William M. Briggs

Statistician to the Stars!

Page 145 of 426

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?


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.



[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.

Realism vs. Anti-Realism I: Introduction — Guest Post by G. Rodrigues

Mathematical realist Blaise Pascal

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.

— Eugene Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”

These are the final words of E. Wigner’s famous essay, which you can find on-line here. Wigner uses the God-haunted word “miracle”, once in the quoted paragraph, several times in the whole essay. But His presence is more palpable when he speaks about the wonderful, unmerited gift, of mathematics; I do not know what was his relation with the Deity, but he may have found himself in the sad predicament of being thankful and having no one to thank for.

The sense of the miraculous, or more prosaically for those who distrust such intrusions of the numinous in our ordinary lives, the sense of wonder, is the beginning of all True Philosophy. There is a puzzle here and an answer must be found. Why is the universe orderly? Not only that, why is the orderliness of the universe of such a nature that it can be described and explained, at least in part (and I would add, only in part) by mathematics? And by supremely abstract mathematics, discovered and developed to solve purely mathematical problems, quite independently of its appropriateness for describing the real world[1]?

A tentative answer is to adopt a realist stance and say that mathematical objects have an extra-mental reality just like the common ordinary objects of our experience like rocks, trees, persons and planets, and in studying them we are, somehow, somewhere, somewhen, discovering objective features of reality. This suggestion needs some considerable spelling out, but to see how it imposes itself forcefully, let us watch W. Quine make the so called indispensability argument[2]:

  1. We should believe the theory which best accounts for our sense experience.
  2. If we believe a theory, we must believe in its ontological commitments.
  3. The ontological commitments of any theory are the objects over which that theory first-order quantifies.
  4. The theory which best accounts for our sense experience first-order quantifies over mathematical objects.
  5. We should believe that mathematical objects exist.

Lest there be any confusion, I hasten to add that I do not find this argument compelling. Premises 2 and 3 are particularly hard to swallow[3]. If I invoke it here it is for two wholly different sorts of reasons: one, the delightful irony in borrowing a stick from your enemy (Quine was a confirmed naturalist) with which to beat your other enemies and two, to once again stress that, given how inimical mathematical realism is to naturalism[4], it is quite telling that Quine felt compelled to adopt it (and expansively redefine naturalism along the way). For otherwise, if mathematical objects are nothing but a product of the mind with no objective basis on reality (the mind itself being, on some accounts, the random material product of a highly contingent history), in the same way as fictions are, then what can possibly explain their appropriateness in the description of reality?

If that is indeed the case, and the Dirac operator of a spin manifold or the curvature of a connection are just as fictitious as novels or children stories, then are we not forced to retreat to the nigh-mystical position of Wigner? And if that is indeed the case, what is the principled distinction between say, the Dirac operator on a spin manifold, and quarks which because of QCD confinement cannot be observed free? Are we not committed to say that quarks are equally fictitious? And if that, then are we not obliged to conclude that science tells us nothing objective about the nature of the world? And if that, should not electrons or evolution by natural selection go the same way of quarks?

But enough of questions and on to the heart of the matter. Mathematical realism is just one among a cluster of related problems involving the ontological status of such seemingly abstract objects as universals, properties, propositions, relations, etc. All these notions are intimately related to one another. For the sake of simplicity, I will lump them all under one banner, although realists of various stripes will insist on all sorts of distinctions.

Here, I will defend not mathematical realism per se[5], but the closely related problem of realism with respect to universals. For those who have read The Last Superstition, you will know that Edward Feser addresses this problem in pages 39-49. Although I will return to some of the arguments made in those pages, here I will take a different route and follow J. P. Moreland’s Universals[6].

The plan for this series is then as follows: first I will present an account of the realist position with respect to universals, the phenomena that it purports to explain and the challenge it presents to anti-realists. Then I will survey some variants of anti-realism with respect to universals and point out, not only the problems they have, but how these problems typically recur in all anti-realist stances. Then I will respond to the more common anti-realist objections. I will wrap things up with a few words on why this seemingly abstruse and irrelevant problem is actually at the heart of many contemporary discussions by (very) briefly surveying one such example and along the way annoy to no end and give offense to those delicate, clueless, liberal souls. At least so I hope[7].

Some caveats are in order. My background is in mathematics, and to a lesser extent in physics. From this, two immediate corollaries follow:

1. As a general rule, mathematicians are notoriously bad expositors; over-abundance of technical detail in contrast to a dearth of understanding. In mathematics, this is somewhat inevitable, as knowing the technical details is more often than not what understanding amounts to. So while I cannot say that I have any of the qualities usually recognized in mathematicians like rigor, attention to detail, etc., you can surely expect that I amnot the exception to the general rule.

2. Of necessity, not being a philosopher, I will say nothing that is original. Or to put it in other words, the only originality I can claim is in my mistakes.

In 2, originality is used in the paltry sense of new or novel; but there is a deeper sense to it, related to the root word origin. To recognize it, it is probably best to step into the world of the arts, literature in particular. The greatness of an author like T. S. Eliot or James Joyce (if these examples offend your tastes, replace them by your own as similar remarks apply) lies in part in the fact that their genius has opened up a clearing in our common cultural heritage, where their voices rise and add up to the chorus (or cacophony: choose your preferred metaphor) of the voices of the Great and Magnificent Dead. There can be no understanding of Joyce, understanding in the deeper senses of literary criticism, without locating him within the total order of literature and clarifying his relationship with his predecessors, Shakespeare and Homer above all.

When we read Joyce in its strongest, say in the final pages of Finnegans Wake, we feel that a limit has been reached and that words have been found to express the hitherto inexpressible, what was always there since the origin, what is definitive of our nature of human beings qua human beings but that would not, and could not have been recognized unless it was first illumined to us. These illuminations then become the guiding lights in the inner theater of our imaginings. Something like this sense of continuity is lost in philosophy with the advent of the Cartesian revolution (and the Hobbesian revolution, and the Baconian revolution, and etc.) where the ties with Plato, Aristotle and their progeny, the Scholastics, were severed. The curt dismissal of a whole tradition without even dignifying to offer a semblance of criticism is not exactly the type of cultural continuity I am thinking of. In cycle after cycle, modern philosophers will raze to the ground the hard won wisdom of the past and build upon the ashes of their forefathers their own metaphysical edifices. But to borrow Kierkegaard’s charge against Hegel, peppered with some rhetorical flavor, no one, including their builders, wants to live in them because the darned things are so damn ugly[8].

The same Kierkegaard, no friend of Aquinas and co., in an intense little book called Repetition, proposes this term to replace the Platonic term of anamnesis or recollection. For Plato we have always known, but upon the shock of being dropped on the bucket of the world we have forgotten, and the travail of Wisdom is to recollect and reawaken what is origin-al within ourselves. Or as Francis Bacon puts it at the beginning of Essay LVIII Of Vicissitude of Things, in his very distinctive diction:

Solomon saith, “There is no new thing upon the earth”. So that as Plato had an imagination, “That all knowledge was but remembrance”; so Solomon giveth his sentence, “That all novelty is but oblivion”.

Kierkegaard means by repetition, not the stale, desiccated reiteration of old formulas, but a re-creation in the Apocalyptic terms of “Behold, I make all things new”. So the third corollary is a plea, and here I am following Feser again, for a renewed look upon the metaphysical tradition of the Scholastics. Not a return to some fabled Golden Age, that never existed anyway[9], but a development and elaboration upon the sound, realist metaphysics and philosophy of nature developed by those men and concomitantly, a gentle nudge to the reader, if any there be, to go search in more appropriate places for a more exhaustive explanation of the issues involved.

I will take as my fourth and last corollary, a warning and a dire one indeed. As the reader may have already observed, I am given, among other sins, to ramblings, digressions[10], asides, footnotes, parenthetical remarks, heavy doses of pedantry and (salutary) exaggerations. Add on top of this the fact that the series will drag itself through four more installments, and you may want to reserve your comments to future posts. Anyway, as the typical villain in a comic book would have it, “I am invincible!” (clenched fists, maniacal laughter), so feel free to Snipe, Snide and Snark; I may even respond in kind. Unless that is, someone bores me to death. Literally.



[1] This is not to deny that many developments in mathematics have indeed occurred in answer to problems posed by other disciplines, most notably physics. But the fact that such developments did come about that way, does not entail that they necessarily had to come about that way, this latter claim being patently absurd as even the most incipient knowledge of modern mathematics (starting about the beginning of the 19th century with the efforts to give calculus a firm and rigorous foundation) shows.

[2] H. Putnam, M. Resnik, etc. have advanced slightly different versions of the indispensability argument. See The Indispensability Argument in the Philosophy of Mathematics for more information.

[3] And then again, the modern strategy to defuse indispensability arguments, appropriately called dispensability arguments, involves rewriting the physical theories to avoid the quantification over mathematical objects. But such rewriting, even when successful, appeals to second-order logic or mereological axioms which are even more controversial and problematic. As Quine quipped, higher order logic is set theory in sheep’s clothing, so it is legitimate to wonder how successful the strategy is given that you avoid reference to mathematical objects (e.g. sets) only by introducing them surreptitiously and by the back door, suitably redressed. Once again I refer the reader to The Indispensability Argument in the Philosophy of Mathematics for more information and references.

[4] I will have occasion to return to this point later on.

[5] The reason why I will not be defending mathematical realism per se is in short, and to quote my lifelong intellectual hero Dr. Johnson, “Ignorance, madam, pure ignorance”. If I were a Platonist realist, I would have available a straightforward account of all of mathematics, but since I reject Platonism for reasons I will not delve into, this move is not available to me. I could still take the neo-Platonist route, which is indeed available, of saying that mathematical objects pre-exist in the mind of God from all eternity, but favoring an Aristotelian-Thomistic metaphysics something more is needed than this simple, stopgap answer. Mathematics is a fascinating and bizarre realm, in more than one sense, and as far as I know, Thomists have not written much about it, and what there is, it is hard to digest — at the level of PhD thesis 700 pages thick, couched in impenetrable jargon.

[6] Further bibliographical references will be scattered throughout the posts for those interested in pursuing these matters.

[7] This is war; the air is burning, shrapnel will be flying everywhere. Better get down on the floor.

[8] Recommended reading: Mortimer Adler, Ten philosophical mistakes.

[9] Such Golden Age proclamations usually betray a singular lack of historical sense.

[10] Here I confess I was really tempted to quote at length the endless ironies of J. Swift’s “A digression in praise of digressions. Just go read it.

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