[This originally appeared as a guest post that I wrote for Richard Chappell’s blog Philosophy, et cetera]

Here’s one of the few canonical philosophical puzzles that I had learned about by the age of five. What’s the truth-value of the following statement?

(L) This statement (L) is false.

The problem, of course, is that if (L) is true then it’s false, and if (L) is false then it’s true. Thus, any theory of truth that assigns a truth-value to (L) is internally contradictory, since the theory will (inter alia) include the contradictory truth-ascription:

(TL) L is true if and only if L is false.

Since there are no true contradictions, a theory of truth must not assign any truth-value to (L) at all. But how do you doing it? If a statement hasn’t got a truth-value, then the usual take is that they are, in some respect, nonsense; that is, they fail to make an assertion — just as “Cat mat on the sat the” fails to make an assertion. The canonical approach to (L) in the 20th century has been to try to come up with some principled means of ruling (L) out of the language by means of setting up the right structure of rules beforehand (just as you can point to the preexisting rules of syntax to show that “Cat mat on the sat the” doesn’t amount to a complete sentence). The most famous attempt, and the inspiration of many of the subsequent attempts, has been Tarski’s attempt to sidestep the Liar Paradox by means of segmenting language into object-language and meta-language layers. The idea being that, if you do this assiduously, you can avoid self-referential paradoxes because self-reference won’t be possible in languages whose sentences can be ascribed truth-values; because they can only be ascribed truth-values within a meta-language that contains the names of the object language’s sentences and truth-predicates for those sentences. I have a lot of problems with this approach; a full explanation of them is something that I ought to spell out (indeed, have spelled out) elsewhere. But here’s a quick gloss of one of the reasons: Tarski and the people inspired by him started setting up ex ante rules to try to rule out self-referential sentences because it’s self-reference that makes the Liar Paradox paradoxical (and that makes for similar paradoxes in similar sentences; exercise for the reader: show how “If this sentence is true, then God exists” is both necessarily true and strictly entails the existence of God). But there’s an obvious and general problem for the method: there are self-referential sentences which are unparadoxical, and indeed self-referential sentences which are true. Here’s an example which may or may not cause trouble for Tarskian theories, depending on the details:

(E) This sentence (E) is in English.

(E) is truth-valuable; and in fact it is true. (If, on the other hand, it had said “This sentence is in French,” it would have been false.) Now, this may cause trouble for the Tarskian method and it may not, depending on the details of a particular account. (Sometimes people want to ban all self-referential sentences; sometimes they are more careful and claim that object languages might be able to name their own sentences but only so long as they don’t contain the truth-predicates for their own language.) But even if (E) is allowed, you haven’t solved the problem. There are plenty of self-referential truth-ascribing sentences that aren’t paradoxical, too. Here’s one:

(EM) Either this sentence (EM) is true, or this sentence (EM) is false.

Unlike (L), this causes no logical paradoxes. If you suppose that it’s false, that means that it turns out to be true — since the second disjunct, “this sentence (EM) is false” turns out to be true; meaning that it cannot be false. But it can be true, without contradiction. So it has to be true, if it has any truth-value at all. That shouldn’t be surprising; it’s an instance of the law of the excluded middle, and all instances of the law of the excluded middle are true.

Now, you might think that (EM)’s relationship to ordinary talk is attenuated enough, and the reasons for thinking it unparadoxical are technical enough, that it might be an acceptable loss if some other technical stuff that saves us from (L) happens to rule out (EM) too. I’d be inclined to agree, except that (EM) isn’t the only example I had up my sleeve, either. Here’s another. In the Prologue to the Travels, Marco Polo wrote,

We will set down things seen as seen, things heard as heard, so that our book may be an accurate record, free from any sort of fabrication. And all who read this book or hear it may do so with full confidence, because it contains nothing but the truth.

Let M be the conjunction of all the assertions that Marco Polo makes in his book. The book contains nothing but the truth if and only if M is true, but that the book contains nothing but the truth is one of the many assertions in the book, so “M is true” is one of the conjuncts of M. Thus:

(M) This conjunction (M) is true, and Marco Polo traveled the Silk Road to Cathay, and served in the court of the Great Khan, and observed the barbarous customs of lesser Armenia, and … and … and ….

But it’s either true or false that Marco Polo’s book contains nothing but the truth; that assertion is a standard bit of understood language (passages just like it are a near-universal feature of traveler’s tales, or other extraordinary stories where the author feels the need to reassure you that she’s not making things up). If your theory of language throws it out as nonsense, then your “theory of language” needs to be thrown out, on the grounds that it’s not semantically serious. (Whatever it’s a theory of may be interesting, but it’s something other than language as it actually exists.)

Now, like Polo, I may have been fudging just a bit in what I said. I suggested that M isn’t paradoxical; I don’t think it is, but there is a way to make it seem paradoxical. Lots of readers have doubted that Polo was telling the truth; some of them, for example, were unimpressed by the evidence that he had ever served in the court of the Great Khan; others weren’t so sure about the tales of dog-headed men or giant birds that consumed elephants. Whatever the case, they believed that Marco Polo made at least two false assertions in his book: (1) the claim about his journeys that they doubted, and (2) the claim that his book contained nothing but the truth. Call these the normal skeptics. I’m sure there were also a few readers (however credulous they would have to have been), who believed that the Travels really did contain nothing but the truth; that is, that there were no false assertions in the book, including the assertion that the book contained no false assertions. Call these the normal believers. But now imagine a third kind of reader, a perverse skeptic — a philosopher, of course — who noticed that you could gloss the contents of the book as M, and who decided that she believed everything that Polo said in the book about his journeys, from the customs of lesser Armenia to the domains of the Great Khan to the giant birds. She believes everything in the book, except … there is one assertion that she thinks is false — that is, (1) the assertion that everything in the book is true, and nothing else.

There are a couple of different ways that you could approach the difficulty. One way is to point out that the perverse skeptic really is being perverse. That’s just not how you can sensibly read the book. Either you think that nothing in the book is false, or you think that at least two things are; the assurance of truthfulness just can’t be a candidate for falseness until something else has been shown false. But if you list the truth-conditions of M, then “M is true” is one among them, and it’s hard to see how you could stop the perverse skeptic from going down the list and picking that one as the only one to be false. Certainly Polo doesn’t say “The rest of the book besides this sentence contains nothing but the truth.” And given that he did say what he did, I’d be hard put to say that “this book contains nothing but the truth” isn’t one of the untruths denied by the sentence, if something else in the book is false.

Another way to approach it is this: you can imagine an argument between the normal skeptic and the normal believer; whether or not one ever managed to convince the other in the end, you can in principle identify the sorts of reasons that they might offer to try to determine whether Polo really did tell the truth about the birds, or about the Khan, or…, and you can say what things would be like if one or the other is true. But what kind of argument could the normal believer and the perverse skeptic have? How would one convince the other? Or, to take it beyond the merely psychological point to the epistemological point, what kind of reasons could the normal believer possibly give to the perverse skeptic to give up the belief that “this book contains nothing but the truth” is false? (She can’t point to all the true statements about his journey; the perverse skeptic already believes in those.) Or, to take it beyond the epistemological point to the ontological point: what sort of truth-makers could even in principle determine whether the normal believer or the perverse skeptic is in the right?

So there is a problem with M, to be sure. But the problem is not the same as the problem posed by L: there’s no logical contradiction involved, so its self-referentiality sets off no logical explosions. And the solution can’t be the same either: the radical move of abandoning the sentence as meaningless works with (L), where there’s just no right way to take it, but it doesn’t help us out with (M), where there obviously is a right way to take it (i.e., as the normal readers take it, and not as the perverse reader takes it).

So there has to be some right way to go about ascribing a truth-value to (M) (and also (E)). Whatever it is, it may very well also explain how we can ascribe a truth-value to (EM). But it certainly cannot also mean that we try to ascribe a truth-value to (L). What is it? Is there some kind of principled and motivated general rule that we can add to our logical grammar, so as to get M and E and maybe EM but no L? If so, what in the world would it be? If not, then what do we do?

(I have my own answers; for the details, you can look up Sentences That Can’t Be Said in the upcoming issue of Southwest Philosophy Review. Or contact me if you’re interested enough to want a copy of the essay. But I want to pose the puzzle and see what y’all think about it as it stands.)

Update 2005-12-08: I fixed a minor error in phrasing. Thanks to Blar for pointing it out in comments.

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!

On 6 December 1989, sixteen years ago today, Marc Lepine murdered 14 women at Montreal’s Ecole Polytechnique. He killed them because they were women; he went into an engineering class with a gun, ordered the men to leave, screamed I hate feminists, and then opened fire on the women. He kept shooting, always at women, as he moved through the building, killing 14 women and injuring 8 before he ended the terror by killing himself.

6 December is a day of remembrance for the women who were killed. They were:

• Geneviève Bergeron, aged 21
• Hélène Colgan, 23
• Nathalie Croteau, 23
• Barbara Daigneault, 22
• Anne-Marie Edward, 21
• Maud Haviernick, 29
• Barbara Maria Klucznik, 31
• Maryse Leclair, 23
• Annie St.-Arneault, 23
• Michèle Richard, 21
• Maryse Laganière, 25
• Anne-Marie Lemay, 22
• Sonia Pelletier, 28; and
• Annie Turcotte, aged 21

I don’t have much to add today, except to repeat what I said last year:

The Montreal Massacre was horrifying and shocking. But we also have to remember that it’s less unusual than we all think. Yes, it’s a terrible freak event that some madman massacred women he had never even met because of his sociopathic hatred. But every day women are raped, beaten, and killed by men–and it’s usually not by strangers, but by men they know and thought they could trust. They are attacked just because they are women–because the men who assault them believe that they have the right to control women’s lives and their sexual choices, and to hurt them or force them if they don’t agree. By conservative estimates, one out of every four women is raped or beaten by an intimate partner sometime in her life. Take a moment to think about that. How much it is. What it means for the women who are attacked. What it means for all women who live in the shadow of that threat.

On what seems like an unrelated topic, I’ve been asked before, and I’m sure I’ll be asked again, what it is that makes me so sympathetic to, and inspires me in, radical feminism, and Andrea Dworkin’s version of radical feminism specifically. That’s a question that gets tossed at anyone who expresses sympathy for or interest in Dworkin’s work, but I guess it’s supposed to be especially puzzling in my case, as someone who’s (1) male and (2) pretty stridently libertarian in my politics. There are a lot of things to say in response, but the one that means the most is to say that Andrea Dworkin takes violence against women seriously. What it means for violence, and the threat of violence, to be so pervasive, systematic, intense, and socially invisible or culturally excused. The demands that places on all of us. The urgency and seriousness of the struggle that it calls for. The fact that I’m male (and that I’ve had to make the painful realization of how often what I’ve said and what I’ve done hurt women, how much it was shaped by, and participated in, the same system of male supremacy that has hurt some of my dearest friends and family so badly) harldy overrides the fact that, well, what she says is true. (I know it’s true, because it’s happened to my friends.) And the fact that my politics are centrally concerned with a radical and comprehensive commitment to human freedom makes the insights offered by Andrea Dworkin (and Catharine MacKinnon and Susan Brownmiller and Robin Morgan and…) more, not less urgently needed. As I’ve written elsewhere (with my friend Roderick Long):

Brownmiller’s and other feminists’ insights into the pervasiveness of battery, incest, and other forms of male violence against women, present both a crisis and an opportunity for libertarians. Libertarianism professes to be a comprehensive theory of human freedom; what is supposed to be distinctive about the libertarian theory of justice is that we concern ourselves with violent coercion no matter who is practicing it—even if he has a government uniform on. But what feminists have forced into the public eye in the last 30 years is that, in a society where one out of every four women faces rape or battery by an intimate partner,2 and where women are threatened or attacked by men who profess to love them, because the men who attack them believe that being a man means you have the authority to control women, male violence against women is nominally illegal but nevertheless systematic, motivated by the desire for control, culturally excused, and hideously ordinary. For libertarians, this should sound eerily familiar; confronting the full reality of male violence means nothing less than recognizing the existence of a violent political order working alongside, and independently of, the violent political order of statism. As radical feminist Catharine MacKinnon writes, “Unlike the ways in which men systematically enslave, violate, dehumanize, and exterminate other men, expressing political inequalities among men, men’s forms of dominance over women have been accomplished socially as well as economically, prior to the operation of the law, without express state acts, often in intimate contexts, as everyday life” (1989, p. 161). Male supremacy has its own ideological rationalizations, its own propaganda, its own expropriation, and its own violent enforcement; although it is often in league with the male-dominated state, male violence is older, more invasive, closer to home, and harder to escape than most forms of statism. This means that libertarians who are serious about ending all forms of political violence need to fight, at least, a two-front war, against both statism and male supremacy …

Here is the speech that Andrea Dworkin gave at the University of Montreal, a year and a day after the massacre:

Feminists should remember that while we often don’t take ourselves very seriously, the men around us often do. I think that the way we can honor these women who were executed, for crimes that they may or may not have committed–which is to say, for political crimes–is to commit every crime for which they were executed, crimes against male supremacy, crimes against the right to rape, crimes against the male ownership of women, crimes against the male monopoly of public space and public discourse. We have to stop men from hurting women in everyday life, in ordinary life, in the home, in the bed, in the street, and in the engineering school. We have to take public power away from men whether they like it or not and no matter what they do. If we have to fight back with arms, then we have to fight back with arms. One way or another we have to disarm men. We have to be the women who stand between men and the women they want to hurt. We have to end the impunity of men, which is what they have, for hurting women in all the ways they systematically do hurt us.

–Andrea Dworkin (1990): Mass Murder in Montreal, Life and Death, 105-114.

And, as I said last year:

To be serious about creating a free and just society, we have to be serious about ending violence against women. As Andrea Dworkin puts it (speaking about sexual assault), I want to see this men’s movement make a commitment to ending rape because that is the only meaningful commitment to equality. It is astonishing that in all our worlds of feminism and antisexism we never talk seriously about ending rape. Ending it. Stopping it. No more. No more rape. In the back of our minds, are we holding on to its inevitability as the last preserve of the biological? Do we think that it is always going to exist no matter what we do? All of our political actions are lies if we don’t make a commitment to ending the practice of rape. This commitment has to be political. It has to be serious. It has to be systematic. It has to be public. It can’t be self-indulgent. And the same is true of every form of everyday gender terrorism–stalking, battery, rape, murder. How could we face Geneviève Bergeron, Hélène Colgan, Nathalie Croteau, Barbara Daigneault, Anne-Marie Edward, Maud Haviernick, Barbara Maria Klucznik, Maryse Leclair, Annie St.-Arneault, Michèle Richard, Maryse Laganière, Anne-Marie Lemay, Sonia Pelletier, Annie Turcotte, and tell them we did anything less?

Take some time to keep the 14 women who were killed in the Montreal massacre in your thoughts. If you have the money to give, make a contribution to your local battered women’s shelter. As Jennifer Barrigar writes:

Every year I make a point of explaining that I’m pointing the finger at a sexist patriarchal misogynist society rather than individual men. This year I choose not to do that. The time for assigning blame is so far in the past (if indeed there ever was such a time), and that conversation takes us nowhere. This is the time for action, for change. Remember Parliament’s 1991 enactment of the National Day of Remembrance and Action on Violence Against Women — the glorious moment when every single womyn in the House stood together and claimed this Day of Remembrance. Remember what we can and do accomplish — all of us — when we work together. It is time to demand change, and to act on that demand. Let’s break the cycle of violence, and let’s do it now.

Remember. Mourn. Act.

Elsewhere

• Toronto Star 2005-12-06: Montreal Massacre victims remembered
• Anarchocyclist 2005-12-05: revolutionary women puts many pieces together nicely.

In the latest news from the world’s greatest deliberative bodies (thanks to Catallarchy 2005-12-02), Texas Republican Joe Barton has continued his diligent work to promote a conservative agenda and protection of individual rights by finding another unregulated industry for the House Energy and Commerce subcommittee’s tender ministrations.

College football is not just an exhilarating sport, but a billion-dollar business that Congress cannot ignore, said committee Chairman Joe Barton, a Texas Republican. Barton’s panel is separate from the House Government Reform panel that tackled steroids in baseball.

So Barton and the committee he chairs will be convening a Congressional hearing next on the compelling State interest of what ranking system collegiate football teams should use to determine the national championship.

The committee announcement called the hearing, scheduled for next Wednesday, a comprehensive review of the BCS and postseason college football.

Too often college football ends in sniping and controversy, rather than winners and losers, Barton said. The current system of determining who’s No. 1 appears deeply flawed.

Well, thank God, says I; it’s about time. If the State doesn’t provide a final arbiter to disputes over who the #1 college football team in the United States is, how will we avoid chaos?

Further reading

• GT 2005-11-23: Uncle Sam is your ISP
• GT 2005-10-27: Well, thank God.
• GT 2004-06-09: Airport! 2004

Did you know …

1. … that Christian anarchism (think William Lloyd Garrison or Leo Tolstoy) is just like anti-abortion terrorism and Christian Reconstructionism?

2. … that if you, personally, don’t mind chipping in for public roads, schools and sewer systems, that constitutes a knock-down refutation of the anarcho-capitalist complaint against taxation?

3. … that anti-capitalist anarchists are in fact Maoists who want a do-over of Bolshevik totalitarianism?

4. … that dismantling the right of habeas corpus is, in fact, a step towards anarchism?

5. … that Republican legislators and lobbyists who occasionally express contempt for government are, in fact, paradigm cases of anarchists?

It’s true! I read it on the Internet.. (Thanks, Guerilla Science.)

Here, at least, is something that anarchists of all sects, organizations, and creeds can come together on: Lisa Jones is a know-nothing blowhard. You can let her know what you think at HeyJones@gmail.com. Here’s my contribution:

Ms. Jones,

I recently read your column, The battle between law and anarchy, for the Rocky Mountain News. You wondered if most political debates today aren’t between right and left, but between anarchism and rule of law. I think you’re probably right, but I can’t say that I’m entirely convinced by your brief in favor of the rule of law.

There’s a lot to wonder about; for example, your comparison of the pacifist Christian anarchism of Leo Tolstoy or William Lloyd Garrison (who described complete nonviolence as one of the highest Christian duties) to the statist politics of the Christian Reconstruction movement seems a bit strained, as does your attempt to compare anti-capitalist anarchists such as Emma Goldman or Mikhail Bakunin to the death march of forced collectivism under Mao Zedong. (For the record, you might try reading the extensive and fierce anarchist polemics against Bolshevik tyranny, such as Goldman’s My Disillusionment in Russia.) I was also a bit puzzled by your attempt to portray Republican lobbyist Grover Norquist as an anarchist, when part of the point of the quip that you refer to (about making government so small you can drown it in the bathtub) is that he doesn’t want to abolish the government.

But for the moment I want to focus on a more theoretical point. In the course of criticising anarcho-capitalism, you say:

But anarcho-capitalists also oppose taxation and the very existence of the state. They want to privatize all public institutions, such as schools, and rely on a self-regulating competitive marketplace instead of government. …

Plus, I don’t mind chipping in for public roads, schools and sewer systems. Insofar as tax revenues are used wisely for the common good, I support limited taxation.

Actually, all anarchists oppose taxation and the very existence of the state. That’s what makes them anarchists rather than statists. But I’m a bit puzzled by the justification you give for limited taxation. If you, personally, don’t mind chipping in for public roads, schools, and sewer systems, then no anarchist would suggest that you shouldn’t be allowed to get out your checkbook and make a donation. But that’s not taxation. Taxation is what happens when other people who don’t want to chip in are forced to do so. Do you think that you have the right to sign away other people’s money without their consent? If not, why does your personal willingness to pay for public goods have anything to do with the argument?

Curiously,
Charles Johnson

Let’s hear your response!