Can Only the Mortalist Love?

From the mail: 

A friend of mine (a philosophy professor) and I were discussing issues of immortality, meaning, and love on Facebook. I explained to him that the love I feel for others in some sense 'seeks' immortality, as the depth of the feeling is such that without that belief, love would be almost too painful for me to bear. He expressed a diametrically opposed view, wherein love REQUIRES that we acknowledge the mortality of both the other and ourselves. This is, he said, because time is only a limited commodity and the time we spend with someone else is only valuable because there is a limited amount of it, and so spending time with someone is only really an act of love for the one for whom time is extremely limited.
 
Your friend seems to be maintaining that only a mortalist (one who maintains that bodily death spells the end of a person) can truly be said to love another person.  Your friend's argument seems to be this:
 
1. The time spent with the beloved is valuable only because it is limited; therefore,
 
2. One cannot love without acknowledging the mortality of both lover and beloved.
 
First of all, I would say that this is a non sequitur.  For even if we suppose that (1) is true, (2) is obviously false.  Gabriel Marcel did not acknowledge the mortality of himself or his wife, and yet he loved his wife.  (On this topic, Marcel is one of the people to read.)  Whether or not love is genuine cannot hinge on whether one is right or wrong about the mortalism/immortalism question.  It would be both churlish and absurd to say to Geach and Anscombe, "You two don't really love each other because you are immortalists!"
 
Your friend might respond by saying that the intensity of a love believed to be undying must be less than the intensity of a love believed to be as mortal as the lovers.  To this I have two responses.  First, the question of intensity is not the same as the question of whether the love is genuine.  The genuineness of love varies independently of its intensity.  Second, it is not obvious that a love believed to end with the lovers must be less intense. One could easily argue the opposite:  if I believe that my love cannot survive bodily death, then I am more likely to practice something like Buddhist nonattachment with respect to the beloved and with respect to my loving of the beloved in accordance with the 'truth' that all is impermanent and therefore  nothing is worthy of a full measure of commitment.  In other words, you could argue against your friend that it is precisely because love can conquer death that you value it as highly as you do, and that because he does not believe this, he ought to value it less.    You could say to him, "Look, if you believe that you and your love will soon pass away, then it is irrational of you to ascribe much value to yourself or your love. Impermanence does not intensify value; it argues lack of value!"
 
Saying this to your friend, you will not convince him ( I am quite sure of that!) but you will neutralize his argument and show that it is not compelling.  And that is about all one can accomplish in a philosophical discussion. But it is also all you need to accomplish to be able to show that your intuitions are rationally acceptable.
 
As for (1), it is arguably false, and for some of the same reasons I have just given.  If contact with the beloved ends utterly with death, then this could be taken to show that the contact was not so valuable  in the first place on the Platonic-Augustinian ground that impermanence argues (relative) unreality and unimportance.  I grant that this is not absolutely compelling, but it is as compelling as the opposite, namely, that impermanence increases value and importance.
 
I'm with you: love is a harbinger of Transcendence; it intimates of Elsewhere.  You won't be able to convince your friend of this, but don't let that bother you.  Any argument he can throw up, I can neutralize.
 
If you haven't read Augustine, you should.  I also recommend P. T. Geach, Truth. Love, and Immortality: An Introduction to McTaggart's Philosophy (University of California, 1979), esp. the last chapter.

Infinity and Mathematics Education

A reader writes,

Regarding your post about Cantor, Morris Kline, and potentially vs. actually infinite sets: I was a math major in college, so I do know a little about math (unlike philosophy where I'm a rank newbie);
on the other hand, I didn't pursue math beyond my bachelor's degree so I don't claim to be an expert. However, I do know that we never used the terms "potentially infinite" vs. "actually infinite".

I am not surprised, but this indicates a problem with the way mathematics is taught: it is often taught in a manner that is both ahistorical and unphilosophical.  If one does not have at least a rough idea of the development of thought about infinity from Aristotle on, one cannot properly appreciate the seminal contribution of Georg Cantor (1845-1918), the creator of transfinite set theory.  Cantor sought to achieve an exact mathematics of the actually infinite.  But one cannot possibly understand the import of this project if one is unfamiliar with the distinction between potential and actual infinity and the controversies surrounding it. As it seems to me, a proper mathematical education at the college level must include:

1. Some serious attention to the history of the subject.

2. Some study of primary texts such as Euclid's Elements, David Hilbert's Foundations of Geometry, Richard Dedekind's Continuity and Irrational Numbers, Cantor's Contributions to the Founding of the Theory of Transfinite Numbers, etc.  Ideally, these would be studied in their original languages!

3. Some serious attention to the philosophical issues and controversies swirling around fundamental concepts such as set, limit, function, continuity, mathematical induction, etc.  Textbooks give the wrong impression: that there is more agreement than there is; that mathematical ideas spring forth ahistorically; that there is only one way of doing things (e.g., only one way of construction the naturals from sets); that all mathematicians agree.

Not that the foregoing ought to supplant a textbook-driven approach, but that the latter ought to be supplemented by the foregoing.  I am not advocating a 'Great Books' approach to mathematical study.

Given what I know of Cantor's work, is it possible that by "potentially infinite" Kline means "countably infinite", i.e., 1 to 1 with the natural numbers?

No! 

Such sets include the whole numbers and the rational numbers, all of which are "extensible" in the sense that you can put them into a 1 to 1 correspondence with the natural numbers; and given the Nth member, you can generate the N+1st member. The size of all such sets is the transfinite number "aleph null". The set of all real numbers, which includes the rationals and the irrationals, constitute a larger infinity denoted by the transfinite number C; it cannot be put into a 1 to 1 correspondence with the natural numbers, and hence is not generable in the same way as the rational numbers. This would seem to correspond to what Kline calls "actually infinite".

It is clear that you understand some of the basic ideas of transfinite set theory, but what you don't understand is that the distinction between the countably (denumerably) infinite and the uncountably (nondenumerably) infinite falls on the side of the actual infinite.  The countably infinite has nothing to do with the potentially infinite.  I suspect that you don't know this because your teachers taught you math in an ahistorical manner out of boring textbooks with no presentation of the philosophical issues surrounding the concept of infinity.    In so doing they took a lot of the excitement and wonder out of it.  So what did you learn?  You learned how to solve problems and pass tests.  But how much actual understanding did you come away with?

The Ground Zero Mosque: The Controversy Continues

And it seems to be heating up as the anniversary of 9/11 approaches.  I suspect dialogue with liberals on this topic is impossible due to what I call the 'two planets problem':  conservatives and liberals live on different planets.  You could cash out the metaphor by saying  that we differ radically in temperament, sense of life, values, and assumptions. But I am getting e-mail from decent and well-intentioned left-leaners who disagree with me about the GZM, so here goes one more time. 

Let's be clear about what the issue is.  To put it as crisply as possible, it is about propriety, not legality.  No one denies that Imam Rauf et al. have the legal right to build their structure on the land they have purchased.  The point is rather that the construction in that place is improper, unwise, provocative, insensitive, not conducive to comity.  To put it aphoristically, what one has a right to do is not always right to do.  But that is to put it too mildly:  the construction of a mosque on that hallowed ground is an outrage to the memories of those who died horrendous deaths on 9/11 because of the acts of Muslim terrorists, terrorists who didn't just happen to be Muslims, but whose terrorist deeds were a direct consequence of their Islamist beliefs. 

Now at this point you either get it or you don't.  A majority of the American people get it, but Obama doesn't.   Lacking the spine to address the real issue — the issue of propriety, not legality — he gave us a lecture on freedom of religion and the First Amendment.  Besides being b-o-r-i-n-g, his pathetic homily amounted to the logical fallacy of ignoratio elenchi.  This fallacy is committed when, mistaking the thesis your interlocutor is advancing, you respond to a distinct thesis that he is not advancing.  We who oppose the GZ mosque do not maintain that its construction is illegal; and because we do not maintain this, Obama and his leftist cohort commit ignoratio elenchi when they insist that it is legal.

Here again we note the 'two planets' problem.'  Leftists just cannot grasp what the issue is as conservatives see it.  Since they do not feel the impropriety of a mosque's being built near Ground Zero, they cannot believe that conservatives feel it either; and so they must interpret the conservative response in some sinister way: as an expression of xenophobia or 'Islamophobia' or nativism or a desire to strip Muslim citizens of their First Amendment rights. 

Supposedly, a major motive behind the construction is to advance interfaith dialogue, to build a bridge between the Muslim and non-Muslim communities.  But this reason is so patently bogus, so obviously insincere, that no intelligent person can credit it.  For it is a well-known fact that a majority of the American people vehemently oppose the GZM.  Given this fact, the construction cannot possibly achieve its stated end of advancing mutual understanding.  So if Rauf and Co. were sincere, they would move to another site.

Here is a little analogy.  Suppose you and I have a falling out, and then I make an attempt at conciliation. I extend my hand to you.  But you have no desire for reconciliation and you refuse to shake hands with me.  So I grab your hand and force you to shake hands with me.  Have I thereby patched things up with you?  Obviously not: I have made them worse.  Same with the GZM.  Once it became clear that the the American people opposed the GZM, Rauf and Co. either should have nixed the project or else had the cojones to say:  we have a legal right to build here and we will do so no matter what you say or how offended you are.

As it is, we have reason to suspect Rauf et al. of deception.

 

A Tea Party Manifesto

Here.  The authors, Dick Armey and Matt Kibbe, make it clear that fiscal responsibility and limited government are the central concerns of Tea Partiers.

The criteria for membership are straightforward: Stay true to principle even when it proves inconvenient, be assertive but respectful, add value and don't taking credit for other people's work. Our community is built on the Trader Principle: We associate by mutual consent, to further shared goals of restoring fiscal responsibility and constitutionally limited government. [. . .]

The big-government crowd is drawn to the compulsory nature of centralized authority. They can't imagine an undirected social order. Someone needs to be in charge—someone who knows better. Big government is audacious and conceited.

Note that the opposition is to big government, not to government as such.  This simple point needs to be repeated again and again in the teeth of liberal-left slander.

By definition, government is the means by which citizens are forced to do that which they would not do voluntarily. Like pay high taxes. Or redistribute tax dollars to bail out the broken, bloated pension systems of state government employees. Or purchase, by federal mandate, a government-defined health-insurance plan that is unaffordable, unnecessary or unwanted.

This is perhaps OK for a manifesto.  But surely government cannot be defined in this slanted way.    But the authors are right to point out the coercive nature of government.  They should have gone on to say that government and its coercion are necessary and legitimate when properly limited. 

For the left, and for today's Democratic Party, every solution to every perceived problem involves more government—top-down dictates from bureaucrats presumed to know better what you need. Tea partiers reject this nanny state philosophy of redistribution and control because it is bankrupting our country.

Spot on.  The main reason the Tea Partiers reject the liberal-left vision of an omnicompetent, omni-intrusive government is purely pragmatic: it is leading us to financial ruin.  This is reason enough to oppose the fiscal irresponsibility of both major parties.  We don't even need to get into the injustices of progressive taxation and redistributionism, and the  assault on individual liberty — though these are powerful additional arguments. 

On Hitchens and Death

I just caught the last third of an interview of Christopher Hitchens by Charlie Rose.  He looks bad, the chemotherapy having done a nasty tonsorial number on him.  But his trademark intellectual incandescence appeared undiminished.  'Brilliant' is a word I don't toss around lightly, but Hitch is one to whom it unarguably applies. Public intellectuals of his caliber are rare and it will be sad to see him go.  Agree or disagree with him, it is discourse at his level that justifies the high regard we place on free speech.

In the teeth of death the man remains intransigent in his unbelief.  And why not?  He lived in unbelief and so it is only fitting that he should die in it as well.  He lived for this life alone; it is fitting that he should die without hope. As I read him, God and the soul were never Jamesian live options.  To cop out now as debility and death approach must appear to him to be utterly contemptible, a grasping for straws, a fooling himself into a palliative illusion to ease the horror of annihilation.

For what he takes to be the illusion of immortality, Hitch substitutes literary immortality.  "As an adult whose hopes lay assuredly in the intellect, not in the hereafter, he concluded, 'Literature, not scripture, sustains the mind and — since there is no other metaphor — also the soul.'" (Here) But to the clearheaded, literary immortality is little more than a joke, and itself an illusion.  Only a few read Hitch now, and soon enough he will be unread, his books remaindered, put into storage, forgotten.  This is a fate that awaits all scribblers but a tiny few.  And even they will drink the dust of oblivion in the fullness of time.

To live on in one's books is a paltry substitute for immortality, especially when one recalls Georg Christoph Lichtenberg's aphorism: Ein Buch ist ein Spiegel, aus dem kein Apostel herausgucken kann, wenn ein Affe hineinguckt. "A book is a mirror:  if an ape peers in, no apostle will look out."  Most readers are more apish than apostolic.

To live on in one's books is only marginally better than to live on in the flickering and mainly indifferent memories of a few friends and relatives. And how can reduction to the status of a merely intentional object count as living on?

The besetting sin of powerful intellects is pride.  Lucifer, as his name indicates, is or was the light-bearer.  Blinded by his own light, he could see nothing beyond himself.  Such is the peril of intellectual incandescence.  Otherworldly light simply can't get through.  One thinks of Nietzsche, Russell, Sartre, and to a lesser extent Hitchens.  A mortal man with a huge ego — one which is soon to pop like an overinflated balloon.

The contemplation of death must be horrifying for those who pin all on the frail reed of the ego.  The dimming of the light, the loss of control, the feeling of helplessly and hopelessly slipping away into an abyss of nonbeing.  And all of this without the trust of the child who ceases his struggling to be borne by Another.  "Unless you become as little children, you cannot enter the kingdom of heaven."  But this of course is what the Luciferian intellect cannot do. It cannot relax, it must hold on and stay in control.  It must struggle helplessly as the ego implodes in upon itself.  The ego, having gone supernova, collapses into a black hole.  What we fear when we fear death is not  so much the destruction of the body, but the dissolution of the ego.  That is the true horror and evil of death.  And without religion you are going to have to take it straight.

Have you read Philip Larkin's Aubade?

What would Hitch lose by believing?  Of course, he can't bring himself to believe, it is not a Jamesian live option, but suppose he could.  Would he lose 'the truth'?  But nobody knows what the truth is about death and the hereafter.  People only think they do. Well, suppose 'the truth' is that we are nothing but complex physical systems slated for annihilation.  Why would knowing this 'truth' be a value?  Even if one is facing reality by believing that death is the utter end of the self, what is the good of facing reality in a situation in which one is but a material system? 

If materialism is true, then I think Nietzsche is right: truth is not a value; life-enhancing illusions are to be preferred.  If truth is out of all relation to human flourishing, why should we value it?

Islam’s Role in the Etiology of Terrorism

WARNING:  Free speech and political incorrectness  up ahead!

Our man on the ground in Afghanistan, Spencer Case, writes:

Here at Forward Operating Base Thunder, the captain has recently returned from leave, bringing with him his propensity for political debate. One hot subject in the office, the Ground Zero mosque, has led to a genuine philosophical question which I’d like to see you take up. The question is this: at what point is it appropriate to credit/blame an “-ism” for the deeds/misdeeds of professed adherents?

To me it seems perfectly correct to say that Islam causes terrorism, that 9/11 was an Islamic attack, and that Islam as an overarching worldview is responsible for certain evils. The captain thinks 9/11 was simply a crazy or evil attack. The fact that the attackers happened to be Muslim, rather than Christian, Buddhist, Communist or what-have-you is purely accidental (Allahu Akbar! notwithstanding).

First of all, the 9/11 hijackers were not 'crazy' or insane or irrational.  They displayed a high degree of instrumental rationality in planning and carrying out their mission.  It is a big mistake to think that evil actions are eo ipso crazy actions.  People who say or suggest this (typically liberals) simply do not take evil seriously or the free will that makes it possible.  They think that people who commit mass murder must be out of their minds.  No! Mass murder can be an entirely rational means for the furtherance of one's (evil) goals.  The 9/11 terrorists knew exactly what they were doing, did it deliberately and freely and consciously and rationally (in terms of instrumental rationality), and they dealt us a severe blow from which we are still reeling.  It is also a mistake to call Muhammad Atta and the boys 'cowards' as Bill O'Reilly and others have done.  On the contrary!  They displayed great courage in carrying out their evil deeds.  The fact that courage is a virtue is consistent with an exercise of courage having an evil upshot.

And your captain is certainly wrong if he thinks that it is an accidental fact about the 9/11 hijackers that they are Muslims.  Intentional actions derive from and reflect beliefs.  People do not act  in a doxastic vacuum.  And what they believe cannot help but influence their actions. A convinced pacifist is highly unlikely to be a suicide bomber.  Compare the number of Buddhist terrorists to the number of Muslim terrorists.  There are many more of the latter than of the former, to put it in the form of an understatement.   Obviously, the content of Buddhist/Muslim beliefs plays an important role in the etiology of pacifist/terrorist acts.

Continue reading “Islam’s Role in the Etiology of Terrorism”

Don’t Mess With Texas: After 9th DWI, Texas Man Gets Life

News accounts like this one give me hope that there is still some common sense left  in this crazy country dominated as it is by the politically correct.  The sentence is just.  Think about it.  This is the miscreant's 9th conviction.  The road to conviction is long.  First there must be an apprehension, then a trial, then a conviction.  How many times was this dude tried without being convicted?  How many times did he drive drunk without being caught? Perhaps hundreds. 

Kline on Cantor on the Square Root of 2

Morris Kline, Mathematics: The Loss of Certainty, Oxford 1980, p. 200:

. . . when Cantor introduced actually infinite sets, he had to advance his creation against conceptions held by the greatest mathematicians of the past. He argued that the potentially infinite in fact depends on a logically prior actually infinite. He also gave the argument that the irrational numbers, such as the square root of 2, when expressed as decimals involved actually infinite sets because any finite decimal could only be an approximation.

Here may be one answer to the question that got me going on this series of posts. The question was whether one could prove the existence of actually infinite sets. Note, however, that Kline's talk of actually infinite sets is pleonastic since an infinite set cannot be anything other than actually infinite as I have already explained more than once.  Pleonasm, however, is but a peccadillo. But let me explain it once more.  A potentially infinite set would be a set whose membership is finite but subject to increase.  But by the Axiom of Extensionality, a set is determined by its membership: two sets are the same iff their members are the same.  It follows that a set cannot gain or lose members.  Since no set can increase its membership, while a potentially infinite totality can, it follows that that there are no potentially infinite sets.  Kline therefore blunders when he writes,

However, most mathematicians — Galileo, Leibniz, Cauchy, Gauss, and others — were clear about the the distinction between a potentially infinite set and an actually infinite one and rejected consideration of the latter. (p. 220)

Kline is being sloppy in his use of 'set.'  Now to the main point.  Suppose you have a right triangle. If two of the sides are one unit in length, then, by the theorem of Pythagoras, the length of the hypotenuse is the sqr rt of 2 = 1.4142136. . . . Despite the nonterminating decimal expansion, the length of the hypotenuse is perfectly definite, perfectly determinate. If the points in the line segment that constitutes the hypotenuse did not form an infinite set, then how could the length of the hypotenuse be perfectly definite? This is not an argument, of course, but a gesture in the direction of a possible argument.

If someone can put the argument rigorously, have at it.

Does Potential Infinity Rule Out Mathematical Induction?

In an earlier thread David Brightly states that "The position on potential infinity that he [BV] is defending is equivalent to the denial of the principle of mathematical induction."  Well, let's see.

1.  To avoid lupine controversy over 'potential' and 'actual,' let us see if we can avoid these words.  And to keep it simple, let's confine ourselves to the natural numbers (0 plus the positive integers).  The issue is whether or not the naturals form a set.  I hope it is clear that if the naturals form a set, that set will not have a finite cardinality!  Were someone to claim that there are 463 natural numbers, he would not be mistaken so much as completely clueless as to the very sense of 'natural number.'  But from the fact that there is no finite number which is the number of natural numbers, it does not follow that there is a set of natural numbers.

2.  So the dispute is between the Platonists — to give them a name — who claim that the naturals form a set and the Aristotelians — to give them a name — who claim that the naturals do not form a set.  Both hold of course that the naturals are in some sense infinite since both deny that the number of naturals is finite.  But whereas the Platonists claim that the infinity of naturals is completed, the Aristotelians claim that it is incomplete.  To put it another way, the Platonists — good Cantorians that they are — claim that  the naturals, though infinite,  are a definite totality whereas the Aristoteleans claim that the naturals are infinite in the sense of indefinite.  The Platonists are claiming that there are definite infinities, finite infinities – which has an oxymoronic ring to it.  The Aristotelians stick closer to ordinary language.  To illustrate, consider the odds and evens.  For the Platonists, they are infinite disjoint subsets of the naturals.  Their being disjoint from each other and non-identical to their superset shows that for the Platonists there are definite infinities.

3.  Suppose 0 has a property P.  Suppose further that if some arbitrary natural number n has P, then n + 1 has P.  From these two premises one concludes by mathematical induction that all n have P.  For example, we know that 0 has a successor, and we know that if  arbitrary n has a successor, then n +1 has a successor.  From these premises we conclude by mathematical induction that all n have a successor.

4.  Brightly claims in effect that to champion the Aristotelean position is to deny mathematical induction.  But I don't see it.  Note that 'all' can be taken either distributively or collectively.  It is entirely natural to read 'all n have a successor' as 'each n has a successor' or 'any n has a successor.'  These distributivist readings do not commit us to the existence of a set of naturals.  Thus we needn't take 'all n have a successor' to mean that the set of naturals is such that each member of it has a successor.

5. Brightly writes, "My understanding of 'there is' and 'for all' requires a pre-existing domain of objects, which is why, perhaps, I have to think of the natural numbers as forming a set."  Suppose that the human race will never come to an end.  Then we can say, truly, 'For every generation, there will be a successor generation.'  But it doesn't follow that there is a set of all these generations, most of which have not yet come into existence.  Now if, in this example, the universal quantification does not require an actually infinite set as its domain, why is there a need for an actually infinite set  as the domain for the universal quantification, 'Each n has a successor'?

6.  When we say that each human generation has a successor, we do not mean that each generation now has a successor; so why must we mean by 'every n has a successor' that each n now has a successor?  We could mean that each n is such that a successor for it can be constructed or computed.  And wouldn't that be enough to justify mathematical induction?

Addendum 8/15/2010  11:45 AM.  I see that I forgot to activate Comments before posting last night.  They are on now. 

It occurred to me this morning that  I might be able to turn the tables on Brightly by arguing that actual infinity poses a problem for mathematical induction.  If  the naturals are actually infinite, then each of them enjoys a splendid Platonic preexistence vis-a-vis our computational activities.  They are all 'out there' in Plato's heaven/Cantor's paradise.  Now consider some stretch of the natural number series so far out that it will never be reached by any computational process before the Big Crunch or the Gnab Gib, or whatever brings the whole shootin' match crashing down.  How do we know that the naturals don't get crazy way out there?   How can we be sure that the inductive conclusion For all n, P(n) holds?  Ex hypothesi, no constructive procedure can reach out that far.  So if the numbers exist out there, but we cannot reach them by computation, how do we know they behave themselves, i.e. behave as they behave closer to home?  This won't be a problem for the constructivist, but it appears to be a problem for the Platonist.

On Strictu Dictu and Holus Bolus

If memory serves, I picked up strictu dictu from an article by the philosopher C. B. Martin. It struck me as a bit odd, but having found it in use by other good writers, I started using it myself. Using it, I am in good company. But classicist Mike Gilleland, who knows Latin much, much better than I do, considers it not a proper Latin phrase at all. See An Odd Use of the Second Supine and More on Strictu Dictu.

So I am inclined to drop strictu dictu. I should take the advice I myself give in On Throwing Latin ( a most excellent post that I cannot at the moment locate). I do strive to practice what I preach. But I will continue to pepper my prose with the unexceptionable mirabile dictu, horribile dictu, difficile dictu, and the like, ceteris paribus of course. And I will not apologize for my use of 'big words' such as ambisinistrous, animadversion, preternatural, desueteude, incarnadine, inconcinnity, unexceptionable, et cetera.   Am I writing for a pack of idiots?

"Why not forget the foreign ornamentation and just say what you want to say clearly and simply and in plain English?"

Well, sometimes I do exactly that. But I refuse to be bound by any one style of writing, or to pander to the appallingly limited vocabularies of my fellow citizens. George Orwell and others who reacted against the serpentine and baroque sentences of their Victorian fathers and grandfathers went too far in the opposite direction.  And now look what we have.  For a poke at Orwell, see here.  Zinnser I criticize here and here.   

It just now occurs to me that it wasn't strictu dictu that I picked up from C. B. Martin but holus bolus.  Holy moly, that too looks like bogus Latin. Perhaps the estimable Dr. Gilleland will render his verdict on this construction as well.

My Angelic Wife

One indicator of her angelicity is her support of my chess activities — in stark contrast to the wives of two acquaintances both of whose 'better' halves destroyed their chess libraries in fits of rage at time spent sporting with Caissa. "Hell hath no fury like a woman scorned," wrote old Will.

I'm no bard, but here's my ditty in remembrance of my two long lost Ohio chess friends:

   Forget that bitch
   And dally with me.
   Else I'll decimate
   Your library.

Innumeracy in the Check-Out Line

The Sarah Lee frozen pies were on sale, three for $10, at the local supermarket. I bought two, but they rang up as $4.99 each. I pointed out to the check-out girl that this was wrong, and she sent a 'gofer' to confirm my claim. Right I was. But now the lass was perplexed, having to input the correct amount by hand and brain. She had to ask me what 10 divided by 3 is. I was nice, not rude, and just gave her the answer sparing her any commentary.

(It's a crappy job, standing up eight hours per day, in a confined space, an appendage of a machine. I make a point of trying to relate to the attendants, male and female, as persons, at the back of my mind recalling a passage in Martin Buber's I-Thou in which he says such a relation is possible even in the heat of a commute between passenger and bus driver.)

But now I can be peevish. They learn how to put on condoms in these liberal-run schools but not how to add, subtract, multiply and divide? And how many times have I encountered pretty young things in bars and restaurants who are clueless when it comes to weights and measures?  At a P. F. Chang's the other day I asked whether the beer I wanted to order was 22 oz.  The girl said it was a pint, "whatever that is." This was near Arizona State and it is a good bet that she was a student there.  How can such people not know that there are two pints in a quart, that a pint is 16 fluid ounces, that four quarts make a gallon , . . . , that a light-year is a measure of distance not of time, . . . .

Can we blame this one on libruls too?  You betcha!  A librul is one who has never met a standard he didn't want to undermine.

You many enjoy John Allen Paulos, Innumeracy.  In case it isn't obvious, innumeracy is the mathematical counterpart of illiteracy.