Posts tagged Bertrand Russell

Gnu’s to me

One of the nice things about my recent journey to Alabama is that I got the chance, along the way, to hang out with my folks in Auburn for a couple days, and, before I left, also managed to drop in at my second favorite used bookstore in the world, The Gnu’s Room. (Now both a used bookstore and a café, apparently; also now enjoying the patronage of the Auburn University Philosophy Department.) Here’s what I scored while I was there; I found all but two of these books sitting together in one stack, apparently recent arrivals. The other two came from the Philosophy shelf. And none of them cost me more than $4.00.

  • Raymond J. McCall (1952/1961), Basic Logic: The Fundamental Principles of Formal Deductive Reasoning, 2nd edition (Barnes & Noble, Inc.). A peculiar and (judging from the Preface) delightfully cranky textbook in logic. The peculiarity comes from the crankiness: McCall is a Catholic Aristotelian who spends the preface railing against the Wolffian perversion of the modern mathematicized logic (which he believes is due to a confusion of material logic and formal logic). He then devotes the entire textbook to a hardcore course in the categorical syllogism with some closing material on the theory of judgment.

  • Mary Hartman and Lois W. Banner (eds.) (1974), Clio’s Consciousness Raised: New Perspectives on the History of Women. An anthology with a great title and a pretty good spread of topics from Feminist Studies Inc., published by Harper & Row. The modal topic is, as usual, women in Victorian America and Victorian England, but several other things get covered too.

  • Evelyn Reed (1969/1970), Problems of the Women’s Liberation Movement: A Marxist Approach. From Pathfinder.

  • Hugh Hawkins (ed.) (1970), The Emerging University and Industrial America. A short anthology of essays — some from participants like Josiah Royce, others from historians looking back — from D.C. Heath’s Problems in American Civilization series.

  • Bertrand Russell (1926), Education and the Good Life. A paperback edition from Avon Books, which looks to be a printing from the early 1960s or so, but I can’t find the date of the reprint.

  • E. David Cronon (ed.) (1963/1969), Labor and the New Deal. A documents reader from the Berkeley Series in American History.

  • Albert A. Blum (1963/1972). A History of the American Labor Movement. An alleged survey of American labor history, published as American Historical Association pamphlets #250, which I read on the plane back from Alabama. It’s actually just a recitation of the AFL-CIO party line on the triumph of state unionism, the wisdom of George Meaney and Walter Reuther, and the glory of the NLRB; any mention of the labor radicals (land-redistributionists, money reformers, the IWW) is only to summarily push them aside in a few opening paragraphs about their utopianism, foolishness, or failure. Blum, remarkably, manages to discuss the big drop-off in unionism from 1919-1929 without even once mentioning either the Palmer Raids or the Red Scare more broadly.

New from the Scriptorium: Part I of Instead of a Book and Part I of the Principles of Mathematics

One of the things I’ve been working on while I’ve been away from blogging is transcribing public domain texts for the Fair Use Repository. I have a few different projects on tap there; right now, what’s worth mentioning are the following two online editions:

  1. Benjamin R. Tucker’s Instead of a Book, by a Man Too Busy to Write One is a classic of individualist anarchism. It’s also a classic of miscellaneous writing; the title (as well as the subtitle, A Fragmentary Exposition of Philosophical Anarchism) refers to the fact that it’s composed of fragments from Tucker’s writing, mainly from Liberty. Bloggers may, thus, feel an odd sense of familiarity in the reading; but for its being arranged topically instead of in reverse chronological order, the way in which Instead of a Book reads — heavily based on dialog and critical engagement, focused on short points, sometimes organizing itself into extended discussion threads between Tucker and other writers — will seem almost indistinguishable from the way that blogs are written today. In any case, Fair Use now has the introductory essays and the entirety of Part I (on The Individual, Society, and the State) available online, including Tucker’s masterful essay on State Socialism and Anarchism, an extended discussion with John Beverly Robinson over non-resistance (i.e., the permissibility of defensive violence) (1, 2, 3, 4), and an excellent long essay by Clara Dixon Davidson on Relations Between Parents and Children. Now it’s on to Part II, on Money and Interest. Stay tuned!

  2. Readers may remember that I mentioned quite a while ago that I’d started on a transcription of Bertrand Russell’s The Principles of Mathematics (1903). Well, after working on it off and on (mostly off) for the last year and a half, the online edition now includes the entirety Part I of Russell’s book (on The Indefinables of Mathematics, which, along with the two appendices, contains most of the work’s sustained discussion of philosophical logic). Notably, it concludes with Russell’s first sustained discussion of Russell’s paradox. From here it’s on to Part II, on the theory of Number.

There’s more to come soon, both for these works and in some other projects I’ve got coming down the pipeline. Read, cite, and enjoy!

The Gift of Reading

Happy Christmas, everyone. Here’s some holiday reading, as a gift from me to you. World War I may not seem like the best topic for the season, but, well, that’s what I’ve been working on lately.

  • At Dulce Et Decorum Est today, you can read a powerful review essay by Phil Shannon, on the Soldier’s Truce of Christmas, 1914 (which I first encountered a year ago, through Kevin Carson’s blog.)

    It was the war that was supposed to be over by Christmas. It very nearly was. A spontaneous soldiers’ truce broke out along the Western Front on Christmas Eve 1914, four months after the start of hostilities.

    Peace on Earth, goodwill to all men — British, French and German soldiers took these usually hypocritical Christmas sentiments for real and refused to fire on the enemy, exchanging instead song, food, drink and gifts with each other in the battle-churned wastes of no-man’s land between the trenches.

    Lasting until Boxing Day in some cases, the truce alarmed the military authorities who worked overtime to end the fraternisation and restart the killing.

    Stanley Weintraub’s haunting book on the Christmas Truce recounts through the letters of the soldiers the extraordinary event, routinely denigrated in orthodox military histories as an aberration of no consequence, but which was, argues Weintraub, not only a temporary respite from slaughter but an event which had the potential to topple death-dealing governments.

  • Some time ago, I put up a copy of Randolph Bourne’s most famous essay, The State, online at the Fair Use Repository. Lots of people had already posted extracts from The State online in all kinds of different forums (usually under the title War is the Health of the State). But as far as I know the Fair Use edition is the only complete online transcription. (The others usually omit Part II, Bourne’s analysis of American politics and the party system.)

    In any case, the more topical news is that I’ve just added two more of Bourne’s essays on the war — essays which, unlike The State, were published within Bourne’s own lifetime. These both come from his time writing for Seven Arts: The War and the Intellectuals is from June, 1917, and A War Diary is from September, 1917. Unfortunately what was true of the Sensible Liberals and New Republic columnists of 1917 could just as easily have been written last week.

    The results of war on the intellectual class are already apparent. Their thought becomes little more than a description and justification of what is already going on. They turn upon any rash one who continues idly to speculate. Once the war is on, the conviction spreads that individual thought is helpless, that the only way one can count is as a cog in the great wheel. There is no good holding back. We are told to dry our unnoticed and ineffective tears and plunge into the great work. Not only is everyone forced into line, but the new certitude becomes idealized. It is a noble realism which opposes itself to futile obstruction and the cowardly refusal to face facts. This realistic boast is so loud and sonorous that one wonders whether realism is always a stern and intelligent grappling with realities. May it not be sometimes a mere surrender to the actual, an abdication of the ideal through a sheer fatigue from intellectual suspense? The pacifist is roundly scolded for refusing to face the facts, and for retiring into his own world of sentimental desire. But is the realist, who refuses to challenge or to criticise facts, entitled to any more credit than that which comes from following the line of least resistance? The realist thinks he at least can control events by linking himself to the forces that are moving. Perhaps he can. But if it is a question of controlling war, it is difficult to see how the child on the back of a mad elephant is to be any more effective in stopping the beast than is the child who tries to stop him from the ground. The ex-humanitarian, turned realist, sneers at the snobbish neutrality, colossal conceit, crooked thinking, dazed sensibilities, of those who are still unable to find any balm of consolation for this war. We manufacture consolations here in America while there are probably not a dozen men fighting in Europe who did not long ago give up every reason for their being there except that nobody knew how to get them away.

    — Randolph Bourne, The War and the Intellectuals ¶ 12

    And:

    The penalty the realist pays for accepting war is to see disappear one by one the justifications for accepting it. He must either become a genuine Realpolitiker and brazen it through, or else he must feel sorry for his intuition and be regretful that he willed the war. But so easy is forgetting and so slow the change of events that he is more likely to ignore the collapse of his case. If he finds that his government is relinquishing the crucial moves of that strategy for which he was willing to use the technique of war, he is likely to move easily to the ground that it will all come out in the end the same anyway. He soon becomes satisfied with tacitly ratifying whatever happens, or at least straining to find the grain of unplausible hope that may be latent in the situation.

    But what then is there really to choose between the realist who accepts evil in order to manipulate it to a great end, but who somehow unaccountably finds events turn sour on him, and the Utopian pacifist who cannot stomach the evil and will have none of it? Both are helpless, both are coerced. The Utopian, however, knows that he is ineffective and that he is coerced, while the realist, evading disillusionment, moves in a twilight zone of half-hearted criticism and hoping for the best, where he does not become a tacit fatalist. The latter would be the manlier position, but then where would be his realistic philosophy of intelligence and choice? Professor Dewey has become impatient at the merely good and merely conscientious objectors to war who do not attach their conscience and intelligence to forces moving in another direction. But in wartime there are literally no valid forces moving in another direction. War determines its own end–victory, and government crushes out automatically all forces that deflect, or threaten to deflect, energy from the path of organization to that end. All governments will act in this way, the most democratic as well as the most autocratic. It is only liberal naïveté that is shocked at arbitrary coercion and suppression. Willing war means willing all the evils that are organically bound up with it. A good many people still seem to believe in a peculiar kind of democratic and antiseptic war. The pacifists opposed the war because they knew this was an illusion, and because of the myriad hurts they knew war would do the promise of democracy at home. For once the babes and sucklings seem to have been wiser than the children of light.

    — Randolph Bourne, A War Diary § 4

  • Third, I’ve also added a series of essays from 1915, which I discovered thanks to Carl Watner’s essay on nonviolent resistance in the most recent Journal of Libertarian Studies. The exchange began with Bertrand Russell’s The Ethics of War, which appeared in the January 1915 number of the International Journal of Ethics. Russell condemned the war and argued If the facts were understood, wars amongst civilized nations would case, owing to their inherent absurdity. (Meanwhile, in one of the more baffling parts of the essay, he did some utilitarian hand-waving to try to offer some rather despicable excuses for wars of colonization and the attendant ethnic cleansing. As usual, good anti-war instincts are betrayed by prejudice when utilitarian pseudo-calculations are allowed to intrude.) Ralph Barton Perry objected to Russell’s criticism, at least as applied to the ongoing war, in Non-Resistance and the Present War. Russell wrote two more articles. One of them a direct rejoinder to Perry, published as The War and Non-Resistance–A Rejoinder to Professor Perry in the IJE. The other, probably the best essay in the exchange, appeared in the Atlantic Monthly, under the title War and Non-Resistance. Of particular note is Section II, in which Russell considers how Britain might be defended from a foreign invasion with no army and no navy, using only the methods of non-violent passive resistance. Although Russell doesn’t quite realize it, the answer he offers amounts, in the end, to doing away with the central State and its organized machinery. With no levers of centralized power to take hold of, the invaders would find themselves in possession of little if anything. Anyway, it’s well worth a read.

Read, and enjoy.

May your holidays be full of light and warmth, joy in fellowship, comfort, and peace.

Chopping logic with nested conditionals: the Impiety Paradox

If there is no God, then She cannot answer our prayers, even if we make them with all our heart. That seems intuitive. (Maybe God doesn’t answer prayers even if She does exist; but we can be sure that She doesn’t if there is no God.) Call this the God-Dependence of Prayer.

As it happens, I don’t pray. This is an empirically verifiable fact. Call this the Impiety Thesis.

But if we suppose that both the Impiety Thesis and the God-Dependence of Prayer are true, is that enough to prove that God does exist? That would seem awkward; especially for the impious, since it’s their very impiety that proves the existence of God. cabrutus (2006-02-09) and Scottish Nous (2006-02-12) think that it might. Let’s start with the following propositional constants:

G =def. God exists
P =def. I pray
A =def. God answers my prayers

We can formalize GDP by saying If God does not exist, then it’s not the case that God answers my prayers if I pray, i.e., ~G → ~(PA). We can formalize IT by saying It’s not the case that I pray, i.e., ~P. Now here’s a formally valid argument from those two premises to prove that G, i.e., that God does exist:

  1. ~G → ~(PA) (given: GDP)
  2. ~P (given: IT)
  3. ~PA (logical addition 2)
  4. PA (material implication 3)
  5. ~~(PA) (double negation 4)
  6. ~~G (modus tollens 1, 5)
  7. G (double negation 6)

Therefore, God exists. Q.E.D., hosanna, and amen.

I’m pointing this argument out not because I think it’s convincing, but rather because Scott and cabrutus each pointed it out as a puzzle. I think the puzzle is extremely easy, and that it simply wouldn’t exist for someone who hasn’t been drilled in the canons of 20th century propositional logic. (Which is not to say that there’s something deeply wrong about the canons of 20th century propositional logic, just that the training tends to have a few odd side-effects.) So here’s the solution, as I see it: we need to use the symbol → to mean material implication (pq =def ~(p & ~q)) if we are going to make the step from premise 3 to premise 4. But if we’re consistently using the symbol → to mean material implication, then premise 1 (GDP) is false, or rather, it’s false wherever premise 2 (IT) is true. But didn’t we agree above that the God-Dependence of Prayer seems intuitively true (whether I pray or not)? Yes, but that’s because we were thinking about what it intuitively means, before we formalize it into premise 1 using truth-functional logical operators. The following is intuitively plausible whether I pray or not:

If God does not exist, then it’s not the case that if I pray, my prayers will be answered.

The following, however, is not:

~G → ~(PA)

… because that’s logically equivalent to:

~G → (P & ~A)

… i.e., If God does not exist, then it’s true both that I pray to God and that my prayers are not answered. Material implication, by definition, can only be false when the antecedent is true and the consequent is false, so denying a material implication is the same as affirming, among other things, the antecedent. But there is no reason to believe that if God does not exist, then it’s true both that I pray to God and that my prayers are not answered unless I do, in fact, pray to God. If I don’t, then I pray to God materially implies that my prayers are answered is true–as is I pray to God materially implies that my prayers are not answered–a false statement materially implies all statements. (There is some reason to believe If it’s true both that God does not exist and I pray to God, then my prayers are not answered, i.e. (~G & P) → ~A. But that’s logically equivalent to ~G → (P → ~A), not ~G → ~(PA).)

The problem here is that we take GDP to be plausible because when we say If God does not exist, then it’s not the case that if I pray, God will answer my prayers, we’re reading the if-then nested in the consequent to express something like a logical entailment, or a causal connection, or a counterfactual conditional, all of which can fail to be true without the antecedent being true. (The counterfactual if I were the King of England, I would be very poor is false; if I were the King of England, I would be very rich. But I am the King of England does materially imply I am very poor; I am the King of England is false, and a false statement materially implies all other statements.) The solution, then, is simply to point out that if → is being consistently used to express material implication, then 1 is false, and only seemed to be true because we formalized GDP incorrectly. And if → is not being used consistently to express material implication, then the attempt to infer 6 from 1 and 5 commits a fallacy of equivocation.

I point this out because I think the fact that it even seemed like an interesting puzzle to modern philosophers is itself interesting. I suspect that if you walked someone through the argument who hasn’t been drilled in introductory modern logic, or who doesn’t remember the drilling very well (those of you who haven’t, or don’t, can correct me if I’m wrong), they’d object at the step from 3 to 4 (from It’s true that I don’t pray or that God answers my prayers to If I pray then God answers my prayers), and the only justification we could give is by drawing out a truth-table for material implication and asking them to accept, on stipulation, that that’s what we mean by If-then. That’s because material implication is a logically useful notion, but (deliberately!) leaves out a lot of what’s meant when we say If this is true, then something else is true. The danger is that we have a distinct tendency to start by meaning what we mean by an ordinary language if-then, and end up formalizing it with material implication, and then shaking our head at the results.

As a historical side note, back in 1894, Lewis Carroll (yes, that Lewis Carroll) wrote an article on logic for Mind, in which he pointed out A Logical Paradox involved in nested hypotheticals of the form If C is true, then if A is true, B is not true (C → (A → ~B)), when combined with a second premise that If A is true, B is true (AB). You can read through the paradox (and accompanying vignette about three barbers) yourself; the reason I mention it here is because modern logicians would tend to be baffled that anyone ever found this puzzling at all: Carroll’s paradox is easily dissolved if you interpret hypotheticals according to the modern notion of material implication. In particular, Carroll suggests the following two very interesting questions in connection with his argument: Can a Hypothetical, whose protasis is false, be regarded as legitimate? and Are two Hypotheticals, of the forms If A then B and If A then not-B, compatible? Most modern logicians would instinctively answer Yes; in fact, it’s always true, and Yes, as long as A is false, because if you read the If A then B as material implication (as modern logicians have been drilled to do), then If A then B is just logically equivalent to It’s not the case that both A is true and B is false, which can be true (indeed, always is true) when A is false, and, as long as A is false, is also perfectly compatible with It’s not the case that both A is true and B is not false. Once you admit both of these two answers, Carroll’s paradox disappears, apparently as nothing more than a relic of an obsolete method of logic and its primitive unclarity about implication. (Carroll, of course, could not be blamed, since the notion of material implication wasn’t current in English mathematical logic until it was introduced by Bertrand Russell a decade or so later, after Carroll had already shuffled off this mortal coil.)

But — to come back to the point, somewhat — solving one technical puzzle is no guarantee that you’ve solved them all, and in this case it turns out that training in the solution that makes it instinctively easy to dismiss the Carroll paradox (based on A → (B → ~C)), makes it instinctively hard to see why you should dismiss the Impiety Paradox here (based on A → ~(BC)). Hammers are good for pounding in nails, but there is always the danger that they will make everything look like a nail, when in fact the world is full of strange and un-nail-ish things. In light of that, it may be a lot less easy to dismiss logical paradoxes as mere obsolete artefacts of primitive logical notation than some philosophers in the last century thought. It is certainly the case that Carroll’s questions about Hypotheticals remain very interesting questions after all this time, in spite of the supposed march of technical progress in logic:

Several very interesting questions suggest themselves in connexion with this point, such as

Can a Hypothetical, whose protasis is false, be regarded as legitimate?

Are two Hypotheticals, of the forms If A then B and If A then not-B, compatible?

What difference in meaning, if any, exists between the following Propositions?

  1. A, B, C, cannot be all true at once;
  2. If C and A are true, B is not true;
  3. If C is true, then, if A is true, B is not true;
  4. If A is true, then, if C is true, B is not true.

–Lewis Carroll (1894), A Logical Paradox, ¶¶ 49–56

Philosophical progress

A couple of notes are in order about new philosophical material on the web. First, I’ve put up some new new material at Philosophy, et cetera; and second, I’ve put up some new old material at the Fair Use Repository.

First, my new new material: Richard Chappell of Philosophy, et cetera generously invited me to contribute some guest posts while he was away at a conference. Here’s the results, such as they are:

Second, there’s quite a bit of new old philosophical material now available at the Fair Use Repository. One of my initial projects for the Fair Use Repository was to increase the availability and visibility of G. E. Moore’s philosophical writing; beginning with a freely available transcription of Principia Ethica (1903) and, after half a year and several atrocious puns on G. E. Moore’s last name, moving on to two other notable works on ethics. The scriptorium has been busy since then, too; the public domain Mooreana now available to the free world now includes:

There’s also lots of new old stuff to peruse besides Moore. Here’s a quick attempt at a break-down:

  1. Bertrand Russell, The Elements of Ethics (1910) is available in full. The essay attempts to sketch out the outlines of a theoretical ethics, based on by Russell’s reading (sometimes his misreading, but what else is new?) of Principia Ethica.

  2. Bertrand Russell, The Principles of Mathematics (1903): Russell’s first great labor towards a logicist account of mathematics. As of today, Preface, Chapter I: Definition of Pure Mathematics, Chapter II: Symbolic Logic, and Appendix B, Russell’s first full statement of the Theory of Types, are available in full online.

  3. Ludwig Wittgenstein, review of of Professor Coffey’s The Science of Logic (1913): the first public record of Wittgenstein’s philosophical views (and one of only three works on philosophy published in his lifetime); this is a merciless review of a logic textbook, written at the invitation of The Cambridge Review in late 1912 and published in early 1913, while Wittgenstein was still an undergraduate at Cambridge. The original (which has apparently not survived) was written in German, and then translated into English by Wittgenstein, with the help of his friend David Pinsent.

  4. T. H. Green, Prolegomena to Ethics (1884): transcriptions of the Analytical Table of Contents (which summarizes the argument of the entire book), the Introduction, the (enormous) first chapter, and Book III Chapter I are now available online.

  5. Lewis Carroll, What the Tortoise said to Achilles (1894) and A Logical Paradox (1895): Lewis Carroll published two articles in the philosophical journal Mind on logical paradoxes (interestingly, he published them as Lewis Carroll, rather than as Charles Dodgson). One of the articles, What the Tortoise said to Achilles, is discussed vigorously to this day. The other, A Logical Paradox was a hot topic in philosophical logic for about 10 years or so after its publication; today it’s almost unknown because people took it for granted that material implication had solved the problem. (Try reading it and see if you feel any intuitive pull towards the paradox.) Still, if there are good reasons to doubt that material implication does a good job of capturing the meaning of conditional statements, there may also be good reasons to start trying to get into the puzzle again. In any case, both articles are now available online.

  6. William James, Essays in Radical Empiricism (1912): James’s elaboration and defense of radical empiricism, the doctrine of a world of pure experience. Ralph Barton Perry’s editorial Preface and James’s first essay, Does Consciousness Exist?, are available in full online.

There’s more where that from. Stay tuned!