Month: August 2010

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.

Doron Zeilberger’s Ultrafinitism

This is wild stuff; I cannot say whether it is mathematically respectable but the man does teach at Rutgers.  It is certainly not mainstream.  Excerpt:

It is utter nonsense to say that sqrt 2

 is irrational, because this presupposes that it exists, as a number or distance. The truth is that there is no such number or distance. What does exist is the symbol, which is just shorthand for an ideal object x that satisfies x2 = 2.

Now what the hell does that mean? A rational number is one that can be expressed as a fraction a/b where both a and b are integers and b is not 0. An irrational number is one that cannot be expressed in this way.  By the celebrated theorem of Pythagoras, a right triangle with sides of 1 unit in length will have an hypotenuse with length = the square root of 2.  This is an irrational number.  But this irrational number measures a quite definite length both in the physical world and in the ideal world.  How can this number not exist?  It is inept to speak of a symbol as shorthand for an ideal object since, if x is shorthand for y, then both are linguistic items.  For example 'POTUS' is shorthand for 'president of the United States.'  But 'POTUS' is not shorthand for Obama.  'POTUS' refers to Obama.  Zeilberger appears to be falling into use/mention confusion.  If the symbol for the sqrt of 2 refers to an ideal object, then said object is a number that does exist.  And in that case Zeilberger is contradicting himself.

What's more, it seems that from Zeilberger's own example one can squeeze out an argument for actual infinity.  We note first that the decimal expansion of the the sqrt of 2 is nonterminating:  1.4142136 . . . .  We note second that the length of the hypotenuse is quite definite and determinate.  This seems to suggest that the decimal expansion must be actually infinite.  Otherwise, how could the length of the hypotenuse be definite?

As an ultrafinitist, however, Zeilberger denies both actual and potential infinity:

. . . the philosophy that I am advocating here is called

ultrafinitism. If I understand it correctly, the ultrafinitists deny the existence of any infinite, not [sic] even the potential infinity, but their motivation is `naturalistic', i.e. they believe in a `fade-out' phenomenon when you keep counting. [. . .]

So I deny even the existence of the Peano axiom that every integer has a successor.

As I said, this is wild stuff.  He may be competent as a mathematician; I am not competent to pronounce upon that question.  But he appears to be an inept philosopher of mathematics.  But this is not surprising.  It is not unusual for competent scientists and mathematicians to be incapable of talking coherently about what they are doing when they pursue their subjects.  Poking around his website, I find more ranting and raving than serious argument.

The ComBox is open if someone can clue us into the mysteries of ultrafinitism.  There is also some finitist Russian cat, a Soviet dissident to boot, name of Esenin-Volpin, who Michael Dummett refers to in his essay on Wang's Paradox, but Dummett provides no reference.  Is ultrafinitism the same as strict finitism?

Bear Canyon Trail in the San Gabriel Mountains

The Bear Canyon Trail (Old Mt. Baldly Trail) is one way to the top of Mt. Baldy (Mount San Antonio) in the San Gabriel Mountains.  My childhood friend John Ingvar Odegaard (the heftier of the two guys depicted below) and I got nowhere near the peak, but we did saunter up to Bear Flat in a manner most leisurely.  We had the trail to ourselves except for a young mother with baby in papoose and an angry rattlesnake who was not glad to see us.  The trail to Bear Flat is a mere 1. 75 miles one way, but fairly steep, gaining 1260' from the trailhead at 4260'.  The trail was delightfully soft, unlike the rocky, ankle-busting tracks I am used to in the Superstitions, and proceeded mostly under an arboreal canopy of oak and other trees.   But the trail opened out here and there onto some nice vistas.  From one, we could see all the way down to the ancestral Odegaard cabin in Baldy Village.

IMG_1802

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Odegaard

Illegal Immigration and Liberal Irresponsibility

Peggy Noonan, America Is at Risk of Boiling Over:

To take just one example from the past 10 days, the federal government continues its standoff with the state of Arizona over how to handle illegal immigration. The point of view of our thought leaders is, in general, that borders that are essentially open are good, or not so bad. The point of view of those on the ground who are anxious about our nation's future, however, is different, more like: "We live in a welfare state and we've just expanded health care. Unemployment's up. Could we sort of calm down, stop illegal immigration, and absorb what we've got?" No is, in essence, the answer.

Exactly right.  One cannot have both an ever-expanding welfare state and a tolerant attitude toward illegal immigration. 

An irony here is that if we stopped the illegal flow and removed the sense of emergency it generates, comprehensive reform would, in time, follow. Because we're not going to send the estimated 10 million to 15 million illegals already here back. We're not going to put sobbing children on a million buses. That would not be in our nature. (Do our leaders even know what's in our nature?) As years passed, those here would be absorbed, and everyone in the country would come to see the benefit of integrating them fully into the tax system. So it's ironic that our leaders don't do what in the end would get them what they say they want, which is comprehensive reform.

Unfortunately, we cannot take at face value what our so-called leaders say they want, especially when they employ gaseous phrases like 'comprehensive immigation reform' which  mean nothing definite.  Obviously, Job One is to stop the influx of illegal aliens.  But try to get someone like Janet 'The System Works'  Napolitano to admit that.  She won't, not in a million years.  It's not in her interest, since illegal aliens are most of them 'undocumented Democrats,' i.e., potential members of her party.  Recently she dodged the fence question with the asinine response, "You can't stop 'em all."  On her JackAss (Democrat) logic, if you can't stop 'em all –which is true — then there is no point in enforcing the border so as to stop more than are being stopped now.

Once Job One is done, then we can advance to the question of how to normalize and integrate the 10-15 million whom we have allowed to enter illegally.  Noonan is absolutely right: we are not going to deport them, nor — I would argue — should we.  Conservative bomb-throwers such as Ann Coulter who call for deportation are almost as irresponsible as Obama and Co.  (To set forth my reasons why we ought not deport  millions of otherwise law-abiding illegals who contribute to our economy and have children who are U S citizens requires a separate post.)

Lest my conservative friends fear that I am turning into a squishy bien-pensant latte-sipping liberal, let me throw this into the mix: the law that allows the U.S. -born offspring of illegal aliens to gain immediate citizenship needs to be changed. 

 

Yet More on the Mosque and Matters Muslim

Malcolm Pollack e-mails from Gotham:

That was an excellent post  about that damned mosque. [. . .]

I have meanwhile been arguing, back at my place, with Bob Koepp over burqa-banning  –  an excellent discussion of which was written at NRO yesterday by Claire Berlinsky. I think you would find it interesting; it's here.

Very interesting indeed, and I agree with you that Berlinsky 'nails it' when she writes:

Because this is our culture, and in our culture, we do not veil. We do not veil because we do not believe that God demands this of women or even desires it; nor do we believe that unveiled women are whores, nor do we believe they deserve social censure, harassment, or rape. Our culture’s position on these questions is morally superior. We have every right, indeed an obligation, to ensure that our more enlightened conception of women and their proper role in society prevails in any cultural conflict, particularly one on Western soil.

I also noted in particular this paragraph of yours:

In the six years I have been running this weblog, I have distinguished between moderate and militant Muslims.  Some of my more conservative friends have criticized me for this distinction, and I am currently re-evaluating it.  This is an open question for me.  Perhaps 'moderate Muslim' is as oxymoronic as 'moderate Communist.'  Communists used our institutions and freedoms to undermine us, and that's a fact.  It is at least an open question whether Muslims are doing the same, with so-called 'moderate Muslims' being like 'fellow travelers' who are not actively engaged in subversion but provide support from the sidelines.

I've done some re-evaluating too; my own views have evolved considerably since 9/11. Prior to that awful day, I had only a general familiarity with Islam, and made a very clear distinction between "radical" or "fundamentalist" Islam and what I imagined to be "mainstream" or "modernized" Islam. After all, like you, I had Muslim friends and acquaintances, and my exploration of the teachings of G.I. Gurdjieff (whom my father actually knew, by the way) had led me some distance into esoteric teachings that derived in part from Sufism.

After 9/11, however, I made it my business to learn more, and I read a great deal about Islamic history and theology  –  with the effect that I came to understand, as Recep Erdogan has put it, that there is no such thing as "moderate" Islam; there is just Islam, and "moderates"  –  meaning, in particular, those who see Islam as fully compatible with life under a secular, pluralistic government  –  are, on any coherent interpretation, heretics and apostates.

See here for what Erdogan said and analysis by Daniel Pipes.

This realization has made it increasingly clear to me that Islam is not, as fuzzy-minded liberals (and even most conservatives) would have it, just another religion, and a peaceful one at that, that has been "hijacked" by "extremists", but an expansionist, totalizing ideology, a highly infectious mind-virus  –  and one that is not only utterly incompatible, in anything resembling its pure form, with Western norms and Western culture, but is also its sworn and implacable enemy.

I don't know whether you are right about this, Malcolm, but it is clear to me that this question must be honestly addressed, and political correctness be damned.

This is, of course, far beyond the pale as far as polite society is concerned, but the threat is, I think, so serious and so clamant that it must be said, and people here need to get used to hearing it. Very few people are saying it yet; Lawrence Auster is perhaps foremost among them, but his audience is small.

The lesson of 1,400 years is very clear: Islam always expands, unless it is made to contract or withdraw by force of arms. It is doing so in Europe, and in Britain, and it will do so here, if we let it. Terrorism is the least of it.

Anyway, sorry to ramble on so. Living here in the bulls-eye, this stuff is on my mind a lot lately.

Good luck with your battle against the D.O.J.!

Paradoxes of Illegal Immigration

Philosophers hate a contradiction, but love a paradox.  There are paradoxes everywhere, in the precincts of the most abstruse as well as in the precincts of the prosaic.  Here are eight paradoxes of illegal immigration suggested to me by Victor Davis Hanson.    The titles and formulations are my own.  For good measure, I add a ninth, of my own invention. 

The Paradox of Profiling.  Racial profiling is supposed to   be verboten.  And yet it is employed by American border guards when they nab and deport thousands of illegal border crossers.  Otherwise, how could they pick out illegals from citizens who are merely in the vicinity of the border?  How can what is permissible near the border be impermissible far from it in, say, Phoenix?  At what distance  does permissibility transmogrify into impermissibility?  If a border patrolman may profile why may not a highway patrolman? Is legal permissibility within a state indexed to spatiotemporal position and variable with variations in the latter?

The Paradox of Encroachment.  The Federal government sues the state of Arizona for upholding Federal immigration law on the ground that it is an encroachment upon Federal jurisdiction.  But sanctuary cities flout Federal law by not allowing the enforcement of Federal immigration statutes.  Clearly, impeding the enforcement of Federal laws is far worse than duplicating and perhaps interfering with Federal law enforcement efforts.  And yet the Feds go after Arizona while ignoring sanctuary cities.  Paradoxical, eh?

The Paradox of Blaming the Benefactor.  Millions flee Mexico for the U.S. because of the desirability of living and working here and the undesirability of living in a crime-ridden, corrupt, and impoverished country.  So what does Mexican president Felipe Calderon do?  Why, he criticizes the U.S. even though the U.S.  provides to his citizens what he and his government cannot! And what do many Mexicans do?  They wave the Mexican flag in a country whose laws they violate and from whose toleration they benefit.

The Paradox of Differential Sovereignty and Variable Border Violability.  Apparently, some states are more sovereign than others.  The U.S., for some reason, is less sovereign than  Mexico, which is highly intolerant of invaders from Central America.  Paradoxically, the violability of a border is a function of the countries between which the border falls.

The Paradox of Los Locos Gringos.  The gringos are crazy, and racist xenophobes to boot, inasmuch as 70% of them demand border security and support AZ SB 1070.  Why then do so many Mexicans want to live among the crazy gringos? 

The Paradox of Supporting While Stiffing the Working Stiff.  Liberals have traditionally been for the working man.  But by being soft on illegal immigration they help drive down the hourly wages of the working poor north of the Rio Grande.  (As I have said in other posts, there are liberal arguments against illegal immigration, and here are the makings of one.)

The Paradox of Penalizing the Legal while Tolerating the Illegal.   Legal immigrants face hurdles and long waits while illegals are tolerated.  But liberals are supposed to be big on fairness.  How fair is this?

The Paradox of Subsidizing a Country Whose Citizens Violate our Laws.  "America extends housing, food and education subsidies to illegal aliens in need. But Mexico receives more than $20 billion in American remittances a year — its second-highest source of foreign exchange, and almost all of it from its own nationals living in the United States."  So the U.S. takes care of illegal aliens from a failed state while subsidizing that state, making it more dependent, and less likely to clean up its act. 

The Paradox of the Reconquista.  Some Hispanics claim that the Southwest and California were 'stolen' from Mexico by the gringos.  Well, suppose that this vast chunk of real estate had not been 'stolen' and now belonged to Mexico.  Then it would be as screwed up as the rest of Mexico: as economically indigent, as politically corrupt, as crime-ridden, as drug-infested.  Illegal immigrants from southern Mexico would then, in that counterfactual scenario,  have farther to travel to get to the U.S., and there would be less of the U.S. for their use and enjoyment.  The U.S. would be able to take in fewer of them.  They would be worse off.  So if Mexico were to re-conquer the lands 'stolen' from it, then it would make itself worse off than it is now.  Gaining territory it would lose ground — if I may put paradoxically the Paradox of the Reconquista.

Exercise for the reader:  Find more paradoxes!

 

On Potential and Actual Infinity

Some remarks of Peter Lupu in an earlier thread suggest that he does not understand the notions of potential and actual infinity.  Peter writes:

(ii) An acorn has the potential to become an oak tree. But the acorn has this potential only because there are actual oak trees . . . .  If for some reason oak trees could not exist, then an acorn cannot be said to have the potential to become an oak tree. Similarly, if the proponent of syllogism S1 thinks that actual infinity is ruled out by some conceptual, logical, or metaphysical necessity, then he is committed to hold that there cannot be a potential infinity either. Thus, in order for something to have the potential to be such-and-such, it is required that it is at least possible for actual such-and-such to exist.

This is a very fruitful misunderstanding!  For it allows us to clarify the different senses of 'potential' and 'actual' as applied to the analysis of change and to the topic of infinity.  First of all, Peter is completely correct in what he says in the first two sentences of the above quotation.  The essence of what he is saying may be distilled in the following principle

If actual Fs are impossible, then potential Fs are also impossible.

But this irreproachable principle is misapplied if 'F' is instantiated by 'infinity.'  If an actual infinity is impossible, it does not follow that a potential infinity is impossible.  For when we say that a series, say, is potentially infinite we precisely mean to exclude its being actually infinite.  A potentially infinite series is not one that has the power or potency to develop over time into an actually infinite series, the way a properly planted acorn develops into an oak tree.   On the contrary, it is a series which, no matter how much time elapses, is never completed.  An actually infinite series, by contrast, is complete at every instant.

Consider the natural numbers (0, 1, 2, 3, . . . n, n +1, . . . ).  If these numbers form a set, call it N, then N will of course be actually infinite.  A set is a single, definite object, a one-over-many, distinct from each of its members and from all of them.  N must be actually infinite because there is no greatest natural number, and because N contains all the natural numbers. 

It is worth noting, as I have noted before, that 'actually infinite set' is a pleonastic expression. It suffices to say 'infinite set.'  This is because the phrase 'potentially infinite set' is nonsense. It is nonsense because a set is a definite object whose definiteness derives from its having exactly the members it has.  In the case of the natural numbers, if they form a set, then that set will have a transfinite cardinality. Cantor refers to that cardinality as aleph-zero or aleph-nought.

But surely it is not obvious that the natural numbers form a set.  Suppose they don't.  Then the natural number series, though infinite, will be merely potentially infinite.  What 'potentially infinite' means in this case is that one can go on adding endlessly without ever reaching an upper bound of the series.  No matter how large the number counted up to, one can add 1 to reach a still higher number. The numbers are thus created by the counting, not labeled by the counting.  The numbers are not 'out there' waiting to be counted; they are created by the counting.  In that sense, their infinity is merely potential.  But if the naturals are an actual infinity, then  they are not created but labeled.

Or consider a line segment. One can divide it repeatedly and in principle 'infinitely.'  But if one does so is one creating divisions  or recognizing  divisions that exist already?  If the former, then the infinity of divisions is merely potential; if the latter, it is actual. 

Peter seems worried by the fact that no human or nonhuman adding machine can enumerate all of the natural numbers.  But this is no problem at all.  If there is an actual infinity of natural numbers, then it is obvious that a complete enumeration is impossible:  the first transfinite ordinal omega has aleph-nought predecessors.  If there is only a potential infinity of naturals, then as many enumerations have taken place, that is the last number created.

Peter seems not to be taking seriously the notion of potential infinity by simply assuming that the naturals must form an infinite set.  He doesn't take it seriously because he confuses the use of 'potential' in the context of an analysis of change, where change is the reduction of potency to act, with the use of 'potential' in discussions of infinity.

But now I'm having second thoughts.  I want to say that from the fact that a line segment is infinitely divisible, it does not follow that it is actually divided into continuum-many points.  But  what about the number of possible dividings?  If that is a finite number, one that reflects the ability of some divider, then how can the segment be infinitely divisible?  But if the number of possible dividings  is a transfinite number, then it seems we have re-introduced an actual infinity, namely, an actual infinity of possible dividings.  In other words, infinite divisibility seems to require an actual infinity of possible dividings.  Or does it? 

Still More on the Ground Zero Mosque

Dorothy Rabinowitz, Liberal Piety and the Memory of 9/11:

In the plan for an Islamic center and mosque some 15 stories high to be built near Ground Zero, the full force of politically correct piety is on display along with the usual unyielding assault on all dissenters. The project has aroused intense opposition from New Yorkers and Americans across the country. It has also elicited remarkable streams of oratory from New York's political leaders, including Attorney General Andrew Cuomo.

"What are we all about if not religious freedom?" a fiery Mr. Cuomo asked early in this drama. Mr. Cuomo, running for governor, has since had less to say.

Messrs. Cuomo and Bloomberg need to be reminded that one cannot derive a 'freedom of unlimited construction' from freedom of religion.  Yes, we Americans are for freedom of religion.  It is enshrined in our Constitution in the very first clause of the very first Amendment: "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof."  Those Muslims who are U. S. citizens enjoy the right to the free exercise of their religion.  But that is not to say that they can do anything anywhere or build anything anywhere.  Or do they have special rights and privileges not granted to Jews and Christians and Buddhists?  Is one of these rights the right to offend with impunity the majority of the citizens of a country that is the most tolerant that has ever existed?  Correct me if I am wrong, but would the Islamic Republic of Iran tolerate the building of a huge synagogue in Teheran? Is there perhaps a double-standard here?

Dr. Zuhdi Jasser—devout Muslim, physician, former U.S. Navy lieutenant commander and founder of the American Islamic Forum for Democracy—says there is every reason to investigate the center's funding under the circumstances. Of the mosque so near the site of the 9/11 attacks, he notes "It will certainly be seen as a victory for political Islam."

Exactly right.  You are very naive if you assume that being conciliatory toward a person or group of persons will in every case cause that person or group to be conciliatory in return.  Not so!  There are people who take conciliation and tolerance and respect for diversity as signs of weakness.  These people are only emboldened in their aggressiveness by your broadmindedness.  It is therefore folly to be too conciliatory.  Jasser is right: a mosque near Ground Zero will be taken as a victory for political Islam.  It will embolden Islamists worldwide.  It may even contribute to there being more Islamo-terrorist attacks in the U.S. and in the West generally.

One of the problems with liberals is their diversity fetish.  It is on clear display in Thomas Friedman's recent NYT commentary on the GZM debate.  He thinks that blocking construction amounts to resistance to diversity!  A slap in the face of openness and inclusion!  What liberals like him can't understand is that diversity, though admittedly a value, is not an absolute value: there are competing values.

It looks as if the mosque will be built.  Well, if it helps defeat the Left in Novermber, then it will have served a worthwhile purpose.