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!

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.

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 → ~(P → A). 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 → ~(P → A) (given: GDP)
2. ~P (given: IT)
3. ~P ∨ A (logical addition 2)
4. P → A (material implication 3)
5. ~~(P → A) (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 (p→q =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 → ~(P → A)

… 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 → ~(P → A).)

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 (A → B). 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 → ~(B → C)). 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

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:

• Philosophy, et cetera 2005-12-05: Freak intelligence, marginal cases, and the argument for ethical vegetarianism, in which I take a critical look at one of the canonical arguments for ethical vegetarianism and how it is typically defended. (I actually think that a version of the argument works, but explaining why requires more detail-work than ethical vegetarians have typically done.)

• Philosophy, et cetera 2005-12-07: The ends in the world as we know it: in which I curse a non-functional comment form, argue for a richer conception of what the world studied by science contains (by way of Michael Thompson’s account of aristotelian categoricals), and reply to some comments on my ethical vegetarianism post.

• Philosophy, et cetera 2005-12-08: If the title of this post is true, then you should read it, in which I invite people to puzzle over some self-referential statements other than the famous Liar Paradox (“This sentence is false” is not the only self-referential statement you can make philosophical hay out of; and it seems likely that treating it as if it were has lead to some philosophical errors about self-reference).

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:

• The Nature of Judgment (1899). One of the essays that launched Moore and Russell’s break from British Idealism. (That’s something of a retrospective judgment, incidentally; in the essay itself Moore’s thesis is that the world is constituted by concepts; it’s the account of concepts that marks the beginnings of a divergence from the idealists….)

• Principia Ethica (1903)

• Moore’s review of The Origin of the Knowledge of Right and Wrong by Franz Brentano (1903), mentioned in the Preface to Principia Ethica.

• The Refutation of Idealism (1903), another locus classicus for Moore’s break with British Idealism (by this point already fully accomplished). This was actually already available through Andrew Chrucky’s wonderful ditext.com, but not well-formatted for citing, and since I needed to cite it elsewhere, I repurposed his text according to the Fair Use Repository conventions.

• Ethics (1912), Moore’s wonderful but little-read sequel to PE

• You can also find Ralph Barton Perry’s February 1904 review of The Refutation of Idealism, which appeared in one of the very first issues of J. Phil.

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!

Sean Martin at common sense philosophy and Richard Chappell at Philosophy, et cetera have lately been puzzling over the claim that so-called sentences such as Caesar is a prime number are not false, but rather meaningless. They’re both inclined to think that this is wrong: it seems obvious enough that there’s a set of all prime numbers, and that Caesar isn’t in it (since everything in it is, inter alia, a number, and Caesar is not), so Caesar is a prime number is simply false. I think that the claim is meaningless rather than false, and that their attempt to give it a meaning commits a classical error in philosophy, of the sort exposed by Wittgenstein in both his earlier and his later work. But this will take some explaining.

To get an idea of why I take Caesar is a prime number to be meaningless, it will actually help to consider the psychological story that Richard suggests to deflate the intuition that it is meaningless. (I think Richard’s on to something in his story, but I think that it has more than a merely psychological bite.) He wonders if some might be tempted to deny it meaning simply because it is so very false, necessarily and obviously so, that no-one would ever even dream of seriously entertaining the thought that it might be true. Then, rather like how something might be so cold that it burns, so some sentences might be so false that they no longer seem it. I think that this is in fact the right track to be on, but to see why it actually supports the intuition for regarding Caesar is a prime number as meaningless rather than false, we need to observe that the difference between this mistake and the mistake involved in humdrum falsehoods such as Caesar was a barkeep is a difference in kind, not merely a difference in degree.

Think about it this way. Suppose that I — intending to say something true in the English language — say Caesar was a Greek. Ordinarily we would take this sentence to be both meaningful and false: Caesar was a Roman, not a Greek. So when I said it, I made a mistake; but there is an open question as to what sort of mistake I made, and you’d have to ask some questions to figure out the best way to understand my error. For example, I might have made a factual error about either Caesar, the man, or about Greeks, the category; if you asked why I said that Caesar was a Greek, I might say that I heard that Caesar was born in Athens, and believed it. Or I might have heard that in Caesar’s day, Greece extended from Anatolia to the Pillars of Hercules. Either of these would be flabbergasting examples of historical ignorance; but they would nevertheless be mistakes about Caesar or about the Greeks. On the other hand, it’s possible that my answers might reveal a linguistic mistake, about the word Caesar or the expression a Greek. For example, I might have thought that a Greek meant anyone born in an ancient Mediterranean culture, or that Caesar was Plato’s family name. In this case I didn’t make a mistake about Caesar, the man, or Greeks, the category. I just made a mistake about the terms that I was using to express myself, and the way to correct me would not be to teach me some history, but rather to clear up my misconceptions about what Caesar and a Greek mean in the sentences in which they are used.

Now let’s return to Caesar is a prime number. Suppose, again, that I said this, and that I wanted to say something true in the English language. What sort of mistake could you understand me as having made? Is there any conceivable matter of fact about Caesar, the man (or prime numbers) that I could be misinformed about which would explain my thinking that Caesar is a prime number? I can’t think of any conditions under which that kind of error would explain the utterance. The only cases that I can conceive, so far as I can tell, are cases in which there is a mistake about meaning, that is, in which I just haven’t got any sort of cognitive connection between my use of Caesar and a prime number in the sentence, and the actual man Caesar or the actual set prime numbers. Maybe I had been taught that Caesar was a name for a constant (equal to 3, say). Or maybe I thought that prime number was a way of saying a powerful member of Roman society. Either of these would, again, involve some flabbergasting ignorance, but what’s important to note here is that it’s not ignorance about Caesar or ignorance about prime numbers. Any position I might be in, such that it would explain my uttering Caesar is a prime number, is just a position in which I haven’t correctly learned how to use the sign Caesar or a prime number, in which I’ve made a mistake about the role that they play in the English language. (You might say: Look, I can think of a factual error you might make about Caesar that would make you think he was a prime number. You might have thought that he, Caesar, was an integer greater than zero, not a man. But do you really think that someone who thinks that Caesar was an integer greater than zero has correctly learned what Caesar means, in any plausible sense of the word meaning?)

The mismatch here is important: the kind of mistakes you can make that would lead you to utter Caesar was a Greek may be either factual or linguistic; but the kind that would lead you to utter Caesar is a prime number are — if what I’ve said is right — only linguistic. That’s a difference in kind between the two cases, and I think it’s a difference in kind that reflects something important about the logical (not just the psychological) status of the two utterances. If you are using English, then when you try to say Caesar is a prime number you are just not succeeding in meaning anything by it. (You may mean something by it in your own idiolect, but that’s another matter.) Gilbert Ryle famously called this sort of mistake a category mistake, and Carnap (who is the immediate source of Sean’s puzzlement) explained the mistake by saying that the name Caesar and the predicate is a prime number have a particular logical syntax — so that Caesar is a prime number, even though it fulfills the rules of English syntax, still fails to fulfill the rules of logical syntax, because part of understanding what Caesar means is understanding that he is not the sort of thing that is either prime or non-prime; and understanding what ____ is a prime number means is understanding that the predicate can only be ascribed to, or withheld from, a number. I think Carnap’s understanding of the situation is actually gravely mistaken, and Ryle’s description is perhaps misleading (for some detailed reasons why, see Edward Witherspoon’s Conceptions of Nonsense in Carnap and Wittgenstein in The New Wittgenstein, and Cora Diamond’s What Nonsense Might Be in The Realistic Spirit). The short of it is that the conclusion is right — Caesar is a prime number hasn’t got any meaning in English — but the diagnosis is wrong, and wrong because it presumes that Caesar and —— is a prime number all have determinate meanings that you can pin down independently of the statements that they occur in; having pinned them down, you can then say Look, the meaning of Caesar is incompatible with the meaning of —— is a prime number; if you try to put them together, they just won’t fit. But expressions have no meaning in isolation; they only get meanings in the context of their significant use within a language (for example, as they are employed in making assertions). If someone goes around saying Caesar is a prime number I don’t know what he means; I don’t know what he means by Caesar, or prime number, or even is a, at least not until I’ve asked him to explain to the point where I can see the sort of linguistic mistake that he’s making. If I ask him, I may find out that he was trying to say one of the things I mentioned above — for example, that Caesar was a powerful Roman, or that 3 is prime. Or I may find out that he was not asserting anything at all, but rather belting out an example of nonsense for philosophical purposes. Or, I may, after all, find out that he was just babbling, as much as if he had said Blitiri bububu. The problem isn’t even that Caesar is a prime number couldn’t have a meaning; I just mentioned a couple meanings it might have. It’s that it doesn’t, because, as people use the words, there isn’t any meaning given to Caesar in the number-place of a mathematical categorization, or to —— is a prime number in the predicate-place of a description of a person. Thus Wittgenstein’s claim that philosophical pseudo-problems are of the same kind as the question whether the Good is more or less identical than the Beautiful (TLP 4.003); the problem with that question is that — at the very least — no meaning has been given to the sign identical when it is used as an ordinal predicative adjective.

Now, if I put myself only in the Wittgensteinian position of saying that one or more parts of Caesar is a prime number hasn’t got a sense, and refuse to take the Carnapian route of saying that they’ve all got senses but those senses entail that the sentence as a whole must not have a sense, then Richard or Sean can always claim that they’ve given the constituent words a commonsensical meaning, and that given those meanings, the sentence is meaningful and false. For example, they both suggest giving Caesar the sense of Caesar, the man, x is a φ the sense of x is an element of the set of φ’s, and prime number the sense of a whole number that is evenly divisible only by itself and 1. But of course is a member of is no better off than is a when I try to imagine a factual error that would explain my saying that Caesar’s a member of the set of prime numbers, and the same thought-experiments that tend to count against the notion of a univocal meaning for is a, no matter what the subject and predicate nominal are, would also tend to count against the notion of a univocal relation of set membership, no matter what the relata are. If there is some general meaning that encompasses all of Caesar was a Greek, Caesar was a Roman, Caesar is a prime number, 3 is an Italian, 3 is a prime number, 3 is an irrational number, etc. then let them give it — but we have a right to expect that whatever meaning they give will have to make it clear how you could make some mistake about matters of fact, and not just the meanings of terms, that would explain how you could utter the category-error cases above.

And no, I don’t think that an appeal to the primitives of mathematical set theory will help here at all. Of course, sets of numbers, nations of people, orchards of trees, and so on may all have some similar formal features; those formal features may make some parallel treatment according to the schema provided by, say, axiomatic set theory possible. But that no more means that Caesar is a Roman and 3 is a prime number express the same relationship than your ability to map planar geometry into polynomial equations using the techniques of analytic goemetry means that geometry really is just algebra (or vice versa). That would also mean that there isn’t any meaningful set consisting of {Caesar, 3, the peach tree in front of my house, …} (since the claim is that no meaning has, so far, been yet given to the notion of a set, or to one or more of the purported elements of the set). If you had high hopes for a set like that, well, I’m sorry.

A parting note. Richard also wants to know about sentences that use empty designators (such as The present king of France is bald or Odysseus was set ashore at Ithaca while sound asleep). Some philosophers (Strawson, for example) think they’re meaningless; others (Russell, for example) that they are false. For what it’s worth, Frege, contrary to popular opinion, did not think that they are meaningless; but he didn’t think they were false either. He thought that they express a thought but have no truth-value (see my exegetical comments at Philosophy, et cetera). But I think that Frege clearly fails to give us a viable alternative — determinate thoughts are either true or false; what it is to have a determinate sense just is to have truth-conditions which are either met or unmet. As for whether Strawson or Russell is right, though, my suspicion is that either one of them could be right, depending on the sentence. There’s no reason to think that just because some uses of names and definite descriptions are tractable by means of Russell’s theory of descriptions or Strawson’s theory of presupposition, that all of them have to be tractable by the same method. Is Odysseus was set ashore at Ithaca while fast asleep a failed attempt to make an assertion, provided that there was no historical Odysseus? Probably. Certainly Russell’s attempts to gloss names such as Odysseus or Apollo with definite descriptions have been failures — see Naming and Necessity for some of the reasons why. Similarly I think that the King of France is bald probably presupposes rather than asserts that there is a present King of France, and so fails to say anything rather than saying something false. On the other hand, there are cases where it seems quite clear that Russell’s theory of descriptions ought to be applied: someone who says Yesterday I interviewed the present King of France! has said something that is both meaningful and false. And there are also cases that I think are simply not clear. I’m not sure whether, say, We are all subjects of the Emperor of North America asserts or presupposes that there is an Emperor of North America; you’d probably need to find out more about the dialogical context in which it was uttered to know whether it asserts falsely or fails to assert.

Richard also wants to know whether the condition that a sentence either violates syntactical requirements or else contains nouns that fail to refer is necessary or sufficient for a sentence to be meaningless. I think that it is not sufficient, for the reasons I give above: there are at least some cases in which sentences with empty designators ought to be treated according to Russell’s theory of descriptions, and those sentences say something false. Nor do I think it is necessary, for there are examples of sentences that neither contain empty designators nor violate any syntactical rules, but which must be meaningless on pain of contradiction. Here’s an example: This sentence is false. Here’s another one: Either this sentence is false or God exists. Clearly the designators in them are not empty: the sentence itself guarantees that they will pick out something. But if there’s any plausible candidate for a syntactic rule that they might be accused of violating, I haven’t found it. If think you’ve got a syntactic rule that you can cite to rule these sentences out, then go ahead, make my day.