William M. Briggs

Statistician to the Stars!

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Realism vs. Anti-Realism IV: (some) Objections to realism—Guest Post by G. Rodrigues

Dr Johnson refutes naturalism thusly

Johnson did not answer …; but talking for victory and determined to be master of the field, he had recourse to the device which Goldsmith imputed to him in the witty words of one of Cibber’s comedies. “There is no arguing with Johnson; for when his pistol misses fire, he knocks you down with the butt end of it.”

— J. Boswell, Life of Samuel Johnson

Dr. Johnson had an unwieldy frame, a face scarred by scrofula, the laughter of a hippopotamus, always left home with a solid stick to defend himself from hoodlums and always argued for victory. After having shot blanks[1], the anti-realist with something like Johnson’s tenacity will go after the realist with the butt end of his pistol. Even if he concedes that realism about universals is very hard to evade as I tried to argue in the previous post, maybe he can find an objection powerful enough to force the realist into a stalemate.

In this fourth installment, I will consider some of the objections put forward against realism. The first two are somewhat technical; they are here because they illustrate the ways in which anti-realists find universals abhorrent, and also to pave the track to the last three, which form the spiritual core of the post.

A. Identity conditions

Some philosophers (Quine in particular, pressed this objection) argue that compared to classes, the identity conditions for universals are obscure. The identity conditions for classes are clear: two classes are identical iff they have exactly the same members. But no such condition exists for universals, and if there are no identity conditions for the posited entities, then how can there be such entities in the first place? This argument can be interpreted in two ways, an ontological and an epistemological one.

The former does not pose a special problem as the realist can always use a variation of Leibniz’s law of the indiscernibility of identicals now applied to universals. If the latter, then the objection seems to be a variation of methodism applied to the identity conditions of universals, that one must know how one knows before one can know, and if one cannot answer the skeptical question of how one knows, then the skeptic becomes the master of the field.

A first possible response is to deny the need for specifying identity conditions for universals. One reason for doing this is that providing non-circular and informative identity conditions for material objects is equally fraught with problems. For example, certain facts of quantum mechanics make the identity conditions for elementary particles highly problematic. Presumably, this does not bother anyone so why should we be bothered by the absence of explicit identity conditions for universals? Following this, we could adopt some form of epistemological particularism, which seems unavoidable anyway on pain of infinite regress. To see how it can be done, consult J. P. Moreland, Universals, chapter 5, pg. 118 ff.

B. Vicious regresses

Some vicious regress arguments have been aimed at realism. The Third Man argument is a particularly notorious one directed against the Platonist version of realism. Since I favor the Aristotelian-Thomist stripe, I will not bother with it and instead focus my attention on an argument devised by F. H. Bradley. It goes like this. The core of the realist doctrine is the instantiation relation, call it R, between concrete particulars, say x, y, etc. and universals X, Y, etc. Now Bradley says the following: for the relation x R X to obtain, and given the realist ontological commitments, then both x and X must enter into a relation with R and so on ad infinitum, and the realist has a vicious regress in his hands.

But the realist can respond that just as one does not need superglue to connect two objects to normal glue in order to tie them together with normal glue, relations do not need to enter in relations with their relata for they to relate those relata to each other. In the same way, the fact that x instantiates X does not need putative higher-order relations R’, R” such that x R’ R and X R” R’ if R is to relate x and X. As a primitive metaphysical fact, the instantiation relation, or nexus or tie if we want to avoid any confusion, connects particulars and universals and does not need any mediators for the relation to obtain.

The two previous objections are admittedly of a technical kind. The next three on the other hand are probably what hover on most anti-realist minds. They usually come tied together by some prior metaphysical commitment, for example, to naturalism. This is spelled out in the fifth and last objection. To be fair though, the problem, from a Thomist point of view, lies in assumptions going back to Descartes and co., naturalism just being the logical outcome of rejecting the Thomist essentialist picture. It is not, as many ignoramuses think, that the Thomist will want to hold on to his metaphysics with its “ghostly” entities as the last bulwark against the onslaught of materialist science that explains, and explains away, everything as congeries of particles in motion. For the Thomist, the modern metaphysical conception of matter is just as wrongheaded, if not more, as the conceptions of the soul or the mind. And just in case it is not clear, let me repeat that the bone of contention is metaphysical, not scientific.

The concept of Ockham’s razor is yet another universal

C. Ockham’s razor

One common complaint is that the realists’ ontology is bloated, dragging in together with the common objects of our experience an extravagant abundance of abstract objects like universals, relations, properties, etc. The anti-realist might even say that universals, for example, are invoked to explain features of language, and that a wielding of Ockham’s razor should instead cut them off. But what are we to make of this suggestion? Given the arguments to the effect that an appeal to universals is necessary to not only explain linguistic features such as predication and abstract reference but that it is also the ground for a robust correspondence theory of the truth, Ockham’s razor only applies if the anti-realist can offer a better and simpler account of such phenomena. However one judges realism, it is clear that such an account has not emerged so the argument has little force.

D. The epistemological objection

A fourth objection is the so-called epistemological challenge. If universals are abstract objects as the traditional realist contends, then they do not exist in space-time[2]. If they do not exist in space-time then they are causally inert. And if they are causally inert how can we ever perceive them and come to know them? In the philosophy of mathematics, the epistemological challenge was launched in the influential article of P. Benacerraf, “Mathematical Truth”. If you are like me and favor an Aristotelian-Thomist metaphysics, reading the article followed by a reading of modern responses to it such as B. Hale and C. Wright’s “Benacerraf’s Dilemma Revisited”[3], for all the undeniable virtues of these articles, it makes for something of an infuriating exercise, for you will note just how much they are suffused with metaphysical assumptions that a Thomist will outright reject.

What do people mean when they say that abstract objects are causally inert? Usually, it is meant in the sense that abstract objects have no efficient causal powers, but efficient causality is just one of the four modes of causality, and its modern usage is a narrow construal of the classical one at that. But why assume that to know the abstract universals greenness or triangularity, there must be a physical chain of efficient causation involved?

For Aquinas, when we sense-perceive that Fido is green, followed by the intellectual act of abstracting the universal greenness[4], the same universal that exists in re in Fido comes to exist post rem in the intellect, in a different mode of being. For Aquinas, an intellect just is the kind of thing that can grasp or get a hold of universals without instantiating them, that is, that can grasp greenness without itself becoming green[5]. This is not only what guarantees the objectivity of knowledge but its truth, the correspondence between the universals abstracted by the mind in act and the universal as instantiated in the concrete particular.

But even leaving Aquinas’ epistemological account aside, it is simply not clear why abstract objects cannot be the objects of thought. For we can think about non-existent objects, such as unicorns, a thing which even the anti-realist must concede. The anti-realist may retort that such fictional objects like unicorns, if they existed would be material objects and thus capable of being perceived and it is precisely because we do not perceive them that we have grounds to say that they do not exist. But this is muddleheaded; for given that abstract objects do not exist in space-time, our failure to perceive them tells us nothing whatsoever. Moreover, given that we can think about them, even pose the question of whether they do exist or not as extra-mental entities, it seems it is at least metaphysically possible that they do exist[6]. And given that we can reason about them, as we surely can, it seems at least possible that we can reason to their existence, which is precisely what the realist will contend he
has done.

E. The naturalist objection

An elaboration of objections C and D is the naturalist charge and contain the metaphysical commitment underlying not only most of the objections but the very rejection of realism. Naturalism is notoriously hard to define; here I will take it to be the view that the spatio-temporal physical universe of entities studied by science, especially the hard empirical sciences, is all there is. Everything that exists is located in space-time and is part of the efficient causal system known as the universe. If naturalism is true, then it is clear that the traditional realist account must be false.

But what arguments are there for naturalism? As far as I can glean from what the Prophets of the Sect affirm, it all boils down to two arguments: first, non-naturalists have no evidence for the existence of non-physical entities and second, the inductive successes of the modern empirical sciences give strong evidence that concrete particulars are the only thing that exist.

Starting with the former, the claim is patently false. This series of posts is evidence for the existence of one type of non-physical entities, universals. And this is just one, rather paltry example. But even if we granted the truth of the claim (which to repeat myself, I do not, not even for a second), the only thing you could squeeze from it is that all the purported arguments for the existence of non-physical entities fail. This does not by itself give warrant to believe in the claim P = “non-physical entities do not exist”. For if it did, it would mean that you would be warranted in believing in P without the least shred of evidence in favor of it which is absurd. So by itself, it is useless.

And we come to the second argument. This argument only has force if we judge the modern, hard empirical sciences to either exhaust the field of knowledge, in the sense that everything can be ultimately reduced to scientific explanations, or that the empirical sciences are the ultimate epistemic arbiter of warranted knowledge. The first is patently false; mathematics cannot be reduced to the empirical sciences. It is false, if the arguments in this series are correct. There are other arguments that purport to show this, but here, the only thing I need to notice is that this is nothing more than a promissory note, something like “We have not pegged it yet, but just you wait”, so the appropriate response is to call on the bluff.

Axioms? Doesn’t that mean…?

The second take is either circular or self-refuting. To put it in a different way: what is the object of proper study of the hard empirical sciences? Material bodies in motion or change. Is it a great wonder that the hard empirical sciences have not found anything besides their object of proper study? This is like a man trying to convince us that there are no stars by saying to look through the microscope and point out that there are none to be found upon looking. This is one of the reasons why many science-fetishists when pressed against the wall to justify their metaphysical foundations, will retreat more often than not to a bizarre concoction of relativism and pragmatism, which itself is ultimately circular or self-refuting. The ultimate irony being that this stance is what most undermines the science to which they pay lip service.

Maybe the naturalist will retort that I am mischaracterizing the argument. What he is saying is that if such non-physical entities existed, then we should expect to see physical effects of their existence. Facepalm. No, we do not expect to see such a thing, because the traditional realist will concede that abstract objects are causally inert, causality understood in the sense of efficient causality operative in the empirical sciences. So what is the naturalist asking? Maybe the naturalist intends the request only against God and such “personal”, “supernatural” entities. The argument is still worthless, but as far this post is concerned, discussion is over.

Oh what the heck, I still want to know what is this particular brand of science-beholden naturalist asking? Let us plumb these depths of irrationality. A personal intervention from God in his life? That is putting the evidential bar a little too high, methinks. I would advise such a person to read the epistle of James 1:5-8. And even if he did witness a miracle what is to stop him from saying that aliens with ultra-advanced technology are just goofing around and thus give a completely naturalist explanation?

Maybe the naturalist is asking for something more modest, a state of affairs that is not explainable by natural science. But what would this be other than a gap argument? Gap arguments are fallacious. There are now three options. One, the naturalist is asking for a gap argument not knowing that it is fallacious, in which case he is clueless. Two, he does know it, in which case it is a mere rhetorical ploy and he is intellectually dishonest. The third and last option is that he knows that gap arguments are fallacious, but given his (self-refuting) epistemic strictures he then must say that there can be no evidence for God. This I presume, is what in some quarters passes for being open-minded and committed to evidence and reason…

Since naturalists tend to be science-fetishists, here is a final argument in favor of realism. Consider any given scientific law, say Newton’s law of gravitation, and for the sake of simplicity assume it obtains exactly in our universe. If the anti-realist is right and only concrete particulars exist then this law is a law about pairs of concrete particulars, concrete material bodies with specific mass and at a specific distance from each other. But if the law is merely a law about concrete particulars it could be a mere “cosmic accident” and there would be no reason why it applies to any future contingent, existent pair of concrete particulars.

In other words, it fails to account for the truth of the corresponding counterfactual conditionals. But what becomes of the predictive power of science if it cannot account for counterfactual conditionals? Vanished, poof, gone with the pigs[7]. To avoid this and other difficulties, we must accept that a law is a relationship between universals and that it applies to all concrete particulars instantiating the relevant universals. For example, in case of Newton’s law the universals involved are mass, force and distance. And insofar as the aim of science is to uncover objective, mind-independent truths, the subjects of those truths, universals, must be objective and mind-independent. Thus, it seems acceptance of science commits us to the existence of universals[8].

As the saying goes, one man’s modus ponens is another man’s modus tollens. Realism is true so naturalism is false. Good riddance.



[1] There is an obvious joke lurking here. But serious, sober philosophical discourse is above such petty vulgarities. (He He He He He).

[2] Sometimes one hears that abstracts objects exist outside of space-time, but this is confused and confusing as “outside” implies a spacial relationship which contradicts the fact that abstracts do not exist in space-time.

[3] Benacerraf’s article appeared in Journal of Philosophy, 70 (1972) 661-680 and is reprinted in Philosophy of Mathematics: Selected Readings, ed. by P. Benacerraf, H. Putnam. The article of B. Hale and C. Wright can be found here.

[4] I am glossing over many details, such as the difference between sense and perception, the role of phantasms, etc. The crucial point is that Aquinas is adamant on a distinction in kind between the animal powers of sensation and perception, memory and imagination on the one hand and the intellectual activity proper on the other, to which the powers of abstraction, concept formation and the various modes of reasoning belong. This distinction, lost to many modern philosophers, is at the heart of many (misguided) objections against realism.

[5] Aquinas’ epistemology follows his metaphysics, as one should expect in a realist. A good starting point to know more about it is S. MacDonald, “Theory of Knowledge” in The Cambridge Companion to Aquinas, ed. by N. Kretzmann and E. Stump.

[6] A modal argument for the necessary existence of abstract objects, numbers more precisely, parallel to Plantinga’s modal ontological argument can be found in S5, God and Numbers by Chad McIntosh. One obvious difference between the two arguments is that the crucial premise in the case of numbers is much harder to dispose of, and is in fact practically all but granted by many (most?) philosophers.

[7] And thus, by shedding a sound, realist metaphysics and philosophy of nature, another typical modern “problem” is born, the problem of induction.

[8] For an elaboration of the argument from science in favor of realism, see D. M Armstrong, What is a law of nature?

Lewandowsky’s Confusion About Statistics

Still at conference, so just a short plug for learning about which you speak.

Stephan Lewandowsky, who believes JFK shot at the moon landings and that’s why the globe has passed the tippling point, or something like that, has said a few words about statistics:

However, our conclusion that the effect [in yet another silly study] is “real” and not due to chance is inevitably accompanied by some uncertainty.

Here is the rub: if the significance level is .05 (5%), then there is still a 1 in 20 chance that we erroneously concluded the effect was real even when it was due to chance—or put another way, out of 20 experiments, there may be 1 that reports an effect when in fact that effect does not exist. This possibility can never be ruled out (although the probability can be minimized by various means).

In his favor, a lot of people who publish too many papers aimed at audiences who are eager to nod their heads sagely at the foibles of their inferiors make the same errors Lewandowsky does. They are widely replicated errors. Which proves that replication in science can often reinforce distortions.

If the significance level is 0.05 it only means that if the p-value is less than or equal to that number, and that you are allowed to declare “success” for your experiment, no matter how silly it is (see the Statistics section on this page for some doozies). What is a p-value? Unfortunately, the definition of this destructive beast is very difficult to remember, so difficult that it is easier to remember what it isn’t.

The p-value is the probability of seeing a statistic as large (in absolute) value as the one you actually did see, given: (1) the values of certain parameters in a model you are using to quantify uncertainty in the numbers are set to a pre-specified number (usually 0), (2) the model itself is unambiguously true, (3) the experiment that generated the data is replicated indefinitely, and (4) the data at hand is measured without error (or if it is measured with error, this error is modeled).

Each word of this cumbrous definition counts, which is why it is so difficult to memorize and to use properly.

You are free to choose the model, the truth of which is usually unknown. For example, you are free to model your data using a hockey stick, even when that’s absurd. You will get a different p-value for every model. One model can give a non-publishable (i.e. significant) p-value, while a second model can give a publishable one. In statistics, there are many models one may choose in any situation. Their name is legion. Many scientists, psychologists in particular, tend to choose poorly.

Now, once you have the model in hand, you still have to pick a statistic. For any given model, there are many. Each statistic will give a different p-value. One statistic (inside a model) will give a non-publishable p-value, another statistic will give a publishable one.

On top of all this is the enormous latitude the scientist has to call the model/statistic pair he used to be relevant to the hypothesis he announces. It could be, and often is, this relationship is tenuous and that a direct reading of the model has little bearing on the “public” hypothesis. Almost always, the hypothesis about the real-life thing is confused and conflated with different hypotheses about the parameters of the model picked. This is not a small error: it is enormous and leads to wild over-certainty. Again, see that page for examples.

And then you are free to manipulate the data itself, tossing away “outliers”, usually defined as data that does not fit your preconceptions. You can do “sub group” analysis. You can say your hypothesis is true only for certain parts of your data. Oh my, it goes on and on.

So in addition to getting the technical definition wrong, Lewandowsky got the practical, boots-on-the-ground definition wrong. He would do well to read “Inappropriate Fiddling with Statistical Analyses to Obtain a Desirable P-value: Tests to Detect its Presence in Published Literature” by Gadbury and Allison for wisdom on this topic.

Conclusion: Especially in dicey areas, and psychology is certainly one of them, there is much more than a 1 in 20 chance that the finding does not confirm the stated hypothesis (about the real-life thing).

Epilogue: Lewandowsky advocates, as do we all, replication to smoke out queer p-values. As an example, Lewandowsky indicates the infamous climate hockey stick has been “replicated,” a sure view, he claims, that the p-values are leading us down a flowery path. Unfortunately, our man has forgotten to include the multiple studies that show the hockey stick is malarkey, as crazy Uncle Joe would say.

There is a psychological term for emphasizing only the evidence which supports your belief and ignoring everything else, but I’ve forgotten what it is.


Thanks to Dr K.A. Rodgers for alerting me to this topic.

James Hansen Was Right

This beverage contributed to humanity’s Tippling Point

Let it not be said that I cannot admit when an enemy is right. When right is right it is right to acknowledge that right.

And James Hansen—that infrequent visitor to the land of careful reasoning, where natives bask in the calm sunshine of the mind—was right. How so?

Our pal Willie Soon sent us an article from one of those progressive places in which Mr Hansen claimed that mankind—and womankind, too, God bless them—had reached a Tippling Point. And by golly, was he on the money.

You’ll forgive me if I am short on details, but I am at a conference in Seattle and last night we made rather merry and my eyes aren’t quite able to focus on the whole of Willie’s link. But it was at least clear as Pugent Sound that Mr Hansen had vigorously argued that we have reached a Tippling Point. And it was so!

Every man and women in my field of vision last night had not only reached that point, but many had ventured well beyond it. How Mr Hansen was able to discern this from his faraway place must remain a mystery to us mere mortals. But claim it he did, and he was right.

Therefore, let us raise our glasses and toast the estimable Mr Hansen. To the Tippling Point!

Regular posts resume tomorrow. I hope.

A House Is A Woman’s Castle—Guest Post By The Blonde Bombshell

Attention men: that green thing is a “duvet cover”. See the text.

A Norwegian study reports that couples who make a concerted effort to divide the housework are more likely to divorce than couples where most of the chores fall to the woman of the house.

The study results may puzzle the modern person, who has been informed from the cradle that gender roles imposed by a patriarchal society are meant to be exposed and shattered into a million little pieces. It is much better that everyone carry their own freight (or do their own laundry) under the banner of fairness.

Lest the reader write off the study results as a case of “Norwegians just being Norwegian”, a recent article in The Atlantic offers circumstantial evidence from a dinner party attended by women (all divorced save for one) in Los Angeles that suggests that the increased divorce rate among the multi-degreed, professional class is skyrocketing.

The Atlantic article recounts the story of a married woman who has a wonderful well-paying job and a house husband, who seems like a pretty cool guy, and content in his role. The wife asked the husband to replace a broken light-bulb in the garage, and he didn’t do the assigned task in a timely manner, which resulted in the wife banging her shin one dark night. She became unhinged, and the result was a costly “emergency therapy session.”

In this instance, most or nearly all of the home chores fell to the man, so it is not fair to use him as an example of what’s wrong with the 50-50 approach to marriage. If this particular union ends in divorce, it could be due the wife’s financial independence or the modern tendency to view marriage as a business contract rather than a sacrament—both reasons that the study authors offer for the increased divorce rates in 50-50 marriages.

What is really going on is that the poor men—from the fjords of Norway and to the suburbs of Los Angeles—do not have a clue. The men do not have the most basic realization that his home is his wife’s castle, and she has very definite customs, habits, and expectations, all of which he hasn’t noticed.

He has never observed that the top sheet has a very definite top and a bottom. He does not recognize that the duvet cover has a several buttons at the bottom, which should be to the foot of a made bed. When he makes the bed, the covers go any which way. The result may be functional, but may not please the eye of the wife.

He doesn’t see the smear of balsamic vinegar on the shelf or the ring of dried ketchup at the neck of the bottle. He doesn’t sense the internal order in the way the dishes are stacked or how the silverware is arranged. He doesn’t care that the clothes are inside-out as he folds them from the dryer. There is a lot going on in his own house that is outside of his awareness.

The trouble is that the wife is perfectly aware. She sees right away that things are out of order. She can either heave a quiet sigh and re-stack the dishes, and tidy up the silverware drawer and be grateful that she has a life’s companion, or she can make a federal case out it, and summon the emergency therapist—or the divorce lawyer.

I don’t have any scientific data to back me up, but I would guess there are between 12 and 20 ironclad expectations that any wife has for her house. These expectations vary from woman to woman. Men in a second marriage will quickly learn that what worked with number one isn’t necessarily going to work with number two.

So, for the upper-income man to stay married, he needs to learn what she wants. (Note: She already knows what he wants.)

Some wives will want an everyday vacuum run and bathroom polish. Others don’t mind a once-a-week vacuum and a deep clean of the tub on Sundays. Some wives are a maniac for order in the kitchen, and won’t go to bed with dishes in the sink.

The strategy of some men (likely those with less education and not as much income) is to have her do the work herself. These louts manage to stay married.

For a man to be king of his castle, the queen has to be happy. As sexist and backward as that sounds, that is the biggest key to martial harmony. Researchers: start your data collection.

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

St. Thomas Aquinas from ‘The Demidoff Altarpiece’ by Carlo Crivelli

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.

This image is green (and black)

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.



[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.

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