The Underground Grammarian

If you think that I am a language Nazi, then pay a visit to the Underground Grammarian. His stern visage reminds me of a passage near the beginning of Franz Kafka's Vor dem Gesetz, "Before the Law." The protagonist seeks entry into the Law, but at the door stands a guard who warns:

     Ich bin maechtig. Und ich bin nur der unterste Tuerhueter. Von Saal
     zu Saal stehn aber Tuerhueter, einer maechtiger als der andere.
     Schon den Anblick des dritten kann nicht einmal ich ertrage.

     I am powerful. And I am but the least of the gatekeepers. From room
     to room there are gatekeepers each stronger than the next. Not even
     I can bear so much as the glance of the third. (tr. BV)

Closure: Some Mathematical and Philosophical Examples

A reader asks, "What is meant by 'closure' or 'closed under'? I've heard the terms used in epistemic contexts,  but I've not been able to completely understand them."

Let's start with some mathematical   examples. The natural numbers are closed under the operation of addition. This means that the result of adding any two natural numbers is a natural number. What is a natural number? On one understanding of the term, the naturals are the positive integers, the counting numbers, the members of the set {1, 2, 3, 4, 5, . . .}. On a second understanding, the naturals are the positive integers and zero: {0, 1,  2, 3, 4 . . .}. Either way, it is easy to see that adding any two   elements of either set yields an element of the same set. It is also easy to see that the naturals are also closed under multiplication. But they are not closed under subtraction. If you subtract 9 from 7,   the result (-2) is not an element of the set of natural numbers.

Now consider the squaring operation. The square of any real number is a real number. So the reals are closed under the operation of squaring. But the reals are not closed under the square root operation. The square root of -4 cannot be 2 since 2 squared is 4; it cannot be -2 either since -2 squared is 4. The square root of -2 is the complex number 2i where the imaginary number i is the square root of -1. The square  roots of negative numbers are complex; hence, the reals are not closed under the square root operation.

Generalizing, we can say that a set S is closed under a binary operation O just in case, for any elements x and y in S, xOy is an element of S. In Group Theory, a set S together with an operation O  constitutes a group only if S is closed under O.

Now for some philosophical examples. Meinongian objects (M-objects) are not closed under entailment. The M-object, the yellow brick road, although yellow is not colored even though in reality nothing can be yellow without being colored. M-objects are incomplete objects. They have all and only the properties specified in their descriptions.  So we say that the properties of M-objects are not closed under property-entailment. Property P entails property Q iff necessarily, if   anything x has P, then x has Q.

What goes for M-objects goes for intentional objects. (On my reading of Meinong, an M-object is not the same as an intentional object: there are M-objects that are not the accusatives of any actual
intending.) Suppose I am gazing out my window at the purple majesty of Superstition Mountain. The intentional object of my perception has the property of being purple, but not the properties of being colored or being extended even though in reality nothing can be purple without being both colored and extended. Phenomenologically, what is before my mind is an instance of purple, but not an instance of colored item. What I see I see as purple but not as colored.

Now consider: If S knows that p, and S knows that p entails q, then S also knows that q. If you acquiesce in the bolded thesis, then you acquiesce in the closure of 'knows' under known entailment. For what you are then committing yourself to is the proposition that a proposition q entailed by a proposition p you know — assuming you know that p entails q — is a member of the set of propositions you  know.

Federalism

My plea for federalism is contained in Can Federalism Save Us?  And so I am pleased to point my readers to Jonah Goldeberg's The Federalist Solution.

Mitt Romney mentioned federalism in a recent speech but he didn't pause to explain what it means.  That was a mistake.  Joe Sixpack has no idea what federalism is.  He probably thinks it means that more power should be handed over to the federal government. It wouldn't have killed Romney to take 30 seconds and provide a crisp definition. 

The same goes for such terms as 'social justice.'  They do not wear their meanings on their faces.  Pols and commentators need to learn the importance of defining one's terms.  Launching into a discussion of socialism, for example, without preliminary clarification of what it is is foolish and unproductive.

But be pithy! Joe Sixpack is a tweeting twit whose attention span is commensurate with the length of his 'tweets.'  Do not these tweeting twits fear that their brains will soon be fit only to  flit?

Of Cranks and Crackpots

London Ed quotes neurologist Steven Novella who makes an insightful observation in Cranks and Physics (the whole of which is well worth reading):

… cranks around the world have been able to form their own “alternative” community, publish their own journals, and have their own meetings. There is just one requirement in this alternative community – acceptance. All ideas are accepted (there is no chaff, all is wheat), that is except for one. Whatever is accepted by mainstream science is wrong [my emphasis]. That is “the one ring” of crank mythology, that brings all crank theories together and in the darkness of their community binds them together. Otherwise they are largely mutually incompatible. Each crank’s “theory of everything” is a notion unto itself, and is mutually exclusive to every other crank’s own theory of everything (unless there is some incidental overlap). So they get together, present their theories without criticism, and all agree that the evil conspiracy of mainstream science must be taken down. Of course, if any of them got their way and their ideas became accepted, they would instantly become rejected by the rest of the crank community as mainstream physics.

Ed comments:

Correct. My enemy's enemy is my friend, whatever my enemy believes. I have seen this effect in Wikipedia a number of times. Cranks unite to defeat the mainstream, orthodox view. Orthodox editors get blocked or banned. Cranks then war with each other, and get banned themselves. The orthodox editors mount appeals to the powers that be – the arbitration committee, none of whom have any expert credentials as far as I can see, and get unbanned. Or they just open 'sockpuppet' accounts and start editing again under a different name. So do the cranks, and the whole nightmare begins again. Another difficulty that Novella omits is 'mainstream' crankery. That is, bad science or quackery that unites its practitioners by financial interest. Homeopathy and 'Neurolinguistic programming' are good examples of this.

This would not matter at all, if Wikipedia were not increasingly used as a 'reliable source' by students, and even some medical researchers, as I noted in an earlier post.

Philosophy, Superman, and Richard C. Potter

I was pleased to hear from Patrick Kurp of Anecdotal Evidence this morning.  He inquired:

About four or five years ago you wrote about an American writer and thinker, perhaps an academic philosopher, who published, I believe, two books and seemed to disappear. You had difficulty finding information about him online. I believe you said he had an interest in East Asian thought. His “career” was eccentric by conventional standards and he seemed to be something of a loner.

Then I remembered a post of mine which begins:

This post examines Richard C. Potter's solution to the problem of reconciling creatio ex nihilo with ex nihilo nihil fit in his valuable article, "How To Create a Physical Universe Ex Nihilo," Faith and Philosophy, vol. 3, no. 1, (January 1986), pp. 16-26. (Potter appears to have dropped out of sight, philosophically speaking, so if anyone knows what became of him, please let me know. The Philosopher's Index shows only three articles by him, the last of which appeared in 1986.)

I don't know whether Potter is the man Kurp had in mind, but the former does satisfy part of Kurp's description.  In any event, the Richard Potter story is an interesting one. 

I recall talking to him, briefly, in the summer of 1981 at Brown University.  I was a participant in Roderick Chisholm's National Endowment for the Humanities  Summer Seminar, and Potter, who I believe had recently completed his Ph.D. at Brown, sat in on a few sessions.  My impression was he that he was unable to secure a teaching position.  I also recall a slightly derogatory comment I made about the Midwest and  how one might have to go there to find employment.  Potter's mild-mannered reply was to the effect that he preferred the Midwest over other geographical regions.  His name stuck in my mind probably because of a paper on the paradox of  analysis he co-authored with Chisholm and because of  the F & P article mentioned above.  See here.  But then he dropped out of  philosophical sight.

A few years back, I did a search and he turned up again as a George Reeves and Superman aficionado.  So here is part of the rest of the Potter story.  Here  is Potter's George Reeves site.

A checkered career, his.

I too enjoyed the Superman series while growing up in the '50s.   Some thoughts of mine on George Reeves are in Superman: The Moral of the Story.

Hats Off to Hentoff: Abortion and Obama

It is often assumed that opposition to abortion can be based only on religious premises. This assumption is plainly false. To show that it is is false, one need merely give an anti-abortion argument that does not invoke any religious tenet, for example:

   1. Infanticide is morally wrong.
   2. There is no morally relevant difference between abortion and
   infancticide.
   Therefore
   3. Abortion is morally wrong.

Whether one accepts this argument or not, it clearly invokes no religious premise. It is therefore manifestly incorrect to say or imply that all opposition to abortion must be religiously-based. Theists and atheists alike could make use of the above argument.

And as a matter of fact there are pro-life atheists. Nat Hentoff is one. In The Infanticide Candidate for President, he takes Barack Obama to task:

     But on abortion, Obama is an extremist. He has opposed the Supreme
     Court decision that finally upheld the Partial-Birth Abortion Ban
     Act against that form of infanticide. Most startlingly, for a
     professed humanist, Obama — in the Illinois Senate – also voted
     against the Born Alive Infant Protection Act. I have reported on
     several of those cases when, before the abortion was completed, an
     alive infant was suddenly in the room. It was disposed of as a
     horrified nurse who was not necessarily pro-life followed the
     doctors' orders to put the baby in a pail or otherwise get rid of
     the child.

 

Internet Crackpots and the Perils of Autodidacticism

One of the (very minor) drawbacks of having a Web presence is that one becomes the target of crackpot e-mail from people like this.  He describes himself as an autodidact, thereby illustrating the perils of autodidacticism. 

And yet some negotiate the straits of autodidacticism quite well, Eric Hoffer for example.  In general, however, he who educates himself has a fool for a pupil. That being said, I advise a modicum of skepticism concerning academic credentials.

If you expect to have 'cred' in the 'sphere, it helps to have established credibility in peer-reviewed venues.  Some of my publications are listed here, at PhilPapers. 

It comes as no great surprise that the crackpot in question is an anti-Semite.

The Voter Photo Identification ‘Issue’

Some positions are so absurd as to be beneath refutation. To respond reasonably to the unreasonable lends them a veneer of credibility to which they are not entitled.  Mockery, derision, and ridicule are often much more appropriate and effective.  Oftentimes, all it takes is a cartoon to refute a stupid liberal.  By the way, this voter ID 'issue' — pseudo-issue, actually — is a perfect example of the lunacy of contemporary liberalism.  But it is worse than lunacy given that the motive (not the reason, they have none) is to encourage voter fraud.  For a leftist, the end justifies the means. Does it take fraud to win?  Then you commit fraud.

Voter ID

Saturday Night at the Oldies: ‘Green’ Songs

I was going to cover 'strange' songs tonight, but then I remembered it is St. Patrick's Day. 

Remember The New Christy Minstrels?  Here is Barry Maguire belting out their 1963 hit,
Green, Green."  It was sanitized, well-scrubbed hootenany stuff like this that caused a lot of my generation to pick up guitars and then find our way back to the more authentic material.  Check out this video of a live performance at an Arizona university.  This was before the '60s became the '60s. But by '65 the cultural as opposed to the calendrical  '60s had arrived with a vengeance and the same Barry Maguire came out with The Eve of Destruction.  Topical songs and social protest came to displace songs about Tom Dooley and workin' on the railroad . . . .

Joan Baez, Green, Green Grass of HomeRed Foley does a great job with this 'green' song.

Hoyt Axton, Greenback Dollar. Here is the Kingston Trio's cleaned-up collegiate version.  Fretkillr's  killer amateur version is modelled on Hoyt Axton's.

Hoyt Axton, Greensleeves

Jim Lowe, Green Door, 1956.

Roy Buchanan, Green Onions.  A guitar-slinger's version.

Finally, a song about the lean green.

And now to bed.

Via Platonica Versus Via Aristotelis

School of athens

I have spoken more than once of the fruitful tension between Athens (philosophy) and  Jerusalem (Biblical revelation). But there is also a tension, and it is also a fruitful one, within Athens. It is depicted, if such a thing can be depicted at all, in Raphael's School of Athens.   Take a gander at the close-up below.  Plato points up, Aristotle, the younger man, points down. The Forms are, in a manner of speaking, up yonder in a topos ouranos, in a heavenly place; his star pupil would, again in a manner of speaking, bring them down to earth.  In a terminology I do not wholly endorse, Plato is an extreme, while Aristotle is a moderate, realist.

The vitality of the West is due, in part, to the fruitful tension between Athens and Jerusalem. And much of the vitality of philosophy derives from the fruitful tension between the Platonic and Aristotelian ways of thinking, not just as regards the problem of universals, but on a wide range of issues.

Plato and aristotle

In the Arena

Say what you want about politicians, they are in the arena taking the heat, under their own names, unlike the wordslingers, too many of them hiding behind pseudonyms, who snipe from the sidelines:

It is not the critic who counts: not the man who points out how the strong man stumbles or where the doer of deeds could have done better. The credit belongs to the man who is actually in the arena, whose face is marred by dust and sweat and blood, who strives valiantly, who errs and comes up short again and again, because there is no effort without error or shortcoming, but who knows the great enthusiasms, the great devotions, who spends himself for a worthy cause; who, at the best, knows, in the end, the triumph of high achievement, and who, at the worst, if he fails, at least he fails while daring greatly, so that his place shall never be with those cold and timid souls who knew neither victory nor defeat. (Theodore Roosevelt, "Citizenship in a Republic," Speech at the Sorbonne, Paris, April 23, 1910.)