William M. Briggs

Statistician to the Stars!

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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.

Rover?

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.

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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.

Eating Chocolate Increases Chance Of Nobel Prize, P< 0.05

Yesterday, those noble Nobel fellows, the same committee that honored President Obama—what was it? six, seven days after he assumed office?—, gave this year’s Peace Prize to the European Union. That’s right: the statue, or cup, or whatever it is they bestow, will be given to the bureaucracy in Brussels.

And it’s no surprise. Why? Because those Europeans eat a lot of chocolate.

Just you take a look at the following picture, culled from Franz Messerli’s masterful New England Journal of Medicine‘s paper Chocolate Consumption, Cognitive Function, and Nobel Laureates (pdf).

Sweet success

It should be obvious, but if not, that horizontal-axis shows chocolate consumption and the vertical-axis shows per-capita Nobel prizes. The more chocolate a nation eats, the more Nobels. The Nobels! There just is no more official designator of truth and goodness.

Masserli says:

There was a close, significant linear correlation (r = 0.791, P<0.0001) between chocolate consumption per capita and the number of Nobel laureates per 10 million persons in a total of 23 countries (Fig. 1).

Look at that astonishingly low p-value! They just don’t come lower than that! That means only one thing: eat enough chocolate and the prize is yours. That’s why the EU won. How could anybody eat more chocolate than twenty-seven entire countries.

I’ll tell you how: twenty-eight or more countries could eat more chocolate. These leads to a statistical predication that next year’s Nobel Peach Prize will go to World. Word is that some are already practicing their part in the acceptance ceremony.

Chocolate can swell the little gray cells—Messerli pegs flavonoids—but our author was on the ball:

A second hypothesis, reverse causation—that is, that enhanced cognitive performance could stimulate countrywide chocolate consumption—must also be considered. It is conceivable that persons with superior cognitive function (i.e., the cognoscenti) are more aware of the health benefits of the flavanols in dark chocolate and are therefore prone to increasing their consumption.

Good news for this hypothesis is that it too is decisively rejected—it also have a disappearingly low p-value. That means it’s true too!

As an afterthought, and in view of complete completeness, Messerli opines (emphasis mine):

Finally, as to a third hypothesis, it is difficult to identify a plausible common denominator that could possibly drive both chocolate consumption and the number of Nobel laureates over many years. Differences in socioeconomic status from country to country and geographic and climatic factors may play some role, but they fall short of fully explaining the close correlation observed.

Indeed they do fall short, stumbling well before the mark. And why? I’ll tell you: there is no p-value for this obviously offhand hypothesis, this whim. Classical statistics assures us: No p-value, no truth. Therefore, this conjecture can’t be so.

Update See also Why Do Statisticians Answer Silly Questions That No One Ever Asks?

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In the interest of full disclosure, the paper included the following statement, typical in medical journals: “Dr. Messerli reports regular daily chocolate consumption, mostly but not exclusively in the form of Lindt’s dark varieties.”

Thanks to @benlauderdale where I first learned of this paper.

Note Given this is the internet and that therefore one can never be certain, we do all know that Messerli is pleased to be jocose?

Realism vs. Anti-Realism II: The realist challenge — Guest Post by G. Rodrigues

The one who will not work fits what is written about the virgins of Israel: he gives birth to wind — but the one who will work gives birth to his own father.

— S. Kierkegaard, Fear and Trembling

Fido instantiates himself onto a real leaf

In this second post I will consider the realist position towards universals and related objects such as propositions, relations, etc. For starters, consider the following three statements:

  1. Fido is green.
  2. Rover is green.
  3. Socrates is green.

Statements (1) through (3) predicate green of certain concrete particulars, Fido and Rover, specific lizards that have been so named (this lizard, that lizard), and Socrates, the famous Greek philosopher. The word “green” is both a noun and an adjective. In all three statements it has the latter, adjectival function. But (1) can be rendered in the logically equivalent “greenness characterizes Fido” where greenness is a noun and thus, presumably, it refers to an existing something.

So prima facie, an ordinary language statement like (1) seems to commit us to the existence of an entity, greenness, that makes (1) true. The realist will take this at face value and say that greenness does exist as an extra-mental object; more precisely, that greenness is a universal multiply instantiated, or exemplified, by the many concrete particulars of our sense experience. It is the fact that Fido and Rover instantiate the universal greenness, and thus have the property or attribute of being green, which grounds the truth of sentences (1) and (2) [1].

Similarly, it is the fact that Socrates does not instantiate the universal greenness[2] that grounds the falsity of (3). Furthermore, it is the instantiation of one and the same universal—greenness—that explains unity within plurality; that is, it is because Fido and Rover both instantiate the same universal greenness that they belong to the natural class of green things and why they resemble each other in this one aspect, while the fact that Socrates does not instantiate said universal is what accounts for him not belonging to the natural class of green things and thus not resembling Fido and Rover in the aspect of greenness.

Besides predication and resemblance, or as it has been historically known, the One over Many, the third phenomena that the realist purports to account is that of abstract reference, that is, the fact that universals themselves instantiate universals, stand in relations, etc. Consider the statements:

  1. Greenness is a color.
  2. Greenness resembles blueness more than it resembles yellowness.

The realist has a straightforward, simple, uniform account of the truth of (4): the universal greenness, being an entity in itself, instantiates a universal—the second-order universal color-ness—and it is that fact that grounds the truth of (4). The same simple, uniform account can be applied to (5), namely, that there is relation of resemblance, an objective feature of the fabric of reality, between the universals known as colors, that accounts for and grounds the truth of (5). Moreover, the realist account gives a simple, plausible explanation for why such statements as (4) and (5) are seemingly necessarily, unchanging truths, that hold in all possible worlds[3], by appealing to the de re necessity of the relations between the relevant universals, themselves necessary beings.

The realist accounts of predication, resemblance and abstract reference can be turned into arguments in favor of realism. Let us consider the latter case. To make the argument more forceful it is useful to drop Green Lizards and work instead with mathematical objects, triangles say. The triangles we encounter in reality are imperfect instantiations of the mathematical notion of triangle, for not only they are not perfect triangles, as being en-mattered they cannot have perfect straight sides, but they also have features that no mathematical triangle has, such as being drawn in sand or in paper or in a computer screen, being of this or that color, being at this or that region of space-time, etc. so that the universal triangularity cannot be identified with any particular concrete triangle.

Furthermore, concrete triangles, or even the class or scattered object of all triangles, are contingent, or it could be the case, and if cosmologists are correct it certainly will, that there was no intellect in the universe
to perceive them. It follows that not only is not triangularity reducible to a thought in the mind, but since the (non-tautological) truths about triangularity are necessary rather than contingent, the subject of such truths, the universal triangularity, is itself mind-independent and a necessary rather than contingent being[4].

Before proceeding, some words are in order about the realist ontological commitments. In the traditional[5] realist account a universal like greenness is an abstract object. Both the universal greenness and the relation of instantiation are abstract in the sense that they are not localized in space-time[6]. Greenness is “in” Fido not in the sense of being localized at the space-time location of Fido, but of being an ontological constituent of the substance known as Fido[7]. Furthermore, the relation of instantiation is a primitive one that is not analyzable in terms of more basic or fundamental entities.

A realist of an Aristotelian bent would now add that universals are ontologically dependent on the particulars that instantiate them, and that apart from them and abstracted away by the mind they are mere abstractions, or beings of reason[8]. To be even more specific, the substance Fido, The Lizard, instantiates a certain substantial form that, speaking somewhat loosely, fixes the range of potencies within the being of Fido, namely the potency for being green that on a normal, healthy lizard like Fido is, becomes actual and instantiated or exemplified, as opposed to say, being hundred-legged or composing long tracts on the problem of universals using silly examples with lizards instead of dogs. A realist after Plato would deny this ontological dependence and insist that universals stand over and apart the particulars that instantiate them. In other words, there can be, and surely there are, uninstantiated universals and thus the Platonist is compelled to posit a third realm to house them.

This then is the realist challenge: either accept the reality of universals, or offer a competing, satisfying account of predication, unity within plurality and abstract reference.

There are objections to the realist account that boil down to a restatement of some form of anti-realism; I will get to them in the next post. There are plausible objections directed against realism and I will also address (some of) them in due time. And then there are the clueless objections. The realm of clueless objections is potentially infinite, as vast and infinite as is human clueless-ness (which the reader will observe is the universal exemplified by the clueless, and only the clueless persons). Trying to peer into such an abyss and guesstimate a clueless objection is a vain affectation. It makes one stoop down to the level of the clueless and there is a serious risk of being confused with one. I dare say that one might as well be one. It is a dirty job but someone’s got to do it; so it might as well be me, as I am just as clueless as the next guy.

An envious Socrates wishes he thought of these arguments

Objection no. 1: Fido is green not because he instantiates the universal greenness but because the surface of Fido is such that it reflects photons within a certain energy range, and only those photons, and that is why we perceive Fido as green. Go learn some physics.

Answer to objection no. 1: So you do not know the difference between metaphysics and physics? Read again what I wrote. I did not say that Fido is green because it instantiates the universal greenness, rather, the fact that Fido is green is the same thing as instantiating the universal greenness. There are no explanatory becauses in the realist (or anti-realist) metaphysical account of predication. The causal story you tell while interesting, is completely irrelevant. Furthermore, even if I granted the cogency of such a causal story, such an analysis will necessarily appeal to universals for these are what ground the truth of such predication statements as that photons have energy levels, or that the the surface of Fido has certain reflection properties, etc. and etc.

Objection no. 2: “Greenness is a color” is a tautology, not a necessary truth. It is that way because of how the words “greenness” and “color” are conventionally defined.

Answer to objection no. 2: This objection is in fact a covert appeal to a form of linguistic nominalism, which will be dealt with in the next post. So you do not know the difference between a real and nominal definition? Yes, it is a contingent historical fact that in the English language, the particular word “greenness” has been made to point to, refer, or denote the property of being green. But once we grasp what the key abstract singular terms “greenness” and “color” point to, refer, or denote, we cannot help but give our intellectual assent to the truth of the statement “greenness is a color”, but also come to recognize that there is no possible world in which greenness failed to be a color, for it is a color by virtue of what greenness is, not by virtue of the contingent fact that the word “greenness” points to, refers, denotes greenness.

Objection no. 3: What a load of tosh; these are just dull and boring word-games.

Answer to objection no. 3: I cannot really retort to the charge of dullness and boringness; but no, these are not just “word-games”. Rather, universals are the link between thought and language on the one hand, and reality on the other, since they are what ground the intelligibility and the truth-conditions of statements like (1) to (5). You are certainly free to reject the realist account, but what you cannot do is evade the issue and say it does not matter; for otherwise when you make a predication statement like (1) you are speaking unintelligible gibberish since you have not deigned to clarify what is the meaning of such statements or what their truth conditions are.

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Endnotes:

[1] Some points of terminology: the meaning of universal was already explained, and should be contrasted with that of particulars that are not multiply exemplifiable (there is only one Fido, one Socrates, etc.). A relation is a universal that applies to pairs, or more generally n-tuples, of objects. For example: the spatial relation of taller than. Aristotelians will also introduce further distinctions in the general class of universals: kinds (substantial forms), properties, accidents, etc. These need not concern us, but for the interested reader, D. Oderberg’s Real Essentialism is a modern defense of Aristotelian-Thomistic essentialism. Propositions assert something, and thus are either true or false. Statements (1) to (3) all express propositions. In this series I will concentrate mainly on universals. For the problems anti-realists face when dealing with propositions see for example A. Plantinga Warrant and Proper Function, chapter 6.

[2] We have no pictures of Socrates, but I think we can be fairly certain that he was not green. If someone cares to dispute this, let him present his evidence.

[3] Possible worlds, the nature of necessity and contingency and allied problems constitute a huge topic, and currently a very popular one, in metaphysics. Here, I will take a possible world to be a possible state of affairs of the whole of reality, and hide beneath this simple statement a good deal of complicated details. See any good introductory book on metaphysics like E. Lowe A Survey of Metaphysics and references therein.

[4] In The Medieval Problem of Universals, Gyula Klima makes the argument particularly vivid. He goes on to discuss the immediate problems facing “naive” forms of Platonist realism and the fairly sophisticated nominalist controversy going on in medieval times.

[5] I say “traditional” because, obviously enough, there are non-traditional realist accounts of universals. Foremost that of D. M. Armstrong, who, because of his naturalist commitments, is compelled to deny that universals are abstract and the attending axiom of localization. For a critique of Armstrong’s views see J. P. Moreland’s Universals, chapter 4, pg. 83 ff.

[6] This is the ontological sense of abstract. Anti-realists will tend to use the word in an epistemological sense, that is, a feature abstracted away from its concrete instantiations by an act of the mind. For the most part, I will be using “abstract” in the ontological sense, but sometimes I will slip into using it in the epistemological sense; context should make clear when I am using “abstract” in this latter sense, e.g. by the use of such expressions as “abstracted away” or “beings of reason”.

While I am at it, a useful rule-of-thumb for distinguishing realists from anti-realists is that the former will start out from ontology, or reality, and build their epistemology from there, while the latter have their starting point in their epistemological stance and then project it onto reality. I freely admit that this description is a simplification, but it does express something true about the actual state of affairs.

[7] Sub-stance, or that which stands under.

[8] There is a subtle epistemological point lurking here. I will return to it when dealing with the epistemological objection to realism. I will also add that the Thomist has available to him the neo-Platonic move of positing universals as existing ante rem, as the archetypes of creation pre-existing from all eternity in the mind of God. This is one way (but not the only one) of escaping some dilemmas like the flip-flopping dilemma, when a universal is instantiated at one moment in time, becomes uninstantiated at a subsequent moment of time and then instantiated again.

The Year Of Faith: What Strange Things People Believe

Rational belief based on evidence

What better way to start the Year of Faith than with this headline:

Experts: Global warming means more Antarctic ice

This was atop an article penned Seth Borenstein, who noticed that Antarctic ice was accumulating at an alarming rate, hitting “a record 7.51 million square miles in September.” “How could this be?” Borenstein surely asked himself. “The theory of catastrophic global climate warming tipping point change would appear to preclude such manifestations.”

Borenstein believes in this theory so much that his earnestness goes well beyond plain acceptance: he desires it be true. Therefore, when confronted by icy observations contrary to his belief, he sought out an explanation to counter it. He was successful and uncovered certain named “experts” who assured him that “A warming world can have complex and sometimes surprising consequences”. Like increasing Antarctic ice.

The man has the touching faith of a child, the kind which seems cruel to challenge. Let us hope the poor fellow did not see yesterday’s report, “Once-in-century October snow across [South Australia].

And then there is our Dear Leader and his relations, foreign. Word is out that the embassy in Benghazi was purposely left thinly armed lest Americans appear imperial and boastful. If we had to lose a Marine here, an ambassador there in our efforts to display a humble and welcoming attitude, well, these would be mere “bumps in the road.” The road leading to world peace, of course. We may thus call this the Beauty Queen foreign policy.

Benghazi was part of his larger strategy of anxiously admitting that America is just as exceptional as everybody else, and his hoping that “dialog” and the subtle negotiating technique of giving in to every demand, à la Iran, will appease our enemies. The theory in which Mr Obama takes comfort is that if you are nice, people will treat you nicely. He is currently hoping that it works with China, which is sailing its newly created navy into disputed waters (which America has sworn—with crossed fingers?—to protect).

In France, the words mère and père will be banned “from all official documents.” No, I know you don’t believe me, but this really is a proposed law. The English, refusing to be trumped by their traditional rivals, have proposed, as Kenneth Minogue tells us, “that the terms ‘husband’ and ‘wife’ should be removed from the 1973 Marriage Act and replaced by ‘parties to the marriage.'”

The theory is that by removing these biased, value-laden words, you remove the ability of people to be biased and to hold the outmoded values expressed by those words. The old terms caused some people to feel badly about themselves, and there is no worse crime than that. State control of language is a doubleplusgood strategy to make us all think well of ourselves.

Regular readers will recognize this definition from the Skeptic’s Dictionary:

Faith is a non-rational belief in some proposition. A non-rational belief is one that is contrary to the sum of the evidence for that belief. A belief is contrary to the sum of the evidence if there is overwhelming evidence against the belief, e.g., that the earth is flat, hollow, or is the center of the universe. A belief is also contrary to the sum of the evidence if the evidence seems equal both for and against the belief, yet one commits to one of the two or more equally supported propositions.

Messrs Borenstein and Obama, and the earnest expurgators in France and England, and indeed ideologues of all stripes, possess this kind of faith, which is a state undifferentiated from desire. When belief leads and trumps observation, the object of faith is false. That which is false cannot be found, hence the unending search and call for “more”—more money, more time, more research, more bodies.

But there is another kind of faith. St Paul tells us that “faith is the substance of things hoped for, the evidence of things not seen.” This is true faith, a rational belief in that which cannot be observed. All of us have this faith, and must have it. All thought necessarily begins with truths which cannot be proved.

The main Object of faith is, of course, well known and it is here where true faith has acquired a bad reputation, while the other kind continues from success to success. But faith in God would only be absurd if its Object was provably false. And it is not. The best, in all of history, the atheist has done is to say God might not exist, which is logically equivalent to God might exist. Thus belief in God cannot be properly labeled irrational. But the belief that “belief in God is irrational” is itself irrational, and is so based on evidence. What a nice thought to take into this year.

The Future of Scientific Publications: Abandon Journals?

A paper undergoes peer review

It took three years–or was it four?—for a paper I submitted to the august journal Annals of Statistics to wend its way through peer review. When it came back to me stamped “Rejected: And Don’t You Dare Try To Resubmit!” I originally thought it was a prank because I did not recall writing it.

However, when I saw contained in the body of this wrongly neglected jewel a marvelous joke—and not a few typos—the memory of authorship returned to me.

Another journal has only recently stopped a bounty hunter from dogging my tracks to collect page charges for an article I wrote perhaps fifteen years ago. Page charges, you ask? Why, many journals require the author to pay for the privilege of publishing. Science is the original vanity press. The economics of publishing are complicated. Journals recover the expense of charging authors by also charging readers. Publishers do add value, though. Example: they provide the service of unburdening the author of his copyright.

David Banks, a statistician at Duke, and eminence of the American Statistical Association, has asked for comments about the publishing process (it was from him that I stole today’s title):

I fear our current approach to publishing does not serve us well. It takes too long, so our best scientists are driven to other journals in faster disciplines. Refereeing is noisy and often achieves only minor gains. And the median quality of reviews is deteriorating due to journal proliferation, pressure on junior faculty to amass lengthy publication lists, and the slow burnout of conscientious reviewers.

All true. So’s this: “Published research often does not replicate”. For papers which rely on statistics, this is the largest sin, as regular readers are well aware.

Banks reminds us the system today was not always thus.

Today’s publication process was essentially invented by Henry Oldenburg, the first corresponding secretary of the Royal Society. He received letters from members describing their research, copied them out in summary form, and mailed those summaries to other members.

It was also the habit of pre-journalified scientists to correspond with one another; letters were passed in lieu of official publication. Yet we admit journals initially were a boon, especially when there was limited reader- and authorship.

Today, though, in statistics alone, there are dozens upon dozens of publications, with more appearing regularly. An advanced computerized statistical model predicts there will be 1.2 journals per statistician by the year 2023—none of which will or need be read. Why the increase? The depressing desire for quantification of the unquantifiable (a particularly dismal trait in statisticians).

It is publish or perish: paper count is the sine qua non of success within the university. Without it, departments would be aswim, unable to decide on promotion or hiring. Remove paper count—the statistic everybody uses while simultaneously decrying—and there will be no objective basis to decide who stays or who is booted.

Trouble is, with an increasing multitude of outlets, anybody can achieve a pleasing sum. This causes other metrics to be sought. Like citation count, or the sounds-like-advertising “impact” factor. Trouble with the latter is that the “best” journals have limited space. And then, because of the charmingly naive view that peer-review is a rigorous filter of truth, authors spend just as much time editing the work of others as they do writing their own papers. And then the true definition of random is found in considering why papers are accepted or rejected.

Are there alternatives to our stultifying system? Sure. I figured the world deserved to read my jocose but rejected jottings. So instead of enduring the desultory review process again, I stuck the paper on this page and on arXiv. Where, to my delight, it was actually read.

Larry Wasserman (whose books on mathematical statistics are highly readable), commenting on Banks’s plea, agrees and said:

I think we should abandon journals completely and just use arXiv.

We should eliminate refereeing completely and let the marketplace of ideas decide the value of a paper.

Sounds nice. But how do you get credit for a letter? Or a blog post? Or an arXiv dump? The worry is somebody suffering from latent accountancy will suggest number of downloads or the like—as if that would not be easy to manipulate.

Well, you shouldn’t get numerical credit. Each person’s work, or potential for same, should be judged on its own as a whole. This requires extra effort for reviewing committees, who would actually have to read instead of count papers, but tough.

This ploy isn’t perfect, either. No system is. For example: Article popularity is a weak gauge of quality. It’s easy to write many papers quickly in “hot” areas (I once attended a conference where everybody started their talk “Wavelets are…”). But some topics are more experimental or are foundational, areas which may never pay off but which are worthy of investment. And there will 1,000 arXiv wavelet-neural-net-“big”-data-of-the-day papers to every probability-really-means-this work.

The system of books, blogs, and backups to arXiv is probably the least worst.

Update Corrected thanks to the ever-watchful eye of JH.

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