Diet Soap Interview

I talk to Doug Lain of the Diet Soap podcast about paraconsistent logic, counterpossible reasoning, analyticity and confirmational holism here. You can also get the episode by just going to iTunes and searching for Diet Soap. It's Episode # 25, entitled "This Podcast Is A Lie."

There's also a short story at the end of the episode. It had to be pretty severely abridged for the podcast, and the print magazine it was originally published in is now defunct, so I put a Creative Commons-licensed version of the whole thing here.

What Calling The LNC "Metaphysical" Won't Get You A Free Pass On

[It's been recently forcefully pointed out to me that a regular, predictable schedule here would be good. Accordingly, I'm going to try to update every Monday and Wednesday for the foreseeable future. We'll see how that goes.]

So I just saw this extremely interesting article by Tuomas E. Tahko, "The Law Of Non-Contradiction As A Metaphysical Principle." (Thanks to William Shultz for the pointer.) From a quick skim, it looks like Tahko is making a useful distinction between the LNC understood just as a logical formula that says that for any sentence, the negation of the conjunction of that sentence and its negation is true, and something more like what I like to call "monaletheism" (a helpful term coined by Ryan Lake), a distinction often run together when the debate about dialetheism is casually referred to as a debate about the Law of Non-Contradiction. After all, the dialetheist can embrace the LNC in the former sense, as long as they're willing to commit to a secondary true contradiction, (P & ~P) & ~(P & ~P) for every simple contradiction (P & ~P) that they are committed to. Moreover, IIRC, the LNC is actually a logical truth in Graham Priest's favored logic LP (Logic of Paradox), and in a talk I saw in Melbourne, Koji Tanaka said that this was a feature of all of the paraconsistent logics that Koji liked. So this seems like a worthwhile distinction to make. As far as Tahko's favored way of expressing it....meh. I more or less agree with Quine on issues of ontological commitment, confirmational holism and the like, so I'm a bit skeptical about how much light is shed on the status of a given truth when we slap the "metaphysical" label on it, but Tahko's explication of what he's getting at with the label seems more or less unobjectionable to me:

"At its simplest, the metaphysical interpretation of LNC amounts to this: the entities of the mind-independent reality are plausibly governed by some sort of principles...as to what kind of properties a certain kind of entity can and cannot have, and further, some of these properties are mutually exclusive. For instance, a particle cannot both have and not have a charge at the same time, or an object cannot be both green and red all over at the same time. It seems that reality just is such that it conforms to the law of noncontradiction. For instance, a particle cannot both have and not have a charge at the same time, or an object cannot be both green and red all over at the same time."

The general spirit of this passage resonates nicely for me with what Frege seems to be getting at when he says that: "[l]ogic is concerned with the laws of truth, not of holding something to be true, not with the question of how men think, but with the question of how men must think if they are not to miss the truth." So far, so good.* What I have a problem with, in Tahko's presentation, comes shortly after that definition:

"Another thing to note before we proceed is that semantic paradoxes such as the Liar do not threaten LNC as a metaphysical principle. Any arbitrariness or vagueness over language has no bearing on LNC understood as a metaphysical principle. A counterexample to the metaphysical version of LNC could only be a true contradiction in the world."

I don't think this works. First of all, I'm deeply skeptical about the idea that the Liar Paradox has much of anything to do with vagueness. Take a typical Liar sentence:

# The sentence marked by the number sign is false.

No one, reading this sentence, has the slightest doubt about what sentence is being referred to, or about what it is to say of any sentence that it is false. Moreover, "true" and "false" certainly seem pre-philosophically to be mutually exclusive properties of sentences, certainly no less mutually exclusive than "red" and "green" as the colors of the entire visible surface of an object. So, unless sentences are not, for some reason, part of "the world" (which is certainly a strange thought, since they certainly *seem* to have an independent existence), then it looks like the LNC-as-a-"metaphysical"-principle as Tahko defines it should apply to the truth-and-falsehood of sentences as well as the redness-and-greenness of visible surfaces.

And what work is "arbitrariness" doing here? Of course, you could argue (as many people do) that any claim that "ungrounded" sentences like the Liar (or its non-paradoxical twin, the Truth-Teller) is either true or false is in some sense arbitrary, but if that line of thought gets you to the result that such sentences are "neither true nor false," you run into familiar problems with Strengthened Liar sentences, like:

$ The sentence marked with the dollar sign is not true.

...and the problem for the orthodox logical/metaphysical position on entities having some properties and not others, and some such combinations of properties being generally impossible, rears its ugly head once more. So, to sum up my objection to Tahko's move for side-stepping the semantic paradoxes, it seems to me that:

(a) Sentences are part of the world,
(b) Different semantic statuses of sentences seem to mutually exclude each other in the same way as e.g. different charges of particles or different colors of visible surfaces, and to equally be the sort of thing that the LNC-as-a-metaphysical-principle-as-defined-by-Tahko would pretty much have to apply to, &
(c) If the problem posed for logical orthodoxy by the Liar has anything to do with either vagueness or arbitrariness, it's far from obvious, and, at first blush, it's not clear how mention of either clarifies why the Liar isn't a problem for the-LNC-as-a-metaphysical-principle.

So, any thoughts out there? Is there a good way of glossing Tahko's discussion that makes his quick dismissal of the Liar more plausible than it sounds to me right now? Let me know what you think.






*Obviously, agreeing with Frege about *that* much is an entirely different matter from agreeing with him that logical truths are "analytic," or are about a metaphysically different sort of reality than other kinds of truths, or anything of the kind. Also, this description of what "logic is concerned with" on the relevant level of analysis shouldn't be taken as ruling out the possibility (unforeseen by Frege, as far as I know) that logical systems can fail to accurately model the way things really are but still be interesting and instrumentally useful tools for formal reasoning about various subjects.

A Quick Thought About Sylvan's Box, Paraconsistency and Truth-Value Gaps

Something occurred to me today and I'm curious to see what people who read this blog think about it.*

(1) Graham Priest has argued (convincingly, from my perspective) in many places that truth-value gaps are impossible. If there is no fact that makes P true, the fact that there is no such fact is sufficient to make it false, and that in any case gaps entail gluts--if a sentence is neither true nor false, then given that falsehood is best understood as truth of negation, by a single instance of the law of double negation, it follows that the sentence is both true and false, so (non-glutty) gaps are incoherent. Of course, there are many places in that extremely rough and condensed summary that a gap theorist could object and defend their position against these considerations, but for the moment, the important point is that it is Priest's position, and, since I don't tend to agree with him about much here, it seems worth noting that we're of the same mind on this.

(2) Priest once wrote a short story called Sylvan's Box in which the plot was explicitly inconsistent. (In it, the late Richard Sylvan (better known as Richard Routley) turns out to have been in a possession of a box that was simultaneously, observably empty and non-empty.) Of course, works of fiction frequently contain inconsistencies (the location of Watson's war wound is a famous stock example), but part of Priest's point in that story was to write something where the inconsistency was unambiguous and explicit, and no one could try to charitably interpret the inconsistency out, or break the story into maximal consistent chunks and look at them individually, or anything of the kind. We have to face up to the fact that there is a flat out contradiction (P & ~P) in the story, and that we are quite capable of (non-trivially) reasoning about it.** Over at Inconsistent Thoughts, Colin put this nicely, by saying that it shows that "we can navigate inconsistent bodies of information without triggering a “psychotic break."***

Now, in so far as this ability-to-maintain-our-sanity is supposed to show that the 'explosion' of inferences derivable from contradictions in classical logic is invalid, and we should instead adopt a weaker, inconsistency-tolerant (paraconsistent) account of the logical consequence relation, I think there's a tension here between that stance and Priest's position on truth-value gaps.

To see what I mean, let's think about a different possible moral you could take from Sylvan's Box (or, for that matter, from Watson's wandering war wound), which is not that P and ~P don't jointly entail any Q, but simply that F(P) and F(~P) don't jointly entail any F(Q). Just as it's false--but true in fiction--that Watson existed, it's true--but false in fiction that explosion is (vacuously) truth-preserving, since, while there are no true contradictions, it is true that works of fiction sometimes portray contradictions as being true. (I've advocated this approach here in the past.) Of course, as a couple of commenters then indicated, there are real questions about the feasibility of developing rigorous formal tools with which to reason about fictional worlds, but let's leave that aside for now, since right now, we're focussed on the narrower project of weighing the respective virtues of the two proposals on the table for how to do so.

Now, at least for anyone who agrees with Priest (and I) about the impossibility of truth-value gaps, I think the following consideration should tilt the balance of things in favor of explosion-fails-in-fiction-but-Sylvan's-box-tells-us-nothing-about-whether-it-really-fails approach:

Fictional worlds are chock-full of (non-glutty) truth-value gaps.

Let's take some obvious examples.

(1) "Sherlock Holmes' brother Mycroft secretly liked to dress up in women's clothing."
(2) "Watson's great-grandfather on his maternal grandmother's side had blue eyes."
(3) "Professor Moriarty once wrote a paper anticipating Russell's Paradox, but he never published it."

Now, since none of these people existed to do any of these things, (1)-(3) are all false, but are they true or false in the world of the stories? It seems to me that, far from our inability to answer these questions being a matter of ignorance, there is absolutely no way that there could be a fact of the matter one way or the other on these issues. The world of these stories is an incomplete one that, far from including information that Mycroft liked to dress in women's clothing *and* that he never did so, fails to include anything on the subject.**** While these issues give us no good reason to doubt [F(P) v ~F(P)] (in each case, I'd say that ~F(P) is true), [F(P) v F(~P)] simply fails to hold. As such, the logical structure of the world of the Holmes stories includes not only (non-trivial) gluts but also (non-glutty) gaps. None of that tells us much of anything about which inferences are valid in the actual case.







*(And yes, I know I promised a follow-up to the post about the metaphysics of change, and yes, I know that it's been a while since I did so, but the thought is fresh and I'm weirdly excited about the point, so this one comes first.)
**(The morals that Priest draws from the story are many and complicated, but for the moment let's leave it at that, since it's at least what many readers take the story to show.)
***(At the time, he asked me a question about Bohr's of the atom to which I never responded, since I forgot about it until now. My punctuality, in general, seems to be sucking this year. In any case, it's the kind of thing that deserves its own post, which I hope to have in the near future.)
****(Part of the reason that the case for the failure of explosion in the world of the Holmes stories is so compelling is that it seems implausible that Watson's inconsistently-placed war wound would entail, e.g. Mycroft's cross-dressing. This appealing feature would be quite lost if we stuck to our guns and started postulating that it was true--and false--in the world because of its incompleteness.)

Let's Not Pretend This NEH Thing Is All That Surprising

Next Week: Follow-Up Post On Presentism And Graham Priest's Theory Of Change

This Week: Curmudgeonage

One of the saddest and funniest things about doing academic philosophy is that, once you start doing it, you quickly figure out that, to a really surreal extent, at least 75% of college-educated people, hell, at least 50% of *academics in other disciplines,* have absolutely no earthly idea whatsoever what your subject matter is. The pilot episode of Buffy the Vampire Slayer includes the following snatch of dialogue:

Buffy: My philosophy, do you want to hear my philosophy?
Willow: Yeah, I do!
Buffy: Life is short.
Willow: Life is short!
Buffy: Not terribly original, I'll grant you, but it's true...Why waste time being all shy, and worrying about some guy, and if he's gonna laugh at you. Seize the moment, 'cause tomorrow you might be dead.
Willow: Oh, that's nice!

Now, I'd submit that Buffy's grasp of what the word "philosophy" refers to, while...uh...not great, is about as good as the average graduate student in English Literature, and considerably better than whoever runs the NEH. More about that in a second.

This is constantly hammered home to me when I meet people who ask what I do for a living, and we have the following conversation:

Them: Oh, what kind of philosophy are you interested in?
Me: Well, my dissertation has to do with dialetheism, which is the position that some sentences are both true and false.
Them (brow furrowing): So...uh...what kind of philosophy is that?

...because they have no idea how to relate their hazy impression of what "philosophy" means to an actual description of a philosophical subject, so they assume you must be doing lead-up to telling them what kind of philosophy you do. Because philosophy means studying the Big, Complicated Thoughts of Great Thinkers. Whatever those might be, y'know, about. A correct answer to "what kind of philosophy are you interested in?" would be in the form of "oh, I'm interested in Great Thinkers X, Y and Z," or better yet a few of them clumped together into a historical period.

(A closely related piece of silliness comes with the question, "oh, who's your favorite philosopher?" I'm always tempted to give some smart-ass answer like "oh, that would be Greg Restall. He's a Great Thinker from Australia in the late 20th and early 21st centuries...")

So that's what you get from college-educated people with no earthly idea what philosophy is about. It actually makes you appreciate the actually slightly less ridiculous line you get from non-college-educated people with no earthly idea of what philosophy is about, accurately exemplified by Buffy and Willow. A lot of people in this category will initially confuse philosophy with psychology, or even sociology, which at least has the virtue of embodying the assumption that philosophy deals with some important, well-defined subject matter. (When I adjunct teach Intro classes at my local community college, I generally ask the class on the first day what they think philosophy is, and I invariably get a lot of answers like "the study of how people think" or "the study of why societies are the way they are" before I get answers that start to approach the ballpark of being vaguely philosophy-like.) Those who know slightly better, but just slightly, will ask you, "oh, what's your philosophy?"

Now...don't get me wrong. That's an inane, cringe-inducing question that displays a deep ignorance of the sort of thing philosophy is about. There's a level on which it makes exactly as much sense as asking a mathematician, 'oh, what's your mathematics?'

But.

That said.

The impression of what philosophy is that's reflected at the Buffy & Willow/community college student level is actually considerably less dumb than the impression of what philosophy is that's reflected at the college-educated-but-clueless level. I say this with a heavy heart as someone with an obvious financial stake in the claim that college makes people smarter, but, in small doses, for a lot of people, in certain ways and on certain issues, college actually makes them dumber, and there's a fair bit of empirical evidence of this phenomenon. Going to college gives them General Impressions Of Things, picked up by osmosis from What Smart-Seeming People At College Seem To Think, and, sadly, from time to time, these General Impressions Of Things are pretty asinine.

(Historical example: Statistically, people with at least some college were far more likely to support the Vietnam War than people with only high school educations. That whole historical narrative about college kids all being anti-war and 'hard hats' being more likely to support the war? Provably, consistently wrong throughout the whole duration of the Vietnam conflict. See here for details. For a fuller discussion, scroll back to p. 345 and keep going until p. 353.)

Inane as "what's your philosophy?" may be, at least it contains within itself a kernel of understanding that philosophy is not just about studying Important People In The Past Who Had Big, Complicated Thoughts (whatever exactly those may be, y'know, *about*), but actually currently thinking about Big, Complicated Thoughts (whatever exactly those may be, y'know, *about*). Sad that a little education seems to kill even that understanding.

So when I read about this absurdity from the NEH, I'm sad, and I'm frustrated, but I'm not even a little bit surprised.

"Is there such a thing as right and wrong? Good and evil?"

Well, you *should* expect whoever's designing grants at the NEH to have heard of meta-ethics, and to be aware that, far from being a "pre-disciplinary question," a gaping hole in the course offerings that it's appropriate to offer a grant for whoever in whatever discipline to offer a class in, meta-ethics has been a thriving sub-discipline of academic philosophy for a long, long time, something that any Intro course worth its salt will touch on, something that every 100-level ethics class offered by every Philosophy Department in the f--ing world will devote a large segment to, and something that there are of course lots of grad and upper-level undergrad seminars specifically devoted to. For sure. There's definitely some sense in which you *should* be surprised, but...really...if you've ever had the "oh, what kind of philosophy are you interested in?" discussion over coffee with that girl with the MA in Post-Colonial Portugese Literature who's eyes just started to cloud over when you told her, *would* you be surprised? Really?

Graham Priest's Theory Of Change

In In Contradiction, Graham Priest argues that all moments of change are necessarily contradictory. What follows is a quick, rough paraphrase of his argument.

Consider any object O changing from being in state S to being in state not-S. For example, imagine that Mark gets very drunk and accidentally smashes his friend Ben's nice glass ash tray. At the moment when it changes from being intact to being broken (i.e. not-intact), is it:

(a) Intact?
(b) Not-intact?
(c) Neither intact nor not-intact?
(d) Both intact and not-intact?

If the answer is (a), then we're not talking about the moment of change, but some moment before the change. If the answer is (b), then we're not talking about the moment but some moment after the change. If the answer is (c), then by double negation that entails (d) in any case. Hence, at the moment of change, it must be both intact and not-intact. Priest thinks this "contradiction theory of change" puts him in a line of thought about change attributable to historical figures like Heraclitus, Zeno, Hegel and Engels. He also extends the thought to accommodate the common intuition that "time flows" as one moment changes into the next, that process being as contradictory as all moments of change.

Now, I'm inclined to view this as a neat little reductio proof against the very idea that there are or could be such things as "moments of change." Change doesn't occur *at moments,* it occurs among moments. That is to say, to say that O goes from being S to being not-S is just to say that at Time T1 it's S and at Time T2 it's not-S, and that's all. To say that an object changes over time, is simply to say that its properties vary across time. (In fact, since I'm a perdurantist about persistence over time, I'd sharpen this by saying that to say that an object changes over time is simply to say that there are differences in the relevant respect among its temporal parts.) Priest is of course aware of this alternative theory of change, which he attributes to Russell and calls the "cinematic" theory of change. The barb here is that this wouldn't be real "change" at all, but a series of static states succeeding each other, like still frames being projected in rapid succession to create the illusion of motion.

Of course, in arguing for the Russellian theory of change against a non-dialetheist partisan of "moments of change," we could just respond to this barb by deriving the contradiction from the notion of moments of change and that would be that. In the rock-paper-scissors rules of standard metaphysical argumentation, inconsistency-avoidance beats vague lingering intuitions every time. In this case, of course, we can't respond that way without begging the question against Priest, so let's see if we can't do better.

The first interesting thing to point out is that Priest, with his talk of time flowing and moments changing into one another, would seem to be deeply committed to the A-Theory of Time, according to which there's an ontologically privileged present moment, and if its not the only moment that exists (as the extreme form of the A-Theory has it), then at the very least, there are real "MacTaggart properties" of pastness, presentness and futurity out there in the world. The alternative B-Theory of Time has it that there are no such properties, no stance-independent fact of the matter about what "the present moment" is, and that words like "now" are just indexicals like "here." It's tellingly relevant that Priest expresses his theory of change with a paraconsistent tense logic, with pastness and futurity operators, and that tense logics have historically been associated with A-Theorists like Prior. It's not clear that from the perspective of the B-Theory, a tense logic with pastness and futurity operators would make any more sense than, say, a "height logic" with tallness and shortness operators, and for about the same reason. Moreover, if the B-Theory is right, and time is just like space, then the varying time slices of objects had better be "static," at least in the sense that all of time equally exists "all the time."

Priest's first problem, then, is that it's awfully hard to reconcile the A-Theory with Einstein's Special Theory of Relativity. As Putnam and others have argued very nicely, without absolute simultaneity, it's hard to make sense of the idea that there could be a fact of the matter about what "the present moment" is. After all, one of the things that seems to be intuitively true about presentness is that if Event A is part of "the present," and Event B is simultaneous with Event A, then Event B is part of the present as well. The problem is that, if simultaneity is relative to reference frames, then A and B could be simultaneous with each other (but not with Event C) according to one reference frame, and B and C could be simultaneous with each other (but not A) according to a different one, and we can keep iterating that principle about simultaneity and presentness until....well, you see where this is going.

So that's Problem #1. Priest's theory of change seems to fly in the face of our best current science. The obvious snarky response to this is that, as a dialetheist, the logical space for Priest would include embracing a contradiction about the Special Theory of Relativity, but this would miss the point. Just because contradictions are, according to the dialetheist, logically possible, doesn't mean that any particular contradiction is particularly plausible, and it seems safe to say that, as far as making Priest's form of dialetheism more plausible and attracting new followers to it, embracing a contradiction about the STR would not be a particularly good move.

This observation leads direction to Problem #2.

A central component of Priest's project of trying to carve out a plausible dialetheism is something called the "classical re-capture." The idea is this. If dialetheism is correct, then some rules of classical logic, like Disjunctive Syllogism, aren't universally truth-preserving. DS is the rule that, given (P v Q) and ~P, we can conclude Q. The problem is that if dialetheism is right, then there could be a situation where P and ~P are both true, but Q is (just) false. In that scenario, since P is true, by the law of disjunction-addition, (P v Q) must true as well, so we have a counter-example to DS.

While this has the happy result of showing that, if dialetheism is true, the explosion proof is invalid (since it relies on DS), it has the unhappy result of rendering invalid a rule that we use all the time in everyday, garden-variety reasoning and which intuitively seems like an obviously correct inference. ("Ryan is either downstairs playing Guitar Hero or in his room sleeping, since those are the only things he ever does. He's not playing Guitar Hero, so he must be sleeping.") Priest accommodates this by saying that, although given the existence of true contradictions, and hence counter-examples to DS, it's not deductively valid, it's at least a probabilistically reliable inference. To get this off the ground, he argues that the statistical frequency of true contradictions is very low, and so, all else being equal, the epistemic probability of any particular contradiction being true is correspondingly low. Hence, classical rules that rely on the assumption that there are no true contradictions still have probablistic force.

So far, so good. But if all moments of change involve true contradictions, then it starts to look like the rate of true contradictions isn't nearly as low as one would think if one thought the only true contradictions involved abstract issues like Liar sentences and naive set theory. Every time we say of an object O that it's in state S when it is in fact at that moment in the process of changing into being in state not-S, we've said something that's both true and false. So it looks to me like, in claiming that change involves contradiction, Priest is playing with fire and putting his "classical re-capture" is serious danger of burning down.

That's Problem #2. Problem #3 is the simplest one. Let's say Priest is right and mere variation of properties that objects have among moments in time wouldn't be real change but merely a succession of static states. Moreover, let's say that on the basis of his intuition that real change exists, there are indeed these strange contradictory moments of change. Now, to adapt a popular argument against mathematical Platonism to this argument, imagine that suddenly, these moments of change stopped happening. (Say, God willed that real change would no longer exist, but that everything else would stay the same.) Ash trays would still go from being intact to being broken, your hair in the shower would still go from being dry to being wet, etc., etc., etc., but there would no longer be contradictory transitional moments. If that happened, how would we ever know? And what difference would it make to anything else? Would people who (in our world) share Priest's intuitions about change not have them? If not, why on earth should we let those intuitions settle this, given that it's much simpler and more cautious to postulate that the observed states of any given object O being (just) S or (just) not-S are the only states there are?

A Half-Baked Thought About The Lottery Paradox, the Preface Paradox and the Philosophy of Science

The following assumptions all seem extremely plausible:

(1) If it is highly probable that P is true, then we are justified in believing P.
(2) If we are justified in believing P, and Q follows from P (i.e. there is no way for P to be true without Q being true as well), we are also justified in believing Q (at least if we believe it on the basis of this inference).
(3) We are never justified in believing things that we know to be false.

So, in a familiar puzzle, there's a lottery with a thousand tickets. One of them is the winner, and the other 999 are the losers. Thus, the probability of any individual ticket losing is 99.9%. By (1), we're justified in believing of each individual ticket that that ticket will lose. (There's no use saying that .99 isn't highly probably enough, since we can construct a Lottery case for any arbitrarily high number of tickets.) By (2), we're justified in believing that *all* of the tickets will lose, because if Ticket 1 loses, Ticket 2 loses, Ticket 3 loses, and all the way to Ticket 1000, it follows from all of that that none of them win.

...but now, of course, we've reasoned our way to a conclusion that conflicts with (3). We know perfectly well that one ticket *will* win. That bit of background information is how we assigned the probabilities of each ticket winning in the first place.

In more usual presentations, (3) might be "we are never justified in believing contradictions," but I'm deliberately *not* putting it that way, because I think the issue runs deeper than that. The Lottery Paradox looks to me like just as much of a problem for the dialetheist, who believes that some (but not all) contradictions are true, as it is for the rest of us. To make it clearer that the dialetheist isn't at any advantage here, we can re-phrase (3) to:

(3*) We are never justified in believing things that we know to be (just) false.

After all, no dialetheist believes that it is both true and false that lotteries have winning tickets. I suppose it's just barely possible that some radical dialetheist might say that we're both sometimes justified and never justified in believing things that we know to be (just) false, but if there are other available options, it certainly sounds like a violation of Priest's rule about not multiplying contradictions beyond necessity, and in any case, the radical dialetheist who picked this option would be conceding something important, since they'd be giving up on the extremely useful and intuitive principle that:

(3**) It is (just) true that we are never justified in believing things that we know to be (just) false.

Put bluntly, a hypothetical dialetheist who denies (3**), claiming that there are true contradictions about whether we're rationally entitled to believe things we know to be (just) false, starts to sounds like he's advocating the sort of dialetheism that Nester advocates in this comic, and we can start to suspect his dialetheism is similarly motivated.

So, in any case, the real issue seems to me to be the rationality of knowingly believing falsehoods, not just knowingly believing contradictions. Of course, given orthodox assumptions about the philosophy of logic, the latter is just a particularly severe case of the former, since contradictions are the only sorts of claims whose falsehood we can be sure of based on nothing more than their logical form.

Some theorists take the Lottery Paradox to be evidence against (2).

Similarly, some people take Moore's "hands argument" against skepticism to be a reductio proof against the universal reasonableness of (2). Moore proves that material objects exist by looking down on his hands and saying "yep, here's one material object and here's another one." One might think that Moore is justified in beleiving that his hands exist, but not that global skepticism is wrong or that the external world exists or any similar such thing. This line of thought has always seems extremely unconvincing to me. If his hands exist, so does the external world. If you don't think he'd be justified in believing the latter, then it seems like the rational thing to do would be to apply Modus Tollens and conclude that he's not really justified in believing the former either.

Regardless of how one feels about the Moore-type cases, however, in the particular case of the Lottery Paradox, rejecting (2) does nothing to get us around the conflict between (1) and (3). This is another reason (in fact, a much more important reason than demonstrating that the dialetheist is in the same boat as the rest of us here) for expressing (3) in terms of *things we know to be false* in general, not *contradictions* in particular. Rejecting (2) does get us out of the inference to the explicit contradiction (P&~P), where P is "one of the tickets will win," but it doesn't get us out of believing something we know to be false. We're still in a position of believing *of each ticket* that it will lose. Given that we know that one of the tickets will win, we know that one of our beliefs about individual tickets must be false, and we're still in flagrant violation of (3).

Of course, one could reject (3), but out of the three obviously available options, rejecting (3) seems like the most bitter pill to swallow. If we read J(P) as something like "given the available evidence, we're entitled to think P is true," then we seem to be putting ourselves in a considerably strange position if we say that J(P) could be true even if we already know perfectly well that P is false.

Given this, it looks to me like by far the most plausible option is to reject (1), and to take the Lottery Paradox to be a nice proof that, at least sometimes, something can be extremely probable, but it can still be the case that we aren't justified in believing it. (Moreover, I doubt that disambiguating different senses of probability will help here, because the 99.9% probability of each ticket losing sounds to me like an *epistemic* probability.) High probability may often, perhaps even usually or almost always, be sufficient for justified belief, but it isn't always suffient for it. (Granted, there's obviously a large and worrying open question here about how to decide which cases are which.)

Of course, the conclusion that the most reasonable reaction to the Lottery Paradox is to reject (1) isn't original to me. Simone Evnine, for instance, argues for the same point in his extremely interesting book "Epistemic Dimensions of Personhood," although he presents the argument there in a substantially different way than I do here.

...and, of course, he also talks about the Preface Paradox, a related puzzle about (1)-(3) that is likely to be brought up in the same breath as the Lottery by anyone (like, e.g., Penelope Maddy in her otherwise excellent book "Second Philosophy") who takes the Lottery Paradox to demonstrate that, although no contradictions are true, we're sometimes justified in having inconsistent beliefs. In some ways, for the point that I'm building to, the Preface Paradox is even more interesting than the Lottery Paradox.

Before we get to it, it's worth briefly thinking about the consequences of rejecting (1) in the lottery case. After all, one might think that we're losing something important by reacting to it that way. Don't we want to be able to assert, e.g. in talking a dim-witted friend out of wasting his money on a lottery ticket, that we're overwhelmingly rationally justified in thinking that their ticket will lose? After all, as a professor of mathematics who I'm very fond of used to tell me, the lottery is in its essence a tax on people who are bad at math. It *is* irrational of your friend to buy a lottery ticket, and that fact might seem to be a consequence of the fact that we're rationally entitled to believe that it will lose.

This worry is groundless. If we reject (1), the obvious thing to say about the claim that your friend's ticket will win is not that we should that we should reserve judgment about it, *but* that the probability is extremely low, and this last fact is sufficient to motivate the claim that it's irrational of your friend to throw his money away on a lottery ticket, and that he'd be better advised to spend it on something he has a better than .01% chance of getting something out of.

So, that preliminary out of the way, let's think about the Paradox of the Preface. The basic issue is the same as the Lottery Paradox, since it seems to be nicely thought of as a puzzle about (1)-(3). You write a book where you carefully research every claim, carefully considering the evidence, alternate interpretations, objections, etc. It is, however, a very long book in which you make a great many claims, and experience has taught you that with so many claims, no matter how careful and rigorous your research, it is extremely probably that you made at least one subtle, undetected mistake somewhere along the line and that as such at least one of your carefully documented, well-thought-out claims will later turn out to be false. Are you doing something irrational if you say in the preface that at least one of the claims in your book is false?

After all, by (1), you are justified in believing that at least one of the claims in your book is false, by (2) you are justified in beleiving that they are all true (since you are justified on the basis of the evidence in believing of each individual claim that it is true), but, once again, this leads to a contradiction that not even a dialetheist could love, and thus belief in it severely violated (3). Once again, rejecting (2) doesn't seem to help much, because even if you don't believe the conjunction of all of your claims, but just believe each of them individually, you still have a total set of beliefs that you know perfectly well can't *all* be true. Given the severe implausibility of rejecting (3), again, we seem to have another nice little proof of the falsity of (1). So far, so good.

But notice that we're in a slightly different epistemic situation than we were in with regard to the lottery case. With any individual lottery ticket, the rational thing is to *reserve judgment* about whether it will win, while advising against acting as if it were the winner, given the high probability that it won't be. With any individual carefully-researched claim in the book, despite the fact that it is highly probable that at least one of them will be false, the rational thing to do is to believe all of them, and (since denying (2) is counter-intuitive and accomplishes nothing) to believe the conjunction while we're at it, and to *disbelieve* the highly probable claim that one of the is false. Despite the high probability that one of them will be false, we shouldn't believe the negation of the conjunction of all of them.

Thinking hard about the Preface Paradox might shed light on a problem in the philosophy of science. Scientific realists believe that we should believe our best current scientific theories are true. (Of course, in practice may formulations of scientific realism are considerably weaker than this, but for our purposes here, it's useful to consider the strongest formulation and see how well we can defend *that.*) One of the best arguments *against* scientific realism comes from the Pessimistic Induction. In the past, many theories that seemed to be well-supported by the evidence have turned out to be false. Putting a little rhetorical flourish on this as Laudan does, we can say that the history of science is a "graveyard" of such theories. Reflecting on the history of scientific revolutions, and the high incidence of well-supported scientific theories turning out to be false in the past, how can we be sure that our best current theories won't meet the same fate? In fact, it seems highly probable that many of our best current theories will meet the same fate. As such, scientific anti-realist argue, we're not justified in believing them to be true.

Now, this is a quick and rough sketch that can't be expected to do justice to a complicated and subtle debate, but for my present purposes, it should be good enough. It's no doubt possible to advance the Pessimistic Induction without talking about probability at all, but familiar formulations of it tend to be expressed that way. Some of the best and the most sophisticated defenses of realism against the Pessimistic Induction are focused on denying the premise that there is a high probability that many of our best current theories will turn out to be false, like Peter Lewis' argument that the Pessimistic Induction commits the base rate fallacy. Other standard realist defenses turn on attempts to deny or blunt the edge of the historical narrative on which that probabilistic assessment is based. "Oh, it's not that our best theories in the past were shown to be *false,* it's that they were shown to be somewhat false, and throughout the history of science our theories have approximated the truth more and more closely, so we can be confident that by now we're approximating the truth *really* closely...."

At the moment, I don't want to comment on any of that one way or the other. I do think, however, that reflection of what the Lottery Paradox (and, even more so, the Preface Paradox) show us about the relationship between probability and justification points the way to a very different defense of realism against the Pessimistic Induction. This solution in no way contradicts any of the other defenses just mentioned...someone could reasonably think that the more optimistic reading of the history of science is the right one, or that the probabilistic inference commits the base rate fallacy, or both, but that *even if* they were shown to be wrong about them, the following defense is still sufficient to save scientific realism:

We can just grant that the anti-realist is completely right that, given the history of science and its "graveyard" of theories once well-supported on the basis of evidence and later shown to be false, there is a high probability, perhaps even an *extremely* high probability that many of our best current theories will turn out to be false.

But it doesn't matter.

The Lottery Paradox shows that sometimes P can have a high probability of being true, and we can still fail to be justified in believing it. The Preface Paradox shows that sometimes P can have a high probability of being false, and we can still be justified in actually believing it to be true.

In the case of our best current science, (2) fails, for precisely the same reason that it fails in the case of the Preface Paradox. We have excellent evidence that our best current theories are true, and on the basis of that, we are rationally justified in believing them, *even though* there is a high probability that many of them will end up in Laudan's "graveyard."

So...any thoughts? Have I lost my mind?

Am I just showing my ignorance of current work in the philosophy of science here? Maybe this is a thought that's been advanced many times before in the literature and decisively shown to be ridiculous. Or maybe no one has advanced it for the simple reason that any half-way intelligent person whose mind it momentarily crosses can immediately see deep flaws in the reasoning that I can't.

Let me know.

Some Final Points About Feser & A Preview of Coming Attractions

[If you have no idea what I'm talking about, see here, and don't worry. By Wednesday, we'll be back to talking about phil of logic.]

So I was going to let it go and use the previous post exploring the connotations of "logician" to transition back to the more usual subjects discussed here, but given some of what's been said in this debate since my original post, I did want to briefly follow up and make a few summary points before changing the subject for good.

(1) This whole thing started when Ed Feser wrote an angry, unhinged blog post explaining why a recently murdered doctor was an evil, worse-than-Dahmer mass murderer who had forfeited his right to live. He also claimed to nonetheless fully oppose “vigilantism.”

(2) None of his critics--not me, not Ryan, not Leiter, not Shipley--have at any point in all of this denied the existence of that supremely unconvincing disclaimer or “lied” about it. The point of my first post on all of this was that it seemed hard to square that claim with the obvious upshot of everything else that he had to say.

In normal contexts, when someone hears about a murder and they respond with “well, y’know, he did deserve to die,” everyone takes that as a bit of positive commentary on the murder. Feser demands that people refrain from taking his words this way, because his “of course I don’t approve of vigilantism” disclaimer magically cancels out the rest of what he said, no matter how hard it is to fit the two together in a coherent framework. Thus, when some of us have noted the presence of the disclaimer but declined to take it very seriously given his overall views, he’s accused us of spewing “lies” and “libel.”

(3) Even if you take Feser’s disclaimer to be (a) sincere, and (b) somehow compatible within a remotely plausible framework with his claims that Tiller was worse than Dahmer, had forfeited his right to live, etc., then it would still be the case that Feser was an enthusiastic apologist for doctor-killing.

On that reading, he didn’t object to the fact that Tiller was killed. He only objected to the fact that the wrong people killed him. Feser (on this reading) would prefer to wait for abortion to be banned and the death penalty applied to abortion doctors. At that point, he would be all in favor of Dr. Tiller being lethally injected or strapped to a chair and electrocuted for the crime of helping women end unwanted pregnancies in safe conditions instead of using coat hangers. Moreover, even a cursory glance at Feser’s original post, which was replete with claims that Tiller was a servant of the demon Moloch, that he was worse than Dahmer in five distinct respects, and so on, should confirm that Feser was extremely enthusiastic in pushing for his position that Tiller had "forfeited his right to live."

Thus, even on this reading--that is, to concede for the sake of argument that Feser’s defenders are entirely right and the rest of us are entirely wrong on how to read his original post--it is a banally obvious statement of fact that Feser is a “doctor-killing enthusiast.” Given that, it says something about the standards of reasoning in force over at W4 that, in this comment thread, Feser calls me a “nasty, unrepentant, shameless bald-faced liar” because I called him a “doctor-killing enthusiast.” Regardless of who is right and who is wrong in the argument we’ve been having, on any possible reading of Feser’s original post, he is indeed a doctor-killing enthusiast.

(4) That said, the reading on which Feser “just” wished that Dr. Tiller’s killing had been carried out by different hands is far from the most natural or reasonable reading of his actual words. The central reason not to take his “of course none of this means I actually approve of the actions of people who take all this ‘abortion doctors are serial killers’ rhetoric at face value...no, no, I wash my hands of that” rhetoric very seriously comes in the form of some forceful arguments by analogy advanced at various points in the debate by Shipley and by Ryan. Here’s Shipley:

"Suppose a racist government refuses to protect a minority from persecution. Don't members of the minority have a right to protect themselves? Or, suppose a government refuses to outlaw rape. Would it not be justifiable to protect women by means outside the law? Do you really believe that there are absolutely no circumstances in which vigilante action is justified?"

After Leiter quoted this item, Feser made a long-winded, detailed-looking reply to Shipley, in which he responded to individual sentences of Shipley’s with lengthy blocks of text, but he conspicuously failed to touch this paragraph. He changed the subject to say that vigilantism might be justified in societies as bad as Nazi Germany, but the U.S. wasn’t as bad as all that. He utterly failed to acknowledge or respond to Shipley’s hypotheticals. I took Feser to task for this omission in my original post on all this, then Feser responded at length to me....but once again conspicuously failed to respond to the content of the paragraph just (once again) quoted. To make the point even sharper, Ryan has been asking anyone who will listen, in the comment thread on his own comic and in some of the comment threads over at W4:

"Suppose that Jeffrey Dahmer wasn’t ever captured. Suppose he were free and still torturing, slaughtering and eating people. And suppose the government refused to do anything to try and stop him. Would you decry the actions of the vigilante who brought him down?”

To date, neither Feser nor any of his defenders has actually answered this question head on, and answered it in the affirmative, saying that, yes, yes indeed, under those circumstances, they really would disapprove of vigilante action to stop Dahmer. To me, this failure strongly suggests that we shouldn’t take Feser’s claim that by saying that Tiller was worse than Dahmer, he wasn’t acting as an apologist for Tiller’s murder very seriously.

That's the point.

Now, enough of that.

On Wednesday, the subject changes to the Lottery Paradox, and what we can learn from it about either the rationality of holding inconsistent beliefs or the relationship between probability and justification.