мои авторитеты

В 1989 году на кампусе Калифорнийского университета в Лос-Анджелесе меня окликнул хасид.
—Молодой человек, вы еврей?
—Предположим, что да.
—Не хотите ли исполнить мицву, наложив тфилин?
—Спасибо, я это уже пробовал. Ничего из этого не вышло.
—Как это так? Исполнение мицвот является Вашей обязанностью.
—Наши мнения расходятся. Я так не считаю.
—А что же Вы считаете? Скажите, кто по-Вашему самый мудрый человек в мире?
Разговор явно шёл по направлению к Менахем-Мендлу Шнеерсону, предполагаемому Божьим помазанником. Я решил резко изменить курс.
—Я считаю, что самым мудрым человеком в мире на настоящий день является Алонзо Чёрч.
Хасид взволновался.
—Как так? Кто это такой?
—Это мой учитель логики. Он преподаёт в нашем университете. Если хотите, я могу Вас познакомить.
—Нет, спасибо… не надо.
На этом разговор и закончился.

Чёрч научил меня, что ничьё мнение никогда не является, и не может быть решающим. К сожалению, его больше нет в живых. В качестве нынешнего авторитета, я назову Карло Гинзбурга.

california dreamin’

Royce’s excursion to Europe and the eastern U.S. fixed in his mind a decided hatred of his native state. California’s provinciality, its ruthless economics, its blind and selfish politics—everything, in fact, but its exquisite natural beauty—filled him with loathing. Compared with the cultural centers that Royce had just left, California had little to offer besides stock speculation, wheat ranching, political charades, racial warfare, and agitation. “Foundation for higher growth we sadly lack. Ideals we have none. Philistines we are in soul most thoroughly. And when we do talk, our topics of discussion are so insufferably finite!’ As a place for philosophical thought, it was execrable. “There is no philosophy in California—from Siskiyou to Ft. Yuma, and from the Golden Gate to the Summit of the Sierras, there could not be found brains enough [to] accomplish the formation of a single respectable idea that was not a manifest plagiarism. Hence the atmosphere for the study of metaphysics is bad, and I wish I were out of it.”
—John Clendenning, The Life and Thought of Josiah Royce, Revised and Expanded Edition, Vanderbilt University Press, 1999, p. 74

The word “logic”, fortunately or unfortunately, rings with varied overtones not all of which are in harmony. One ear may be deaf to what excites another, and great care must be taken in claiming that the “logic” of a subject has been found or revised. As one of my undergraduate professors once told me, “When you question a man’s logic you question his taste,” which may explain the contempt of some mathematicians for logical studies. Now that there seems to be a chance for formal logic to have a wider audience, all the more care is required. Easy victories waste too much time in celebration. Formal methods should only be applied when the subject is ready for them, when conceptual clarification is sufficiently advanced. This is not to discourage experimentation—only the party giving. Modal Logic is a good example: colorful axioms have been strung up all over, but few couples are dancing. Maybe Quantum Logic is another example, but at least the mathematics being served at that party is vastly more sophisticated than the Coca-Cola of the modal logicians. Besides, those who study the foundations of quantum physics readily agree that the fight has only just begun.2 [2 A general reference is J. M. Jauch, Foundations of Quantum Mechanics (Addison-Wesley, Reading, Mass. 1968). A related discussion and some interesting new ideas have been initiated in C.H. Randall and D.J. Foulis, “An Approach to Empirical Logic”, in American Mathematical Monthly 77 (1970) pp. 363-374.] Whether, then, the claim of a carry-over for modal logic is going to be justified is to my mind a very moot point and is one of the main motivations for attempting this essay.3 [3 Reservations about modal logic, mingled with some optimism, have been expressed by George Lakoff, “Linguistics and Natural Logic”, in Semantics of Natural Language, ed. by D. Davidson and G. Harman (D. Reidel Publishing Company, Dordrecht, Holland 1972) pp. 545-665. Note especially the final section of Concluding Remarks. The point about presuppositions and three-valued logic does not seem to be entirely well-taken, however, in view of van Fraassen’s well-known analysis in terms of supervaluations. This does not mean that the connections between “natural” and “formal” logic are all that clear.]
—“Background to Formalization”, Dana S. Scott, in Truth, Syntax and Modality, edited by H. Leblanc, Studies in Logic and the Foundations of Mathematics, Volume 68, 1973, pp. 244-273, at p. 245

In what important and often neglected sense are there many worlds? Let it be clear that the question here is not of the possible worlds that many of my contemporaries, especially those living near Disneyland, are busy making and manipulating. We are not speaking in terms of multiple possible alternatives to a single actual world but of multiple actual worlds. How to interpret such terms as “real”, “unreal”, “fictive”, and “possible” is a subsequent question.
—Nelson Goodman, “Words, Works, Worlds”, Erkenntnis, Volume 9 (1975), Number 1, pp. 57-73, at pp. 57-58; reprinted in Ways of Worldmaking, Hackett, 1978, p. 4

Richard Montague was a small, very dapper, compact, cufflink of a character. He was dressed in a neat blue suit, a snowy white shirt, and a matching crimson tie. We had met for drinks in mid-town Manhattan—he, Daniel Gallin, and I. His hands, I noticed, were square, the fingernails manicured and covered with a clear polish. A logician by profession, Montague had a reputation for great technical brilliance. His papers were adroit, carefully written, biting, and completely beyond the intellectual grasp of all but a handful of analytic philosophers.
    For some reason he was ill at ease that afternoon, and looked fitfully around the hotel’s bar, as if he suspected somehow that nothing was going to turn out properly. Beyond the bar, in the lobby of the hotel, there was an absurd canary cage in which a pair of yellowish birds were cheeping nervously, complaining, I am sure, about the price of drinks or room service.
    We talked of taxes and politics and How on Earth do you survive in this place—meaning New York. Then the discussion turned to mathematics and Montague cheered up. He had just commenced his research program into formal grammars and had published a series of papers of truly monstrous technicality. He liked to imagine that he and Chomsky were rivals. “There are,” he said, “two great frauds in the history of twentieth-century science. One of them is Chomsky.”
    I reached for the peanuts.
    “And the other?”
    “Albert Einstein,” Montague said decisively, glad that I had asked.
    —David Berlinski, Black Mischief: Language, Life, Logic, Luck, Mariner Books, Second Edition, 1988, pp. 139-140

Bonus links: Richard Montague’s obituary signed by Montgomery Furth, C.C. Chang, and Alonzo Church; reviews by Sacha Arnold of more or less improper treatments of Richard Montague in literary fiction, Less Than Meets the Eye by David Berlinski and The Mad Man by Samuel R. Delany, and The Semantics of Murder by Aifric Campbell.

we know what we are

Jerry Fodor and Massimo Piatelli-Palmarini propound the following analogy in their letter to the TLS Editor:

Our difficulty with Darwin is very like our difficulty with our stockbroker. He says the way to succeed on the market is to buy low and sell high, and we believe him. But since he won’t tell us how to buy low and sell high, his advice does us no good. Likewise, Darwin thinks that the traits that are selected-for are the ones that cause fitness; but he doesn’t say how the kinds of variables that his theory envisages as selectors could interact with phenotypes in ways that distinguish causes of fitness from their confounds. This problem can’t be solved by just stipulating that the traits that are selected for are the fitness-enhancing traits; that, as one said in the 1960s, isn’t the solution; it’s the problem.

Matthew Cobb, a contributor to the evolutionist advocacy blog owned and operated by Jerry A. Coyne, Ph.D and a Professor in the Department of Ecology and Evolution at the University of Chicago, fancies himself to have made short work of this argument. But misunderstanding the analogy between evolving through natural selection and succeeding on the market by buying low and selling high is a clear symptom of being out of one’s mind in the following, precisely defined sense:

  1. Natural selection is said to be responsible for evolving all functions of living organisms.
  2. The mind counts among the functions of some living organisms.
  3. The mind of some living organisms is capable of making intensional distinctions such as the one between being renate and being cordate, or the one between being an even prime number and being equal to the positive square root of four.
  4. Natural selection is incapable of making intensional distinctions.
  5. Natural selection cannot evolve the capacity to make intensional distinctions.
  6. Some minds have functions that cannot have evolved through natural selection.
  7. Some functions of living organisms cannot have evolved through natural selection.

At this point, to echo Sir Winston Churchill, we know exactly what you are as a living organism; we are just haggling about something that determines your price.

Crossposted to [info]larvatus, [info]philosophy, and [info]real_philosophy.

the necessity of acedia


    Lo naturale è sempre sanza errore,
ma l’altro puote errar per malo obietto
o per troppo o per poco di vigore.
    The natural is always without error,
but the other may err through an evil object
or through too much or too little vigor.
    —Dante, Purgatorio, Canto 17, 94-96

“To love is to risk not being loved in return.” This slogan, sometimes traced to Leo F. Buscaglia, or credited to Rollo May, proliferates in self-help manuals, many of them cast in a religious mold. Therein lies a contradiction. If God is love, he cannot but love every man. Then, if to love is to risk not being loved in return, it follows that men cannot love God for want of risk of not being loved by Him.

Nothing in this rebuttal depends on the meaning of is. If God is love, the inference goes through with the copula being interpreted as a relation of identity, predication, or belonging. It might be argued that in loving God man runs the risk of not being loved in return, in the event of His non-existence. But it is implausible that love—unlike its collateral attitudes such as fear—could be predicated without presupposing the existence of the lover and the beloved alike. There is something wrong with our homiletic premisses. Love does not require the risk of not being loved in return. Or else, God is something other than love.

‎vere tu es deus absconditus deus sui salvator

As is well-known, God helps those who help themselves, which renders God’s help rather superfluous. Now, let us consider an apposite God, one who is committed to helping exactly those who do not help themselves. We bear in mind that, unlike Russell’s barber, who is free to shrug off as impossible his duty to shave those, and only those, who do not shave themselves, the perfection of God requires that he actually do everything he is committed to do. Then is our God under obligation to help Himself?

(Originally published on 20 January 1993.)

Crossposted to [info]larvatus and [info]philosophy.

torkel franzén is dead

Looking back over fifteen years of Usenetting, I gratefully recall one man selflessly expending his time and effort on making it a better place. Torkel’s learned and benevolent presence single-handedly made up for a myriad ephemeral and persistent sophistical frauds striving to overwhelm our forum with self-serving nonsense. I am proud to have benefitted from his learning and character.
    Torkel Franzén earned his PhD in philosophy in 1987 for work on provability and truth, available online and in hard copy in the imprint of Acta Universitatis Stockholmiensis, deposited at university libraries worldwide. He was a world-class expert on incompleteness and inexhaustibility and an able and tireless expositor of the use and abuse of Gödel’s Incompleteness Theorems. Torkel will be remembered and celebrated for his incisive contributions to logic and his magnanimous bestowals of honesty and wisdom in public discourse. My condolences for this untimely loss go out to his friends and family.

0.0.0 the voice of the turtle

L’IDÉE est tout. Le nom propre n’est que l’exemple et la preuve de l’idée.
THE IDEA is all. The proper name is not but the example and the proof of the idea.
—Alfred de Vigny, Réflexions sur la vérité dans l’art1

    The Fragestellung of John Robert Ross’ 1986 study of universal grammar,2 recounts a familiar legend as follows:

    The following anecdote is told of William James. I have been unable to find any published reference to it, so it may be that I have attributed it to the wrong person, or that it is apocryphal. Be that as it may, because of its bull’s-eye relevance to the study of syntax, I have retold it here.
    After a lecture on cosmology and the structure of the solar system, James was accosted by a little old lady.
    “Your theory that the sun is the center of the solar system, and that the earth is a ball which rotates around it, has a very convincing ring to it, Mr. James, but it’s wrong. I’ve got a better theory,” said the little old lady.
    “And what is that, madam?” inquired James politely.
    “That we live on a crust of earth which is on the back of a giant turtle.”
    Not wishing to demolish this absurd little theory by bringing to bear the masses of scientific evidence he had at his command, James decided to gently dissuade his opponent by making her see some of the inadequacies of
    “But what does this second turtle stand on?” persisted James patiently.
    To this, the little old lady crowed triumphantly,
    “It’s no use, Mr. James—it’s turtles all the way down!”

Continue reading 0.0.0 the voice of the turtle