Maverick Philosopher

Saturday Night at the Oldies: Mimi Fariña

Let's not forget Joan Baez's sister, Mimi (1945-2001).  Interestingly, the girls' father is the noted physicist Albert Baez (1912-2007).  I remember a physics teacher in high school  showing us an instructional film made by one Albert Baez.  We were surprised to hear that he was Joan's father.  We hadn't heard of him, but we sure had heard of her.  This was around 1965.

Joan and Mimi sing a lovely version of Donovan's "Catch the Wind."  Speaking of Donovan, here he and Joan collaborate on another unforgettable 'sixties tune, "Colours."  Finally, Mimi, her husband Richard, and Pete Seeger in Pack Up Your Sorrows.

A Problem With the Multiple Relations Approach to Plural Predication

Consider

1. Sam and Dave are meeting together.

2. Al, Bill, and Carl are meeting together.

3. Some people are meeting together.

Obviously, neither (1) nor (2) can be decomposed into a conjunction of singular predications.  Thus (2) cannot be analyzed as 'Al is meeting together & Bill is meeting together & Carl is meeting together.'  So it is natural to try to analyze (1) and (2) using relational predicates.  (1) becomes

1R. Meeting(Sam, Dave)   In symbols: Msd

But if 'meeting' is a dyadic (two-place) predicate, then we should expect (2) to give way to

2R. Mab & Mbc & Mac.

Unfortunately, (2R) is true in circumstances in which (2) is false.  Suppose there are three separate meetings.  Then (2R) is true and (2) false.  To get around this difficulty, we can introduce a triadic relation M* which yields as analysans of (2):

2R*. M*abc.

But then we need a tetradic relation should Diana come to the meeting.  And so on, with the result that 'meeting together' picks out a family of relations of different polyadicities.  But what's wrong with that?  Well, note that (1) and (2) each entail (3) by Existential Generalization in the presence of the auxiliary premise 'Al, Bill, Carl, Dave, and Sam are people.' 

But then we are going to have difficulty explaining the validity of the two instances of Existential Generalization.  For the one instance features a dyadic meeting relation and  the other a triadic.  If two different relations are involved, then what is the logical form of (3) -- Some people are meeting together -- which is the common conclusion of both instances of Existential Generalization?  If 'meeting together picks out a family of relations of different 'adicities, then (3) has no one definite logical form.

Does this convince you that the multiple relations approach is unworkable?

REFERENCE:  Thomas McKay, Plural Predication (Oxford 2006), pp. 19-21.

 

Hitch Lives

Here.

Irreducibly Plural Predication: 'They are Surrounding the Building'

Let's think about the perfectly ordinary and obviously intelligible sentence,

1. They are surrounding the building.

I borrow the example from Thomas McKay, Plural Predication (Oxford 2006), p. 29.  They could be demonstrators.  And unless some of them have very long arms, there is no way that any one of them could satisfy the predicate, 'is surrounding the building.'  So it is obvious that (1) cannot be analyzed in terms of 'Al is surrounding the building & Bill is surrounding the building & Carl is surrounding the building & . . . .'  It cannot be analyzed in the way one could analyze 'They are demonstrators.'  The latter is susceptible of a distributive reading; (1) is not.  For example, 'Al is a demonstrator & Bill is a demonstrator & Carl is a demonstrator & . . . .'  So although 'They are demonstrators' is a plural predication, it is not an irreducibly plural predication.  It reduces to a conjunction of singular predications.

We Philosophize Best With Friends

Aristotle says that somewhere, but I forgot where.  In any case, it is true as I verified once again yesterday in Tempe, where I met up with Steven Nemes, Mike Valle, Peter Lupu and his student Scott.  Before joining them I stopped at the library where I borrowed Thomas McKay's Plural Predication and Douglas Hyde's I Believed. 

The conversation went on for about five hours from 2 to 7.  The 19 year old Nemes has made a fairly thorough study of my book on existence (see here for links to the ten posts he has written about it) and we discussed some topics from the book.  He really understands me, and has a keen eye for problems potential and actual.  I jokingly call Nemes my nemesis.  We also discussed free will and Biblical inerrancy.  Steven floated some interesting ideas that he then today began to work out in this post.

It occurred to me today that Peter and I, sitting and smoking out in front of the Churchill cigar emporium, did a good job of instantiating the role of Sidewalk Socrates, a role Peter learned from his friend and teacher, Sidney Morgenbesser.  "There are people who have a passion for discourse, who are addicted to debate, who live in a world of constant conversation, and Morgenbesser was among the purest examples of the type."  The description fits Peter as well.  But I chided Peter for being a 'corrupter of youth' when he offered Steven cigarettes.

 

Richard Taylor on Goodness: Critical Remarks

Richard Taylor, Good and Evil: A New Direction (Prometheus 1984),  p. 134:

Goodness . . . is simply the satisfaction of needs and desires . . . the fulfillment of purposes. The greatest good for any individual can accordingly be nothing but the total satisfaction of his needs,
whatever these may be.

There seems to be a tension in this passage, between the first sentence and the second, and I want to see if I  can bring it into the open.

Taylor plausibly maintains that nothing is good or evil in itself or intrinsically. If a thing is good, it is good only relative to a being who wants, needs, or desires it. If a thing is evil, it is evil only relative to a being who shuns it or is averse to it. In a world in which there are no conative/desiderative beings, nothing is good or evil. This is plausible, is it not?

Imagine a world in which there is nothing but inanimate objects and processes, a world in which nothing is alive, willing, striving, wanting, needing, desiring. In such a world nothing would be either good or evil. A sun in a lifeless world goes supernova incinerating a nearby planet. A disaster? Hardly. Just another value-neutral event. A rearrangement of particles and fields.  But if our sun went supernova, that would be a calamity beyond compare -- but only for us and any other caring observers hanging around.

Taylor's point is, first, that sentences of the form 'X is good (evil)' are elliptical for sentences of the form 'X is good for Y.' To say that X is good (evil) but X is not good (evil) for some Y would then be like saying that Tom is married but there is no one to whom Tom is married. Taylor's point, second, is that these axiological predicates can be cashed out in naturalistic terms. Thus,

D1. X is good for Y =_df X satisfies Y's actual wants (needs, desires)

D2. X is evil for Y =_df X frustrates Y's actual wants (needs, desires).

It is clear that good and evil are not being made relative to what anyone says or opines, but to certain hard facts about the wants, needs, and desires of living beings.  That we need water to live is an objective fact about us, a fact independent of what anyone says or believes.  Water cannot have value except for beings who need or want it; but that it does have value for such beings is an objective fact.

Taylor's view implies that there is no standard of good and evil apart from the actual wants, needs, desires, and aversions of conative/desiderative beings. Goodness consists in satisfaction, evil in frustration. But satisfaction and frustration can exist only if there are indigent beings such as ourselves. It follows that nothing that satisfies a desire or fulfills a need or want can be bad. (p. 126) It also follows that no desire or purpose is either good or evil. (p. 136) For if good and evil emerge only upon the satisfaction or frustration of desires and purposes, then the desires and purposes themselves cannot be either good or evil.  The rapist's desire to 'have his way' with his victim, qua desire, is not evil, and the satisfaction of desire via the commission of rape is not evil, but good, precisely because it satisfies desire!  (Glance back at the above definitions.)

We now have a reason to toss Taylor's book out the window.  But I want to point out a rather more subtle difficulty with his theory. 

If goodness is relational in the manner explained, how can there be talk of the greatest good of an individual? Glance back at the quotation. Taylor tells us that the greatest good for an individual is nothing but the total satisfaction of his needs.  This is a higher-order state of affairs distinct from a ground-level state of affairs such as the satisfaction of the desire for water by a cool drink. What need does this greatest good satisfy?

Suppose I satisfy all my needs, wants and desires. How can this higher-order state of satisfaction be called good if a thing is good only in relation to a needy being? There would have to be a higher-order need or want, a need or want for total satisfaction, and the goodness of the first-order satisfaction would have to consist in the satisfaction of this higher-order need. But this leads to a vicious infinite regress.

Taylor should say about the satisfaction of desire what he says about desire, namely, that it is neither good nor evil. Consider the desire to drink a beer. By Taylor's lights, drinking a beer is intrinsically neither good nor evil. It is good only insofar as it satisfies some desiderative being's desire. Thus the goodness of drinking a beer is nothing other than the satisfaction of the desire to drink beer. The desire itself, however, is neither good nor evil, and the same goes for the satisfaction or frustration of this desire.

My critical point is that Taylor is using 'good' in two senses, one relative, the other absolute, when his own theory entitles him to use it only in the relative sense. By his theory, a good X is a satisfactory X: one that satisfies some desiderative/indigent being's need, want, desire, for X. But then desire can't be said to be good or evil, as Taylor himself realizes on p. 136. Similarly, the satisfaction of desire cannot be said to be good or evil. Otherwise, the satisfaction of desire would have to be relative to a higher-order desire. Hence Taylor is not entitled to speak of the "greatest good for any individual" as he does in the passage quoted.

'Guns on the Street'

It's a liberal phrase, a silly phrase, a phrase that aids and abets thoughtlessness. Liberals speak of the 'guns on the street' and of  getting them off the street. Now I've walked down many a street in
many a city in this world, but I have yet to see any guns on the street. But I have seen them in the hands of people. The liberal tendency is to blame the instrument not the agent. You hear this sort of thing all the time: Guns have killed X people in Y time. A gun can do no such thing. Do liberals know this? They must, but then why do they talk as if they don't? So maybe they don't know it.

I didn't leer at the girl, my eyeglasses did. I didn't insult my colleague, my tongue did. Tookie Williams is not responsible for brutal murders, society is. It's the same sort of nonsense.

Don Colacho's Aphorisms

Ah, the webbiness of the Web!  I used an aphorism of Nicolás Gómez Dávila three days ago for purposes of logical analysis and received a comment from one 'Stephen' who is the proprietor of an interesting site devoted to translations of Don Colacho's aphorisms.  The blog is appropriately entitled Don Colacho's Aphorisms.  Please do check it out if you are a lover of aphorisms.  His are even better than mine, if I do say so myself.  Here is an example:

“Social” is the adjective that serves as a pretext for all swindles.

Excellent! If I may be permitted to supply an example: social justice.

Another good aphorist is Deogolwulf, proprietor of The Joy of Curmudgeonry.  Here is an example of one of his fewtrils:  "The common man is never so clever as the politician says and never so stupid as the politician believes."

John Pepple on the Need for a Cultural Revolution

I drew your attention to John Pepple's weblog, I Want a New Left, a few days ago.  Pepple identifies himself as a leftist, but what's in a label?  If he were characteristic of leftists, which he isn't, I would  have little or no problem with them.  I find myself wholly in agreement with his post, We Need a Cultural Revolution.  His topic is violent crime among the poor, and how the rebellious attitudes propagated by the 'Sixties Left have had terrible consequences for the poor without harming the well-off who spread the pernicious attitudes and who, after sloughing off their rebelliousness, slid comfortably back into the establishment.  Excerpts, emphasis added:

The problem goes back to that cultural revolution called the Sixties, because this sort of thing [extreme gang violence] did not happen before that decade. Part of that decade was the rise of the left’s cultural dominance, and the left (whether the old left or the new left) has always been soft on crime. Pushing poor people into crime makes sense to the left because such criminals are seen by them as heroes against the evil capitalists. But in fact poor people who turn to crime basically rob other poor people, which means that the total gain for the poor is zero. Moreover, once businesses in poor neighborhoods realize they have to deal with criminals, they raise prices, either because they have to hire more security people or because they have to compensate for the goods lost through theft. Once again, this doesn’t really help the poor.

That is spot on.  Leftists coddle criminals and the unproductive while penalizing productive behavior via taxation and regulation.  But by attacking those who create wealth, they make everyone poorer.  Fetishizers of equality, leftists would rather have everyone poor and equal rather than tolerate inequalities that benefit the worst off.

Douglas Hyde: From Communist to Catholic

I am now reading Archie Brown, The Rise and Fall of Communism (HarperCollins 2009).  Over 700 pages.  The author's name is hardly donnish, but he is Emeritus Professor of Politics at Oxford University.  There is a chapter entitled "The Appeals of Communism," and in it I came across a reference to Douglas Hyde:

For some who joined the Communist Party, a search for belief and a craving for certainty were important parts of their psychological make-up.  One English Communist, Douglas Hyde, moved from being a young Methodist lay preacher, with an interest also in other religions, to becoming a Communist activist for twenty years, finishing up as news editor of the CPGB party newspaper, the Daily Worker, before resigning from the party in 1948 to become a proselytizing member of the Catholic Church.  Although Hyde's political memoir, I Believed, written in the late Stalin period, is also a reasoned attack on Communist Party strategy and tactics, it holds that a majority of those attracted to Communism in those years were 'subconsciously looking for a cause which will to fill the void left by unbelief, or, as in my own case, an insecurely held belief which is failing to satisfy them intellectually and spiritually.' (p. 125)

People have strong doxastic security needs.  They need a system  of belief and practice to structure their lives. Few can tread the independent path.  In the 2oth century many bright and earnest young people sought meaning and structure in Communism.  In the 21st century radical Islam fills a similar need.  Both snares and delusions, of course.  It is arguably better to have no ideals rather than the wrong ideals, no beliefs rather than false and pernicious ones.

More on Douglas Hyde.

"Some of Us Just Go One God Further"

I've seen this quotation attributed to Richard Dawkins. From what I have read of him, it seems like something he would say. The idea, I take it, is that all gods are on a par, and so, given that everyone is an atheist with respect to some gods, one may as well make a clean sweep and be an atheist with respect to all gods. You don't believe in Zeus or in a celestial teapot. Then why do you believe in the God of Isaac, Abraham, and Jacob?

What Dawkins and the gang seem to be assuming is that the following questions are either senseless or not to be taken seriously:   'Is the Judeo-Christian god the true God?'  'Is any particular god the true God'  'Is any particular conception of deity adequate to the divine reality?'  The idea, then, is that all candidates for deity are in the same logical boat. Nothing could be divine. Since all theistic religions are false, there is no live question as to which such religion is true. It is not as if there is a divine reality and that some religions are more adequate to it than others. One could not say, for example, that Judaism is somewhat adequate to the divine reality, Christianity more adequate, and Buddhism not at all adequate. There just is no divine reality. There is nothing of a spiritual nature beyond the human horizon.  There is no Mind beyond finite mind.  Man is the measure.

That is the atheist's deepest conviction.  It seems so obvious to him that he cannot begin to genuinely doubt it, nor can he understand how anyone could genuinely believe the opposite.  But why assume that there is nothing beyond the human horizon? The issue dividing theists and atheists can perhaps be put in terms of Jamesian 'live options':

EITHER: Some form of theism (hitherto undeveloped perhaps or only partially developed) is not only logically and epistemically possible, but also an 'existential' possibility, a live option;

OR: No form of theism is an existential possibility, a live option.

Theist-atheist dialog is made difficult by a certain asymmetry: whereas a sophisticated living faith involves a certain amount of purifying doubt, together with a groping beyond images and pat conceptualizations toward a transcendent reality, one misses any corresponding doubt or tentativeness on the part of sophisticated atheists. Dawkins and Co. seem so cocksure of their position. For them, theism is not a live option or existential possibility.  This is obvious from their mocking comparisons of God to a celestial teapot, flying spaghetti monster, and the like. 

For sophisticated theists, however, atheism is a live option. The existence of this asymmetry makes one wonder whether any productive dialog with atheists is possible.

Companion post:  Russell's Teapot: Does It Hold Water?

The Hatfields and the McCoys

Whether or not it is true, the following  has a clear sense:

1. The Hatfields outnumber the McCoys.

(1) says that the number of Hatfields is strictly greater than the number of McCoys.  It obviously does not say, of each Hatfield, that he outnumbers some McCoy.  If Gomer is a Hatfield and Goober a McCoy, it is nonsense to say of Gomer that he outnumbers Goober. The Hatfields 'collectively' outnumber the McCoys. 

It therefore seems that there must be something in addition to the individual Hatfields (Gomer, Jethro, Jed, et al.) and something in addition to the individual McCoys (Goober, Phineas, Prudence, et al.) that serve as logical subjects of number predicates.  In

2. The Hatfields are 100 strong

it cannot be any individual Hatfield that is 100 strong.  This suggests that there must be some one single entity, distinct but not wholly distinct from the individual Hatfields, and having them as members, that is the logical subject or bearer of the predicate '100 strong.'

So here is a challenge to William the nominalist.  Provide analyses of (1) and (2) that make it unnecessary to posit a collective entity (whether set, mereological sum, or whatever) in addition to individual Hatfields and McCoys.

Nominalists and realists alike agree that one must not "multiply entities beyond necessity."   Entia non sunt multiplicanda praeter necessitatem!  The question, of course, hinges on what's necessary for explanatory purposes.  So the challenge for William the nominalist is to provide analyses of (1) and (2) that capture the sense of the analysanda and obviate the felt need to posit entities in addition to concrete particulars.

Now if such analyses could be provided, it would not follow that there are no 'collective entities.'  But a reason for positing them would have been removed.

On Islam and Toleration (Peter Lupu)

In his post titled A Mosque Grows near Brooklyn Bill made the following statement:

“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.”

This statement in turn provoked the following critical commentary by Prof.  Richard Hennessey:

Now I personally know a number of Muslims. I can assure you that at least one of them is very liberal, at least one of them is tolerant in attitudes and behavior, and at least one of them is not working to “undermine our way of life.” The three universal statements that I see staring out at us from the quoted paragraph are all then false, as even the most rudimentary acquaintance with old Aristotle’s logic and its “square of opposition” would have you see.

 I have no doubt that Prof. Hennessey knows at least one liberal Muslim, at least one tolerant Muslim, and at least one Muslim who is not intent on undermining the American way of life. So it seems that Prof. Hennessey conclusively refuted Bill’s statement. Did he?

 Let us distinguish between four categories of what the term ‘Muslim’ or ‘Islam’ might mean:

(a) ‘Muslim’ or ‘Islam’ might refer to a *religion* just like ‘Christianity’, ‘Judaism’, ‘Buddhism’, etc;

(Peter is of course aware that the noun 'Muslim' cannot be used to refer to the religion, Islam; his point is that 'Muslim' as an adjective in 'Muslim religion' can used to refer to the religion, Islam.)

(b) ‘Muslim’ or ‘Islam’ might refer to a *class of people* whose heritage is Islam or adopted Islam as their religion;

(c) ‘Muslim’ or ‘Islam’ might refer to *Islamism*, a radical form of Islam that declared a war on Western Culture;

(d) ‘Muslim’ or ‘Islam’ might refer to a country that has Islam as its official religion.

We are now in the position to evaluate Bill’s claim and Prof. Hennessey’s critical comments as quoted above relative to each of the above categories. Clearly, Prof. Hennessey is right when Bill’s claim is evaluated relative to category (b). But then again no one who reads Bill’s post thinks that he meant to say that every person whose heritage is Islam or adopted this religion is intolerant, anti-liberal, and intent to undermine Western Culture (See Bill’s reply in his Addendum and Corrigendum (7/22). Nevertheless, Prof. Hennessey scores one run here.

What about Bill’s statement interpreted in light of category (a)? One way of so doing is asking the following question: Does Islam as a religion promote the values of liberalism, toleration, and the Western way of life? I challenge Prof. Hennessey to answer this question. So far as I know, Islam as a religion does not promote any of these values. So at least in the eyes of this umpire Bill scores one run here. Thus far, the score is tied one to one.

When it comes to (c), the verdict is fairly clear: I doubt that anyone, including Prof. Hennessey, would challenge the notion that Islamism or Muslim Extremists abhor liberalism, toleration, and the Western way of life. So, what about (d)? Once again I think it is fairly clear that in most Muslim countries there is very little tolerance of other religions and certainly it is prohibited and dangerous to promote alternative religions. Moreover, most of the countries that have Islam as their official religion are anti-liberal and do not tolerate very well the Western way of life. At least this is so for the last ten or so years.

So it seems that Bill is right on three counts, whereas Prof. Hennessey is right on one count. Final score: three to one in favor of Bill, unless Prof. Hennessey wishes to challenge this umpire's score card. I invite him to do so.

I Need to Study Plural Predication

Here is a beautiful aphorism from Nicolás Gómez Dávila (1913-1994), in Escolios a un Texto Implicito (1977), II, 80, tr. Gilleland: 

Stupid ideas are immortal. Each new generation invents them anew.

Clearly this does not mean:

1. Each stupid idea is immortal and is invented by each new generation anew.

So we try:

2. The set of stupid ideas is immortal in the sense that every new generation invents some stupid idea or other.

(2) is much closer to the intended meaning. The idea is that there are always stupid ideas around, not that any one stupid idea is always around. (2) seems to capture this notion. But (2) presents its own puzzles. A set is a collection, and a collection is not the mere manifold of its members: it is "a further entity over and above them" as Michael Potter puts it in Set Theory and its Philosophy (Oxford 2004, p. 22).

Potter speaks of collections versus fusions. The distinction emerges starkly when we consider that there is a distinction between a singleton collection and its member, but no distinction between a 'singleton' fusion and its member. Thus Quine is distinct from {Quine}, the set consisting of Quine and nothing else. But there is no distinction between Quine and the sum or fusion, (Quine). {Quine}, unlike Quine, has a member; but neither (Quine) nor Quine have members. A second difference is that, while it makes sense to speak of a set with no members, the celebrated null set, it makes no sense to speak of a null fusion. The set consisting of nothing, the null set { } is something; the fusion of nothing is nothing.

Getting back to stupid ideas, what I want to say is that 'stupid ideas are immortal' can be understood neither along the lines of (1) nor along the lines of (2). The generality expressed is quite obviously not distributive, but it is not quite collective either. We are not expressing the idea that there is some one entity "over and above" its members to which immortality is being ascribed. 'Stupid ideas' seems to pick out a fusion; but if a fusion is a pure manifold, how can it be picked out?  

The puzzle is that immortality is not being predicated of each stupid idea, but it is also not being predicated of some one item distinct from stupid ideas which has them as members, whether this one item be a mathematical set or a mereological sum.

We know what we mean when we say that stupid ideas are immortal, but we cannot make it precise, or at least I can't make it precise given my present level of logical acumen.

So rather than contribute any stupid ideas of my own, I will go to the library and check out Thomas McKay's Plural Predication.  

 

Saturday Night at the Oldies: Carmelita, Juanita, and the Wicked Felina

Warren Zevon, Carmelita.  Linda Ronstadt's version.  Stay clear of heroin and Pioneer chicken, both.

Flying Burrito Brothers, Juanita. Lyrics:

'No  affection' were the words that stuck on my mind
When she walked out on me for the very last time.
Oh mama sweet mama can you tell me what to say?
I don't know what I've done to be treated this way.

In a cold dirty room that's where I found myself
With a bottle of wine and some pills off the shelf.
Oh mama sweet mama can you tell me what to say?
I don't know what I've done and I'm feeling so ashamed.

Then an angel appeared she was just 17
In a dirty old gown (town?) with a conscience so clean
Oh mama sweet mama can you tell me what to say?
She's brought back the life that I once threw away.

Delightfully ambiguous:  Is Juanita the girl who walked out or the one who saved him?  Or both?

Marty Robbins, El Paso.  "Cradled by two loving arms that I'll die for/One little kiss and Felina, good-bye."

The Axiom of Infinity as Easy Way Out?

I posed the question, Can one prove that there are infinite sets?  Researching this question, I consulted the text I studied when I took a course in set theory in a mathematics department quite a few years ago. The text is Karl Hrbacek and Thomas Jech, Introduction to Set Theory (Marcel Dekker, 1978). On pp. 53-54  we read:

It is useful to formulate Theorem 2.4 a little differently. We call a set A inductive if (a) 0 is an element of A; (b) if x is an element of A, then S(x) is an element of A. [The successor of a set  x is the set S(x) = x U {x}.]

In this terminology, Theorem 2. 4 is asserting that the set of natural numbers is inductive. There is only one difficulty with this reformulation: We have not yet proved that the set of all natural numbers exists. There is a good reason for it: It cannot be done, axioms adopted so far do not imply existence of infinite sets. Yet the possibility of collecting infinitely many objects into a single entity is the essence of set theory and the main reason for its usefulness in many branches of abstract mathematics.  We, therefore, extend our axiomatic system by adding to it the following axiom.

The Axiom of Infinity. An inductive set exists.

Intuitively, the set of all natural numbers is such a set.

Therefore, if we turn to the mathematicians for help in answering our question, we get the following. There are infinite (inductive) sets because we simply posit their existence! Thus their existence is not proven, but simply assumed. Philosophically, this leaves something to be desired. For it is not self-evident that there should be any infinite sets.  If there are infinite sets, then they are actually, not potentially, infinite.  (The notion of a potentially infinite mathematical set is senseless.)  And it is not self-evident that there are actual infinities.

I will be told that there is no necessity that an axiom be self-evident.  True: axiomhood does not require self-evidence.  But if an axiom is an arbitrary posit, then I am free to reject it.  Being a cantankerous philosopher, however, I demand a bit more from a decent axiom.  I suppose what I am hankering after is a compelling reason to accept the Axiom of Infinity.

A comparison with complex (imaginary) numbers occurs to me.  They are strange animals.  But however strange they are, there is a sort of argument for them in the fact that they 'work,' i.e. they find application in alternating current theory the implementation of which is in devices all around us. But can a similar argument be made for the denizens of Cantor's Paradise?  I don't know, but I have my doubts.  Nature is finite and so not countably infinite let alone uncountably infinite.  But caveat lector:  I am not a philosopher of mathematics; I merely play one in the blogosphere.  What you read here are jottings in an online notebook.  So read critically.

 

Nietzsche's Definition of 'Nihilist'

Der Wille zur Macht #585 (Kroener Ausgabe): 

Ein Nihilist ist der Mensch, welcher von der Welt, wie sie ist, urteilt, sie sollte nicht sein, und von der Welt, wie sie sein sollte, urteilt, sie existiert nicht.

A nihilist is one who judges of the world as it is, that it ought not be, and of the world as it ought to be, that it does not exist.

My translation is as beautiful as the German original.  Don't you agree?

Mel Gibson, Misplaced Moral Enthusiasm, and Real Threats

Mel Gibson is in the news again.  What I said about him on 1 August 2006 bears repeating:

What's worse: Driving while legally drunk at 87 miles per hour in a 45 mph zone, or making stupid anti-Semitic remarks? The former, obviously. And yet a big stink is being made about  Gibson's drunken rant. I call this misplaced moral enthusiasm.

Calling a Jew a bad name won't kill him, but running him over in your speeding 2006 Lexus LS 430 will. On the one hand, offensive words that no reasonable person could take seriously; on the other hand, a deed that could get people killed.

Here is what Gibson said: "The Jews are responsible for all the wars in the world," and, addressing the arresting officer, "Are you a Jew?" Now compare Gibson with Iran's Mahmoud Ahmadinejad who repeatedly has called for the destruction of the State of Israel. Ahmadinejad's is speech that incites unspeakable violence, unlike Gibson's drunken rant which is no threat to anyone. So let's forget about Gibson, and concentrate on real threats.

Necessitas Consequentiae versus Necessitas Consequentiis

Take the sentence, 'If I will die tomorrow, then I will die tomorrow.' This has the form If p, then p, where 'p' is a placeholder for a proposition. Any sentence of this form is not just true, but logically true, i.e., true in virtue of its logical form. Now every sentence true in virtue of its logical form is necessarily true. (The converse, however, does not hold: there are necessary truths that are not logically true.) Thus we can write, 'Necessarily(if p, then p)'  or

1. Nec (p -->p).

The parentheses show that the necessity attaches to the consequence, represented by the arrow, and not to the consequent, represented by the terminal 'p.' (When speaking of conditionals, logicians distinguish the antecedent from the consequent, or, trading Latin for Greek, the protasis from the apodosis.) Thus the above is an example of the necessitas consequentiae. This, however, must not be confused with the necessitas consequentiis, which is exemplified by

2. p-->Nec p.

In (2) the necessity attaches to the consequent. It should be obvious that (1) does not entail (2), equivalently, that (2) does not follow from (1). For example, although it is necessarily true that if I will die tomorrow, then I will die tomorrow, it does not follow, nor is it true, that if I will die tomorrow, then necessarily I will die tomorrow. Proving fatalism cannot be that easy. For even if I do die tomorrow, that will be at best a contingent occurrence, not something logically necessitated. (Think about it.)

To confuse (1) and (2) is to confuse the necessity of the consequence with the necessity of the consequent. This is an example of what logicians call a fallacy, i.e., a typical error in reasoning, and in particular a modal fallacy in that it deals with the (alethically) modal concepts of necessity and possibility and their cognates.

Class dismissed.

Can Federalism Save Us?

I fear that we are coming apart as a nation.   We are disagreeing about things we ought not be disagreeing about, such as the need to secure the borders.  The rifts are deep and nasty.  Polarization and demonization of the opponent are the order of the day.   Do you want more of this?  Then give government more say in your life.  The bigger the government, the more to fight over.  Do you want less?  Then support limited government and federalism.  A return to federalism may be a way to ease the tensions, not that I am sanguine about any solution. 

Federalism, roughly, is (i) a form of political organization in which governmental power is divided among a central government and various constituent governing entities such as states, counties, and cities; (ii) subject to the proviso that both the central and the constituent governments retain their separate identities and assigned duties. A government that is not a federation would allow for the central government to create and reorganize constituent governments at will and meddle in their affairs.  Federalism is implied by the Tenth Amendment to the U.S. Constitution: "The powers not delegated to the United States by the Constitution, nor prohibited to it by the States, are reserved to the States respectively, or to the people." 

Federalism would make for less contention, because people who support high taxes and liberal schemes could head for states like Massachusetts or California, while the  conservatively inclined who support gun rights and capital punishment could gravitate toward states like Texas. 

The fact of the matter is that we do not agree on a large number of divisive, passion-inspiring issues (abortion, gun rights, capital punishment, affirmative action, legal and illegal immigration, taxation, wealth redistribution, the purposes and limits, if any, of governmental power  . . .) and we will never agree on them.  These are not merely 'academic' issues since they directly affect the lives and livelihoods and liberties of people.  And they are not easily resolved because they are deeply rooted  in fundamental worldview differences.  When you violate a man's liberty, or mock his moral sense, or threaten to destroy his way of life, you are spoiling for a fight and you will get it.

Worldview differences in turn reflect differences  in values.  Now values are not like tastes.  Tastes cannot be reasonably discussed and disputed  while values can.  (De gustibus non est disputandum.) But value differences, though they can be fruitfully discussed,  cannot be objectively resolved because any attempted resolution will end up relying on higher-order value judgments.  There is no exit from the axiological circle.  We can articulate and defend our values and clarify our value differences.  What we cannot do is resolve our value differences to the satisfaction of all sincere, intelligent, and informed discussants. 

Consider religion.  Is it a value or not?  Conservatives, even those who are atheistic and irreligious, tend to view religion as a value, as conducive to human flourishing.  Liberals and leftists tend to view it as a disvalue, as something that impedes human flourishing.  The question is not whether religion, or rather some particular religion, is true.  Nor is  the question whether religion, or some particular religion, is rationally defensible.  The question is whether the teaching and learning and practice of a religion contributes to our well-being, not just as individuals, but in our relations with others.  For example,  would we be better off as a society if every vestige of religion were removed from the public square?  Does Bible study tend to make us better people?

For a conservative like Dennis Prager, the answer to both questions is obvious.  As I recall, he gives an example something like the following.  You are walking down the street in a bad part of town.  On one side of the street  people are leaving a Bible study class.  On the other side, a bunch of  Hells [sic] Angels are coming out of the PussyCat Lounge.  Which side of the street do you want to be on?  For a conservative the answer is obvious.  People who study the Bible with its Ten Commandments, etc. are less likely to mug or injure you than drunken bikers who have been getting in touch with their inner demons  for the last three hours.  But of course this little thought experiment won't cut any ice with a dedicated leftist.

I won't spell out the leftist response.  I will say only that you will enter a morass of consideration and counter-consideration that cannot be objectively adjudicated.

My thesis is that there can be no objective resolution, satisfactory to every sincere, intelligent, and well-informed discussant, of the question of the value of religion.  And this is a special case of a general thesis about the objective insolubility of value questions with respect to the  issues that most concern us.

Another  sort of value difference concerns not what we count as values, but how we weight  or prioritize them.  Presumably both conservatives and liberals value both liberty and security.  But they will differ bitterly over which trumps the other and in what circumstances.  Here too it is naive to  expect an objective resolution of the issue satisfactory to all participants, even those who meet the most stringent standards of moral probity, intellectual acuity, knowledgeability with respect to relevant empirical issues, etc.

Liberal and conservative, when locked in polemic, like to call each other stupid.  But of course intelligence or the lack thereof has nothing to do with the intractability of the debates.  The intractability is rooted in value differences about which consensus is impossible.  On the abortion question, for example, there is no empirical evidence that can resolve the dispute.  Empirical data from biology and other sciences are of course relevant to the correct formulation of the problem, but contribute nothing to its resolution.  Nor can reason whose organon  is logic resolve the dispute.  You would have to be as naive as Ayn Rand to think that Reason dictates a solution.

Recognizing these facts, we must ask ourselves: How can we keep from tearing each other apart literally or figuratively?  Guns, God, abortion, illegal immigration -- these are issues that get the blood up.  I am floating the suggestion that federalism and severe limitations on the reach of the central government are what we need to lessen tensions. 

Example:  Suppose Roe v. Wade is overturned and the question of the legality of abortion is returned to the states.  Some states will make it legal, others illegal.  This would be a modest step in the direction of mitigating the tensions between the warring camps.  If abortion is a question for the states, then no federal monies could be allocated to the support of abortion.  People who want to live in abortion states can move there; people who don't can move to states in which abortion is illegal. Each can live with their own kind and avoid having their values and sensibilities disrespected.

I understand that my proposal will not be acceptable to either liberals or conservatives.  Both want to use the power of the central government to enforce what they consider right.  Both sides are convinced that they are right.  But of course they cannot both be right.  So how do they propose to heal the splits in the body politic?

Will Liberals Ever Retire the Race Card?

Why should they?  As good leftists, they believe the end justifies the means, and their shameless race-baiting is a means conducive to their ends.  It works.  That's why they do it.  They must at some level have an inkling of what vile people they are to employ such a  shabby tactic, but whatever sense of moral decency is left in them is quickly smothered by their lust to win at all costs.

And it is indeed a well-rehearsed tactic which amounts to collusion on the part of liberal-left journalists and others to smear conservatives.  This from the Christian Science Monitor:

When conservatives were criticizing Mr. Obama for his connection to the Rev. Jeremiah Wright in 2008, some JournoList members discussed a counterstrategy.

The Daily Caller writes that Spencer Ackerman, then of the Washington Independent, "urged his colleagues to deflect attention from Obama's relationship with Wright by changing the subject. Pick one of Obama's conservative critics, Mr. Ackerman wrote, 'Fred Barnes, Karl Rove, who cares – and call them racists.' "

See also Thomas Sowell's Race Card Fraud.  Excerpt:

The latest attack on the Tea Party movement, by Ben Jealous of the NAACP, has once again played the race card. Like the proverbial lawyer who knows his case is weak, he shouts louder.

This is not the first time that an organization with an honorable and historic mission has eventually degenerated into a tawdry racket. But that an organization like the NAACP, after years of fighting against genuine racism, should now be playing the game of race card fraud is especially painful to see.

You should also read the posts in my Race category. There is plenty of documentation there of the race-baiting and scumbaggery which are the now the marks of contemporary Democrats, liberals, and leftists.

And you should do your bit to push back.  The next time some scumbag of a liberal calls you a racist for standing up for fiscal responsibility or the rule of law, say this:  You lie about us, we'll tell the truth about you.

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.

The Christian Delusion

According to Michael Martin, The Christian Delusion "completely destroys Christianity."  The folks at Triablogue are not impressed.

Stephen Braude on the Gold Leaf Lady

Fascinating.  Stephen Braude is a very good philosopher who writes on the paranormal.  I am currently reading, and recommend, his Immortal Remains.  He evinces the right blend of skepticism and openmindedness.  Here is his website.

Another Strange Tale of the Superstitions

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.

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 . . .

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.

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.

 

Come to the USA

Here.

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 Trouble With Larry

I share Steve Burton's misgivings about the work of Lawrence Auster.  We need a broad coalition to defeat leftists and Islamists.  A certain amount of intramural squabbling  is to be expected and may even be healthy, but not if it ramps up to internecine warfare.

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.)

Thinker and Doer

The thinker, because he is a thinker, cannot naively live his life of thought, but must be tormented by doubts regarding it.  The doer, because he is not a thinker, can naively live his life of action.

The Vital Imperative: Live Well, Live Now

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?

Freud or James? Wish-Fulfillment or Inducement to Strenuous Living?

Sigmund Freud (1856-1939), The Future of an Illusion:

It would indeed be very nice if there were a God, who was both creator of the world and a benevolent providence, if there were a moral world order and a future life. But at the same time it is
very odd that this is all just as we should wish it for ourselves.

William James (1842-1910), "The Moral Philosopher and the Moral Life":

The capacity of the strenuous mood lies so deep down among our natural human possibilities that even if there were no metaphysical or traditional grounds for believing in a God, men would postulate one simply as a pretext for living hard, and getting out of the game of existence its keenest possibilities of zest.

Both of these passages support the view that God is a posit, a postulate, a projection. But there is a striking difference. Freud, seeing the origin of the God-projection in weakness, takes this as
discrediting the God-idea. Having its genesis in our neediness, the God-idea is false or at least unworthy of belief. James, however, viewing the God-idea as an expression of our robustness, takes this fact as a verification of the idea of God.

Of course, there are two different notions of truth in play. I don't know whether Freud ever discussed theories of truth, but I'd guess he is a correspondence-theorist: an idea is true if it corresponds to reality. But James is a pragmatist: an idea is true if it works, if it is something good for us to believe in the long run. For James, we get more out of the game of existence when we believe in God and all that entails: a moral world order that places an ethical demand on us; an ultimate explanation of why anything exists and why we exist; a final guarantor of the veridicality of our ideas; a provider of sense and purpose; a repository of hope; a securer of immortality and adjustor of happiness and virtue.  Believing in God, we live better, richer, fuller lives; we wring from existence its  "keenest possibilities of zest."

To resolve the debate between Freud and James one would have to get clear about the nature of truth and its connection to human flourishing. The problems are deep and perhaps insoluble. But that doesn't stop them from being fascinating and worth pursuing. And we don't know they are insoluble. If we believe that they are soluble, that truth about ultimates is attainable, and we strive for it, then too we will wring from "the game of existence its keenest possibilities of zest."

Companion post:  Freud on Illusion, Delusion, Error, and Religion

The Losertarian Party

Politics is a practical business: it is about the gaining and maintaining of power for the purpose of implementing programs and policies that one believes to be beneficial, and for opposing those whose policies one believes to be deleterious. As the Converse Clausewitz Principle has it, it is war conducted by other means.  For this very reason, I stay clear of it except for voting and blogging: I am by inclination and aptitude a theoretician, a "spectator of all time and existence" to borrow a marvellous phrase from the  Plato's Republic. But part of the theoretician's task is to understand the political. And if I understand it, I understand that the Libertarian Party, though it might be a nice debating society, is a waste of time practically speaking. That's why I approve of and borrow Michael Medved's moniker, 'Losertarian Party.' These adolescents will never get power, so what's the point? It's a party of computer geeks, sci-fi freaks, and adolescents of all ages, the sort that never outgrow Ayn Rand.  Open borders, legal dope, ACLU-type extremism about freedom of expression.  Out of the mainstream and rightly so.

So Ron Paul made a smart move when he joined the Republicans, and his son Rand seems more conservative than libertarian. 

As I said, politics is a practical business. It's about winning, not talking. It's not about ideological purity or having the supposedly best ideas; it's about gaining the power to implement good ideas.  The practical politician understands that quite often  Le mieux est l'ennemi du bien, the best is the enemy of the good.

A Day on the Salt River

Mike Valle and I spent four and a half hours floating down the Rio Salado on truck tire inner tubes yesterday.  That's Mike and a bit of my left knee in the first shot.  The second depicts some thirsty wild horses.  The third offers a fine view of Red Mountain.

What is Philosophy?

I found the following on Keith's blog.  It is so good I simply must reproduce it here.

The nearest thing to a safe definition of the word "philosophy", if we wish to include all that has been and will be correctly so called, is that it means the activity of Plato in his dialogues and every activity that has arisen or will arise out of that.

(Richard Robinson, "Is Psychical Research Relevant to Philosophy?" The Aristotelian Society, supplementary volume 24 [1950]: 189-206, at 192.)

This is in line with my masthead motto which alludes to the famous observation of Alfred North Whitehead:

The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato.  I do not mean the systematic scheme of thought which scholars have doubtfully extracted from his writings.  I allude to the wealth of general ideas scattered through them.  [. . .] Thus in one sense by stating my belief that the train of thought in these lectures is Platonic, I am doing no more than expressing the hope that it falls within the European tradition. (Process and Reality, Corrected Edition, The Free Press, 1978, p. 39)

John Pepples Wants a New Left

During our lazy float down the Rio Salado today, Mike Valle and I had a lot to talk about. He mentioned a new blog he had come across entitled I Want a New Left. The author, John Pepples, aims to develop a self-critical leftism.  Now, having read quickly through most of his posts, I am a bit puzzled by the same thing that puzzles Mike:  why does Pepples hang on to the 'leftism' label?

But labels aren't that important.  What is important are the issues and one's stances on them. On that score, conservatives like me and Mike share common ground with Pepples.  In his biographical statement he says that in college he majored in mathematics and took a lot of physics courses. "But this was during the late 60s and early 70s, when much questioning was occurring, and I ended up as a grad student in philosophy."  Sounds very familiar!  The 'sixties were a heady time, a time of ferment, during which indeed "much questioning was occurring."  I started out in Electrical Engineering but also "ended up as a grad student in philosophy."  I did, however, have a bit more luck career-wise and didn't experience the same difficulties getting into print.

Why did so many of us 60s types end up in philosophy?  Because we were lost in a strange land, traditional understandings and forms of world-orientation having left us without guidance, and we needed to ascend to a vantage point to reconnoiter the terrain, the vantage point that philosophy alone provides.

Political change, a species of the genus doxastic change, is a fascinating topic.  I recently stumbled upon an effort by a distaff blogger who documents her transition from a comfortable enclave of mutually reinforcing Democrats to the more open world of contemporary conservatism, and the hostility with which her turncoat behavior was rewarded.  She calls her blog Neo-Neocon.

Fruitful Conversation

E. M. Cioran, Drawn and Quartered, p. 163:

Conversation is fruitful only between minds given to consolidating their perplexities.

A brilliant aphorism. Philosophy, as Plato remarks (Theaetetus 155) and Aristotle repeats (Metaphysics 982b10),  has its origin in wonder or perplexity.  Fruitful philosophical conversation, rare as it is and must be given the state of humanity, is therefore a consolidation and appreciation of problems and aporiai, much more than an attempt to convince one's interlocutor of something. Herein lies a key difference between philosophy and ideology.

NASA Then and Now

In the '60s, under the leadership of JFK, NASA put a man on the moon.  Forty years later, under the 'leadership' of BHO, 'NASA' has become an acronym for

Nurturing Arab Self Awareness.  (From an e-mailer to the O'Reilly Factor)  Image found here.

On second thought, the e-mailer's suggestion can be improved upon:  Nurturing Arab Self Acceptance.

As for the cartoon below, I needn't point out to my astute readership that the Arabs did not invent mathematics.

From the Mailbag: Faith and Modality

An astute reader e-mails, 

First, sometime ago I recommended John Bishop's Believing by Faith: An Essay in the Epistemology

and  Ethics of Religious Belief . If you have yet to read the book, I would recommend his new article

on Faith in the Stanford Encyclopedia of Philosophy. You may be particularly interested in

sections 7-10.

 

Second, I do not know a great deal about possible worlds semantics, and am taking a great risk of embarrassing myself in questioning your  argument that "Necessarily, something exists" - but I think

that I will take a stab at it!

 

I am assuming that "Necessarily something exists" = "In at least one possible world, at least one

thing exists." Is this correct?

 

No.  The first sentence is equivalent to 'In every possible world, at least one thing exists.'  In other words, there is no possible world that is empty: every world has at least one item in it.  But this is consistent with there being no one item that exists in every possible world.  Suppose every being is contingent, where a contingent being is one that exists in some but not all possible worlds.  Then there would be no one being that exists in all worlds, and 'Necessarily something exists' would be made true by the fact that each world has something or other in it.  But if there is a necessary being (defined as a being that exists in all worlds), then of course the sentence in question is also true.

 

1. Does not your argument depend upon the assumption of 'modal realism' - that all possible worlds

actually exist, a highly questionable assumption?

 

No, because I am using the 'possible worlds' language only as a façon de parler, a graphic and intuitive way of representing modal relationships which I find helpful.  (Unfortunately, most of my readers are completely 'thrown' by it!) In other words, I could have stated the argument without mentioning possible worlds.  Here is a partial schedule of intertranslation, where 'world' is short for 'broadly logically possible world':

 

X is a necessary being =df X exists in all worlds

X is a contingent being =df X exists in some but not all  worlds

X is an impossible being =df X exists in no world

X is an actual being =df X exists in the actual world

(Note that if x is contingent, it doesn't follow that x is actual, nor conversely)

X is a possible being =df X exists in some world

X is essentially F =df X instantiates F-ness in every world in which X exists.

X is accidentally F =df X instantiates F-ness in some but not all worlds in which X exists

X is necessarily F =df X instantiates F-ness in every world in which X exists, and X exists in every world.

(Example: God is necessarily, not just essentially, omnipotent.)

Proposition p is necessarily true =df p is true in all worlds

P is contingently true =df p is true in some but not all worlds

And so on.

 

Now isn't that neat? The modal notions are explicated in terms of the familiar quantifiers of predicate logic.  The schema facilitates modal reasoning.  For example, if x is necessary, does it follow that x is possible?  Yes, because if x exists in all worlds, then it exists in some worlds. If x is possible, does it follow that x is contingent?  No, because if x exists in some worlds, that leaves it open that it exists in all worlds.  If x is noncontingent, does it follow that x is necessary?  No, because if it is not the case that x exists in some but not all worlds, it does not follow that x exists in all worlds:  x might exist in no world.

 

You characterize modal  realism  as the doctrine that "all possible worlds actually exist."  No philosopher maintains that every world is absolutely actual.  There is only one possible world that is absolutely actual: all the rest are merely possible.  Now there is a philosopher, David K. Lewis, who maintains that there is a plurality of worlds, all on an ontological par, and thus all equally real; but he denies that there is such a property as absolute actuality.  For him each world is actual at itself, but no world is actual simpliciter or absolutely.  I reject Lewis's view which could be called extreme modal realism.  Almost everyone rejects it.  Lewis's idea, which is both brilliant and crazy at the same time, is that modality can be reduced to purely extensional terms via definitions like the ones I gave above.  But few follow him in that.  The above definitions do not allow one to eliminate modality by quantifying over worlds, because the worlds in question are possible, and 'possible' is a modal term.

 

So, to answer what I take to be your question, my argument does not presuppose extreme modal realism.  In fact, it does not require that we take any stand at all on what exactly possible worlds are.  But I do presuppose realism to this extent:  I asssume that modality is not merely epistemic. Thus the possibility that I be sleeping now instead of blogging is a 'real possibility' in that it is subsists independently of what I or anyone know or believe.  It is not possible merely in the epistemic sense of 'possible for all I know,' but possible independently of what I know.

 

2. Does not your use of 'exists' in premises 4 and 5 treat it as, or assume that it can be used as,  a

'real predicate'  rather than merely a 'grammatical predicate' (B. Russell) - again a questionable if

not false assumption?

 

I discuss this is various articles and in my 2002 book A Paradigm Theory of Existence.  I argue, among other things, that Russell's theory of existence, which is closely related to Frege's, is a complete nonstarter, wrong from the ground up.  There is something on Russell's theory in Paul Edwards' Heidegger's Confusions: A Two-Fold Ripoff. 

 

In 'possible worlds' lingo, we say things like this:  There are possible worlds in which Socrates exists but is not the teacher of Plato. Now of course those worlds are all merely possible because we know (or reasonably believe) that in the actual world Socrates is the teacher of Plato.  So what does it mean to say that Socrates exists in those worlds?  Let W be a merely possible world.  To say that x exists in W is to say that, had W been actual, x would have existed.  A merely possible world in which Socrates is not the teacher of Plato is a world which is such that, had it been actual, then Socrates would have existed without being the teacher of Plato.

 

My correspondent continues with several more questions/objections which I don't understand.  In any case the above gives us plenty to discuss.

Kerouaciana

A page of links of interest to the Kerouac aficionado.  And if you haven't seen Bill Buckley's Kerouac interview, here it is, featuring a drunken Kerouac with interspersed commentary by Burroughs, Ginsberg, Steve Allen, Gregory Corso, and John Clellon Holmes.

The 'Stickiness' Metric

'Stickiness' is a measure of the average length of time a reader remains at a website.  Personally, I am more impressed by the 'stickiness' of a site than its raw traffic (measured in unique visitors and page views).  Here at TaxProf Blog is  a ranking of the 'stickiest' law prof blogs.  (Via Legal Insurrection.) Ladder Man will no doubt gnash his teeth over the fact that Volokh Conspiracy is in the number one slot handily beating out his two blogs.  It comes as no surprise that Instapundit is first in traffic but last in 'stickiness.' 

Why is Ladder Man so-called?  Because he is a status-obsessed careerist, a  social climber, given  to ranking things.  You won't find much by way of content at his academic gossip site. 

A Cantorian Argument Why Possible Worlds Cannot be Maximally Consistent Sets of Propositions

A commenter in the 'Nothing' thread spoke of possible worlds as sets.  What follows is a reposting from 1 March 2009 which opposes that notion.

................

In a recent comment, Peter Lupu bids us construe possible worlds as maximally consistent sets of propositions.  If this is right, then the actual world, which is of course one of the possible worlds,  is the maximally consistent set of true propositions.  But Cantor's Theorem implies that there cannot be a set of all true propositions. Therefore, Cantor's theorem implies that possible worlds cannot be maximally consistent sets of propositions.

1. Cantor's Theorem states that for any set S, the cardinality of the power set P(S) of S > the cardinality of S. The power set of a set S is the set whose elements (members) are all of S's subsets. Recall the difference between a member and a subset. The set {Socrates, Plato} has exactly two elements, neither of which is a set. Since neither is a set, neither is a subset of this or any set. {Socrates, Plato} has four subsets: the set itself, the null set, {Socrates}, {Plato}. Note that none of the four sets just listed are elements of {Socrates, Plato}. The power set of {Socrates, Plato}, then, is {{Socrates, Plato}, { }, {Socrates}, {Plato}}.

In general, if a set S has n members, then P(S) has 2ⁿ members. Hence the name power set. Cantor's Theorem that the power set of a set S is always strictly larger that S is easily proven. But the proof needn't concern us.  It is available in any standard book on set theory.

2. Suppose there is a set T of all truths, {t₁, . . . , t_i, t_{i + 1}, . . .}. Consider the power set P(T) of T. The truth t₁ in T will be a member of some of T's subsets but not of others. Thus, t₁ is an element of {t₁, t₂}, but is not an element of { }. In general, for each subset s in the power set P(T) there will be a truth of the form t₁ belongs to s or t₁ does not belong to s. But according to Cantor's Theorem, the power set of T is strictly larger than T. So there will be more of those truths than there are truths in T. It follows that T cannot be the set of all truths.

3. Given that there cannot be a set of all truths, the actual world cannot be the set of all truths.  This implies that possible worlds cannot be maximally consistent sets of propositions.   I learned the Cantorian argument that there  is no set of all truths from Patrick Grim. I don't know whether he applies it to the question whether worlds are sets.

4. As far as I can see, the fact that possible worlds cannot be maximally consistent sets does not prevent them from from being maximally consistent conjunctive propositions.

A commenter in the 'Nothing' thread spoke of possible worlds as sets.  What follows is a reposting from 1 March 2009 which opposes that notion.

................

In a recent comment, Peter Lupu bids us construe possible worlds as maximally consistent sets of propositions.  If this is right, then the actual world, which is of course one of the possible worlds,  is the maximally consistent set of true propositions.  But Cantor's Theorem implies that there cannot be a set of all true propositions. Therefore, Cantor's theorem implies that possible worlds cannot be maximally consistent sets of propositions.

1. Cantor's Theorem states that for any set S, the cardinality of the power set P(S) of S > the cardinality of S. The power set of a set S is the set whose elements (members) are all of S's subsets. Recall the difference between a member and a subset. The set {Socrates, Plato} has exactly two elements, neither of which is a set. Since neither is a set, neither is a subset of this or any set. {Socrates, Plato} has four subsets: the set itself, the null set, {Socrates}, {Plato}. Note that none of the four sets just listed are elements of {Socrates, Plato}. The power set of {Socrates, Plato}, then, is {{Socrates, Plato}, { }, {Socrates}, {Plato}}.

In general, if a set S has n members, then P(S) has 2ⁿ members. Hence the name power set. Cantor's Theorem that the power set of a set S is always strictly larger that S is easily proven. But the proof needn't concern us.  It is available in any standard book on set theory.

2. Suppose there is a set T of all truths, {t₁, . . . , t_i, t_{i + 1}, . . .}. Consider the power set P(T) of T. The truth t₁ in T will be a member of some of T's subsets but not of others. Thus, t₁ is an element of {t₁, t₂}, but is not an element of { }. In general, for each subset s in the power set P(T) there will be a truth of the form t₁ belongs to s or t₁ does not belong to s. But according to Cantor's Theorem, the power set of T is strictly larger than T. So there will be more of those truths than there are truths in T. It follows that T cannot be the set of all truths.

3. Given that there cannot be a set of all truths, the actual world cannot be the set of all truths.  This implies that possible worlds cannot be maximally consistent sets of propositions.   I learned the Cantorian argument that there  is no set of all truths from Patrick Grim. I don't know whether he applies it to the question whether worlds are sets.

4. As far as I can see, the fact that possible worlds cannot be maximally consistent sets does not prevent them from from being maximally consistent conjunctive propositions.

Is Rhode Island in Violation of the Supremacy Clause?

Rhode Island is already doing what Arizona is fixin' to do come the end of this month. As William A. Jacobson, Associate Clinical Professor of Law, Cornell Law School,  reports over at Legal Insurrection, ". . . Rhode Island already has implemented the critical piece of the Arizona law [S.B. 1070], checking the immigration status of people stopped for traffic violations where there is a reasonable suspicion, and reporting all illegals to federal authorities for deportation."

Will Eric Holder and colleagues at the DOJ be going after Rhode Island?  If not, why not?  I'm not legally trained, but isn't there supposed to be something wrong with selective enforcement? Isn't there something objectionable about suing Arizona for a violation of the Supremacy Clause of the U. S. Constitution while turning a blind eye to Rhode Island, not to mention those sanctuary cities such as Los Angeles which are, because of their sanctuary laws, really in violation of the Clause in question?

One gets the impression that the reasons adduced in the complaint are just a smokescreen to hide venal and  'political' motives.  A need to curry favor with Hispanics in order to stay in office?  A desire to flood the country with potential Democrats so as to secure a permanent victory for the Left?

Actually, the latter is what this is all about to anyone astute enough to penetrate the thick veil of liberal-left mendacity.  Obama and the boys have no desire to control the border or solve the problem of illegal immigration. This is why they mouth and hide behind the vacuous phrase 'comprehensive immigation reform.'  Like 'change,' it means nothing definite.  To them, that is a virtue allowing as it does for maximal obfuscation.

Gallup Poll: Americans Oppose Federal Suit Against AZ Immigration Law

Here.  The notion that the Obama Justice Department would waste millions suing  a state for passing a law that mirrors the content of a Federal law is absurd on the face of it, especially when the same Justice Department turns a blind eye to sanctuary laws which actually do violate the Supremacy Clause; but also from a purely political standpoint the suit is idotic harming as it does the Dems' chances in the November elections and beyond.

By the way, did you see Sarah Palin on The O'Reilly Factor tonight?  Mr. Bill did a good job grilling her and exposing the shallowness of her thinking about illegal immigration. She has obviously given little thought to the problem of the 12 or so million illegals already in the country, many of whom stay out of trouble, have jobs, and have children who are U. S. citizens.

Terry Goddard

He is the Arizona Attorney General.  I just watched Greta van Susteren ask him repeatedly whether the DOJ should drop the inane lawsuit against the state of Arizona anent S. B. 1070, and he would not answer the question.  What a weasel! Of course, he's a Dem.  Perhaps the weasel should replace the jackass as the emblem of that sorry party.