Realism vs. Anti-Realism III: The anti-realist response — Guest Post by G. Rodrigues

We have no space to follow St. Thomas through all these negative heresies; but a word must be said about Nominalism or the doubt founded on the things that differ. Everyone knows that the Nominalist declared that things differ too much to be really classified; so that they are only labelled. Aquinas was a firm but moderate Realist, and therefore held that there really are general qualities; as that human beings are human, amid other paradoxes. To be an extreme Realist would have taken him too near to being a Platonist. He recognized that individuality is real, but said that it coexists with a common character making some generalisation possible; in fact, as in most things, he said exactly what all common sense would say, if no intelligent heretics had ever disturbed it.

— G. K. Chesterton, Saint Thomas Aquinas, The Dumb Ox

In this post I will consider the anti-realist (Chesterton’s “intelligent heretics”) response to the realist challenge. Anti-realism comes in several varieties as one would expect: we have nominalism (universals do not exist) and conceptualism (universals are mere beings of reason), and within these major genera there are then several species[1]. For what concerns me here, the disagreement between conceptualists and nominalists is much less important than their common denial of the extra-mental reality of universals, so I will purposely lump the two together.

After a short introduction, I will divide anti-realist strategies in two major trends: linguistic and class-based ones. Ideally, these two sections should be read side by side to get a feel for the parallel arguments made against the two strategies, as the same problems tend to recur in all nominalist accounts. I will not probe this phenomenon in any depth, although I will drop a hint here and there. A third section will be devoted to the form of nominalism that is in better shape, trope nominalism. I have looked extensively for ways to present it and its criticism, in my judgment conclusive, but found it impossible to do it fairly within the constraints of a blog post, so the comments will be brief. For more information, look up J. P. Moreland’s Universals, chapters 2 and 3, the book that will, once again, be my main source. For a bird’s eye view of nominalism, see Nominalism in Metaphysics.

Before proceeding two important caveats. First, this is the longest post in the series. There is a frightening amount of ground to cover and I will be moving at a fairly brisk pace. Second, I will be arguing against (some) anti-realist positions. In many cases, the objections can be responded to and the dialectic continued. Since the post must be finite and of a reasonably short length, I have to cut off the dialogue at some point. It is a judgment call, biased in favor of the realist. So if you want the whole story, you know what to do: hit the books.

The bottom metaphysical question is: what makes P-things P? Realists account for this by an appeal to universals. Anti-realists deny the extra-mental reality of universals and related abstract objects such as propositions and relations, and only accept the existence of particulars. They want to connect language and thought directly with reality without the mediating link of universals. The reasons why they want to do it can be stated in the form of objections against realism and will be considered in the next post. Here, I will just gauge their response to the realist challenge.

Recall four basic examples of sentences from the previous post:

1. Fido is green.
2. Rover is green.
3. Socrates is green.
4. Greenness is a color.

To be successful, the anti-realist has to offer a paraphrase of sentences like these that either entirely eliminates or reduces universals to the objects allowed by his ontology. Two major strategies are linguistic nominalism, in which universals are eliminated in favor of words or concepts with general application, or class nominalism, where a universal is reduced to its extensional content or class of instances[2]. Trope nominalism is a beefed up version of class nominalism.

A. Linguistic nominalism

Linguistic strategies seek to eliminate universals by employing translation devices, some of them fairly sophisticated such as those developed by W. Sellars, to show that the realist’s claim that universals are needed is illusory. Starting with predication, the nominalist can paraphrase (1) as:

• 1a. The term “green” correctly applies to Fido.

As for similarity, the nominalist can say that Fido and Rover resemble in the aspect of greenness because the term “green” correctly applies to both.

There are several problems with the linguistic strategy. First, linguistic predicates are neither sufficient nor necessary to specify a universal. They are not sufficient for there are contrived predicates that correspond to no universal whatsoever (exercise to the reader[3]). They are clearly not necessary, for “Fido is green” would still be true even if no human being thought it or uttered the corresponding sentence, or if humans never existed in the first place. The simple fact is that universals are far more numerous than linguistic predicates; the former are infinite in number but the linguistic predicates thought or thought-able, uttered or utter-able in principle by the whole humanity, past, present and future, is finite.

Second, the linguistic nominalist owes us an account of what it means to say that a term applies correctly to explain predication and similarity. The term “green” correctly applies to Fido and it does not apply to Socrates, but what accounts for the difference? A first answer is to simply say that it is a brute, primitive fact. “Green” correctly applies to Fido because Fido is green and that is it. If the realist complains that this is trivial and uninformative, the nominalist will concede it is and then reply that the realist explanation is only superficially more informative, with the disadvantage of dragging in a boatload of extra objects. But how cogent is this?

For starters, it commits one to a staggering amount of brute facts, so much so, that this has been called “Ostrich nominalism”. If you refuse to play the explanatory game, you can hardly say that you have won it. Also, contrary to what the nominalist suggests, correct application of a term does not seem to be a primitive fact but analyzable, for
we say that “green” applies correctly to Fido because Fido is green, not the other way around. But there are other problems.

Whether or not the predicate nominalist gives a non-circular account of correct term application, he is in a very awkward position. For green lizards existed long before human language came unto the world, so it seems he is committed to say that language creates properties and that Fido was not green until the first human thought it or uttered it, a barely comprehensible suggestion. As a bonus, this makes clear that an account of the modal status of necessary truths like (4) above is beset by severe problems.

Finally, words are universals too. For I utter this particular word “green”. Since my first language is Portuguese, I can also utter the particular word “verde“. And Socrates also uttered a “green” word, presumably in Greek. And now I will again utter “green”, a different utterance from my first one. But all these utterances (or thoughts, if you go the conceptualist route) all express the same thing, or in the philosophical jargon, are different tokens of the same word type, so we again have a problem of unity within plurality.

In fact, how is even communication possible in the first place if all these utterances do not express the same thing? But if they do, as they surely must, what can it be other than the corresponding universal word type? So how can the nominalist disentangle this self-imposed knot? He cannot offer a reductive analysis of word types in terms of words, for that would be circular. Maybe he can say that it is because words resemble each other. But in what sense? If he says that it is because these words correctly apply to the same objects, he is just going in circles. And even if some sense can be attached to it, a vicious regress looms large in the horizon because the nominalist is appealing to the typed relation of resemblance, and thus to a universal (see below for more details). It seems then that reference to universals has not been eliminated.

B. Class nominalism.

Class[4] nominalism takes its cue from set theory and replaces universals by their extensional content so that (1) gets paraphrased as “Fido is a member of the class of green things”. Class nominalism suffers from similar ills that plague linguistic nominalism. As in linguistic nominalism, classes are neither sufficient nor necessary to specify universals. In the literature, this goes by the name of the companionship and imperfect community problems.

An easy example of the first is given by two obviously different universals with empty extension, e.g. unicorn-ness and griffin-ness. If the nominalist objects that these name nothing at all, and even if we buy this retort, the problem still persists because we can find examples of different, instantiated universals with the same extensional content. Consider a possible world in which there is only one object, a green ball. Then greenness and roundness have exactly the same extensional content. Conversely, a distinct class of particulars is not a sufficient condition for there being a distinct universal. This is left to the reader as an exercise[5].

How does the class nominalist account for predication and resemblance? We can ask in virtue of what is Fido in the class G of green things. If the nominalist says because Fido is green, then this is uninformative and circular. If he answers because it has the property green, he concedes the point to the realist. The nominalist can always assert that class membership is a primitive, unanalyzable relation, just as the realist asserts that the instantiation relation is primitive. But in order to assert that Fido is in G, we must be given the class G and scan it in order to see that Fido is in it; but this is false to the facts for in order to assert that Fido is green we only have to check Fido and not anything external to it.

If the nominalist wants to construe membership in G as membership in {x: G(x)} where G(x) is the predicate “x is Green” then of course, it suffices to assert G(x) but this concedes the point to the realist that class membership is not primitive. A related problem is that the identity conditions for the class G change in time as green things come and go out of existence. The universal itself does not change, independently of how many times it is exemplified, but the class of green things does change because its identity conditions change.

Maybe one way out is to partition the concrete particulars in resemblance classes and then the question becomes how to non-circularly pick them. This form of nominalism is called resemblance nominalism. One possible way is to select a paradigmatic exemplar. The class of green things will then be the class of things that resemble the green exemplar. The problem with this is what is the criterion to select the paradigmatic exemplar if not itself an exemplar of circular reasoning? And if there are different paradigmatic exemplars, how do we know that we obtain the same class independently of the exemplar picked? Maybe the nominalist can pick a maximal class such that any two particulars in it resemble each other (and if you are a mathematician and want to sound cute, you add, apply Zorn’s lemma). But this does not work[5]. What the class nominalist would like to say is that Fido green-resembles Rover and not green-resembles Socrates. The problem with this answer however, is that what the nominalist is trying to account for is greenness, so to use it to separate the “bad” resemblance cases from the “good” ones is circular.

Taking the cue that resemblance is resemblance in some respect, we can construct a vicious regress in the following way. Unless the resemblance relation is specified the class is not specified either, in other words, the resemblance relation is a universal and has a type. Therefore, resemblance in respect to something—color —is once again appealing to a universal. Maybe, we can eliminate this universal by appealing to its resemblance class; let us throw a bone to the nominalist and allow him to proceed unencumbered without having to explain in what this higher-order resemblance relation amounts to. But then this itself will make appeal to a higher order relation of resemblance, and the nominalist either has not eliminated universals or he has a vicious regress in his hands.

Things do not fare much better on accounting for abstract reference or the necessary modal status of universals and the truths about them. In the first place, taking classes as the referents of abstract singular terms fails because as already observed, classes are neither sufficient nor necessary to specify universals. Maybe the nominalist can construe the class in terms of scattered objects. Applying this to (4) we get:

• 4a. Necessarily, the scattered object of all green things is a colored thing.

This is indeed a true statement, but is it is a faithful translation of (4)? In other words, are the truth conditions preserved? Colors and colored things are not the same kind of entities and different predicates apply to them, so by the indiscernability of identicals, (4b) is not saying the same thing as (4). But even if we accepted this translation, this strategy does not work for other universals: for an example, just replace greenness for humanity. Two further problems with translation strategies in general are first, that they tend to be ad hoc, with no clear pattern emerging on how to uniformly account for all cases and second, for those that pursue the eliminative route, it commits them to the implausible position that things like triangularity or humanity do not exist and talk about them is ultimately talk about words.

C. Trope nominalism.

In the previous section we have seen that the class nominalist would like to say that Fido green-resembles Rover and not green-resembles Socrates. This is precisely what a trope nominalist will say. The trope nominalist replaces the realist’s universal greenness by a multiplicity of green tropes, one for each green instance. Fido has a particular green trope and Rover its own distinct particular green trope and so on. On this view, tropes[6] are simple qualities and an object is a collection or bundle of tropes.

Before tackling predication and resemblance, it is best to see what the trope nominalist makes of abstract reference. As we have seen, a realist takes abstract singular terms to be the proper names of existing things, universals. Eliminative nominalists have to scrounge all sorts of convoluted strategies to deal with abstract reference. The trope nominalist could be a denialist, but instead most trope nominalists, upon recognizing the difficulties facing such strategies, will say that abstract singular terms do name something, just not universals but sets of resembling tropes.

From this, the account of predication follows. If the universal greenness is replaced by the set of green tropes, to say that Fido is green is just to say that Fido has a trope that belongs to the set of green tropes. As for resemblance, the trope nominalist will say that Fido and Rover resemble each other in the aspect of green because they each possess a green trope that qualitatively resemble each other.

As a first remark, note that since tropes are simple qualities, resemblance classes are correctly formed and their formation is immune to the companionship and imperfect community problems. On the other hand, the price to pay is not only the introduction of a new category of entities, tropes, but also a commitment to the paraphernalia of set theory. And the trope nominalist still owes us an account of what a trope is if he is to evade the charge of avoiding realism by positing an extravagant ontology, what is the exact nature of the relationship of a trope with the object that possesses it, the nature of the qualitative resemblance relation between tropes, etc. As an example, consider the latter.

The trope nominalist could follow his strategy to its natural conclusion and posit resemblance tropes, that is, to treat relations the same way as other universals. This immediately raises the prospect of a vicious regress. One strategy is to back down and say that it is just a brute fact that green tropes resemble each other more than blue tropes. But then, for all the bells and whistles, tropes have not done the explanatory work they are supposed to do. So at best this is unsatisfactory, at worse, it generates a vicious regress parallel to those of linguistic and class nominalism.

Much more could be said, in both response and counter-response. My suggestion is for the reader to consult the references. I cannot however, resist the temptation to lodge one objection first raised by Wolterstorff. How innocent is opening the door to sets in one’s ontology? Well, sets have their members necessarily. Accordingly, given any set, it is impossible that it have members other than those it in fact has. Since greenness is the resemblance set of green tropes, it follows that this set necessarily has the members that it has. In particular, it follows that the green trope possessed by Fido necessarily is a member of this set.

There are two options now: if the green trope possessed by Fido individuates it, that is, only Fido could have possessed such a green trope, then it seems we are committed to assert that Fido existed necessarily. If the green trope possessed by Fido is not necessarily possessed by Fido and Fido alone, the tie between tropes and their possessors is loose and accidental. But this suggestion seems incorrect as it makes the identity conditions of tropes, and a fortiori the identity conditions of sets of tropes, unintelligible. But even so, the necessity problem still remains, for it still is the case that the set of green tropes could not have failed to be what it is. In particular, the number of green things (and human things and…) could not have failed to be what it is. But this surely is false.

Scanning the argument, the nominalist could dispute that sets have their members necessarily. The problem with trying to deny this is that, contrary to the class nominalist, the trope nominalist does not have the resources to cash out set talk in terms of concrete particulars, since tropes and sets were introduced precisely to overcome the difficulties with class nominalism. So he is stuck with sets of tropes, and sets, being abstract objects constructed out of its members and with identity conditions fixed by said members, have their members necessarily.

D. Conclusion.

If I could summarize this (long) post in one sentence, it would be: universals cannot be eliminated. I do not expect the unsympathetic reader to fully agree with me, but it should at least be clear that evading them is notoriously very hard to do.

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Endnotes:

[1] D. M. Armstrong has, with the veritable patience of an entomologist, surveyed various varieties of nominalism in Universals and Scientific Realism, vol. 1: Nominalism and Realism.

[2] One could object that the anti-realist is making an appeal to abstract objects, namely sets. The objection can be circumvented, since he can hold that a class of concrete particulars is itself a concrete particular in one of several ways: by identifying the class with the scattered concrete object composed of all the concrete particulars in the class, by translating set talk in terms of their members, etc. Quine and most trope nominalists bite the bullet and do admit sets into their ontology. Although this is a concession, the concession is to the existence of abstract objects not universals, and particularly well behaved ones, so the realist cannot proclaim victory. Not immediately, anyway.

[3] Virtually every introductory course or book on metaphysics contains a discussion of the problem of universals. One reference is E. Lowe, A Survey of Metaphysics, chapters 19, 20. M. Loux, Metaphysics, a Contemporary Introduction dedicates chapters 1 and 2 to the problem. The first chapter gives one example of a self-referential predicate that does not correspond to any universal. A less exotic example can be found in J. P. Moreland, Universals, pg. 29.

[4] For technical reasons (e.g. Russel’s paradox) it is important to maintain a distinction between sets and classes. Here, I will not bother with such technicalities and will use the two words interchangeably.

[5] An example of the imperfect community problem is in E. Lowe, A Survey of Metaphysics, pg. 357 ff. Lowe is working with the more complicated maximal definition of resemblance class, but the problem arises just the same with simpler definitions.

[6] Also called abstract particulars. This can be confusing, depending on how exactly the trope nominalist conceives a trope, but abstract usually is taken in the epistemological sense.