Russell's Paradox, Quine's Argument and the Empirical Refutation of the Law of Non-Contradiction (The Russell's Paradox Series, Part II of IV)

In my last post, I said the following to defuse the idea that any particular scheme for determining which sets exist, whether the unrestricted comprehension axiom of naive set theory or the more conservative axioms of various later theories, is something we can be particularly confident about:

"The realm of sets, if it exists, is notoriously epistemically inaccessible to us. (In fact, as Benaceraff famously pointed out, if we assume that it exists, it still seems to be the case that, if every set in that realm disappeared tomorrow, we'd never know.) Even if we assume that there's a compelling case for set-theoretic realism--i.e. for the conclusion that at least some sets exist--the question of which sets exist is still very much open."

OK, so, given that, what reason do we have (if any) to suppose that at least some sets exist? Here's what Stephen Yablo says, in his article "A Paradox of Existence":

"About fifty years ago, Quine convinced almost everyone who cared that the argument for abstract objects, if there was going to be one, would have to be a posteriori in nature. And it would have to be an a posteriori argument of a particular sort: an indispensability argument representing numbers, to use that example, as entities that ‘total science’ cannot do without."

If that's one's reason for granting the at least some existence of sets, though, we clearly don't need all the sets you get from the unrestricted comprehension axiom. For example, the sets in the ZFC cumulative hierarchy should be (way, way) more than enough to reconstruct the fragment of mathematics you need for our best current scientific theories.

Remember that the original context of this series of posts is Graham Priest's argument for dialetheism on the basis of the antinomies of naive set theory. It seems to me, though, that we have to start by having a pretty damn good reason to accept unrestricted comprehension if we're going to be willing to sacrifice Non-Contradiction for its sake. Of course, if we're going to engage in the project of arguing with dialetheists (which is, after all, what I'm doing here), "your premises must be wrong because I don't like your conclusion" isn't much of a counter-argument. Fortunately, in this case, we can do better.

After all, to review:

(1) The most plausible argument for thinking that any sets exist at all is the indispensibility argument,
&
(2) To set-theoretically reconstruct the fragment of mathematics that's actually indispensible to our best-supported scientific theories, you don't need as many sets as unrestricted comprehension gets you,
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(3) As I argued last time, if we lack evidence one way or the other about what exists in some realm of reality to which we have no direct access, it makes sense to conservatively assume that its logical structure doesn't radically depart from the logical structure of the parts of reality we are familiar with. This seems like a good general principle that everyone can accept--e.g. dialetheists who (like Priest) don't think that there are any counter-examples to the Law of the Excluded Middle have every reason to reject evidentially unmotivated claims that such counter-examples exist in some strange, epistemically inaccessible domain of reality.

Putting (1)-(3) together, it looks like, unless we've already been convinced of dialetheism by some other argument, the paradoxes of naive set theory give us no reason to believe in the existence of sets with inconsistent properties. Considered as an independent argument for dialetheism (which is how Priest seems to view it), we have excellent, non-question-begging reasons to reject one of the crucial premises.

So far, so good. Does this mean, though, that no argument for independent argument for dialetheism could be mounted on the basis of the existence of inconsistent mathematical objects, given our limited epistemic access to such objects, the conservative principle (3) above, and so on?

Actually, no. Indispensibility cuts both ways. Here's what I say about that in my dissertation:

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Now, this suggestion--that our best reason to believe that the total universe of sets fails to contain the Russell Set is that we are only justified in being realists about the sorts of mathematical entities that our best-confirmed scientific theories are ontologically committed to--has a consequence that many of my fellow monaletheists[*] might find extremely unattractive. So as not to look like I’m skirting the issue, it’s worth pausing for a moment to spell it out, and to explain why I regard it not as a bug but as a feature.

While Priest usually likes to portray the intellectual adjustment involved in admitting the possibility of true contradictions as a smaller change than it might appear, one without sweeping consequences for our practices of reasoning--we’ll come back to this point with a vengeance in Chapter Seven, when we consider his “classical re-capture”--in other, more enthusiastically optimistic moods, he likes to speculate about the wide-ranging consequences that the jump to the ‘realm of the transconsistent’ might have.

"In modern science, the inferentially sophisticated part is nearly always mathematical. An appropriate mathematical theory is found, and its theorems are applied. Hence, a likely way for an inconsistent theory to arise now in science is via the application of an inconsistent mathematical theory. Though the construction of inconsistent mathematical theories (based on adjunctive paraconsistent logics) is relatively new, there are already a number of inconsistent number theories, linear algebras, category theories; and it is clear that there is much more scope in this area. The theories have not been developed with an eye to their applicability in science—just as classical group theory was not. But once the paraconsistent revolution has been digested, it is by no means implausible to suggest that these theories, or ones like them, may find physical application—just as classical group theory did. For example, we might determine that certain physical magnitudes appear to be governed by the laws of some inconsistent arithmetic, where, for example, if n and m are magnitudes no smaller than some physical constant k, n + m = k (as well as its being the case that n+ m ≠k). There are, after all, plenty of episodes in the history of science where we came to accept that certain physical magnitudes had somewhat surprising mathematical properties (being imaginary, non-commuting, etc.). Why not inconsistency?"

The suggestion may seem absurd, but consider the analogy of physical geometry. For thousands of years, pretty much everyone was what we might think of as a “Euclidean monist,” meaning that they took it as obvious that there could only be one shortest path between any two points, and that they understood this not just as a claim about the particular hypothetical realm of one axiomatic system but as a (a priori knowable) claim about physical reality as well. Even when non-Euclidean geometries started to be developed, they were largely regarded as esoteric curiosities that couldn’t possibly model anything in the real world. If a student went to Immanuel Kant’s table at his tavern in Konninsberg and suggested to the great man that future science might plausibly one day falsify Euclidean monism and allow for multiple non-equivalent shortest paths between two physically real points, the young man would have presumably been laughed out of the place. Yet, history has rendered the opposite verdict; Einstein has shown that the true geometry of space-time is non-Euclidean, and so much the worse for our spatial intuitions.

Of course, for the student to demand without special evidence or argument that Herr Professor Kant accept that this was possible (particularly in any richer sense than epistemically possible, where ‘epistemically possible’ is taken to mean something like ‘having a status such that one should keep an open mind about it’) would be to beg the question against Euclidean monism, and the good professor would have been fully rationally entitled to decline to do so. Similarly in this case, if we take Priest’s rhetorical question as a demand that we (monaletheists) take his wild speculation about inconsistent magnitudes seriously as a possibility. The problem, of course, as the Einsteinian case shows, is that the lesson of the history of science seems to be that even intuitively well-grounded claims about impossibility can be falsified, and that we shouldn’t be dogmatically closed off to the (epistemic) possibility that we’re wrong about (logical and mathematical) possibility. Priest lays out a fanciful sort of scenario where monaletheist assumptions about logical and mathematical possibility are in fact falsified by empirical research.

"Let us suppose that come to predict a collision between an enormous star and a huge planet. Using a standard technique, we compute their masses as x1 and y1 respectively. Since masses of this kind are, to within experimental error, the sum of the masses of the baryons (protons and neutrons) in them, it will be convenient to take a unit of measurement according to which a baryon has mass 1. In effect, therefore, these figures measure the number of baryons in the masses. After the collision, we measure the mass of the resulting (fused) body, and obtain the figure z, where z is much less than x1 + y1. Naturally, our results are subject to experimental error. But the difference is so large that it cannot possibly be explained by this. We check our instruments, suspecting a fault, but cannot find one; we check our computations for error, but cannot find one. We have a puzzle. Some days later, we have a chance to record another collision. We record the masses before the collision. This time they are x2 and y2. Again, after the collision, the mass appears to be z (the same as before), less than x2 + y2. The first result was no aberration. We have an anomaly.

"We investigate various ways of solving the anomaly. We might revise the theories on which our measuring devices depend, but there is no obvious way of doing this. We could say that some baryons disappeared in the collision; alternatively, we could suppose that under certain circumstances the mass of a baryon decreases. But either of these options seems to amount to a rejection of the law of conservation of mass (-energy), which would seem to be a rather unattractive course of action.

"Then someone, call them Einquine, fixes on the fact that the resultant masses of the two collisions were the same in both cases, z. This is odd. If mass has gone missing, why should this produce the same result in both cases? An idea occurs to Einquine. Maybe our arithmetic for counting baryons is wrong. Maybe the appropriate arithmetic is one where z is the least inconsistent number, and p (the period of the cycle) = 1. For in such an arithmetic x1 + y1 = x2 + y2 = z, and our observations are assumed without having to assume that the mass of baryons has changed, or that any are lost in the collisions! Einquine hypothesizes that z is a fundamental constant of the universe, just like the speed of light, or Planck’s constant."

The story goes on, but the general idea should be clear enough. We have a localized change of the arithmetic assumed by our best science, one that doesn’t require us to change the way we count match-sticks, any more than the non-Euclidean curve of space-time stops us from making Euclidean assumptions about how to make geometrically complicated bank shots when we play pool, but which is just as deadly to monaletheism as Einstein’s discovery was to Euclidean monism. Of course, the details of this story could doubtless be nit-picked in many ways, but I very much doubt that someone in the late eighteenth century trying to imagine a way that science could falsify Euclidean monism could do any better. It’s in the nature of scientific revolutions that, before they come along, they’re not only unpredictable but often almost completely unimaginable. Similarly, at the level of detail that’s Priest’s given us, there’s no way to be sure whether (even in the extreme, strange, counterpossible hypothetical situation being considered) revising the underlying arithmetic of our theory from a classical to a paraconsistent one would be the most rational response. As per our discussion at the end of the introduction, recalcitrant evidence can always be taken as evidence against many different parts of our overall package of beliefs, and any given proposal for belief-revision has to be reasoned out on the specifics of the case, specifics that are unknowable in consideration of these sorts of extreme hypotheticals. So we can’t be too confident in advance that, even in this specific scenario, the best scientific move would be the one Priest hypothesizes.

That said, if Priest’s scenario came true, and it turned out that the best, most reasonable response was to formulate a scientific theory to which inconsistent mathematical entities were indispensible, then, by my lights, we should be realists about such entities, just as we have a good reason to be realists about as much set theory as we need to make sense of our best current science. Thus we have the potentially unattractive consequence mentioned earlier: my solution to Russell’s Paradox leaves the empirical/mathematical back door open for dialetheism. If the empirical results were to go in certain extremely unexpected directions, then inconsistent mathematical results would give us an excellent reason to abandon monaletheism.

As I said, this strikes me as not a bug but a feature of my solution. A belief that no evidence would ever dislodge is a dogma, and one doesn’t need to subscribe to all the details of Karl Popper’s epistemically impoverished theory of justification to agree with him that one of the great lessons of the last few hundred years of scientific progress is that unfalsifiability is a mark of theories that don’t deserve to be taken seriously. If monaletheism is intuitively compelling, there are no good arguments for dialetheism, and the consequences of accepting dialetheism are unappetizing, then we’re within our rational rights to retain the monaletheist structure of our beliefs, but we should always keep the door open for the world to push back against those beliefs and show us that we’re wrong.

Of course, we don’t have a right to even this limited conclusion until we’ve satisfactorily blocked the single strongest argument for dialetheism, which is the argument from the Liar Paradox. It is to this, then, which we now turn.






[*"Monaletheism" is the view that contradictions are never true. When being careful, I like to talk about "monaletheism" rather than "the LNC" as the view being challenged by dialetheists because, technically speaking--if by "the LNC" one just means the logical formula that tells us that for any conjunction of a claim and its negation, the negation of that conjunction is true--then dialetheists don't generally reject the LNC. That formula continues to be a logical truth in systems like Priest's favored logic LP. It's just that dialetheists who accept it also think it has true--and false--counter-examples.]

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But wait! Doesn't this amount to solving Russell's Paradox and the Liar Paradox in different ways, despite their deep structural similarity? And doesn't that violate the Principle Of Uniform Solution?

Stay tuned for next Monday's post to find out!

Russell's Paradox and Logical Conservativism (The Russell's Paradox Series, Part I of IV)

Graham Priest often treats Russell's Paradox as the basis of a positive argument for dialetheism. He has even said that in certain respects it is a more invulnerable dialetheist argument than the argument from the semantic paradoxes, since there's no issue of meaningfulness--since it concerns sets rather than sentences, one can't get around it by denying that some sentence is meaningful.

This is, of course, not the only dialetheist position on the paradox. JC Beall, if I understand him correctly, follows Hartry Field in separating the paradox into two versions, the traditional set-theoretic one, and a paradox about the property 'does not apply to itself'--Beall accepts classical orthodoxy about the former and handles the latter dialethetically, just as Field accepts classical orthodoxy about the former and handles the latter by denying the relevant instances of the Excluded Middle. To me, the Field/Beall position on the taxonomy of the paradoxes seems bizarre. Russell's Paradox is about sets, and the 'does not apply to itself' paradox is about properties. They have similar structures, but what of it? Lots of paradoxes have Russell's-Paradox-ish structures, and saying that this means that the 'does not apply to itself' paradox is a version of Russell's Paradox strikes me as making no more sense than describing the Liar as 'the sentence version of' Russell's Paradox. (In fact, I'm inclined to think that, in so far as "applies to" can be paraphrased as something like "is said of itself in a true sentence", the "does not apply to itself" paradox has a lot more in common with the Liar than it does with Russell's Paradox.) In both cases, one can talk that way if one wishes, but it doesn't strike me as shedding much light on anything. I think that things are kept clearer by regarding the 'does not apply to itself' paradox as an interesting puzzle in its own right that doesn't have much of anything to do with Russell's Paradox.

In any case, a third possible dialetheist position on Russell's Paradox might be to take naive set-theoretic realism and the associated contradictions as something that one might as well accept once one has accepted dialetheism, but something which the non-dialetheist has no particular reason to be bothered about unless they are confronted with some separate compelling argument for dialetheism. Someone who held this position might think that, e.g. the Liar Paradox formed the basis for a compelling argument for dialetheism, and consistent solutions to the Liar are severely wanting, so, given the existence of Liar sentences, we should all be dialetheists (at which point we would have no particularly good remaining reason to reject the unrestricted comprehension axiom of naive set theory), but that, in the absence of other reasons to accept true contradictions, there's nothing particularly problematic about orthodox, consistent views about set theory.

Now, I'm not a dialetheist of any sort, and I think that the Liar Paradox can be plausibly solved within a consistent framework. (In fact, once I'm done with the Russell's Paradox series, I've been thinking about starting up a series on my preferred solution to the Liar.) That said, in this and in follow-up posts, I want to argue that dialetheists should accept Dialetheist Option #3.

To see why, let's start with what I'd like to think of as something like the Principle of Logical Conservativism (PLC), which is a special case of a general rule of ontological caution. Here's how I describe it in my dissertation:

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Any time we expand our ontology, the following seems like an eminently reasonable principle of caution:

• Until we have concrete evidence to the contrary, we should take whatever principles we previously took to apply to absolutely everything whatsoever to apply to the newly discovered objects as well.

By analogy, when we discover the existence of a distant galaxy that we have not been yet able to send probes to photograph, or SETI messages to search for alien life in, the fact that we can imagine or describe perpetual motion machines gives us no reason to think that aliens living on one of the planets of the newly discovered galaxy have developed such a machine. As far as we know, such machines are impossible. If, however, when we send the probes and the SETI messages, we make contact with aliens living in that galaxy, and they show us what seem to be perpetual motion machines, after careful consideration of their evidence, we should be prepared to revise our old ideas about physical possibility. Just so for sets and logical possibility.

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To expand on the thought a bit:

At one point in In Contradiction, Graham Priest says that his view that the cumulative hierarchy of sets postulated by ZFC and similarly orthodox set-theoretic options is an interesting mathematical structure that mathematicians may have their own reasons to choose to concentrate on, but that the whole universe of naive set theory--including sets with contradictory properties, such as the Russell Set and the set of all ordinal numbers--also exists, is "quite compatible" with a view often expressed by more conservative theorists who are agnostic about the existence of any sets outside the cumulative hierarchy. To me, this exactly misses the point--assuming that one has a reason to believe that at least the sets in the cumulative hierarchy exist, a reasonable stance might be (i) confidence that no sets with inconsistent properties, like the Russell Set and the set of all ordinal numbers don't exist, grounded in a general confidence that no objects have inconsistent properties, combined with (ii) agnosticism about the existence of sets that are outside of the cumulative hierarchy but whose existence would be compatible with what we know about the logical structure of reality in general.

The realm of sets, if it exists, is notoriously epistemically inaccessible to us. (In fact, as Benaceraff famously pointed out, if we assume that it exists, it still seems to be the case that, if every set in that realm disappeared tomorrow, we'd never know.) Even if we assume that there's a compelling case for set-theoretic realism--i.e. for the conclusion that at least some sets exist--the question of which sets exist is still very much open.

Different set theories have different comprehension axioms that give us different results about that question, and we don't have any direct evidence that settles the question of which one gets us the right result. The unrestricted comprehension axiom of naive set theory gives us a particularly simple and clear-cut formula for deciding which sets exist, but one which, as far as we know, can't be the right one, since, as far as we know, there are no true contradictions. If we had evidence of the existence of sets with inconsistent properties, then unrestricted comprehension might be the best option, but that's not the situation that we're in.

Now, a fair-minded critic might start to worry at this point that I'm throwing in this conditional--and the "concrete evidence to the contrary" clause in the principle of caution, above--to make my stance on all this sound more fallibilistic and open-minded than it really is. After all, given the Benacerraf-style worries just mentioned, what would ever count as concrete evidence of the existence of inconsistent sets?

All I can say is that, if you share this concern, you should stay tuned for the next installment!

Nolan & Co. On Moral Fictionalism (Pt. 2)

(Read Pt. 1 here.)

Daniel Nolan, Greg Restall and Caroline West have an interesting article called Moral Fictionalism versus the Rest available in its longer form here and in a shorter form in the Australasian Journal of Philosophy, 83 (2005), 307–330. (Thanks to Greg Restall for popping up in the comments last time to direct people to the longer version available online, after someone noted that they couldn't access the actual AJP article from where they are. For the sake of convenience, when I refer to page numbers in what follows, they'll be for that online version.

I was initially interested to see the article mostly because meta-ethics is a strong secondary interest for me at this point, and I was delighted to see some of my favorite figures in my primary area of interest (phil of logic) tackling it. In the last post, I started out by briefly going through other meta-ethical options, setting the whole thing up in terms of how these other options make sense of our intuition that it is somehow correct to say that "torturing children for fun is wrong" and somehow incorrect or mistaken to say that "playing Wii Golf is wrong."

I went on to say that the "distinction surely has to do with our moral intuitions, and for shaved apes like us to 'have moral intuitions' is surely ultimately for us to have a certain sort of neurological event, one resulting from genetics, environment or some eccentric combination of the two. If moral properties exist, and they are non-physical (as they certainly seem like they would be), no remotely plausible causal story relates them to humans having moral intuitions about them.

"At this point, of course, one may go in any number of directions. For example, one can try to make sense of moral properties so they aren't non-physical. Volumes can be (and have been) written about this proposal in all of its myriad flavors--synthetic reductionisms, sentimentality theories and so on--but for the moment I'll just say that, while I've argued for this kind of approach in the recent past, at the moment I find the prospects for this sort of project fairly bleak."

If you're interested in why I tend to find those prospects fairly bleak, see my subsequent post on why I think typical, initially plausible-sounding naturalistic stories about moral realism tend to collapse into relativism. Of course, some sort of frankly relativistic realism of one sort or another might well be the right option (keeping in mind that not all forms of relativism are as silly as the simple variety that introductory ethics instructors the world over spend the first day of class demolishing), but, for now, let's put that to one side.

If not non-naturalistic moral realism, and not naturalistic moral realism, then what? Well, there's always outright error theory, but if we're interested in capturing our intuition that it's somehow correct to say that "torturing children for fun is wrong" and somehow mistaken to say that "playing Wii Golf is wrong," then standard forms of error theory aren't real options.

An additional choice on the market today is Blackburn/Timmons/Gibbard-style "quasi-realism." I find it unattractive mostly because I'm a minimalist about truth, and, while every figure mentioned in the last sentence claims the same thing, I think that their view amounts to a theory of truth no less "substantive" than coherence, young-Wittgenstein-style correspondence and so on. (Note that this is not a criticism that Nolan & Co. make, although I think they should.) See below for an explanation of all that.

Meanwhile, at this point, it might start to look like all the possible options are wrong, and we're in serious trouble. Indeed, it's precisely because this is how things look that I find fictionalism so interesting. It lets have our "some moral statements seem correct and others seem incorrect" cake and not only eat it too but wash it down with both a shot of Respectably Naturalistic Picture Of The World and a Plausible View About Truth chaser. What's not to like?

Before going much further, it's worth fleshing out for a moment what "fictionalism" means. Any fictionalist view about moral statements is one according to which moral discourse is like fictional discourse. What semantic status an apparently correct moral statement like "torturing children for fun is wrong" has according to any version of fictionalism, then, is a matter of what status the fictionalist in question takes apparently correct fictional statements like "Sherlock Holmes is a detective, not a carpenter" to have. There are, at this point, at least two options (actually, there are definitely a lot more, but, for the time being, let's stick with just these two, since one of them is the Restall/Nolan/West-preferred and the other helps us bring out some interesting things about it):

(1) What we can call "truth-fictionalism," which stems from the view that the natural language sentence "Sherlock Holmes is a detective" is true, although its surface grammar has to be re-interpreted a bit. When we say "Sherlock Holmes is a detective, not a carpenter," we really mean "In fiction, Sherlock Holmes is a detective, not a carpenter." Similarly, with whatever the meta-ethical version of a fiction operator may be implicitly affixed the beginning of the sentence, "torturing children for fun is wrong" is true as well, despite the fact that we're neither postulating a really existing property of wrongness nor playing quasi-realist games with the notion of truth.

(2) What we can call "falsehood-fictionalism," which stems from the view that the natural language sentence "Sherlock Holmes is a detective" is just as false as "Sherlock Holmes is a carpenter," but, while discussing fiction, it's correct to assert the former and incorrect to assert the latter. If we take the surface grammar seriously, and we take reference failures to guarantee falsehood in the typical Russellian sort of way, the falsehood of any statement one makes about Sherlock Holmes one way or the other would seem to be straightforward enough. The appropriateness or inappropriateness of asserting any such (false) sentence, however, is a function not just of their truth or falsehood but of the purpose of fictional discourse, and similarly, even if "torturing children for fun is wrong" is, strictly speaking, just as false as "playing Wii Golf is wrong", it's still correct to assert the former and incorrect to assert the latter. This difference in correctness is not a matter of the way that the world is (since, on this view, the world lacks properties like "wrongness") but simply a matter of the function of moral language.

Before we go any further, it's worth addressing one bit of taxonomy--why not call (1) a version of moral realism and (2) a version of error theory? This seems to me to be largely a matter of decision and convenience. If one describes any view according to which moral statements are true as realist and any view according to which they are false as error-theoretic, we can talk about realist fictionalism and error-theoretic fictionalism, but I think that the shape of things is clearer if we reserve the word "realism" for views according to which the world contains really existing moral properties and the word "error theory" for views according to which there's no sense in which some moral statements are more correct than others.

A more interesting question, to my mind, is the one of what the difference is between (2) and quasi-realism. Both "falsehood-fictionalism" and quasi-realism agree that (a) the world isn't obliging enough to provide us with metaphysical facts to make true statements like "torturing children for fun is wrong", but (b) the nature of our moral discourse still makes some such statements (but not others) correctly assertible. Where they come apart is on the question of whether (c) is therefore true.

My gloss on this would be that the main difference is that falsehood-fictionalism is a view that you get when you start out from quasi-realist-like assumptions, but you take minimalism about truth seriously. (I'm certainly not claiming that you have to be a minimalist to be a (2)-style fictionalist. Indeed, Nolan/Restall/West, while advocating (2)-style fictionalism in the linked article, don't claim to be minimalists, and indeed seem quite prepared to cede the term to the quasi-realist. Rather, my claim is that minimalists who agree with the starting points of the quasi-realist story necessarily have to become (2)-style fictionalists in order to remain consistent.) If truth is nothing more than T-Schema instances--or, arguably equivalently, "'P' is true" never means anything above and beyond what P means--then, if I ascribe a non-existent property to something, my statement is straightforwardly false. (If, say, we call the fictional color in H.P. Lovecraft's classic horror story "The Colour Out Of Space" 'glack,' our statement "snow is glack" is obviously and straightforwardly false.) It doesn't matter how our discourse about that property works, what useful function might be served by that bit of our language, or what the conditions might or might not be for in any sense 'correctly' or 'appropriately' asserting that something has that property. None of those things can enter into our assessment of the truth or falsehood of the statement, because there's nothing more to truth than the instances of the T-Schema. The quasi-realist's move is, inevitably, to build things about assertion into their account of truth, and at this point, I can't for the life of me see how their view about truth is any less "robust" or "substantive" than, say, the picture-theory version of correspondence. The picture-theorist, after all, accepts all instances of the T-Schema, they just tell a substantive, definitional story about what all those instances have in common.

(Of course, if the quasi-realist wants to frankly admit that they have a substantive theory of truth and frankly argue for that theory and against any kind of minimalist or deflationary option, that's their right, and any such proposal needs to be carefully considered on its merits. What's annoying is that quasi-realists tend to wrap themselves up in the banner--and inherited intuitive appeal--of minimalism, when their implicit theory of truth is really anything but.)

(As a further sidenote to all this, depending on how a (2)-style fictionalist fills out her preferred story about moral language, (2)-style fictionalism might amount to a version of expressivism, if we use that term to refer not just to quasi-realism but to a whole family of related views, like Ayer's non-cognitivism and Hume's projectivism. Hume, remember, took moral statements to be false. When we paint the world in the colors of our moral reactions to it, we are misrepresenting it, not doing something non-descriptive.)

In any case, before saying anything more about (2)--of which the Nolan/West/Restall position is a variation--we should take a harder look at option (1), "truth-fictionalism." What's wrong with that?

One objection might be that, even if the "implicit fiction operator" story is a plausible reconstruction of what ordinary speakers are getting at when they make positive assertions about Sherlock Holmes--if you say "Sherlock Holmes lived on 221b Baker Street" and I offer to pour through the records of the place to prove that no such person ever occupied it, the obvious response would be "you know that's not what I mean"--it still isn't a particularly plausible reconstruction of what ordinary speakers mean when they talk about wrongness. I'm not sure how devastating this objection is, given cases of fictional discourse whose fictionalness isn't universally agreed on. For example, if Robin is an agnostic who doubts the historicity of the Exodus, and Jane is a devout Christian fundamentalist who takes the Bible as the inerrant Word of God, and one of them thinks that Aaron was Moses' brother and the other of us was sure that Aaron was Moses' son, Jane and Jill don't seem to talking past each other. The (1)-style fictionalist could perhaps make sense of this by saying that both our statements have an implicit "according to the Bible..." operator B(...), and our disagreement about whether B(P) universally entails P is beside the point.

On the other hand, the (2)-style fictionalist might claim to have a more straightforward account of this case...and thus, by analogy, a more straightforward account of what's going on when Mark the Robust Non-Naturalistic Realist and Ryan the Fictionalist disagree about whether abortion is wrong. The (2)-style fictionalist could gloss the Jane and Robin case by saying that the statements they are asserting directly contradict each other, neither being prefaced by any sort of implicit operator, and that their disagreement about whether whatever the correct answer is is assertible because, say, they know it to be true, or because, despite its falsity, the function of fictional discourse entitles us to assert it, is quite irrelevant to the case. Similarly, in the Mark and Ryan case, the claims "abortion is wrong" and "abortion is not wrong" directly contradict each other, and their disagreement about whether the correct answer is assertible because it captures the moral facts or whether it's a matter of the function of moral language is quite beside the point.

This leads directly into another advantage for (2)-style fictionalism over (1)-style fictionalism. "According to morality, abortion is wrong" and "according to morality, abortion is not wrong" don't contradict each other. (They might implicitly contradict each other if we make the background assumption that our moral fiction is internally consistent, but that needs to be separately argued for. Famously, ordinary fictions are often quite inconsistent. "In the Sherlock Holmes stories, Watson's war wound is on his right shoulder" and "in the Sherlock Holmes stories, Waston's war wound is not on his right shoulder" are both true. There are desperate ways of interpreting away such inconsistencies, but they fail when we come to deliberately inconsistent works of fiction like Graham Priest's playful short story "Sylvan's Box.") (1)-style fictionalism, in other words, faces a Frege-Geach problem about whether the logic of moral discourse is going to end up being revisionary. The (2)-style fictionalist, on the other hand, would seem to have no such problem. Even if one is a truth-preservationist about validity, since moral statements are just ordinary statements, some moral arguments are valid and others are invalid (although, of course, none are sound) and there will be nothing revisionary about any of this. (Similarly, the inference from "snow is glack" and "if snow is glack, grass is glack" to "grass is glack" is valid.) So far, so good.

Indeed, West, Nolan & Restall put quite a bit of emphasis on Frege-Geach, and the attractiveness of their avoidance of the problem. (See, for example, p. 25 of the linked article.) There are, however, some tricky issues about how thoroughly they've escaped Frege-Geach, and I'll end on a quick look at that point.

To start to get a handle on it, we can ask a basic question:

What's the value of moral discourse, given that it doesn't have the value of "getting at the truth"?

In the case of fictional discourse with the rules of assertion that go with it (according to the (2)-style fictionalist), the whole story might simply be that the pleasure of conversationally recreating the details of our favorite novels and short stories is an extension of the original pleasure of reading them, and that might be all there is to it. Moral discourse, however, seems to serve richer human purposes. It seems to be intimately linked to all sorts of things that definitely do exist. Even if there's no such thing as wrongness, and as such it's not true that "torturing children for fun is wrong", it's still true, in a typical discussion about the matter, regardless of their meta-ethical views, all participants prefer that no one tortures children for fun, are upset by the idea, disapprove of other people doing so and plan not to do so themselves. Presumably, even if we take truth out of the equation, the remaining purpose and importance of continuing to engage in moral argumentation has something to do with all of this.

In their discussion of the advantages of moral fictionalism over standard error-theoretic accounts, Nolan & Co. write:

"A fourth advantage of moral fictionalism over eliminitavism has to do with its capacity to salvage the important role moral discourse is widely thought to play in coordinating attitudes and regulating interpersonal conflict in cases where people disagree about what they are to do, especially where collective action is needed or the proposed actions of different people interfere with each other." (p. 21)

In filling in the details of how one sort of plausible fictionalist story about this might work, they go on to say that one "reply might be to connect non-moral preferences and what is true in fiction via internalist bridge laws (though care must be taken in stating these). If the fiction is set up in such a way that it is guaranteed that what is good-in-the-story that the people engaged in the story have certain non-cognitive attitudes towards it, then coming to realize that some course of action does have certain moral properties according to the story should prompt the realization that the action is one that the agent has certain attitudes towards.

"Or the fictionalist could tell an externalist story: it might be the case that, by and large, people contingently want to bring about situations which are true according to the fiction. According to the externalist, no mere cognitive belief alone will affect people's preferences, but that does not mean that people may not alter their preferences to reflect what is true in the fiction." (p. 22)

The last point, it seems to me, could be more happily paraphrased as something like "people may have an over-arching preference for their behavioral preferences to line up with what, in the fiction, is 'right.'" (Indeed, given Motivational Humeanism--a view, which, anecdotally, it seems to me is accepted by an awful lot of philosophers with realist views about morality--there's a certain sense in which the fictionalist is in no worse boat than a robust moral realist. Even if there are moral facts, and even if we have access to them, people will only be motivated by them to the extent that they happen to have a desire to be moral.) In any case, all of this talk of regulating preferences brings us back to Frege-Geach.

It seems obvious that it's at least possible to have inconsistent approvals, preferences or plans. I can prefer for two mutually inconsistent things to happen, I can approve of them both, and I can plan to do both. My preferences and approvals will never be fully satisfied and my plans will never be fully carried out, but this can be true without inconsistency rearing its ugly head. (For example, I might plan to always carry out every promise I ever make to anyone about anything, but be psychologically incapable of making good on this.) Conversely, I might not have any preference, approval or plan one way or the other about some issue.

It might seem, though, that part of the value of moral discourse is that it helps reduce both the inconsistency and the incompleteness of my attitudes. Therein, indeed, might lie much of the usefulness of careful, rational discussion of moral issues. So far, so good.

But, given the first option sketched above (internalist bridge laws), it seems like the incompleteness and inconsistency of my plans will tend to infiltrate into the moral fiction and this useful purpose will be undermined. It could be that, even in idealized circumstances, I would still equally prefer for P and ~P to come true, or have no preferences one way or the other. If the moral story we've all been telling to each other seems humans started to develop ideas about morality is "designed" so as to line up with our preferences or plans (or even hypothetical preferences or plans formed under idealized circumstances), then won't it reflect the inconsistency and incompleteness of our (actual or hypothetical) plans and preferences?

OK, but what about the externalist option? Going with that, it could be that the fictional world of rights, duties and the rest described by our moral discourse is both complete and consistent, and that "by and large" people happen to have the happy trait of over-archingly preferring to line up their behavioral preferences with the imaginary properties that exist in that world. Outstanding! Even here, though, problems of consistency and completeness arise. Without infallibly internalist bridge laws, the fictional world of moral obligations might be as complete and consistent as external reality--there might be a "Moral Law of the Excluded Middle" and a "Moral Law of Non-Contradiction"--but why suppose that things have worked out that way? If morality is a human construction--like the world of the Sherlock Holmes stories, it's something we made up--why should it be any more complete or consistent that the Holmes stories are?

Take a typical case of reflective equilibrium, where a conflict between immediate moral intuitions is used to help us to regiment them into a consistent system, in precisely the sort of way that's important to the function of moral discourse described above (to help regulate preferences and coordinate collective action): the argument against consequentialism based on the second version of the Trolley Problem. We start by pointing out that in all morally relevant ways, the switch-pushing case and the fat-man-pushing case seem to be equivalent, and thus reason that "if it's OK to push the switch, it's OK to push the fat man." We then assert that it's not OK to push the fat man, and conclude that it's not OK to push the lever. So far, so good, and all precisely the sort of thing the fictionalist is supposed to be able to make sense of, despite the fact that they take all of the statements with the moral predicate "OK" in them to be, strictly speaking, false.

Why, however, should we still take this to be a valid argument, given that the moral fiction, being a human construction, might well contain inconsistencies? Surely, what it's correct to assert about rightness and wrongness is a function of which things are right and wrong according to the story, and, in the story, (a) if it's OK to push the switch, it's OK to push the fat man" and (b) "it's not OK to push the fat man" could both be true in the story without (c) "it's not OK to push the switch" being true in the story. After all, (d) it's OK to push the fat man" might, in principle, also be true in the world of the story if we have no guarantee that it's an entirely internally consistent story.

Of course, the fictionalist could stick to their guns and say that validity isn't a matter of correct-assertibility-preservation, and certainly not of truth-according-to-some-fictional-story-preservation, but a matter of truth-preservation in the actual case. This is fair enough, but I think that at the end of the day, the fictionalist is faced with an unpleasant choice:

(1) They could accept a correct-assertibility-preservation account of logical validity at the price of accepting revisionary conclusions about the logic of moral discourse, which is to say, re-introducing the Frege-Geach Problem, the avoidance of which was supposed to be a major selling point of the account*,

or

(2) They could accept a truth-preservation account of logical validity at the price of destroying the value of moral argumentation. That is to say, they could continue to say that some logical arguments are valid and others are invalid and that the rules for deciding which are which are the same as they are for arguments about anything else, at the expense of logical validity being an important virtue for moral arguments. If, after all, moral statements are always false (so the point of moral arguments can't be to convince us that the conclusions of those arguments are true), and logically valid arguments can take us from moral premises which it is correct to assert to moral conclusions that it is not correct to assert, then why should moral fictionalists care whether or not some argument is valid?









*Restall, as a logical pluralist, might have the resources to accept this with a shrug--perhaps the logical consequence relation appropriate for moral argumentation is inappropriate for other contexts--but Nolan, who has argued extensively (in his work on counterpossible conditionals) in defense of a monist view about logic, should presumably be more troubled. I'm not sure what West's position is. In any case, in the article, they jointly present fictionalism's alleged avoidance of Frege-Geach-style problems as a major selling point.

Follow-Up On Free Will and the "Logical" Problem of Evil (The Hitler Sperm Post)

In my last post, I argued that Plantinga's version of the free will defense (whereby the bare logical possibility of e.g. demons causing earthquakes is supposed to solve the "logical problem of evil") is a non-starter. If one is concerned about (a) the logical compatibility of the appearance of extreme suffering by innocents with the existence of all all-PKG deity, that's easily enough demonstrated, without any need to bring out to the sort of conceptual technology about actualizing possible worlds that Plantinga deploys. If, on the other hand, one is concerned with the considerably more interesting question of (b) the logical compatibility of the existence of an all-PKG deity with the real extreme suffering of really existing innocents caused in the way that we know it to be really caused, then the demonic free will maneuver clearly fails. What the maneuver demonstrates, at best (i.e. if there's a viable free will defense against the problem of evil in general, which I deny) is (c) the logical compatibility of the existence of an all-PKG God with the real extreme suffering of really existing innocents. And, I argued, (c) only sounds interesting because, if one isn't paying close attention, it looks like (b). We know that earthquakes are caused by the autonomous operation of natural processes in pretty much the same way that we know that the Haitian children who died in last year's earthquake weren't Chalmersian zombies or holograms.

That seems clear enough, but an interesting further question remains--whether some sort of free-will-based solution can at least solve a severely restricted form of the "logical problem of evil" where we confine our attention to human evil. (If that much turned out to be true, some entirely separate defense would still be needed in order to demonstrate the logical compatibility of the existence of all-PKG deity with the existence of natural evil.) I suggested that:

(i) If one is a compatibilist about free will (as I think one should be), there's quite obviously no case to made that God couldn't actualize a possible world with free will and no evil. As far as I know, Plantinga's published arguments against compatibilism tend to be a matter of foot-stomping and table-banging.

&

(ii) Even if compatibilism is wrong, this hardly establishes the logical possibility that libertarianism is right. There are tricky issues here, but it's at least prima facie unclear that the notion that our decisions could be neither random nor causally inevitable is an internally conceptually coherent one. (Think about, for example, the rollback argument.)

&

(iii) Even if some form of libertarianism is both internally incoherent and the account that best captures our intuitive concept of free will, it hardly follows that the libertarian's proposed conditions for free will are ever met in the actual case. This might seem irrelevant, since we're supposed to be talking purely about bare logical possibility, but if libertarianism is incompatible with what we know about the concrete world as a result of the deliverances of the empirical sciences, then--a la the point above about demons and earthquakes--an obvious argument can be made that no form of the free will defense gets around any interesting form of the logical problem of (even human) evil.

So far, so good, but I ended with a promissory note for something better. I said that I'd go on to give an argument that even if (i)-(iii) were all wrong, no form of the free will defense succeeds in demonstrating the possible co-existence of an all-PKG deity and, for example, the Holocaust. I also promised I'd use the phrase "Hitler sperm" in my explanation.

To get the second part out of the way:

Hitler sperm.

To go into greater detail:

There are many strange things about free will defenses in general. One is that they tend to rely on the assumption that not only would a just God want human beings to be the sort of creatures that are generally capable of making free decisions, but that He would unrestrictedly allow them to exercise that capacity and to carry out their freely-decided plans...except when some other, non-divine agent stops them from doing so, the normal operation of some divinely-established natural process stops them, etc. This is a significant point: Consider that proponents of the free will defense take the importance of free will to explain (or possibly explain, or whatever) why a just God wouldn't stop Hitler. Consider too that no one takes the generic statement "humans have the capacity to freely decide between various courses of action and act on those decisions" to be falsified by the fact that human police agencies sometimes catch murderers and rapists before they carry out their freely-decided courses of action and lock them up in confined places where they will be unable to do so (or, even more efficiently, execute them so they are too dead to do so). Why, then, should we suppose that the same generic statement would have been falsified by, for example, God supernaturally intervening (in a way that, obviously, no one would have ever known about) to move the briefcase bomb that almost killed Hitler in 1944 a few feet closer to the Führer, or arranging for there to be one hole in one fence somewhere so positioned as to have saved even one single one of Hitler's millions victims? How can one coherently believe that (1) "a just God would allow his creatures free will" explains God's failure to stop even one person on one occasion from carrying out their freely-decided plans, but also that (2) free will continues to exist in a world where people are constantly stopped from implementing their plans by everything from the intervention of other agents to heart attacks, freak accidents and so on?

Recall that Plantinga-style invocations of free will rely on the radical claim that it would be impossible for even all omnipotent being--presumably "omnipotent" in the sense of "being constrained only by the boundaries of logical possibility"--to actualize a version of the world in which human beings had free will and even one fewer Jew died in the Holocaust. Now, a theist could grant that the generic statement "humans have free will" would still have been true even if God had saved an additional one or two of the six million, but argue that a just God would have to allow not just the existence of free will in general but "at least exactly as much free will as humans actually have in the actual world." That is to say, a just God could allow people's plans to be foiled by the actions of other people, by the normal operation of divinely-established natural processes and so on, but he wouldn't act directly to stop any person from making or carrying out any decision about anything. We can think of this as a bit like a strange cosmic counterpart to the constitutional prohibition on Congress making a bill of attainder.

This is, to say the least, a lot less intuitive than the simpler version of the free will defense. The burden would certainly be on the theist to explain why we should take this modified version seriously. Beyond that, though, there's one last important point to be made about this:

Even if we accept for the sake of argument that the actual world is not deterministic, that compatibilism is not a viable theory of free will but that libertarianism is, and that the actual world conforms to the libertarian picture of free will....

....and we accept for the sake of argument that, for some reason, a just God would always allow every person in existence to carry out their plans unless stopped in some other way than by direct divine intervention....

....it still doesn't follow that an all-PKG God couldn't have prevented Adolf Hitler from ordering the extermination of European Jews. Standard glosses on omniscience (the "K" part of "all-PKG") have it that God knows everything that will ever happen as well as everything that has ever happened. (Whether to cash this out in terms of "foreknowledge" or atemporal knowledge of all of time is irrelevant for our present purposes.) This is, happily, quite compatible with libertarianism. (If one goes with "foreknowledge" rather than "atemporal knowledge," there are some complications, but if one is willing to grant the possibility of backward causation, it all works out well enough.) Even if some entity knows which radically self-caused free decisions I will make at some point in the future, I can still be the cause of that decision, fulfilling whatever one's favorite libertarian requirements for free will might be.

Given that, an all-PKG deity would know everything Hitler would do in his life, every radically self-caused free decision that Hitler would (if allowed to come into existence) would make before He allowed the particular sperm and the particular egg that became Hitler to come into contact with each other. As such, even given the extreme, strange, ad hoc claim that we assented to above (that, for whatever reason, an all-good God would never intervene to stop anyone from exercising their free will in any way that they were not constrained from doing by the normal rules of His governance of the natural world or by the decisions of other agents), unless one ascribes free will to sperm, there is absolutely no reason why a just God couldn't or wouldn't actualize a possible world in which libertarian free will existed but the Holocaust did not.


(BTW, thanks to my good friend Ryan Lake for an extremely informative discussion about this a while back. Like most of what I say about free will, the clever bits are mostly due to his influence.)

Plantinga and the Problem(s) of Evil

In Monday's post about the atheist bus campaign, I suggested that, given the powerful anti-theistic arguments available to us, "God probably doesn't exist" dramatically under-states the case. Even allowing for general fallibilism, a more accurate formulation would be "we can be as sure of God's non-existence as we can be of anything." While most of the post was spent taking apart the stranger bits of conventional wisdom often spouted by people with "middle of the road" positions on God--"science and religion can't conflict because they concern different subjects," "you can't prove a negative"--I did mention the Problem of Evil in passing, saying that (a) there were purely logical problems with making sense of the notion of an "all-powerful" being existing, that (b) "we have powerful empirical evidence against the existence of God in the form of the Problem of Evil," and that (c), given that we have no evidence for the existence of God, even if we didn't have any evidence against the existence of God--i.e. even if (a) and (b) were both false--then, in that "all else being equal" hypothetical, atheism would be rationally mandatory purely as a matter of ontological simplicity.

In the comments, Simon Bunckenburg asked:

"Hi, re your treatment of the problem of evil. I'm suprised you do not mention Platinga's free will response? seems to make sense to me."

To quickly review for readers who may not be familiar with this, it's customary to separate out "the logical problem of evil" from "the evidential problem of evil." A standard way to explain the distinction is that the former problem is about whether the existence of evil makes it logically impossible that God exists, whereas the latter problem is about whether the existence of evil makes it merely extremely improbable that God exists. Plantinga's version of the Free Will Defense isn't intended to address the "evidential problem of evil," but merely to show that the existence of evil doesn't make the existence of God logically impossible. While normal Free Will Defenses at best only account for human evil, Plantinga's is notable because he extends it to natural evil by pointing out that, for example, it is at least logically possible that earthquakes could be caused by demons exercising their free will.

So, the obvious, standard way to reply to Simon would be to point out that my only claim about the Problem of Evil in my post was that the existence of evil constitutes "powerful empirical evidence against the existence of God", and that Plantinga's response doesn't touch that claim, and that indeed it isn't intended to touch it. The reasons why I'm devoting an entire post to this, instead of just giving that one-sentence response in the comments, are that:

(1) For a variety of reasons, I'm not entirely satisfied with the standard way of chopping up the Problem of Evil into "logical" and "evidential" forms,
&
(2) In any case, even if I was completely comfortable with standard procedure here, I'd strongly reject the claim that Plantinga has refuted the "logical" form of the problem. I think that his version of the Free Will Defense (like all versions of it) fails for all sorts of interesting reasons, worth mentioning.

(Note that if you want to skip all the epistemic stuff and just see what I have to say about Plantinga, I mark the break between my discussions of (1) and (2) with a ************.)

On (1), I'd start by noting that, while I'm in a distinct minority here on the contemporary philosophical scene, I reject the whole notion of epistemic probability. (I've posted about this before, and may again, but for now I'll just note that I agree with the conclusions Simon Evnine comes to in his discussion of the Lottery and Preface Paradoxes in his book Epistemic dimensions of personhood. Briefly: the right lesson to draw from the paradoxes is that high probability is neither universally necessary nor universally sufficient for epistemic justification.) A second, related point, is that I'm a confirmational holist. (I think all of rational inference is a matter of coming up with the best total explanation of the evidence, where "total explanation" includes logical and metaphysical components as well as more obviously "empirical" ones, and it's all intertwined.) Putting the two together, let's go back to something I said about the refutation of theories in my last post:

"If a consequence of Astronomical Theory A is that such-and-such planet will be at such-and-such position at a certain time, and at the relevant time, we observe the relevant position and the planet isn't there, that's evidence against Astronomical Theory A. (Similarly, an obvious consequence of theism is that unnecessary suffering shouldn't exist, but it does exist, in great quantities, and the theist has no convincing way to explain it away. This is evidence against theism.) Without this sort of negative evidence, the process of doing science would be unrecognizable."

Let's try to be a bit more precise about all of this:

Is the refutation of Astronomical Theory A "logical"? Well, in the example, the conclusion that Astronomical Theory A is false comes at the end of a valid and sound logical argument (an instance of Modus Tollens), and I don't accept that probability has anything to do with it. In that sense, it's certainly logical. On the other hand, there are in any such cases any number of creative ad hoc maneuvers one could go through in order to deny the first premise of that argument ("if the theory were true, such-and-such planet would be observed at such-and-such position at a certain time"). If we stick to our guns and continue to assert that first premise and thus the conclusion as well, it's because we've examined these explanations and decided that our best overall theory of the world is a simpler one where we don't try to explain away the evidence in these complicated ways. Note, however, that I'd say precisely the same thing if someone tried to get around the conclusion by denying the validity of Modus Tollens (for example, by postulating true contradictions and pointing out that, given that assumption, it follows that MT isn't universally truth-preserving, since 'if P, then Q' 'P', 'Q' and '~Q' would all be jointly true). My attitude wouldn't be "either the probability of the conclusion being false is 0, which licenses me to dogmatically ignore all dissenters, or it's over 0, in which case I have to prefix key parts of the argument with the word 'probably'", but rather that everything's on the table and has to be evaluated case-by-case.

Given my Quinean epistemic picture, then, I'd argue that there's just one Problem of Evil. Given the existence of all sorts of apparently gratuitous suffering and evil, should we believe in God?

********************

On (2), I'd note first that we need to be careful about delineating exactly what Plantinga is trying to do. Just showing that the appearance of the existence of extreme suffering by innocent people is logically compatible with theism doesn't require anything nearly so complicated as Plantinga's manuevers. If you're friendly to qualia, there's Ryan's excellent zombie solution, and with a little creativity one could come up with something similar that doesn't involve qualia to show that the appearance of innocent people suffering in an extreme ways is some sort of illusion. This is all a lot more simple and elegant than banging on about free will and God's ability to actualize certain possible worlds. It isn't sufficient for Plantinga, though, because he seems to aspire to a slightly more interesting project: he wants to show that even if we take the appearance of extreme suffering by innocent people seriously, and postulate that it is just as it appears, this assumption is compatible with the claim that God exists.

That project is considerably more interesting, and I think he pisses it away in a spectacularly uninteresting way when he starts talking about demons exercising their free will by causing earthquakes. If successful (which I don't take it to be....see below) that technically shows that the real existence of extreme suffering is compatible with the existence of God, but it doesn't show that the real existence of extreme suffering caused in the way that it is really caused is compatible with the existence of God. The project "show that God's existence is logically compatible with something we all know to be true (even if there's some sense in which we can't absolutely rule out extreme fantastical scenarios on which it would be false)" becomes totally uninteresting and pointless if the price of the compatibility is that you have to continue to admit that the existence of God is logically incompatible with something else that we equally well all know to be true (even if there's some sense in which we can't absolutely rule out extreme fantastical scenarios on which it would be false). We know damn well that earthquakes aren't caused by demons, just as we know damn well that the inmates at Auschwitz weren't Chalmersian zombies. The two claims have precisely the same epistemic status. Showing that "the existence of earthquakes that really kill and maim really existing and really conscious innocent children" is logically consistent with the existence of God has no value if you aren't also showing that "the existence of earthquakes really caused in the way we know them to be caused that really kill and maim really existing and really conscious innocent children."

So, even if Plantinga's maneuver were successful in his project, there would still be an interesting "logical problem of evil" that his solution wouldn't touch, and, in fact, I would argue that that the version addressed by his solution only ever looked interesting because, if you squint, it looks like the filled-out version spelled out at the end of the last paragraph.

Still, Plantinga's solution might at least defeat the interesting logical problem of evil when it comes to human evil, right? Like, a separate solution is needed to show that God's existence is logically compatible with natural evil, but showing it for human evil would still be worthwhile.

Well...

The first problem is that, given compatibilism about free will, it's obviously not the case that God couldn't actualize deterministic possible worlds where everyone fulfilled the conditions for being free and there was no moral evil. Arguing for compatibilism is a much bigger project--there's a vast literature there--but for now I'll just report that (a) I'm a compatibilist, and (b) that I'm fairly unimpressed with Plantinga's dismissals of compatibilism, which he doesn't tend to take seriously enough to provide much of anything resembling an argument against.

The second, related, problem is that even if you accept that libertarians are right and compatibilists are wrong about the conditions for free will--which I don't--Plantinga has only demonstrated the logical possibility of the co-existence of God with human evil given the significant further assumption that it's logically possible for the libertarian's conditions for free will could be fulfilled. (After all, one could take e.g. Naomi Arpaly's position, eloquently argued for in her book Merit, Meaning and Human Bondage that we do desire free will, but that it's quite possible to wish for deeply impossible things.) I actually think that there are considerable reasons to doubt that this would be logically possible. Depending on exactly how one understands the details, free will as conceived by the libertarian might seem to require a form of causation that is neither deterministic nor random, and it's just not obvious that this notion can be cashed out in a logically coherent way.

Finally, even given the joint assumptions that (a) the libertarian is right about the conditions for freedom, and (b) it's at least possible for those conditions to be fulfilled (plus, of course, some additional controversial assumptions, like, "free will is more good than genocide is bad"), it's not clear that any of this establishes the possible co-existence of God with the specific sorts of extreme human evil that actually exist.

If you're the sort of theistic libertarian who finds that last claim intriguingly strange--given both libertarianism about free will, and the assumption that a just God would allow his creatures free will, how could all that not at least add up to a solution to the logical Problem of Evil?--then stay tuned for next week, because that will be the subject of Monday's post. As an extra feature, I promise to use the phrase "Hitler semen" in my answer.

Science, Religion And Two Very Silly Claims Often Made By Agnostics

If the people running the atheist bus campaign had asked me, I would have balked at the word 'probably' and pushed for something like, "We Can Be As Sure Of The Non-Existence Of God As We Can Of Anything, So Stop Worrying And Enjoy Your Life." Then they would have pointed out that my version is a lot clunkier than theirs, and that it would be harder to fit on the side of a bus in letters big enough for people to read as it rolled down the street, and I would have said, OK, despite my deep commitment to fallibilism about absolutely everything (and, yes, that includes fallibilism, and no, you can't run a self-refutation argument against fallibilism on that point, unless you want to beg the question by simply assuming that certainty is a requirement for knowledge), I'm slightly uncomfortable with the word "definitely", but I'll accept it as a necessary simplification for the sake of space.

As it happens, Richard Dawkins, being prominently involved in the project, actually did argue for the phrasing "almost certainly." Whether or not this is equivalent to my "as sure as we can be about anything" formulation presumably depends on whether Professor Dawkins thinks that we can be absolutely certain about anything. (I'm not sure.) My position, at any rate, is that (a) the Stone Paradox is just as much of a logical problem for the claim that an omnipotent being exists as Russell's Paradox is for naive set theory, (b) we have powerful empirical evidence against the existence of God in the form of the Problem of Evil, and that, (c) given the total absence of anything resembling evidence for the existence of God, even if there were no evidence against the existence of God, and theism were a logically coherent position, and we were in an "all else being equal" situation, atheism would still win hands down as a matter of sheer ontological simplicity.

(If I tell you that an invisible three-inch-tall elf is jumping around on my right hand as I type, tap-dancing and singing show tunes at a frequency that no human or piece of recording equipment can detect, your response will obviously and correctly be active disbelief. No rational person would respond with, "well, it's probably wiser for us all to be humble and admit that no one really knows whether or not there's an elf....")

Despite all of this, a lot of nice enlightened tolerant liberal agnostic types balk at the claim that we can be confident about the non-existence of God, citing the deeply silly and confused claim that "you can't prove a negative." A related and equally silly objection comes from people who, often in the context of tut-tutting at the involvement of folks like Dawkins in things like the atheist bus campaign, say (often in a tone that indicates that they take themselves to be delivering a great insight) that "there can't be a conflict between science and religion because they concern different subjects."

(Note that, while I have heard one or two people who do philosophy for a living express similar sentiments--even the best of us have days where we haven't had enough coffee in the morning to think straight--I'm mostly talking about "the folk" here, or rather a certain very recognizable subsection of the folk who read the New York Times, listen to National Public Radio and studiously avoid having "extreme" or "strident" opinions about anything.)

The force of that second objection, of course, relies on playing with an ambiguity about the word "science." If by "science", you mean to narrowly refer to chemistry, physics, biology and so on, then, sure, it's true that there's no direct logical conflict between theism itself and the deliverances of these fields. Of course, many religions do make specific claims that can and do conflict with the findings of physics, chemistry, biology and so on--creationism being only the most obvious example--but other religious views are specifically designed to avoid such conflicts, and certainly the claim "an all-powerful, all-knowing, all-good being exists" doesn't by itself directly conflict with the findings of any of those fields.

If, however, by "science", one means to refer more broadly to the overall project of trying to understand the world in a rational, evidence-driven way--with chemistry, physics, biology and the rest being important elements of that project, but not the whole of it--then, yes, "science" in that sense does indeed conflict with religion, in so far as the Problem of Evil gives us an extremely convincing empirical, evidential argument against theism, there's no evidence for the existence of God, and the sorts of considerations of simplicity, non-adhocness and so on that necessarily drive theory selection in every part of the overall project should lead us to favor atheism.

The first objection is even stranger. Of course you can prove a negative. I'm constantly amazed by the number of otherwise bright, college-educated people who have somehow gotten it into their heads that it's impossible to do so. If by "prove," one means "show by means of evidence," then, remember, Sir Karl Popper thought that the whole of science was a matter of disconfirming theories--conjectures and refutations--and never a matter of confirming them. Even if one isn't willing to go quite that far, it's still indisputably true that we often have evidence that shows us that certain things are not the case. If a consequence of Astronomical Theory A is that such-and-such planet will be at such-and-such position at a certain time, and at the relevant time, we observe the relevant position and the planet isn't there, that's evidence against Astronomical Theory A. (Similarly, an obvious consequence of theism is that unnecessary suffering shouldn't exist, but it does exist, in great quantities, and the theist has no convincing way to explain it away. This is evidence against theism.) Without this sort of negative evidence, the process of doing science would be unrecognizable.

(Also, of course, given the logical law of double negation, any evidential confirmation of any claim P is also a confirmation of the negation of ~P.)

If by "proof", one does not mean "demonstration by evidence" but "proof" in the strict sense used by mathematicians or logicians, then the claim that "you can't prove a negative" becomes, if possible, even sillier and stranger than it was when we understood "proof" evidentially. There are simple, elegant and decisive proofs of the fact that there's no largest prime number, that there's no set of all ordinal numbers, and so on. So, whether one means "prove" in this narrow sense or in a broad enough sense to include evidential confirmation, the claim that one can't prove a negative is bizarre.

Still, can we specifically prove this negative (that God doesn't exist), in the strict, narrow sense of "prove" just discussed? I think so, yeah.

One of the most famous negative proofs in the history of philosophy and mathematics is Bertrand Russell's refutation of naive set theory, which goes like this:

Start with the claim that, for every description you can come up with, there's a set of all and only and only the objects that match that description. Question: What about the set of all sets that are not members of themselves? Is it a member of itself? If it is, it isn't, and it isn't, it is. Either way, we've got a contradiction.

Here's the equivalent for God:

Start with the claim that a being exists who can do anything. Question: What about creating a stone so heavy that He Himself cannot lift it? If He can create it, then there's something the being that can do anything can't do (create the stone), and if He can't, then there's something the being that can do anything can't do (lift it). Either way, we've got a contradiction.

"But, wait," you say, "can't we just be more careful and re-define omnipotence to avoid these problems? Let's just say that God can do pretty much anything, but there are some limits imposed by logical possibility."

Sure, you can say that. Similarly, the naive set theorist could respond to Russell's Paradox by being more careful about how to express their unrestricted comprehension axiom. They could just say that for pretty much any description we can come up with, there's a set of all and only the objects that meet the description, but that there are some restrictions on this imposed by logical possibility. Or they could reject one of the logical laws used to derive the contradiction. Or they could pull a Modus Ponens where everyone else opts for Modus Tollens, and take Russell's Paradox as an argument for the existence of true contradictions. (Graham Priest does, in fact, take precisely this line, and people who've read this blog before know that, while I disagree with Priest, I take his argument very seriously.) There's a general lesson here: given a conflict among one's beliefs, there are always many different ways of changing those beliefs to resolve the conflict. The process of rational belief revision is all about carefully weighing the options and choosing the best and most plausible alternative. Considerations of simplicty, non-adhocness and so on will come into play, and no solution can be absolutely ruled out in advance.

....which brings us back to where we started. Can we be absolutely certain that God doesn't exist? Nah. But we can be as sure about that as we can about anything, and the bus-campaigner's adjective "probably" severely understates the case.

So, I Have A Full-Time Job For Next Year

It's a one-year (but renewable for up to two more) non-tenure track Assistant Professor position in the Philosophy Department at the University of Ulsan. 3/3 teaching load, mostly Intro but with some opportunity to teach advanced undergraduate classes.

And, yes, that's the Ulsan in South Korea. (The teaching, fortunately, is entirely English-language.) And the school year starts on September 1st.

So, unless some unexpected last minute glitch comes up with getting a visa or some such, I'll be moving to Korea in mid-August.

A Quick Thought About Meta-Ethics

Think about statements (1)-(3)....

(1) Bob seems tall to me.
(2) Bob is a tall guy.
(3) Bob is 6'5.

....and compare them to statement (4):

(4) Murder is wrong.

Of (1)-(3), which one is most like (4)?

If your answer is (1), then you're endorsing a sort of extreme moral relativism whereby the only properties tracked by moral statements are individual preferences. If I think abortion is OK, and you think that it's wrong, we aren't really disagreeing. It's just wrong for you, but not for me. (As Kang says in the classic Simpsons Halloween segment, "abortions for some and miniature American flags for others!")

If your answer is (2), then we've moved to a more moderate and interesting form of relativism. It is, after all, possible to be mistaken about tallness and to be shown your mistake with evidence and arguments. (E.g. "Wow, that guy's tall!" "No, he isn't, man. He just looks tall because of the angle that photo was taken at. Plus, look at his shoes...") Still, exactly what (or, more to the point, "vaguely what") "tall" means surely varies depending on the time, place and context of utterance. Tall-in-12th-century-China and tall-in-21st-century-America are not the same.

The view that moral statements like (4) should be thought of on the model of (3)--combined with the claim that at least some such statements are true is, of course, objectivist moral realism. This is an attractive view for a variety of reasons, but, at least from a naturalistic point of view, it's often hard to make sense of. The easiest, most natural way of cashing out objectivist moral realism--that moral facts exist eternally outside of space and time--is immediately confronted with obvious epistemic difficulties, more or less equivalent to Benacerraf-style worries about numbers-as-abtract-objects. If there were such non-naturalistic moral facts, how would we ever know about them? What reason would we ever have to think that our moral intuitions, refined by some sort of process of reflective equilibrium, even roughly, non-coincidentally tracked them?

One sort of story one could tell to try to reconcile objectivist moral realism with some kind of respectably naturalistic metaphysical and epistemic framework would be to identify moral properties with whatever cluster of properties "out in the world" happen to provoke the right sort of intuitive responses in people under the right circumstances. When cashing out this sort of meta-ethical stories, it's fashionable to talk a lot about evolution, and to invoke analogies to Chomskyan "language engines." This provides at least a rough model, and lets the whole enterprise bask in the reflected glory of more scientifically rigorous disciplines.

Now, at this point, the obvious line of skeptical reply involves questioning the evidence, unfavorably comparing the rich body of rigorous empirical research backing up Chomskyan ideas about language with the paperclips and chewing gum that tend to be used to hold together any remotely plausible-sounding meta-ethical story about a "moral engine." The next interesting question is whether the end result of that line of attack is that the naturalistic objectivist moral realist needs to work harder, and that for now we should all be cautious agnostics about the whole thing, or that the "moral engine" research program is dead in the water....but I don't want to get into that now.

Instead, let's just assume for the sake of argument that the "moral engine" concept is right on the money. Evolution programs us to have certain instinctive reactions to certain things in reliable ways (perhaps excepting sociopaths and other genetic abnormalities, people whose cultural brainwashing has overwhelmed and overridden their instinctual moral reactions, etc.), and that's what our moral language tracks. Just to finish off the picture, we can throw in some Kripkean stuff about "rigidification" here to explain just how concepts like "wrongness" relates to various items of external reality. (Now, our view is basking in the combined reflective glow of Chomsky, Darwin and Kripke. It's unstoppable!) So far, so good.

Now, this means we can be mistaken about moral claims not just because we make logical mistakes in moral arguments, but because the core intuitions that lie at the justificatory base of the whole structure are flawed in some way (genetic abnormality, cultural brainewashing, etc.) One can argue flawlessly, be aware of every relevant counter-example, etc., have thought of everything, but can have intuitions that differ from the ones that fix our common moral language and thus be morally mistaken.

This is an important point, because without this, the whole project collapses into a kind of relativism.

Now, surely moral language existed two thousand years ago. (I.e. post-Plato, post-Aristotle, just before the rise of Christianity, etc.) That said, a lot of judgments of right and wrong that seem clear-cut now were nowhere to be seen then.

Slavery existed, but hardly anyone (if anyone) thought that slavery was universally morally wrong. Different people had different views about men, women and gender, but if anyone thought that men and women should have completely equal rights, then not a lot of them were writing this down. (The notion of "rights" itself doesn't seem to track much of anything in e.g. ancient Greek moral philosophy.)

Etc., etc., etc.

Now, all of this is plausibly explained by empirical progress in terms of common knowledge of relevant non-moral facts, by cultural blinders and prejudices that have been overcome, by bad moral reasoning that's been corrected, etc., and all of that's fair enough. Imagine, however, the following (admittedly silly and fantastical) discovery:

Some substance that was, up until a couple of thousand years ago, trapped deep beneath the surface of the earth, slowly started to leak upward at that time until it eventually made it into the world's supply of drinking water, and we've all been drinking it ever since. This substance causes a specific sort of brain disease that doesn't in any way impair or impede people's power of *reasoning* but does have one major consequence, but does slightly alter people's moral intuitions in a specific way: it makes them identify more with the plight of those who are different from them in various respects, in a way that makes a process of reflective equilibrium more likely to end up with them being sympathetic to the plight of slaves, women, religious minorities, etc.

Thus, given the sort of naturalistic objectivist view sketched out above, we should all (upon the discovery of this substance and its effect on our moral intuitions) realize that we were mistaken in coming to the conclusion that, for example, "slavery is morally wrong." Not because of any logical flaw in our reasoning, not because we weren't clever or imaginative enough in formulating examples and counter-examples and considerations, but because our deepest moral intuitions were defective, because they differed from the ones that the genetics would have predisposed us to if all else had been equal, the ones involved in the rigidification of moral language. Remember, earlier, our recognition of the possibility of these sorts of mistakes was essential. Without it, the view collapses into relativism.

So....thoughts?