Author: Bill Vallicella

A Mosque Grows Near Brooklyn

Here.  Where is the money coming from?

Sarah Palin calls the building of this mosque an "unnecessary provocation."  As opposed to what, a necessary provocation?  But don't let Palin's infelicitous language distract you from the serious point she is making.  It is indeed  a  provocation, and the Islamists are testing us to see how far they can go and to see how weak and supine we are.  Will New Yorkers, sophisticated liberal fools that  many of them are, put up with this abomination a couple of blocks away from where their fellow citizens died horrible deaths because of a terrorist attack fueled by Islamist ideology?

The fact that the building of this mosque will be perceived as a provocation by a majority is sufficient reason to block its construction.  How can its construction do anything to improve relations between decent Muslims and the rest of us?

The first clause of the First Amendment of the U.S. Constitution guarantees the "free exercise" of religion.  True.  But is Islam a religion?  You will say, "of course!"  But perhaps you should be a bit more thoughtful.  Islam is a political ideology as much as it is a religion, and in this respect it is unlike Buddhism, or Christianity, or Judaism.  I have never heard any Jew call for the destruction of any Islamic state.  Muslims, however, routinely call for the destruction of the Jewish state.  When I lived in Turkey in the mid-nineties I was warned that preaching Christianity there could get one thrown in prison — not that I was about to do any such thing.  And Turkey in those days was a relatively 'enlightened' country compared to the rest of the non-Jewish Middle East. 

Muslims aren't very 'liberal,' are they?    They are intolerant in their attitudes and their behavior.  Now the touchstone of classical liberalism is toleration.  Toleration is good, but it has limits.  (See the posts in the category Toleration.)  So why should we tolerate them when they work to undermine our way of life?  The U. S. Constitution is not a suicide pact.  We are under no obligation to tolerate the intolerant. 

I said above that Islam is as much a political ideology as a religion. That is reflected in the fact that they have nothing like our church-state separation.  And please note that church-state separation has a good foundation in the New Testament at Matthew 22: 21: "Render therefore unto Caesar the things which are Caesar's, and to God the the things that are God's."  Please point me to the Koranic verse that enshrines the same idea.

Apologists say that Islam is a religion of peace.  Now 'peace' may be one of the meanings of Islam, but its dominant meaning is 'submission to the will of Allah as revealed to the propher Muhammad in the Koran.'  Let us also not forget that Muhammad was a warrior.  Was Jesus a warrior?  Buddha?  A religion founded by a warrior.  An interesting concept, that.  Somehow, I am more drawn to a religion whose founder says, "He who lives by the sword shall die by the sword."

So here is something to think about. The First Amendment guarantees freedom of religion.  But to apply the Amendment, one must raise and answer the logically prior question, What is a religion?    I rather doubt that the Founders had Islam in mind when they ensured the right to the free exercise of religion.  So we need to ask the question whether Islam counts as a religion in a sufficiently robust sense of the term to justify affording it full First Amendment protection.  To the extent that Muslims work to infiltrate and overturn our institutions and way of life, to the extent that they violate church-state separation, to the extent that they demand special privileges and refuse to assimilate, to that extent they remove  themselves from any right to First Amendment protection.

Addendum and Corrigendum (7/22)

I made a mistake in the last paragraph that I will now correct.  Although the sentence "I rather doubt that the Founders had Islam in mind when they ensured the right to the free exercise of religion" was true when I wrote it, expressing as it did a fact about my mental state, I now see that it is simply false that the Founders did not have Islam in mind.  See The Founding Fathers and Islam.  I thank Mark Whitten for the correction. 

But I do not retract my main point, which is that we ought to give careful thought to the question whether, as I put it above, "Islam counts as a religion in a sufficiently robust sense of the term to justify affording it full First Amendment protection. "  I am raising this as a question.  So-called liberals, however, being politically correct and therefore opposed to truly open discussion, will no doubt haul out their list of abusive epithets: racist, xenophobe, Islamophobe . . . .

I should point out that 'Islamophobe,' a term employed by the benighted Karen Armstrong, the renegade nun, is a particularly silly expression that only a liberal could love.  A phobia is an irrational fear.  If you use the word in any other way you are misusing it.  Fear of militant Islam is a rational fear.  One would hope that Armstrong, a Brit, would have a better grip on the English language.  These' -phobe' constructions are a dead giveaway that one is dealing with a PC liberal.  Take 'homophobia.'  Those who oppose homosexual practices neither fear it nor fear it irrationally.  Some have arguments against it.  In this case, then, the construction is doubly idiotic.  As for 'xenophobe,' that is a real word of English, but our benighted liberal pals seem not to know what it means.  It means 'irrational fear of foreigners.'  It does not mean 'someone who combats liberal-left nonsense.'  As one who has travelled the world and has lived for extended periods in Austria, Germany, and Turkey, I am hardly one who could be called a xenophobe.  Someone who opposes the infiltration of  his country by militant Muslims is not a xenophobe:  his fear is rational and it is directed not at Muslims qua Muslims but at Muslims qua militant subversives.

Over at Gnosis and Noesis, Professor Richard Hennessey rather pedantically and uncharitably picks at my "Muslims aren't very 'liberal,' are they?"  Do I mean that no Muslim is liberal?  Of course not.  A universal proposition can be refuted by a single counterexample.  (And it is worth noting en passant that a necessary universal proposition can be refuted by a single merely possible counterexample.)  Since it is obviously false that no Muslim is liberal, it is uncharitable to take my sentence as expressing that proposition.

One cannot assume that a sentence of the form Fs are Gs is always elliptical for a sentence of the form All Fs are Gs, or that a sentence of the form Fs are not Gs is always elliptical for a sentence of the form No Fs are Gs.  For example, 'Old people go to bed early' would not naturally be taken to mean that all old people go to bed early, which is plainly false, but that most do, or that old people tend to go to be early, or something similar.

Professor Hennessey seems also to be ignoring the context of my remarks, which is the construction of  mega-mosque near Ground Zero.  That, I submit, is an outrageous  provocation, a bit like building a Japanese  Shinto shrine in close proximity to the U.S.S. Arizona. (See here.)  I don't see how any rational person can fail to see that or fail to see that such a project cannot possibly bring together moderate Muslims and the rest of us.  And so it is reasonable to interpret the project as an initiative on the part of militant Muslims to take advantage of our tolerance and naivete in order to spread their religion and culture whose values are antithetic both to the Judeo-Christian tradition and to our Enlightenment values.

So that is the context in which a sentence like "They are intolerant in their attitudes and their behavior" is to be read.  The 'they' refers to militant Muslims: Muhammad Atta and the boys,  their enablers and supporters, those who flog and stone to death adulterers, those who would would impose Sharia, the clitorectomists, the Muslim fathers who murder their own daughters for adopting Western ways.  Our constitution forbids "cruel and unusual punishment."  Perhaps Hennessey can point me to the passage in the Koran that does the same.  And then there are Muslim taxicab drivers who refuse to pick up blind people with seeing eye dogs because of some lunatic Muslim aversion to dogs.  Others won't transport a person who has an alcoholic beverage in a closed container. That sort of fanaticism has no place in America.  I could go on, but the point is clear.

Just at the threat to the West in the 20th century was Communism, the threat to the West in the 21st is radical Islam. Both are totalitarian and internationalist.  Both are extremely skillful in recruiting young fanatic followers.  In one way the threat posed by militant Islam is far more dangerous than that posed by the Commies.  The Commies, being atheists and materialists, had a good reason not to deploy their nukes.  Muslims have no such reason.  (And it seems clear that they will soon be getting nukes thanks to Obama the Appeaser.) They are eager to move on to their crude paradise wherein they will disport endlessly with black-eyed virgins and get to wallow in the sensuousness that is forbidden them here.

For more on this delightful topic, see my Islamism category.

Another Strange Tale of the Superstitions

IMG_0310 The Superstition Mountains exert a strange fascination.  They attract misfits, oddballs, outcasts, outlaws, questers of various stripes, a philosopher or two, and a steady stream of  'Dutchman hunters,'  those who believe  in and search for the Lost Dutchman Gold Mine. This nonexistent object has lured many a man to his death.  More men than Alexius von Meinong's golden mountain, for sure.    Adolf Ruth, for example, back in the '30s.

Such appears to be the case once again this last week.  Three Utah prospectors, their brains addled by gold fever, entered this wild and unforgiving inferno of rocks and rattlesnakes  unprepared and appear to have the paid for their foolishness  with their lives.  Here is the story.

Or at least that is the story so far.  But there has to be more.  Why July when the temperature approaches 120 degrees Fahrenheit and the monsoon humidity adds a  further blanket of discomfort?  It is not as if they haven't been here before.  A couple of them were rescued last year.

And how do you get lost, if you are not totally stupid?  The central landmark of the entire wilderness is Weaver's Needle depicted in the first shot above.  It is visible from every direction, from the Western Sups to the Eastern Sups.  To orient yourself, all you have to do is climb up to where you can see it.  And then head for it.  To the immediate west and east of it are major trails that lead to major trailheads.

And why was no trace of them found despite  intensive searching with helicopters and dogs?  It is possible to fall into an abandoned mine shaft.  But all three at once?  Their plan, supposedly, was to search by day and sleep in a motel at night.  But then they wouldn't have gotten very deep into the wilderness and the chances of finding them dead or alive would have been pretty good.

IMG_0282 Maybe it was all a scam.  Maybe they never entered the wilderness at First Water.  They left their car there and hitchhiked out in an elaborate ruse to ditch their wives and families and their pasts.  But I speculate.  (If a philosopher can't speculate, who the hell can?)

I've hiked out of First Water many times, winter and summer.  I know a trail that you don't and is not on any maps that leads to Adolf Ruth's old camp at Willow Springs.  I've got half a mind to take a look-see . . .

On the Illicit Use of ‘By Definition’

What is wrong with the following sentence:  "Excellent health care is by definition redistributional"?  It is from a speech by Donald Berwick,  President Obama's nominee to head the Centers for Medicare and Medicaid Services, speaking to a British audience about why he favors government-run health care.

I have no objection to someone arguing that health care ought to be redistributional.  Argue away, and good luck! But I object strenuously to an argumentative procedure whereby one proves that X is Y by illict importation of the predicate Y into the definition of X.  But that is exactly what Berwick is doing.  Obviously, it is no part of the definition of 'health care' or 'excellent health care' that it should be redistributional.  Similarly, it is no part of the definition of 'illegal alien' that illegal aliens are Hispanic.  It is true that most of them are, but it does not fall out of the definition.

This is the sort of intellectual slovenliness (or is it mendacity?) that one finds not only in leftists but also in Randians like Leonard Peikoff.  In one place, he defines 'existence' in such a way that nothing supernatural exists, and then triumphantly 'proves' that God cannot exist! See here.

This has all the advantages of theft over honest toil as Russell remarked in a different connection.

One more example.  Bill Maher was arguing with Bill O'Reilly one night on The O'Reilly Factor.  O'Reilly came out against wealth redistribution via taxation, to which Maher responded in effect that that is just what taxation is.  The benighted Maher apparently believes that taxation by definition is redistributional.  Now that is plainly idiotic: there is nothing in the nature of taxation to require that it redistribute wealth.  Taxation is the coercive taking of monies from citizens in order to fund the functions of government.  One can of course argue for progressive taxation and wealth redistribution via taxation.  But those are further ideas not contained in the very notion of taxation.

Leftists are intellectual cheaters.  They will try to bamboozle you.  Listen carefully when they bandy about phrases like 'by definition.'  Don't let yourself be fooled.

"But are Berwick, Peikoff, and Maher really trying to fool people, or are they merely confused?"  I don't know and it doesn''t matter.  The main thing is not to be taken in by their linguistic sleight-of-hand whether intentional or unintentional.

 

Dissecting Leftism and Jihad Watch

Leftism and Islamism are the two main threats we face.  (Sorry, Al, your global warming is about as much a threat to us as your marital cooling.)  Both threats are totalitarian and  the threat is 'synergistic' inasmuch as leftists tolerate and enable militant Islam, which is obviously inimical to their modus vivendi, all the while displaying the most vicious intolerance of Christianity which is little or no threat to them.  I develop this theme in What Explains the Hard Left's Toleration of Militant Islam?

To help you think clearly about these important matters, I recommend Dissecting Leftism and Jihad Watch.

The Existence of Infinite Sets

A reader asked whether one can  prove that there are actually infinite sets.  Well, let's see.

It occurs to me that 'actually infinite set' is a pleonastic expresson. If there are infinite sets, then they are actually infinite, such that a potentially infinite set would be no set at all. For if there are mathematical (as opposed to commonsense) sets at all, then they are quite definite objects whose identity conditions are supplied by the Axiom of Extensionality: two sets are the same if and only they have all the same members. A mathematical set is not exhausted by its membership — it is not a mere plurality — since it is a one to their many; nevertheless, sets are rendered determinate by their members. (Let us for the moment not worry about singletons and the null set which give rise to their own difficulties.) 

It is worth noting that in Georg Cantor's oft-quoted definition, a set (Menge) is a collection of "definite and separate objects." (Contributions to the Founding of the Theory of Tranfinite Numbers, sec. 1) If the members of a set are definite and separate, then the same is true of the set itself. We could say that a math. set inherits its determinacy from the determinacy of its members. 

My point is that, if there are mathematical sets at all, then there is nothing potential, indeterminate, incomplete, or unfinished about them. Each such set is a definite single item distinct from each of its members and from  all of them.  It is a one-over-many. So if there are any infinite sets, then they are actually infinite sets, which is to say that talk of 'actually infinite sets' is redundant.

So our question becomes, Can one prove that there are infinite sets?

I don't know if one can prove it, but one can give an argument. (If a proof is a valid deductive argument the premises of which are self-evident, then damn little can be proven. In particular, the axioms of ZFC are far from self-evident, not that set theorists claim self-evidence for them. Is it self-evident that a null set exists?  Hardly.)

Here is an argument, where 'set' is short for mathematical (as opposed to commonsense) set.

1. There are sets.

2. There are infinitely many natural numbers: no finite cardinal is the number of natural numbers. Therefore,

3. If the natural numbers form a set, then they form an infinite set. (1, 2)

4. The natural numbers form a set.   Therefore,

5. The natural numbers form an infinite set. (3, 4) Therefore,

6. There exists an infinite set. (5)

This is a valid argument, and it renders reasonable its conclusion. But it does not prove its conclusion unless there are proofs for its controversial premises (1) and (4). I argued for (1) in Sets, Pluralities, and the Axiom of Pair.  But what is the argument for (4)?  Why must we think of the natural numbers as forming a set?

But Is It True?

Peter and I were having lunch with a pretty lady yesterday.  While recounting some paranormal experiences, he expressed doubt as to whether they were true.  The lady, quite sympathetic to the experiences and their contents, but having come under the influence of the PoMo crowd, piped up, "There is no truth."  Peter shot back, "So it is true that there is no truth?"

Peter's response was 'knee-jerk,' reflexive, not reflective.  He didn''t need to reflect.  His was a stock response, but none the worse for being stock or easily come by.  It is a prepared line that you should all have at the ready when confronted with  PoMo nonsense.  Not that it will do you much good with the PoMo crowd.

The probative force of Peter's riposte is devastating.  What's amazing, though, is that the Pomo types are not moved by it.  I think this shows that truth is not their concern.  Something else is, power perhaps. It is no surprise that leftism is alive and well within the precincts of PoMo.  I'd have to think about it some more, but 'conservative post-modernist' smacks of being an oxymoron.

Let S be a declarative sentence.  Then surely

E. 'S' is true iff S.

The equivalence schema (E) doesn't say much.  But what it says suffices to refute the claim that there is no truth.  For anyone who asserts 'There is no truth' makes an assertion which is equivalent to "'There is no truth' is true."  And so truth comes back into the picture.  Truth, she's a wily bitch.  Drive her out of the front door, she comes in through the back.  And I don't think it matters how minimalist  is your theory of truth.  My argument does not assume that truth is a metaphysically substantive property.  Even if no property  at all corresponds to the predicate ' is true,' that predicate has a sense.  If it had no sense, then (E) would be gibberish, like

E*. 'S'  is schmue iff S.

I'd have to think about it some more, but it looks as if the equivalence schema by itself suffices to refute the PoMo nonsense that there is no truth.  For even if there is no property of truth, and truth is merely the sense of the predicate 'is true,' that sense cannot be denied.  It's always and necessarily along for the ride.

 

Does Sincere Belief in an Afterlife Entail Religious Zealotry?

Spencer Case e-mails:

Greetings from Afghanistan. I’d very much like to hear your response to a sketch of an argument I’m developing. It goes as follows:

1. Suppose an afterlife is obtainable based on one’s performance in this life. If this afterlife is as I understand it, it must have an infinite value while all the goods in this life have only finite values. In fact, the value of afterlife goods (as I clumsily name them) must be infinite on two planes: quantitative and qualitative; quantitative because the duration of the reward is infinite, qualitative because, I assume—and I think, based on some recent blog posts of yours I’ve read, you would agree—no mortal goods, or accumulation of them, can be qualitatively better than the eternal goods to be found in the afterlife, even when we do not consider duration (this not the case with Islamic fundamentalists, who are promised virgins. But let that pass). Perhaps there is even a punitive afterlife with similar disvalue. 

I agree with this conception of the afterlife.  To put it in a slightly different way, the goods of this life are vanishing quantities axiologically speaking as compared to the goods of the afterlife as portrayed in sophisticated conceptions.  (We agree to set aside crude conceptions such as we find in popular Islam: endless disporting with black-eyed virgins, getting to do there all the sensual things that are forbidden here, etc.)

2.  If this ranking system is correct, it is hard to see how it could ever be rational for one to pursue any set of mortal goods—no matter how well they rank on the finite scale—when one could spend the same time and resources in the pursuit of the afterlife goods or avoiding afterlife evils, which are both endless in duration and of infinitely great quality. If extreme fasts are pleasing to God, and increase my chances of obtaining salvation by a tiny bit, then the rational thing for me to do is to live in such an ascetic state for as long as possible, unless it prevents me from doing other activities that could do even more to promote my own salvation.

Well, Spencer, you have put your finger on a genuine and serious problem, a problem I will rephrase in my own way.  If (i) this world and its finite goods is soon to pass away, and if (ii) one sincerely believes that there is a world to come the value of whose goods infinitely surpasses the values of the goods here below, and if (iii) whether or not one participates in this Higher Life or is excluded from it (either by being sent to the Other Place or by being simply annihilated at death) depends on how one lives in this world, then how can it be rational to pursue mortal goods beyond what is necessary for living in accordance with the precepts of one's religion?  The rational course would be to orient all one's activities to the achievement of the afterlife goal.

For example, if a young person is a Roman Catholic and sincerely believes the teachings of his church, especially as regards what are called the Last Things, and this person is free of such encumbrances as children or aged parents to care for, and has the health and other qualifications necessary to join a monastery, then why doesn't the person do so, and join the most rigorous monastery to be found?  Wouldn't that be the most rational course of action given (i) the end in view, (ii) one's beliefs about this end, and (iii) one's beliefs about the means for securing this end?

Converts often follow this course.  Unlike those who have been brought up in a faith,  they are seldom lukewarm.  They have found the truth with a majuscule 'T' (they think) and their authenticity demands that they act on it.  Thomas Merton, for example, after renouncing his worldly life and joining the RC church was not content to be a good practicing Catholic, or become a parish priest even; no, he had to go all the way and join not just any monastic order but the Trappists!  One can appreciate the  'logic' to it.  And then there is Edith Stein, the brilliant Jewish assistant of Edmund Husserl.  She was not content to convert to Catholicism; she abandoned her academic career and all the usual worldly blandishments (sex, love, children, travel, etc.) to spend the rest of life behind the walls of a strict Carmelite convent until the Nazis murdered her at Auschwitz.

I hope the conversion  'logic' is clear:  if in a few short years we will be pitched head first into Kingdom Come, then pursuing and fretting over the baubles of this life is like re-arranging deck chairs on the Titanic.

Let's note en passant that the same 'logic' is found in the thinking of adherents to nonreligious ideologies.  Thousands of young people, some of them among the best and the brightest, sacrificed their lives to the Communist illusion in the 20th century.  They wasted their lives in pursuit of a fata morgana, while at the same time contributing unintentionally and indirectly to the murder of over 100 million people.

3.  Anyone who pursues only afterlife goods in this way is a paradigm case of a religious zealot.

This formulation needs improvement.  Merton and Stein did not pursue ONLY afterlife goods.  They pursued  this-worldly goods too but only insofar as they were instrumental to the achievement of afterlife goods. (I ignore Merton's lapses.)  A better formulation is as follows:

3*.  Anyone who pursues afterlife goods primarily, and this-worldy goods only insofar as they are instrumental in the achievement of afterlife goods, is a religious zealot.

I can accept (3*), but I would add that being a zealot is not necessarily bad, despite the fact that the word generally carries a pejorative connotation.  Aren't we all legitimately zealous when it comes to the preservation of our lives and the lives of those animals and humans in our care?  Suppose Al Gore is right, and global warming is about to do us all in, then GW zealotry would be justified would it not?

4.  So, accepting these very basic religious propositions makes one rationally committed to religious zealotry and denying our normal reasons for acting.

I don't think your conclusion follows in quite the way you intend it.  For one thing, you seem to be assuming that zealotry as such is bad.  But surely not all zealotry is bad.  To modify a saying of Barry Goldwater: Zealotry in the defense of liberty is no vice!  (He had 'extremism' where I have 'zealotry.')  You may also be assuming that the religious claims are false.  Suppose they are true.  Then one would have a good reason for denying/modifying our normal reasons for acting.  (The same would hold in the case of nonreligious ideologies.)  A 'normal' person, if if he is a practicing adherent of a religion, pursues all sorts of pleasures and diversions which do not advance him toward his spiritual goal, but rather, in many cases, impede his realization of it.  The 'normal' Buddhist, for example, does not carry the precept "Conquer desire and aversion!" to the point where he eats whatever is put on his plate.  (If a fly lands in his soup he does not practice nondiscrimination and eat the fly with the same relish or lack thereof with which he eats the rest of the soup.)  But if our Buddhist really believed Buddhist teachings would it not be rational for him to modify 'normal' behavior and bend every effort towards achieving enlightenment?

What I hope this shows is that religious belief (at least in the religions you and I are most likely to debate about) disallows moderation, which I take it, is a bad thing. What I especially like about this argument is it seems to be an argument that appeals to conservatives, because conservatives are most likely to have strong intuitions against ideologies that tell us to ignore our ordinary reasons for acting.

I think you are right that religious belief, if sincerely professed and lived, disallows moderation of the sort that the average  worldly person displays.  But it is not just religious belief that has this property.  So do many ideologies or action-guiding worldviews.  I gave the example of Communism above.  Other examples readily come to mind. 

You are assuming that moderation of the sort displayed by 'normal' worldly people is a good thing.  But if Communism or Catholicism were true, then moderation of that sort would not be good!  True-blue reds devoted all their energies to their chimerical Revolution  just as true Christians consecrate their lives, without reservation, to Christ.  They don't 'hedge their bets' they way most people do.  Whether that singlemindedness is good or bad depends on whether the underlying beliefs are true or false.  Of course we now know that Communism is a god that failed, but the religious God is safely insulated in a Beyond beyond our ken.

So if your thesis is that sincere belief in an afterlife entails (or maybe only leads to) religious zealotry, and is for that reason  objectionable, then I don't think you have made your case.  Genuine belief in an afterlife will lead to behavior that is 'abnormal' and 'immoderate'  as measured by the standards of the worldly.  But this won''t cut any ice unless worldly standards can be shown to be correct and truly normative, not just statistically 'normal.'

Of course, as you’ve no doubt noticed, this argument does not take into account epistemic uncertainty. Uncertainty about the existence of the afterlife might make it more rational for us to go ahead and pursue other goods. I haven’t yet done the research in probability theory, but I’d be willing to guess our levels of epistemic confidence in religious propositions would have to be very low in order for it to be rational to pursue anything else.

This is another  important side to the problem of balancing the claims of this world with the claims of the next.  People fool themselves into thinking they KNOW all sorts of thinks they merely BELIEVE.  Now it seems to me that no imtellectually honest person can claim to KNOW (using this word strictly) that there is an afterlife: the evidence from parapsychology, though abundant, is not conclusive, and the philosophical arguments, though  some of them impressive, are not compelling.  But I do KNOW the pleasures of good food, and strong coffee, and fine cigars, and chess, and good conversation, and scribbling away as I am now doing, all of them activities which are not necessary for my salvation, and perhaps stand in the way of it.  (Not to mention disporting with ladies of the evening, etc.)

So what is the rational thing to do given my epistemic predicament in which what I KNOW is confined to this ephemeral world which cannot be worth much, and my access to the other is via mere belief and the occasional religious/mystical experience whose veridicality is easily called into question?

A difficult question.  I don't know that there is an afterlife, and I don't know that there isn't.  It strikes me as highly irrational to live for this life alone since it is nasty, brutish, short, miserable, full of natural and moral evil, and of scant value if it doesn't lead to anything beyond it.  It also seems irrational to forego every positive value in this world which is not conducive to otherworldly salvation on the strength of mere belief in that otherworldly possibility.

So my tentative answer is that the rational course is to  inquire ceaselessly into the matter in a critical, exploratory and tentative spirit; avoid being bamboozled by the dogmas of churches and sects which claim to have the Truth; enjoy the limited goods of this life in a measured way while realizing that, in and of themselves, they are of no ultimate value.

In short, be neither a worldling nor a monk.  Be a philosopher! (Not to be confused with being a paid professor of it.)

Sets, Pluralities, and the Axiom of Pair

In a thread from the old blog, resident nominalist gadfly 'Ockham'/'William' made the fascinating double-barreled claim that:

. . . (a) there are such things as sets and (b) the axiom of pairs is false. Briefly, I claim that 'a set of x's' is just another way of saying 'those x's'. The fundamental error of set theory is using a logically singular expression {a, b} to refer to what in ordinary language a plural term refers to, using an expression such as 'a and b' or similar.

I take O to be saying that there are sets, but they are not the sets we read about in standard treatments of axiomatic set theory, and whose properties are all and only the properties ascribed to them in axiomatic set theory, Zermelo-Fraenkel with Choice, to be specific. Suppose we call the latter mathematical sets, and the former ordinary language (commonsense) sets. Then what O is claiming is that there are ordinary language (OL) sets, but there are no mathematical sets. That there are no mathematical sets on O's view follows from O's denial of the Axiom of Pair, a crucial ingredient of ZFC. Here is a formulation of the latter:

PAIR. Given any x and y, there is a set {x, y} the members of which are exactly x and y.

X and y can be either sets or nonsets. So given that Socrates exists and that Plato exists, it follows by PAIR that a third item exists, namely, {Socrates, Plato}. (I use 'there is' and 'there exists' interchangeably.) That a third item exists is what I affirm and what O denies. For O, the plural term 'Socrates and Plato' does not refer to a single third item, the set consisting of Socrates and Plato; and yet it does refer to something, a thing that is an ordinary language set. For O, there are exactly two items in our example, Socrates and Plato, and not three, as I claim.

Let us say that the referent of a plural term such as 'Socrates and Plato' or 'the British Empiricists' or 'the Hatfields' is a plurality. A plurality is an ordinary language set. A gaggle of geese, a pride of lions, a coven of witches, a bunch of grapes, a pack of wolves — these are all pluralities or OL sets. That there are OL sets, or pluralities, is presumably not in dispute. Nor, I think, could anyone rationally dispute their existence. That there is such a thing as a pair of shows cannot be reasonably denied; that the two shoes form a mathematical set can be reasonably denied at least prima facie.

If I understand O, he is saying that all reference to sets is via plural referring expressions such as 'these books,' 'Dick Dale and the Deltones,' 'the barristers of London,' etc. There is no reference to any set via a singular referring device such as the singular definite description, 'the set consisting of these books.'

Now consider the question whether there are sets of sets. I claim that it is a fact that there are sets of sets, and that this fact causes trouble for O's nominalist view that all sets are pluralities. Consider the Hatfields and the McCoys. These are two famous feuding Appalachian families, and therefore two pluralities or OL sets. But there is also the two-membered plurality of these pluralities to which we refer with the phrase 'the Hatfields and the McCoys' in a sentence like 'The Hatfields and the McCoys are feuding families.'

If, however, a plurality of pluralities has exactly two members, as in the case of the Hatfields and the McCoys, then the latter cannot themselves be pluralities, but must be single items, albeit single items that have members. That is to say: In the sentence, 'The Hatfields and the McCoys are two famous feuding Appalachian families,' 'the Hatfields' and 'the McCoys' must each be taken to be referring to a single item, a family, and not to a plurality of persons. For if each is taken to refer to a plurality of items, then the plurality of pluralities could not have exactly two members but would many more than two members, as many members as there are Hatfields and MCoys all together. Compare the following two sentences:

1. The Hatfields and the McCoys number 100 in toto.

2. The Hatfields and the McCoys are two famous feuding Appalachian families.

In (1),'the Hatfields and the McCoys' can be interpreted as referring to a plurality of persons as opposed to a mathematical set of persons. But in (2), 'the Hatfields and the McCoys' cannot be taken to be referring to a plurality of pluralities; it must be taken to be referring to a plurality of two single items.

Or consider the following said to someone who mistakenly thinks that the Hatfields and the McCoys are one and the same family under two names:

3. The Hatfields and the McCoys are two, not one.

Clearly, in (3) 'the Hatfields and the McCoys' refers to a two-membered plurality of single items, each of which has many members, and not to a plurality of pluralities. And so we must introduce mathematical sets into our ontology.

This is connected with the fact that '___ is an element of . . .' in axiomatic set theory does not pick out a transitive relation: If x is an element of y, and y is an element of z, it does not follow that x is an element of z. Socrates, a nonset, is an element of various sets; but he is clearly not a member of any of these set's power sets. (The power set P(S) is the set of all of S's subsets. Clearly, no nonset can be a member of any power set.) But if there are no mathematical sets, and every set is a plurality, then it seems that the elementhood or membership relation would be transitive. A set of sets would be a plurality of pluralities such that if x is an element of S and S an element of S *, then x is an element of S*. My conclusion, contra 'Ockham,' is that we cannot scrape by on OL sets, or pluralities, alone. We need mathematical sets or something like them: entities that are both one and many.

REFERENCES

Max Black, "The Elusiveness of Sets," Review of Metaphysics, vol. XXIV, no. 4 (June 1971), 614-636.

Stephen Pollard, Philosophical Introduction to Set Theory, University of Notre Dame Press, 1990.

Plato

Both his greatness as a thinker and the probity of his quest for truth are revealed in the fact that Plato is not only the father of the Theory of Forms, but also the author of the most penetrating criticisms of them.

(By the way, the above aphorism is crafted in such a way as to demonstrate that the antecedent of a pronoun need not be its antecedent in the order of reading.)

The Vital Imperative: Live Well, Live Now

Wtc1 This is it. This is your life, right here and right now. The present is as real as it gets. If you are not doing with your life right now what you think you ought to be doing with it, then you are doing something wrong.

After the 2001 attack on the World Trade Towers, The New York Times published short pieces on those who had perished. The story of one fellow in particular remains in memory. He was a bond trader whose  office was high up in one of the towers. A man in his late thirties, early forties, his dream was to live in a small town in the Rockies and operate a bait and tackle shop. But first he had to earn his grubstake, or so he thought. So he slaved away in the certain present for an uncertain future. He did what he did not love so that he might do what he did love. He did what he did not love for a present that never came.

His living was not a true living, but a postponing, a placing after. He placed his real life after his present life, forgetting that the present alone is real and that the present,  not the future, is in one's secure possession.

When St Augustine was asked what he would do if he knew he would die in the next hour, he replied, "Nothing other than what I am now doing." He was living as he thought he ought to be living, realizing   rather than postponing his Ideal.

From these lessons we may infer a Vital Imperative: As far as possible, live in the present as if the next hour were to be the hour of your death. How do you want death to find you? Living self-sufficiently in the riches of the moment? Or standing on tip-toe craning your head toward a nonexistent future?