free variable

Here’s a fascinating series of questions designed to determine how consistent one’s attitudes about morality are. If, like me, you don’t appreciate the classic “undergraduate moral philosophy problem” sorts of discussions, you might not enjoy the questions, but they are few and short, and there’s an interesting argument at the end.

I won’t spoil the punchline, but I will say that I agreed with it. In addition, according to the quiz, I am perfectly morally consistent. I might have to print that out and put it in a diploma frame.

Almost a year ago, I posted a short note about how to set Polytonic Greek in the LaTeX typesetting system, inspired by my difficulties in typesetting a chapter epigraph for my dissertation, and included with it a challenge to my readers: namely, say something clever about the (unattributed) quote I had included as an example:

οὐ γὰρ μήποτε τοῦτο δαμῇ εἶναι μὴ ἐόντα·
ἀλλὰ σὺ τῆσδ’ ἀφ’ ὁδοῦ διζήσιός εἶργε νόημα

Today, someone did. Congratulations are due to D Jagannathan, who had something clever to say both about the quote itself — which is from the work of the presocratic philosopher Parmenides of Elea — and about the perils of using LaTeX to set texts in non-Latin alphabets. Fine work!

One (imperfect) way to render the quote into English, given by John Burnet in 1892, is “For this shall never be proved, that the things that are not are; and do thou restrain thy thought from this way of inquiry.” Parmenides is either my favorite or second-favorite presocratic, and I like this quote for two reasons: first, it is remarkably Tractarian for something written around two-and-a-half millennia before Wittgenstein destroyed positivism; second, it could be read to describe logic programming or mechanical proof search.

While I was unable to resist one of the basest impulses of computer scientists (viz., quoting philosophers in an effort to distance oneself from the fact that one is essentially in an engineering discipline; see also here), this quote at least was plausibly connected to the chapter it headed. I was, however, able to resist the temptation to include this quote in its original language in the final version of my dissertation. (Indeed, the only moment of weakness I had with regard to non-English languages was in the dedication, where it seems a little indulgence is justifiable.)

Pancakes taste awesome but are bad for you; these are both necessary properties of pancakes. To attempt to design “pancakes” that are not unhealthy will surely result in pancake-like foodstuffs that are only marginally less healthy but taste substantially worse. As such, so doing is not only a waste of time, but a crime against logic.

I speak from substantial experience, both with contingency and with pancakes.

Over Christmas, I added a couple of t-shirt designs to my Spreadshirt shop. Unlike prior designs, which primarily depict characters from imaginary children’s books and/or 16th-Century debates about the nature of free will, the new designs are depictions of famous paradoxes: the “devil’s tuning fork” and the Russell set. If you’d like one of these designs on a product that’s not yet available, let me know and I’ll cons it up for you.

Ack

I recommend to everyone — but especially to my friends finishing dissertations, and doubly especially to those in Computer Science — Olin Shivers’ amazing acknowledgments section from the scsh manual, which I first encountered as a young Scheme nerd a long time ago. (Philip Greenspun’s gloss on Prof. Shivers’ acknowledgments is pretty delightful as well; scroll ahead to the second block quotation and prepare to be amazed.)

Irrationality

Speaking of acknowledgments, I make brief and jocular reference to the “preface paradox” in the draft preface of my dissertation. This is one of my favorite paradoxes (originally due to David C. Makinson). The basic idea is that a writer believes every individual claim in a manuscript is true (or else he or she would not have committed them to paper); however, some writers claim that their work inevitably will be found to contain some errors. As a consequence, writers are in the curious position of believing the conjunction of every claim in a book and believing the negation of the conjunction of every claim in a book. Whether or not this is irrational is — I guess — an open question with a few plausible solutions.

I’ve just received an advance copy of K. Mooch’s eagerly anticipated Time-out for Contingency (first mentioned here); I’m glad to be able to share this delightful excerpt with you:

In subsequent pages — which I do not reproduce here for reasons of space and copyright — Daddy demonstrates that, even given a transitive reachability relation between possible worlds, assuming the possible permissibility of placing one’s feet on the table introduces a contradiction. My full review is still pending, but I am already sure that this book will quickly come to be regarded as the Iliad of Kripke-inspired children’s fiction.

Apparently, it’s possible to get a doctorate in “Islamic philosophy” without being able to recognize a faulty syllogism (or even a few infelicitously chained together). I know this because, according to this MEMRI dispatch, Iranian professor Hasan Bolkhari has a doctorate in “Islamic philosophy,” and he makes perhaps the most ridiculous sequence of claims I’ve seen in a long time. I’d say that Bolkhari handily defeats even “Spurious George” (not his real name), who was a clueless philosophy student I knew as an undergrad and who represents my benchmark for utter rhetorical incoherence.

I won’t bother attempting to describe the argument; it’s too warped. You’ll have to read it yourself, but be warned that Bolkhari’s sentiments are thoroughly appalling. Also remember that Tom and Jerry cartoons were produced by Warner Bros.

I’m currently listening to Acroyear2 from the album “LP5” by Autechre

Brian Weatherson points out that, as far as some physicists are concerned, existence is a property.

Here are two interesting observations of indexical expressions from Gillian Russell: Indexicals in the Wild and Indexicals in the Wilder.

Mark Liberman and Brian Weatherson are both writing about “silly talk” about their disciplines — for example, asking a philosopher for a list of some of “[his] sayings.”

In my experience, once you get far enough along, just about every discipline is a veritable comedy goldmine in this regard. I recall someone asking Andrea — upon hearing that she had an academic interest in the Arthur legends — what she thought about the veracity of The Da Vinci Code. (She doesn’t remember this, though, so it may be apocryphal.) She does, in any case, regularly field questions about whether her dissertation work (on Middle English romances) has led her to compose a great deal of original fiction. My grad minor work, which was mostly in analytic philosophy, produced snickers from people who don’t consider, say, the problems of the conditional or of vague predicates to be worthy of investigation.

I have often claimed that computer science is special in this way, since computers are ubiquitous but computer scientists are not. As a result, people are confused by the presence of the word “computer” in the name of my discipline, and are inclined to assume that I have something vaguely to do with their wireless network or Start menu. (Frankly, I’m more confused by the “science” part of my discipline’s name.) I have gotten the following sorts of reactions upon disclosing the most general information about my present work:

1. “Well, you’ll make a lot of money someday!” Perhaps (although the technology bubble remains burst). However, I am subject to the whims of the academic job market and a desire to remain in the upper Midwest. Furthermore, if money were my primary concern, it would be absolutely stupid for me to work on a Ph.D. instead of getting a job and investing for n extra years. (Personally, I’d have kept the consulting gig I had out of college, in which I made a grad student’s annual salary in a month.) This comment is by far the most common, and usually comes after someone is flummoxed by the fact that my wife, as a PhD candidate in literature, has no opinion on John Grisham’s latest.
2. “Hey, you’ll have to help me get Word to mail merge/choose between these commodity PC parts/perform some other computer-related task that you’re not qualified to do.” Do you ask an astronomer to fix your binoculars? I have no idea how to use any interesting features of Word if the paperclip doesn’t tell me what to do (I haven’t used it since 1996 or so), and I don’t know anything about which brand of DVD burner is a “better deal.” This is not to say that I mind helping people with computer trouble when I can — I don’t — but that being a computer scientist has not initiated me into some Gnostic succession of secret knowledge about popular computing topics.
3. “So, when you finish your Ph.D., are you going to program computers or fix them?” This is particularly unfortunate, as the person who asked me had a doctorate in another potentially-misunderstood field: German literature. (Perhaps I should have asked whether the lyrics of Rammstein or those of Die Toten Hosen compared more favorably to Goethe.) I have fixed computers for a paycheck before; it is fun for a while, but 10+ years of postsecondary education in order to enable such a career is at least minor overkill. Likewise, if I simply wanted to program computers, I could have dropped out of elementary school in order to hone my then-burgeoning AmigaBASIC skills.

Having to field silly questions, though, has made me much more careful to avoid this behavior myself. Erring on the side of caution has a pleasant side effect: instead of forcing people to discuss their work in social situations, I can confine the conversation to avocational topics. (After all, what would you rather talk about?) On a positive note, the preponderance of “silly talk” when nonspecialists discuss academic disciplines should serve as a wake-up call to academics: there are many levels at which we can discuss our work, and the burden is on us to make what we do clear, relevant, and accessible to laypersons.

If you have a good story about an entertaining misconception relating to your discipline (and I am certain that some regular readers do), feel free to drop it in the comments.

Josh Parsons, whose excellent aesthetic evaluation of world flags I’ve linked to in the past, has a great perl script online that generates pseudo-Tractarian epigrams. Sample output:

15 Russell’s merit is to have shown that the logical symbolism of Frege and Russell is a fact.

15.1 Propositions stand to one another in that total relation that holds between questions.

15.11 An atomic symbol is determined by the propositions, and by these being all the propositions.

15.111 Roughly speaking: every structure is also a senseless tautology.

15.112 In logic, every fact is also every picture: the atomic object itself is, so to speak, a substance.

15.113 It is clear that everything exists independently of the reality itself.

This is truly hilarious stuff, on several levels. My inner nerd, though, secretly pines for distinct “Pears/McGuinness” and “Ogden” versions. (For a chaser, track down Mark Pilgrim’s auto-generated Kant or elsewhere.org’s classic postmodernism generator.)

I’m currently listening to Double – From Partita For Violin Solo No.1 in B minor from the album “Segovia Collection vol. 4: J.S. Bach” by Andrès Segovia

Newly monitored

I noticed Gillian Russell’s blog logicandlanguage.net because she linked to a post of mine on various applications of modal logic for computer science. Her site is interesting and well-written, and several of her interests align with the subfields of philosophy that I follow. As icing on the cake, Prof. Russell established her site on the 5th of March — an auspicious date for the genesis of any creative endeavor.

Re-reading that modal logic post reminded me that there has been very little computer science content here lately. I do have a few pieces that I’m working on in my spare time about CS pedagogy; the overall level of CS and PL content should increase in coming weeks.

Embalming

I was part of a collaborative composition with other members of the idm-making list recently. The project was organized as an “exquisite corpse,” which is best described as a parlor-game cousin to Baroque continuous variation forms. You can hear the results at Michael Upton’s site; my section, sadly, is the one that doesn’t fit in all that well.

A little burn in the pocket

Last year Atlanta Falcons quarterback Michael Vick denied internet rumors about his sexuality by calling in to a radio show and saying “I’m not even going to feed in to that. Everybody who knows me, knows how I get down.” Unfortunately for Vick, now the state court of Gwinnett County, GA knows how he gets down, too.

I’m currently listening to Op 59 Nr.1 in F Rasumovsky I Allegro from the album “Beethoven – Complete String Quartets” by Alban Berg Quartett

Brian Weatherson points out that the excellent (and free) Stanford Encyclopedia of Philosophy has just been awarded a challenge grant from the National Endowment for the Humanities. This is very good news, especially considering both the paucity of quality peer-reviewed scholarly articles on the Internet and the current climate for academic publishing. You can find out more about how to support this extremely worthy cause here.

I’m currently listening to Hard to Handle from the album “Shake Your Money Maker” by The Black Crowes

Au revoir, putain!

To be fair, it’s probably a stretch to file this under “Philosophy,” since the notorious charlatan’s oeuvre mimicked philosophy, but had little impact on legitimate philosophers; furthermore, “his antics [have] contributed significantly to the widespread impression that contemporary French philosophy is little more than an object of ridicule.” (The source for this remark was a 1992 letter by Barry Smith of The Monist, available here; for more gleeful Derrida-bashing, see Mark Goldblatt.)

I should also note that I suggested “Derrida” as a dog name before we acquired the schnauz’ — doing so would of course enable one to say: “Crumb! I’ve got to clean up some Derri-do.” (“Otto” is much better, and — fortunately! — his “antics” are limited to attempted ham acquisition, rather than rank intellectual flimflammery.)

Brian Weatherson has a blog post on vague adverbs; it is interesting by itself, as are the attached comments. His claim — that an adverb is probably vague if we can construct a Sorites sequence for “adverb predicate” where every instance of predicate is a clear instance of predicate — reminds me of some thoughts I had on Roy Sorensen’s 1985 paper “An argument for the vagueness of ‘vague.’” (Unfortunately, I cannot find this paper online.)

Basically, Sorensen’s argument (if I recall it correctly) was that we could construct a Sorites argument for “vague” by constructing a chain of predicates called “n-small” such that a natural number was “n-small” if it was either “small” or less than n. Clearly, “0-small” is vague, since a natural number can only satisfy it if it satisfies the vague predicate “small.” The problem gets trickier as we increase n, since whether or not each predicate is vague depends on whether or not there are numbers greater than n that satisfy “small,” which obviously hinges on the extension of “small.” This is a cute argument, but I found something viscerally unsatisfying (so to speak) about it upon first reading.

I initially thought my problem with the paper could have been rectified by changing the title to “An argument for the Sorites-susceptibility of ‘Sorites-susceptible,’” but that doesn’t quite solve the problem. The problem is not about disjunction in predicates; if it were, we would be in trouble indeed as disjunction is useful. Obviously, disjunction of two nonvague predicates does not introduce vagueness, and disjunction of a vague predicate with tautology (i.e. “either x is small or x is equal to itself”) does not introduce vagueness. If the extension of a predicate P is dependent on the extension of a Sorites-susceptible predicate, however, then P is Sorites-susceptible.

I suppose I see vagueness (or, more properly, Sorites-susceptibility) as “infecting” compound sentences the way that the introduction of not-a-number affects computer floating-point calculations, or in which undefined expressions affect the meaning of programs in denotational semantics; if the end result depends on an out-of-band value (like “not-a-number” or bottom), then the out-of-band value infects the result. Dependence, of course, is tricky to prove even without vagueness in the mix; in particular, my “solution” doesn’t address whether or not “dependence” is knowable! I am not claiming that this is a more tenable approach to the vagueness of ‘vague’ than Sorensen’s, but it is certainly an interesting topic to think about.

If the title of this post makes sense, think about it for a minute.

There’s a fascinating series of posts on this sort of sentence at the Language Log, which is rapidly becoming one of my favorite weblogs. The first, Plausible Angloid Gibberish, describes the phenomenon — that of a meaningless sentence that appears meaningful at first blush. Mark Liberman then observes that these sorts of sentences have something in common with endless-staircase pictures, and David Beaver presents an analysis of such a sentence in the wild.

Personally, I think that these sentences are somewhat better envisioned as the “devil’s tuning fork” — I perceive the devil’s tuning fork when I’m just glancing at it out of the corner of my eye, perhaps not focusing on it, as a three-pronged fork. Upon closer examination, the image falls apart, and it’s not clear what’s left — one knows why it isn’t a three-pronged fork, but one can’t exactly make sense of where the illusion falls apart. (Upon extremely close examination, it is just confusing; it took me about half an hour to make the above figure!) I may just have unusual patterns of perception, but the “devil’s tuning fork” is a more compelling visual paradox for me than the endlessly-rising staircase.

Some would argue that this is the same phenomenon witnessed in the Sorites paradox, of local validity but global invalidity. Look above, at the two halves of the devil’s tuning fork. On the left, there is clearly part of a two-pronged fork, but on the right there are clearly three prongs. When one puts them together, where does one become the other? Where does the figure stop making sense? It seems that, if the epistemicists are right, a solution to this problem will also be a solution to the Sorites. (I’ll have more to say on the matter once I’ve formulated an opinion about Roy Sorensen’s Vagueness and Contradiction, which I’ve been reading lately.)

I’m currently listening to Symphony no.49 in F minor, “La Passione”: Adagio from the album “Haydn: Symphonies nos. 26, 35 and 49″ by Northern Chamber Orchestra / Nicholas Ward

Die Fledermaus ran this weekend. It was the last time the Madison Opera performed in its current venue; a massive new arts complex will be complete in time for Turandot in the fall. We performed with the Ruth and Thomas Martin translation, which is, as far as I can tell, not particularly faithful to the original German text. On the other hand, it seems to amuse the audience, so it can’t be all bad. One notable place where the Martin text introduces some “innovative” dialogue is in Act III, where Eisenstein is disguised as a lawyer and is talking to Rosalinde and Alfred.

note to non-Fledermaus-savvy readers: The basic plot of the first act of the operetta (which sets up the circumstances for the scene I’m describing) is this: Eisenstein is about to part with his wife Rosalinde (to serve a brief jail sentence for a bar fight) when his friend Falke comes to invite him to a party. Falke is only setting Eisenstein up for an elaborate practical joke, but E. is oblivious. As soon as they leave, Rosalinde is joined by an old flame, Alfred, who attempts to seduce her. The prison warden arrives to arrest Eisenstein; faced with the unpalatable option of having to admit that she is having a late supper with a man other than her husband, Rosalinde hands Alfred over to the warden in her husband’s place.

Eisenstein is furious at Rosalinde and Alfred, but cools somewhat when he realizes that he won’t have to serve his prison sentence, since Alfred is already imprisoned in his place. Rosalinde insists that she, as his wife, is in a position to positively identify him, to which he replies “ah, but a wife can’t testify against her husband!” (The libretto implies that Viennese law entailed something stronger than spousal privilege, in which it was not even possible to testify against a spouse; such a clause surely wouldn’t fly in a contemporary legal system.) This clearly sets up rules that produce an untenable situation. It appears to have something in common with several well-known paradoxes; the no-win constraints (but not the structure) recall the barber paradox.* If R. is E.’s wife, then she cannot identify him (by law); however, if R. is not E.’s wife, then she cannot identify him (because she has no basis to do so).

Fortunately for the dramatic arc of the scene, the Martins avoid metalogical reflection or procedural crime drama-style trickery on a solution to the dilemma; Eisenstein is identified by his maid and a comic finale ensues.

*The barber paradox is that of a barber who shaves all and only men who do not shave themselves. It is a set-membership paradox — the barber cannot either be a member of the set of people that he shaves (because he shaves only men who do not shave themselves) or the set of people that he does not shave (because he shaves all men who do not shave themselves). The Eisenstein “paradox” depends on modalities (and different modalities on either side: legal permissibility and knowledge), and as such is not a logical paradox — Rosalinde is merely placed in a position in which she cannot utter a particular sentence, not in which she is forced into a contradiction.

John Halleck helpfully points out a couple of caveats about my recent post on modal logic and PL applications. First, I assert that “all or most” of the classical connectives are truth-functional, “depending on whom you’re willing to believe.” John reminds me that it’s never safe to make generalizations about logic; my assertion, of course, is untrue for formalists. John also points out that my example using time as possible worlds, in which I state that it is necessarily false that I watched SportsCenter last week, is not true in every modal system; it fails in the temporal logics of (the aptly-named) Arthur N. Prior. John recommends Prior’s Papers on Time and Tense and Past, Present, and Future.)

Finally, John reminds me of J. Jay Zeman’s fine modal logic text online. I’ve referred to this one a few times while writing on logic, so I really should have linked to it sooner. It uses prefix notation, which is perhaps off-putting if you didn’t have a similar programming culture to the one in which I was indoctrinated as a computer science undergrad.

I’m currently listening to Vorspiel/Prélude from the album “Wagner – Die Meistersinger von Nürnberg (Karajan, Dresdener Staatskapelle)” by Herbert von Karajan & Staatskapelle Dresden

My friend Dorian raised an interesting question the other day: Assume that you are negotiating with someone, and the strength of your position depends on a certain fact F. You know F; we’ll describe this state of affairs as Yk F. Presumably, you also know that you know F (Yk Yk F), and perhaps turtles all the way down, if you keep thinking about it.

UPDATE (6/1/2004) The KK principle is not uncontested; I don’t know whether I believe it or not. Certainly if I believed it when I first wrote this, I am less sure now.

The person you’re negotiating with may know F as well, which is one fact (we’ll call this Pk F). Furthermore, she may know that you know F as well: thus, Pk Yk F. The question, is this: How many times must an alternating sequence of Pk and Yk repeat before it quiesces? That is, does Pk Yk Pk Yk Pk F tell you (or your opponent) anything more than Yk Pk Yk Pk Yk Pk F? We didn’t, I believe, reach a consensus on this; I thought that you learned nothing new after Yk Pk Yk F, while Dorian asserted that that point occured after Pk Yk Pk Yk F. Neither of us was particularly confident in the rigor of our case, though, and I conceded that it might be context-dependent. Hopefully, this is a fun puzzle to think about (at least, if you don’t already have some formalism that makes this result into an axiom).

There are certainly, I would imagine, benefits to one’s chess and/or bridge game from having a good grasp on this sort of puzzle.

By way of trying to get a more rigorous approach to this problem, I began thinking about systems for epistemic and doxastic logic in general. Apparently, the standard work in this area is Knowledge and Belief: An Introduction to the Logic of the Two Notions by Jaakko Hintikka. I haven’t read this, but the impression I get from reading papers that cite it is that it is fairly difficult.

It seems to me that treating knowledge or belief as a modal operator is not as straightforward as treating, say, necessity or possibility as one. Furthermore, belief (at least), is suceptible to the lottery paradox: that is, one may be certain that any single lottery ticket is not a winner (Nw L_n), but one would be foolish to assert that Nw L₁ & L₂ & … & L_n. This, however, is a problem of degrees; even total certainty is something less than necessity. The problem of treating knowledge as necessity is perspicuous when one reads a Sherlock Holmes story — if knowledge really were like necessity, then we would know the logical consequences of facts we know, and Holmes’ deductive ability would be unremarkable.

Perhaps a better analogy for knowledge is presented by intuitionistic logic: certainly, knowledge does not fulfill the law of excluded middle, in the sense that Yk (p v ~p) is not a tautology (while necessity — M (p v ~p) — is), just as there may not exist either a proof or a disproof of a certain theorem. It seems, also, that it is difficult or impossible to “know” what someone else knows (and, contrary to my first paragraph, many have argued that it is difficult or impossible to know what you know); therefore, it seems that we are rapidly in the realm of belief, and therefore, degrees, with the quiescence puzzle.

I’ll likely write more on this as I have some clearer ideas. Don’t hold your breath!

Here is a great article by Alvin Plantinga. It’s a well-presented and often-amusing article, that is ostensibly a set of advice to Christian philosophers, but which really does a good job of unpacking why philosophy is so hostile to Christianity, and what the relation between philosophy and Christianity should be for the Christian philosopher. Here’s a (somewhat lengthy) quote:

Of course she [a young Christian student of Quine's] will note certain tensions between her Christian belief and her way of practicing philosophy; and she may then bend her efforts to putting the two together, to harmonizing them. She may devote her time and energy to seeing how one might understand or reinterpret Christian belief in such a way as to be palatable to the Quinian. One philosopher I know, embarking on just such a project, suggested that Christians should think of God as a set(Quine is prepared to countenance sets): the set of all true propositions, perhaps, or the set of right actions, or the union of those sets, or perhaps their Cartesian product. This is understandable; but it is also profoundly misdirected. Quine is a marvelously gifted philosopher: a subtle, original and powerful philosophical force. But his fundamental commitments, his fundamental projects and concerns, are wholly different from those of the Christian community-wholly different and, indeed, antithetical to them. And the result of attempting to graft Christian thought onto his basic view of the world will be at best an unintegral pastiche; at worst it will seriously compromise, or distort, or trivialize the claims of Christian theism.

Here are a few delightful fragments from Xenophanes of Colophon (with Diels-Kranz numbers); feel free to apply them to your current favorite ecclesiastical/theological controversy:

DK 21B14 Mortals believe that the gods are born
and have human clothing, voice, and form
DK 21B16 Ethopians say that their gods are flat-nosed and dark
Thracians that theirs are blue-eyed and red-haired
DK 21B15 If oxen and horses and lions had hands
and were able to draw with their hands and do the same things as men,
horses would draw the shapes of gods to look like horses
and oxen to look like oxen, and each would make the gods’ bodies have the same shape as they themselves had

(source: Richard D. McKirahan, Jr. Philosophy Before Socrates. Hackett Publishing Co. Indianapolis. 1994.)

Since I just posted about logic, I should probably post a link to John Halleck’s great logic system interrelationships page. There’s a lot of information in those pages, and they were quite helpful to me when I was trying to prove various things about axioms and their relationship to frame conditions.