in terms of qualitative similarity — now at the level of tropes — does no more than relocate the question".


Red is the property of red things, but the color Red is not Red otherwise Red would be a property of the property Red. But Red has properties - Red is a color, Red is not a shape and Red is not Green. So Red has properties and to have properties is to exist.

But what is the relationship between “Red” and its instances? That is the problem.


Maybe philosophers like David Armstrong see a problem where there is none. The problem of universals is just a mirage.

If that is indeed true, the question just becomes: How can we be able to relate to Armstrong's and other realists' faulty reasoning?

Here Michael Devitt writes in "Ostrich Nominalism or Mirage Realism?":

The One over Many is a pseudo problem. Why, then, are philosophers so beguiled by it? I suspect that the reason is an implicit commitment to the “ ‘Fido’‐Fido” theory of meaning. This theory starts from the appealing idea that the meaning of a proper name like ‘Fido’ is the object it names, Fido. The theory generalizes this view of meaning to all terms. The theory has had a persistent hold over the minds of philosophers and many others.


It is easy to see how this theory leads us to universals. Consider ‘That rose is red’. This sentence, like all others, has a certain complexity. It has two terms, the singular term ‘that rose’ and the general term ‘red’, of different grammatical categories and playing quite different roles. How can the ‘Fido’‐ Fido theory cope with this complexity? It has to see the two types of term naming two types of entities: the different roles of the terms require different types of entities. The entity named by ‘that rose’ is a particular rose; that named by ‘red’ is the universal, redness, which can be shared by many particulars. The One over Many begins to look like a real problem

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