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Saturday, March 28, 2015


Back in 2010, while I was writing and posting my serial Autobiography, I  created a second blog on which, over a period of several months, I wrote and posted a short book called FORMAL METHODS IN POLITICAL PHILOSOPHY.  It was a reasonably chewy technical book with proofs of a variety of important theorems [not original with me, of course!], including Kenneth Arrow's famous General Possibility Theorem for which he won the Nobel Prize.  The little book included my animadversions against the much misunderstood Prisoner's Dilemma, a summary of my formal critique of Rawls' theory, and a good deal else.

Google tells me that in the last five years, there have been a total of 42,129 visits to the Formal Methods blog, which is not bad when you consider the subject matter.  From time to time I check it, and it still gets ten, fifteen, twenty, even twenty-five hits a day.  I figure out there in the world are a couple of professors who send their students to it for some quick background on technical stuff.

Until yesterday.  Yesterday there were 228 visits to that five year old series of mathematical posts!

What on earth is going on?  Is there some Bulgarian mathematical version of REDDIT that gave me a shout out?  If anyone can enlighten me, I woud appreciate it.  Who knows?  In the immortal words of Mel Brooks, I may be "world famous in Poland."

Friday, March 27, 2015


Well, having made a fool of myself by making an off-hand remark about Israeli marriage law without knowing what I was talking about, I shall now once more put my foot in my mouth by offering a speculation about Iran, about which I know even less.  [By the way, a correspondent who knows whereof she speaks informs me that Jews in Israel can only marry other Jews in Israel in an Orthodox ceremony, compelling Israeli Jews who are unwilling to go through such a ceremony to travel outside the country to be married elsewhere, whereupon that foreign marriage is recognized by Israeli law.  That is totally different from what I wrote, but it does strike me as being of the same order of horribleness.]

There has been a great deal of discussion in recent days about the supposed contradictions in the Administration's policy regarding Iran.  The contradictions are said to be these:  In Iraq, we are fighting alongside Iran against  ISIL;  in Yemen we are opposed to the recent overthrow of the Yemeni government, which is supported by Iran, so we are in effect fighting against Iran;  in Syria, we are fighting with Iran against ISIL and against Iran in its support of the Assad regime; all the while we are attempting to negotiate an agreement with Iran regarding Iran's nuclear program, which if accomplished would relieve Iran of the crippling economic sanctions under which it has been laboring for some years.  Taking all in all, it is said, our actions may very well have the effect of strengthening Iran's position in  the region, despite the fact that Iran is our enemy, whom we ought in all ways to be attempting to weaken.

Let us leave to one side the fact that this sounds very much like the elaborate maneuverings of the ancien régime in France in the seventeenth and eighteenth centuries.  I should like to ask some questions designed at least to begin a conversation about the unexamined presuppositions of American Middle East policy.  I ask questions because I do not know enough to hazard answers;  but I ask the questions nevertheless because I am dissatisfied with those unexamined presuppositions.

First, why would it be so unacceptable for Iran to develop nuclear weapons as to justify our launching a war to stop them?  Now, I have all my adult life been unalterably opposed to the existence, threat of use, and use of nuclear weapons, and I was working hard, publicly, to oppose their existence and use before most of the readers of this blog were born, so I cede pride of place to no one when it comes to a commitment to nuclear disarmament.  I was opposed to the development of the American nuclear arsenal and to the development of the Soviet nuclear arsenal.  I was opposed to the development of nuclear  weapons by France, Great Britain, China, Pakistan, and India.  I am opposed to Israel's current possession of a sizable nuclear arsenal, and I am opposed to the attempts by North Korea and Iran to develop nuclear weapons.  But I was not in favor of invading India or Pakistan or China or France or Great  Britain or Israel to stop them from developing nuclear weapons, and I do not see any reason to consider Iran's efforts to develop nuclear weapons different from the successful efforts by Israel.

It is said that it would destabilize the region were Iran to develop nuclear weapons.  Did Israel's development of nuclear weapons destabilize the region?  Not noticeably.  Did the development of nuclear weapons by Pakistan and India destabilize that region?  Very definitely.  Did we contemplate invasion?  Of course not.

Iran, it is said, seeks greater influence in the Middle East.  Every nation in the world seeks greater influence in its region, or, as in the case of the so-called Great Powers, in the world as a whole.  That is the nature of realpolitik, as pursued by every nation with the military and economic power to play the great game.  All nations, including the United States, claim to be pursuing the highest ideals selflessly, and none of them is doing anything of the sort.

Here is my central question:  Why should we not choose to make a self-interested alliance with Iran, rather than with Saudi Arabia or Israel or Egypt?  Is there something we can gain by such an alliance that would adequately compensate us for what it might cost us?  If so, why should we not consider it?

Would this threaten the existence of Israel?  It is difficult to see how, considering that at the present moment Israel is the only nation in the region capable of threatening a potential enemy with nuclear obliteration.  But could we not make the protection of Israel a non-negotiable condition of an alliance with Iran that would enable Iran to expand its influence?

In 1953, John Foster Duller and his brother Allan, under orders from President Eisenhower, engineered a coup that deposed Mohammed Mossadegh, the democratically elected secular Prime Minister of Iran [the casus belli being Mossadegh's decision to nationalize Iran's oil resources.]  I think we all know how that finally turned out.

So, I ask again:  Would it be in the self-interest of the United States to form an alliance with Iran?

Wednesday, March 25, 2015


I hope to communicate today to my students an idea that they may find rather difficult to grasp, or so I fear.  Perhaps if I have a go at explaining it here, the effort will help me to clarify my exposition.  Let me say, by way of setting the scene, that today I shall try to bring together into a single integrated account the four strains of argument I have been developing in my course:  Marx's economic analysis of capitalism, Marx's historical account of the development of capitalism, the modern mathematical formalization of the classical and Marxian tradition of Political Economy, and my literary critical explanation of the extraordinary language of the first six or seven chapters of Capital.  The reading assigned for today is my 1981 essay, "A Critique and Reinterpretation of Marx's Labor Theory of Value."  That essay, which so far as I can determine, in David Hume's words, fell stillborn from the presses, is a rather difficult read for philosophers, containing as it does a good deal of linear algebra.  [Linear Algebra, which is mother's milk to economists, is actually quite elementary undergraduate math for a math major, but as C. P. Snow observed many decades ago, we live in a society of two cultures, and philosophers whose intellectual sophistication knows no bounds confront a page of mathematics as though it were Linear B.]

The idea, in a sentence, is this:  The narrative accompanying a mathematical model frequently contains a good deal of information that finds no formal representation in the model, and it is a mistake to think that the deductions from the model constitute a proof or endorsement of those elements present only in the narrative.  In the case of Marx's theory, the distinction between labor power and labor, which Marx claims is the key to understanding the origin of profit in a capitalist system, actually finds no representation in  the formalism implicit in Marx's argument and made explicit by the modern mathematical formalization of that argument.  The goal of my essay is two-fold:  First, to demonstrate that the labor/labor-power distinction plays no formal role in Marx's argument, and that all of his results can be reproduced for any arbitrarily chosen commodity as "substance of value;"  and Second, to find an alternative formalization of what I believe to be Marx's correct analysis and critique of capitalism.

There are a number of examples of this sort of mismatch between a formal argument and the accompanying narrative.  My favorite is the narrative that has grown up around the so-called Prisoner's Dilemma.  I shan't reproduce here my analysis of that familiar example, from Game Theory, of a two-person non-zero-sum game in which each player has two pure strategies.  Those who are interested will find it in the book-length tutorial I wrote on The Use and Abuse of Formal Methods in Political Philosophy, archived at  Other examples, considerably more important at one time in U. S. military affairs, are the mismatches between the narratives of deterrence and nuclear war and the game theoretic analyses accompanying them.  [To be found in my unpublished book, The Rhetoric of Deterrence, also archived.]

If one prefers a more light-hearted example, one can consider the practice adopted by some Grade School teachers of drawing circles as happy faces and squares as Sponge Bob Square Pants when introducing little children to Geometry.  Sooner or later, the children must learn that the mathematical properties of a circle are independent of whether a happy or sad face is drawn in it.



Tuesday, March 24, 2015


No sooner had I returned from Paris, jet-lagged to deliver a difficult two and a half hour lecture on the mathematics of Marx's labor theory of value than March Madness hit.  I am sure my American readers will understand that as a resident of Chapel Hill, I am required by city ordinances to be a fan of the UNC Chapel Hill basketball team, and to root, secondarily, for Duke in all circumstances in which they are not playing UNC.  This, plus two weeks of accumulated mail, has kept me from my principal responsibility, viz. this blog.  Herewith a first effort to catch up.  K. Reader posted the following comment to my Parable of the Butcher and the Analytic Philosopher: 

"I am an avid reader of your blog. As a non-native speaker I am fascinated by your use of "he" and "she". Are there any rules?  I like the fact that the butcher is "she" and the philosopher "he" - at least in this post."

There are no rules, but perhaps I can tell a story to explain my own practice.  Forty years ago, I was running a small interdisciplinary left-wing undergraduate major that I had started called Social Thought and Political Economy.  I created a Freshman/Sophomore course called "Introduction to Social Theory" as a general background for students interested in the major.  One day, as I was lecturing, some students challenged my constant and exclusive use of the masculine pronoun.  I thought about their criticism, and decided they were right.  What to do?  I could, of course, studiously avoid the singular for the plural ["If people choose to disobey the law, they may risk prosecution" rather than "If a person chooses to disobey the law, he may risk prosecution."]  But that is clumsy.  And I am constitutionally unable to use the singular in the first part of a sentence and the plural in the second part ["If a person chooses to disobey the law, they may risk prosecution."]  So, after some reflection, I decided simply to alternate masculine and feminine pronouns unless the subject dictated one or the other [I did not refer to Marx as "she" half the time.]  This is not hard once you get used to it, and it solved the problem nicely.  Over time, I have backed off from rigid alternation, but I continue to mix them up.  The butcher in my parable just came out female.  It could as easily have been the other way about.

Friday, March 20, 2015


The responses to my observations about anxiety dreams got me thinking about Willard Van Orman Quine, Erik Erikson, and Calypso.  What, you might ask, could the connection possibly be?  It is like this:

Erikson, somewhere [I think in Childhood and Society], observes that people have styles in dreaming.  Some people always dream in Technicolor, others dream in Black and White.  Some folks have cluttered dreams, filled with all manner of dream elements, as psychoanalysts call them;  others have very spare dreams, with only a few elements.  This does seem to be a matter of style -- those who dream in Technicolor, for example, will do so whether the feeling tone of the dream is anxiety, erotic desire, anger, or simple curiosity.

Inasmuch as I graduated from Harvard in 1953 after taking one undergraduate and two graduate logic courses with Quine, I naturally was reminded by Erikson's observation of a line in Quine's elegant little collection, From a Logical Point of View, which was published that year.  In the lead essay, "On What There Is," Quine describes himself at one point as having a "taste for desert landscapes" -- a fact, he suggests, that inclines him to spare ontologies.

Quine, all of us students knew, had rather eclectic cultural tastes, and so it was obvious where he had found the title for his book.  The source was a Calypso song made popular by the young Harry Belafonte whose refrain is "So from a logical point of view/Always marry a woman uglier than you."  I recall thinking that this was a really nifty choice of a title.


I first visited South Africa in the early months of 1986, when the system of Apartheid was in full force and operation.  South Africa was a vibrant, exciting, functioning democracy -- for Whites.  There were a number of first-rate universities, for Whites, a lively intellectual scene, a cultural scene with music, dance, and visual arts, at least one first rate newspaper [The Daily Mail and Guardian], and a far greater awareness in academic circles of the writings of Marx than I could find anywhere in the United States. 

The system of Apartheid [or "apartness" in Afrikaans] had carried out a thoroughgoing relocation of non-whites into racially defined enclaves called "Homelands," which in law, if not in fact, were considered quite literally to be separate countries.  Strict "influx control" laws restricted the presence of non-Whites in the White cities after dark, forcing African, Colored, and Indian men and women to travel long hours each day from their "townships" or their "informal communities" [shack settlements] into the cities where they worked.  The Townships ringing the White cities were deliberately laid out so as to make them easy to police and -- if the state deemed it necessary -- closed off entirely.

And yet, in Johannesburg, Cape Town, Pretoria, and Durban, it was quite possible for a White man like me to spend weeks on end without ever directly encountering the five-sixths of the population excluded from the civil society and cultural life of the country.  The academics I met read the same left-wing journals I read, their sphere of reference was virtually identical to mine, I felt quite at home with them, even though I had flown ten thousand miles to spend six weeks in their country [lecturing on Marx at the University of the Witwatersrand, or Wits, in Johannesburg.]

All of this has been on my mind as I have been reading about the appalling election in Israel.  Contemporary Israel, like pre-liberation South Africa [its military partner, back then], is a vibrant, lively nation where a radical intellectual from America can feel quite at home, so long as he does not look too closely.  Intellectually, musically, culturally, it feels familiar, albeit foreign, much as France or Spain or Italy does.  It is fatally easy to suppose that Israel is our natural ally, a kindred spirit in the family of nations, a place that an American or a Frenchman or a Swede could call home.

But the plain truth is that Israel is running its own version of the system of Apartheid.  The treatment of land is typical of an apartheid system.  In South Africa, the borders of the Homelands, ostensibly the natural boundaries of ethnically and linguistically unified areas [KwaZulu, Sotho, !Qhosa, and so forth]. were actually very carefully drawn so as to reserve the best agricultural land for the White Afrikaner farmers, leaving the infertile land with little water for the Homeland residents.  The denial to non-Jews of even such elementary rights as marriage perfectly mirrors the treatment of non-Whites in the old South Africa.

The simple fact is that the phrase "Jewish democracy," like the phrases "Christian democracy" and "Islamic Democracy," is a contradictio in adjecto. 

Israel, it is said, is our most important strategic partner in the region.  I confess that I can see no reason of realpolitik for this judgment.  From a purely self-interested perspective, it would make a good deal more sense for the United States to form a strategic alliance with Iran.  On the other hand, it would indeed make a great deal of moral and ideological sense to forge strong bonds with a truly democratic Israel.  If such an Israel ever surfaces, I would be the first to call for such an alliance.

Wednesday, March 18, 2015


I am back, exhausted from the trip home and preparing to give a two and a half hour lecture this afternoon!  But I had to rush a brief post to bring everyone up to date on the latest doings of my younger son, Tobias Barrington Wolff.  Here is a link to a University of Pennsylvania site where you can find the text of an amicus brief Tobias has submitted to the Supreme Court in an up-coming case on the recognition of same-sex marriages across state lines.  Tobias has forbidden me to refer to him as the leading Gay Rights legal scholar in America, but I am permitted to say that he is one of the leading Gay Rights legal scholars in America.  This brief is an evidence of the legitimacy of that encomium.

I am very fearful that along about the time I begin lecturing this afternoon, I shall fall asleep.  Will the students notice?  An interesting question.  When I was a twenty-one year old Teaching Fellow at Harvard, I lived in terror that I would simply forget to go to one of the sections I was teaching.  [This actually happened to me the next year.]  I was utterly oblivious to the fact that most of them would have been thrilled.  One of my persistent anxiety dreams takes the form of suddenly realizing, two or three weeks into a semester, that there is a course I am supposed to be teaching that I have never shown up for.  I rush off to the class, where the students are all waiting impatiently.  It is, as I say, a dream!