So when we left off our story, Barwise and Etchemendy were modelling Russellian propositions with Aczelian hypersets, and the Liar Sentence came out false, but this fact wasn't included in "the world," because if it was, that would violate the "coherence condition" preventing a set-theoretic proposition-object and its "dual" from both being present in a model.
They describe this consequence as "counter-intuitive." I'd describe it as absolutely incoherent.
In any case, when they turn to Austinian propositions, one of the big advantages of the shift was supposed to be that this "counter-intuitive" consequence can be avoided. Remember, Austinian propositions include the situations they are about--so, e.g. if you are at a card game and you mistake the player holding the 3 of Hearts for Jill and claim that "Jill has the 3 of Hearts," the proposition comes out false even if by coincidence Jill actually is playing cards across town and she does happen to have the 4 of Hearts.
As such, the proposition being expressed by any given use of the LS is about some specific situation, since all propositions are on the "Austinian" model. How does this help?
Well, as in the Russellian case, the LS always comes out false. We can see why by analogy to the behavior of the Truth-Teller ("This sentence is true.") In situations that don't include any semantic facts, the Truth-Teller is false, since there is nothing to make it true. In situations that include semantic facts, the Truth-Teller is sometimes true and sometimes false, depending on what those semantic facts are...i.e. in a situation that includes the semantic fact that the Truth-Teller of that situation is true, it's true, and in a situation that includes the semantic fact that the Truth-Teller of that situation is false, it's false. Where these "semantic facts" about the Truth-Teller are supposed to come from, since they obviously don't supervene on the non-semantic facts, is a bit of a mystery to me, but whatever. Let's move on.
The Liar behaves in exactly the same way, with one major difference. The relevant semantic facts are always excluded from the situation used to determine its truth value. Why? Well, if we allowed them to included, that would give us the result that each Liar was both true and false, and that would violate the coherence rule. So it's in "the world," but not the part of it used to evaluate the truth-value of the proposition.
So the Liar of a situation that doesn't have any semantic facts in it is false--just false and not true, which is a neat trick--and the semantic fact that "the Liar of Situation 1 is false" is included not in Situation 1 but in Situation 2. Sure, Situation 2 has a Liar of its own, which is made false because there is nothing in Situation 2 to make it true (after all, the semantic fact that the Liar of Situation 1 is false is about the Liar of Situation 1, not this new Liar, so it is irrelevant), and its falsehood is a fact not of Situation 2 but of Situation 3. On and on forever.
Two comments seem to be in order about this picture.
The first is that, at the beginning of the book, Barwise and Etchemendy rejected Tarski's hierarchy-of-artificial-languages solution because it was arbitrary, didn't really solve anything on the intuitive level, etc. I agree with them on that. It is interesting, though, given that, that the situation-theoretic hierarchy they posit seems to be structurally exactly parallel to Tarski's languages model.
Secondly, and more importantly, it seems to me that the one fact being excluded from the situations is the only one that cannot be plausibly excluded from them. It is, in fact, the ONLY thing that belongs in them. If the Liar Sentence really does express a proposition, then the one and only thing its about is its own truth value. That semantic fact is the one and only fact of any kind that belongs in its Austinian "situation," so a Liar that really was 'about' a situation without semantic facts, or even without this one relevant semantic fact, is simply an incoherent non-possibility.
As such, taken as a defense of the Law of Non-Contradiction--and, as an attempt to explain why the Liar does not have its prima facie property of being true if false and false if true, that's what it amounts to, even without a dialetheist who actually asserts that it is both true and false as the conscious target target--it boils down to the following argument.
"There are no counter-examples to the LNC, therefore the Liar is not a counter-example to the LNC."
That's a perfectly valid instance of universal instantiation, but those of us who want to defend the LNC in the context of an actual argument are going to have to do better than that.
Sunday, February 3, 2008
Friday, February 1, 2008
Barwise and Etchemendy, Pt 1 (Russellian Case)
Last weekend, I read Jon Barwise and John Etchemendy's book "The Liar: An Essay on Truth and Circularity." The post is in two parts, divided up in a way that I hope will be intuitive.
The book is, as the name suggests, an attempt to get around the Liar Paradox. I'm sure anyone likely to glance at this book already knows plenty about it, but just for easy reference, here's the Liar Sentence again.
LS: This sentence is false.
Now, in all fairness to them, the book came out in the same year as "In Contradiction," so you can't blame them for not arguing convincingly against dialetheism, which was after all not much on the scene in 1987. On the other hand, to the extent that they are trying to "solve" the semantic paradoxes, though, they are at least trying to show that e.g. the Liar Sentence does not have its prima facie feature of being true if it is false and false if it is true. In practice, the set of arguments that would beg that question is necessarily co-extensive with the set of arguments that would beg the question against the dialetheist's position that the Liar Sentence really *is* both true and false.
Barwisee and Etchemendy argue that sentences like the LS, or, more precisely, the propositions expressed by those sentences, are false, but that, remarkably, they are not also true. And this despite the fact that they assume bivalance--every proposition is either true or false, and there are no truth value gaps.
How do they accomplish this minor miracle?
First things first, they model propositions as set-theoretic objects. This doesn't sound possible for self-referential sentences, given that standard Zermello-Frankel set theory forbids self-membership. As such, they go with Peter Aczel's "universe of hypersets," an exciting-sounding phrase for an alternate set theory (which contains the Zermello-Frankel universe of well-founded sets) in which circularity is permitted. (The sets in the orthodox hierarchy exist in Aczel's conception of the universe of sets, they just don't exhaust it. "Hypersets" are just sets outside of the hierarchy.) On the face of it, the adoption of Aczel's set theory to shed light on the semantic paradoxes sounds like it would let set-theoretic paradoxes through the back door, since these are kept out of orthodox set theory by the cumulative hierarchy of sets where sets can only have sets beneath them in the hierarchy as members. Not so, Barwise and Etchemendy claim, since Aczel has shown that we don't need the cumulative hierarchy to ban things like the Russell Set (the set of sets that are not members of themselves), we just need the set/class distinction. The Russell Set is not as set at all but a class, and there's no class of sets that are not members of themselves.
(If this sounds dangerously arbitrary, dear reader, I'm with you. In fact, here's a question I haven't been able to get a good answer to yet. If anyone wants to help me out in the comments, please jump in, since I suspect that I'm missing something important here. If we invented a new term that was neutral between sets and classes, like "grouping," where a grouping can be either a set or a class, then can't we re-instate the paradox by reference to a Russell Grouping? If not, why not?)
In any case, using Azcel hypersets, they establish models of propositions for both the "Russellian" and "Austinian" conceptions of propositions. (It's not clear how much of a historical/exegetical claim they are making about either Russell's or Austin's actual views in using these terms.) True Russellian propositions are made true by the world as a whole, and true Austinian propositions are made true by particular situations. (For example, the Austinian proposition "Jill has the 3 of Hearts," about a particular game, is false if the speaker has mistaken Lucy for Jill, but by coincidence Jill has the 3 of Hearts in another game across town.) Barwise and Etchemendy prefer the Austinian conception, although they first model Russellian propositions not just because problems in that model set up the Austinian model, but because (like the relationship of Zermello-Frankel sets and Aczel's hypersets) the Russellian sets are ultimately contained in the universe of Austinian sets.
Now, once we start the formal modelling--and this is true for both the modelling of Russellian propositions and later for the model of Austinian propositions--we get to my first and most important problem with the book.
(1) They blatantly beg the question, but making one of the rules of the model that no set-theoretic proposition-object and its "dual" will be included. Translated out of the set-theoretic context, this means that they set it up as a rule in advance that no proposition will be true and false. "We included a formal rule to ban inconsistency and, amazingly, no inconsistencies were generated by he model!"
This rule has, as you might expect, some funny consequences once the whole thing gets going. In the Russellian case, the result is that, since the world does not make the LS true, it is false, but the fact that its false is not included in "the world." Yes, you read that right. The world does not include the fact that it is false. Why not? Because, if it did, then the LS would be true as well as false, since it claims that it is false and the world which makes it true or false would include the fact that it is indeed false.
Yep.
Now, they trumpet the fact that the fact that the LS is false gets to be included in "the world" as a great advantage of the Austinian alternative. On the face of it, it would be....except...well....we'll get to that next post.
The book is, as the name suggests, an attempt to get around the Liar Paradox. I'm sure anyone likely to glance at this book already knows plenty about it, but just for easy reference, here's the Liar Sentence again.
LS: This sentence is false.
Now, in all fairness to them, the book came out in the same year as "In Contradiction," so you can't blame them for not arguing convincingly against dialetheism, which was after all not much on the scene in 1987. On the other hand, to the extent that they are trying to "solve" the semantic paradoxes, though, they are at least trying to show that e.g. the Liar Sentence does not have its prima facie feature of being true if it is false and false if it is true. In practice, the set of arguments that would beg that question is necessarily co-extensive with the set of arguments that would beg the question against the dialetheist's position that the Liar Sentence really *is* both true and false.
Barwisee and Etchemendy argue that sentences like the LS, or, more precisely, the propositions expressed by those sentences, are false, but that, remarkably, they are not also true. And this despite the fact that they assume bivalance--every proposition is either true or false, and there are no truth value gaps.
How do they accomplish this minor miracle?
First things first, they model propositions as set-theoretic objects. This doesn't sound possible for self-referential sentences, given that standard Zermello-Frankel set theory forbids self-membership. As such, they go with Peter Aczel's "universe of hypersets," an exciting-sounding phrase for an alternate set theory (which contains the Zermello-Frankel universe of well-founded sets) in which circularity is permitted. (The sets in the orthodox hierarchy exist in Aczel's conception of the universe of sets, they just don't exhaust it. "Hypersets" are just sets outside of the hierarchy.) On the face of it, the adoption of Aczel's set theory to shed light on the semantic paradoxes sounds like it would let set-theoretic paradoxes through the back door, since these are kept out of orthodox set theory by the cumulative hierarchy of sets where sets can only have sets beneath them in the hierarchy as members. Not so, Barwise and Etchemendy claim, since Aczel has shown that we don't need the cumulative hierarchy to ban things like the Russell Set (the set of sets that are not members of themselves), we just need the set/class distinction. The Russell Set is not as set at all but a class, and there's no class of sets that are not members of themselves.
(If this sounds dangerously arbitrary, dear reader, I'm with you. In fact, here's a question I haven't been able to get a good answer to yet. If anyone wants to help me out in the comments, please jump in, since I suspect that I'm missing something important here. If we invented a new term that was neutral between sets and classes, like "grouping," where a grouping can be either a set or a class, then can't we re-instate the paradox by reference to a Russell Grouping? If not, why not?)
In any case, using Azcel hypersets, they establish models of propositions for both the "Russellian" and "Austinian" conceptions of propositions. (It's not clear how much of a historical/exegetical claim they are making about either Russell's or Austin's actual views in using these terms.) True Russellian propositions are made true by the world as a whole, and true Austinian propositions are made true by particular situations. (For example, the Austinian proposition "Jill has the 3 of Hearts," about a particular game, is false if the speaker has mistaken Lucy for Jill, but by coincidence Jill has the 3 of Hearts in another game across town.) Barwise and Etchemendy prefer the Austinian conception, although they first model Russellian propositions not just because problems in that model set up the Austinian model, but because (like the relationship of Zermello-Frankel sets and Aczel's hypersets) the Russellian sets are ultimately contained in the universe of Austinian sets.
Now, once we start the formal modelling--and this is true for both the modelling of Russellian propositions and later for the model of Austinian propositions--we get to my first and most important problem with the book.
(1) They blatantly beg the question, but making one of the rules of the model that no set-theoretic proposition-object and its "dual" will be included. Translated out of the set-theoretic context, this means that they set it up as a rule in advance that no proposition will be true and false. "We included a formal rule to ban inconsistency and, amazingly, no inconsistencies were generated by he model!"
This rule has, as you might expect, some funny consequences once the whole thing gets going. In the Russellian case, the result is that, since the world does not make the LS true, it is false, but the fact that its false is not included in "the world." Yes, you read that right. The world does not include the fact that it is false. Why not? Because, if it did, then the LS would be true as well as false, since it claims that it is false and the world which makes it true or false would include the fact that it is indeed false.
Yep.
Now, they trumpet the fact that the fact that the LS is false gets to be included in "the world" as a great advantage of the Austinian alternative. On the face of it, it would be....except...well....we'll get to that next post.
Monday, January 28, 2008
Sunday, January 27, 2008
Follow-up: "Interesting but Inconsistent?"
While looking at the discussion after my last post--for those who missed it, I made a really dumb attribution mistake that was thankfully corrected, and it was forcefully brought to my attention that my original example relied on an understanding of conditionals deeply controversial among precisely the same sort of people likely to find Impressive Scientist X examples compelling, but I argued that the same point could be made without bringing in the material conditional, and that there are simpler explanations of e.g. Bohr's failure to derive random crazy things from his inconsistent atomic theory than that he was somehow unknowingly working with an "underlying paraconsistent logic"--something closely related occurred to me.
There's a phrase that's used a lot in these discussions as if we all knew what it meant. I'm not sure that it's so clear. That's "interesting but inconsistent theory."
(The phrase "non-trivial," often appended to "interesting but inconsistent," adds bupkis. All it means is that not everything will follow from the theory, i.e. that interesting but inconsistent theories should be reasoned about paraconsistently or not at all. OK. If you believe that the moon is both made of green cheese and not made of green cheese, that theory will be "non-trivial" in precisely the same sense, but I doubt anyone would call it "interesting" in the relevant sense.)
Well, what is an 'interesting' theory? I mean, I think I know what it means before modified with "but inconsistent," but after that's there, I'm not so sure any more. Normally, when talking about consistent theories, I would take "interesting theory" (in the sense that seems to be driven at, not "interesting" as in "crazily unexpected" or anything like that) to mean "plausible theory," i.e. one that might very well turn out to be true. Or, applied to out-dated theories, one that it would have been rational to regard as quite possibly true given the evidence available at the time, even if we now understand that it is false.
Now, full-blown dialetheists banding about the phrase "interesting but inconsistent theory" might mean exactly this, since they think it's possible in principle for something to be inconsistent but true. What I'm interested in at the moment is what this "interesting but inconsistent phrase" means to people who bandy it around who are on the 2nd Grade of Paraconsistent Involvement discussed in the last post, the "I'm not a dialetheist, but..." crowd who are still holding back from the 3rd Grade where you admit that some of these theories may be true.
So, if you aren't a dialetheist, you still believe in the Law of Non-Contradiction, hence you believe that it is categorically impossible for an inconsistent theory to turn out to be true and there has never been a situation where it would have been rational on the basis of any sort of empirical evidence to believe that an inconsistent theory was true, what does "interesting but inconsistent theory" mean?
Interestingness also can't just boil down to a degree of predictive accuracy*, right? If so, interesting-but-inconsistent theories would be too easy to generate and lose the aura of respectability they gain from Bohr-type examples. After all, for any hotly disputed scientific area, where one theory predicts a bunch of effects with a certain amount of experimental support, and an obviously logically inconsistent competitor theory predicts a bunch of other effects, and there are a certain amount of experimental support for those two, if someone blandly asserted that the disputed phenomenon both existed and didn't exist, and was thus able to claim the experimental successes of both competitors for this claim (like, "if X exists, we expect to see some Y's and if it doesn't, we'd expected to see some Z's, so I expect to see both Y's and Z's..."), would that make the new conjunctive theory "interesting"?
Anyway, I'm throwing this open to the floor. On the assumption that it's never rational to believe an inconsistent theory to be actually true, what does it mean to call one 'interesting'?
*...although why we'd be interested in predictive accuracy, except as an indicator of truth, is for the most part mysterious to me.
There's a phrase that's used a lot in these discussions as if we all knew what it meant. I'm not sure that it's so clear. That's "interesting but inconsistent theory."
(The phrase "non-trivial," often appended to "interesting but inconsistent," adds bupkis. All it means is that not everything will follow from the theory, i.e. that interesting but inconsistent theories should be reasoned about paraconsistently or not at all. OK. If you believe that the moon is both made of green cheese and not made of green cheese, that theory will be "non-trivial" in precisely the same sense, but I doubt anyone would call it "interesting" in the relevant sense.)
Well, what is an 'interesting' theory? I mean, I think I know what it means before modified with "but inconsistent," but after that's there, I'm not so sure any more. Normally, when talking about consistent theories, I would take "interesting theory" (in the sense that seems to be driven at, not "interesting" as in "crazily unexpected" or anything like that) to mean "plausible theory," i.e. one that might very well turn out to be true. Or, applied to out-dated theories, one that it would have been rational to regard as quite possibly true given the evidence available at the time, even if we now understand that it is false.
Now, full-blown dialetheists banding about the phrase "interesting but inconsistent theory" might mean exactly this, since they think it's possible in principle for something to be inconsistent but true. What I'm interested in at the moment is what this "interesting but inconsistent phrase" means to people who bandy it around who are on the 2nd Grade of Paraconsistent Involvement discussed in the last post, the "I'm not a dialetheist, but..." crowd who are still holding back from the 3rd Grade where you admit that some of these theories may be true.
So, if you aren't a dialetheist, you still believe in the Law of Non-Contradiction, hence you believe that it is categorically impossible for an inconsistent theory to turn out to be true and there has never been a situation where it would have been rational on the basis of any sort of empirical evidence to believe that an inconsistent theory was true, what does "interesting but inconsistent theory" mean?
Interestingness also can't just boil down to a degree of predictive accuracy*, right? If so, interesting-but-inconsistent theories would be too easy to generate and lose the aura of respectability they gain from Bohr-type examples. After all, for any hotly disputed scientific area, where one theory predicts a bunch of effects with a certain amount of experimental support, and an obviously logically inconsistent competitor theory predicts a bunch of other effects, and there are a certain amount of experimental support for those two, if someone blandly asserted that the disputed phenomenon both existed and didn't exist, and was thus able to claim the experimental successes of both competitors for this claim (like, "if X exists, we expect to see some Y's and if it doesn't, we'd expected to see some Z's, so I expect to see both Y's and Z's..."), would that make the new conjunctive theory "interesting"?
Anyway, I'm throwing this open to the floor. On the assumption that it's never rational to believe an inconsistent theory to be actually true, what does it mean to call one 'interesting'?
*...although why we'd be interested in predictive accuracy, except as an indicator of truth, is for the most part mysterious to me.
Wednesday, January 23, 2008
A Thought About Underlying Logics
My apologies for the weeks between this and the last post. I'm back in Miami, slugging through my reading list, and I should be posting at a much more frequent clip from now on.
Meanwhile, I have a thought (not really a full thought, but at least the beginning of one), not about dialetheism per se but about what Graham Priest calls the "second grade of paraconsistent involvement."
Just for future reference, his "grades" are:
1st: "Gentle-strength paraconsistency" (you reject the principle that anything follows from a contradiction)
2nd: "Full-strength paraconsistency" (you think there some inconsistent but interesting, non-trivial theories)
3rd: "Industrial-strength paraconsistency" (some of those theories may be true)
4th: "Dialetheism" (some of those theories *are* true)
#
Standard apologetics for the usefulness of paraconsistent logic often include historical examples of inconsistent but non-silly theories. It generally goes something like this. "Impressive Scientist X believed P and he also believed Theory Q, and he knew that Theory Q entails that not-P, but he didn't derive just any claim R, so the underlying logic he was using was clearly not classical."
Now, on the face of it the only sort of explosive logical rule that this situation would be any kind of challenge to would be a claim in the language of epistemic logic that Bxp & Bx~p entailed Bxq for any q. [Of course, (Bxp & Bx~p) is not a contradiction. Only (Bxp & ~Bxp) would be a contradiction.]
Sadly, this has nothing to do with what the historical examples are there for. The historical claim here is not that according to any sort of classical logic, it should follow from Scientist X believing P and ~P that Scientist X will believe that Q for any Q. Rather, the point is that if Scientist X believes that P and he believes that ~P, then classical logic would give him permission to draw the conclusion that Q. The fact that he never exercised this privilege is then seen as evidence that he was (albeit unconsciously, when we're talking about figures who predated the development of paraconsistent logic) operating according to paraconsistent rules of inference in which there are strict limits on what you can derive from a contradiction.
Now, I have severe doubts about the very idea that either scientific practices (or, worse yet, as is sometimes claimed, natural languages) have "underlying logics," but for the moment I'm going to put that to one side.
Instead, let's go for a simple analogy.
Einstein believed in the Special Theory of Relativity.
Einstein never drew the conclusion that "if it is not the case that it is not the case that it is not the case that it is not the case that it is not the case that the Special Theory of Relativity is true, then it is not the case that it is not the case that it is not the case that it is not the case either that Hitler won World War II or that the national flag of Australia is a pirate flag containing a jewel, that, under magnification, is revealed to be a detailed map of the surface of Mars with an X marking the spot where Elvis has high tea every afternoon at four with the Mad Hatter and a ghostly semi-physical representative of the Hegelian world-spirit."
But wait!
According to classical logic, the entire quoted claim is entailed by the truth of the Special Theory of Relativity. (Unless, of course, I slipped up while counting the number of negations.) If the STR is true then it follows that if you put an odd number of negation signs in front of the proposition that it is true, you have a false claim, and any conditional statement with a false antecedent is true, regardless of whether the consequent is true or false.
...so Einstein never drew that conclusion, or any of the infinite number of other similar conclusions classical logic would have given him permission to draw. Does it therefore follow that his "underlying logic" must have been some alternative non-classical logic, where strict rules are in place to reign in the sorts of consequents that can be put on these conditionals?
Meanwhile, I have a thought (not really a full thought, but at least the beginning of one), not about dialetheism per se but about what Graham Priest calls the "second grade of paraconsistent involvement."
Just for future reference, his "grades" are:
1st: "Gentle-strength paraconsistency" (you reject the principle that anything follows from a contradiction)
2nd: "Full-strength paraconsistency" (you think there some inconsistent but interesting, non-trivial theories)
3rd: "Industrial-strength paraconsistency" (some of those theories may be true)
4th: "Dialetheism" (some of those theories *are* true)
#
Standard apologetics for the usefulness of paraconsistent logic often include historical examples of inconsistent but non-silly theories. It generally goes something like this. "Impressive Scientist X believed P and he also believed Theory Q, and he knew that Theory Q entails that not-P, but he didn't derive just any claim R, so the underlying logic he was using was clearly not classical."
Now, on the face of it the only sort of explosive logical rule that this situation would be any kind of challenge to would be a claim in the language of epistemic logic that Bxp & Bx~p entailed Bxq for any q. [Of course, (Bxp & Bx~p) is not a contradiction. Only (Bxp & ~Bxp) would be a contradiction.]
Sadly, this has nothing to do with what the historical examples are there for. The historical claim here is not that according to any sort of classical logic, it should follow from Scientist X believing P and ~P that Scientist X will believe that Q for any Q. Rather, the point is that if Scientist X believes that P and he believes that ~P, then classical logic would give him permission to draw the conclusion that Q. The fact that he never exercised this privilege is then seen as evidence that he was (albeit unconsciously, when we're talking about figures who predated the development of paraconsistent logic) operating according to paraconsistent rules of inference in which there are strict limits on what you can derive from a contradiction.
Now, I have severe doubts about the very idea that either scientific practices (or, worse yet, as is sometimes claimed, natural languages) have "underlying logics," but for the moment I'm going to put that to one side.
Instead, let's go for a simple analogy.
Einstein believed in the Special Theory of Relativity.
Einstein never drew the conclusion that "if it is not the case that it is not the case that it is not the case that it is not the case that it is not the case that the Special Theory of Relativity is true, then it is not the case that it is not the case that it is not the case that it is not the case either that Hitler won World War II or that the national flag of Australia is a pirate flag containing a jewel, that, under magnification, is revealed to be a detailed map of the surface of Mars with an X marking the spot where Elvis has high tea every afternoon at four with the Mad Hatter and a ghostly semi-physical representative of the Hegelian world-spirit."
But wait!
According to classical logic, the entire quoted claim is entailed by the truth of the Special Theory of Relativity. (Unless, of course, I slipped up while counting the number of negations.) If the STR is true then it follows that if you put an odd number of negation signs in front of the proposition that it is true, you have a false claim, and any conditional statement with a false antecedent is true, regardless of whether the consequent is true or false.
...so Einstein never drew that conclusion, or any of the infinite number of other similar conclusions classical logic would have given him permission to draw. Does it therefore follow that his "underlying logic" must have been some alternative non-classical logic, where strict rules are in place to reign in the sorts of consequents that can be put on these conditionals?
Sunday, December 23, 2007
Reading List
I got the preliminary reading list for my qualifying exams today. Here it is.
#
Jon Barwise and John Etchemendy, The Liar.
JC Beall (ed.), Liars and Heaps.
JC Beall and Brad Armour-Garb (eds.), Deflationism and Paradox.
George Boolos, Logic, Logic and Logic.
Vann McGee, Truth, Vagueness, and Paradox.
Michael Hallett, Cantorian Set Theory and Limitation of Size.
Colin McGinn, Logical Properties.
Penelope Maddy, Realism in Mathematics.
Robert Martin (ed.), Recent Essays on Truth and the Liar Paradox.
Graham Priest, In Contradiction (2nd edition).
Graham Priest, Doubt Truth to Be a Liar.
Graham Priest, Beyond the Limits of Thought (2nd edition).
Graham Priest, Towards Non-Being.
Graham Priest, JC Beall and Brad Armour-Garb (eds.), The Law of Non-Contradiction.
#
Jon Barwise and John Etchemendy, The Liar.
JC Beall (ed.), Liars and Heaps.
JC Beall and Brad Armour-Garb (eds.), Deflationism and Paradox.
George Boolos, Logic, Logic and Logic.
Vann McGee, Truth, Vagueness, and Paradox.
Michael Hallett, Cantorian Set Theory and Limitation of Size.
Colin McGinn, Logical Properties.
Penelope Maddy, Realism in Mathematics.
Robert Martin (ed.), Recent Essays on Truth and the Liar Paradox.
Graham Priest, In Contradiction (2nd edition).
Graham Priest, Doubt Truth to Be a Liar.
Graham Priest, Beyond the Limits of Thought (2nd edition).
Graham Priest, Towards Non-Being.
Graham Priest, JC Beall and Brad Armour-Garb (eds.), The Law of Non-Contradiction.
Saturday, December 8, 2007
Rawls and Dialetheism
Some things I've been thinking about while wrapping up my "History of Ethics" paper....
Rawls, in his "Theory of Justice," makes it clear that his primary enemy is utilitarianism. His grand project is to come up with a plausible more or less Kantishly-flavored alternative to it. Despite this, he praises utilitarianism for giving us a single consistent principle of justice, thereby ruling out the possibility of conflicting obligations. He admits that this would be best, but since he doesn't find their one principle defensible, he thinks the next best thing is to postulate a lexical ordering of obligations, such that when obligations stemming from Principle A conflict with alleged obligations rooted in Principle B, the A-obligations always win and so on down the line.
Now, to the extent that I'm a moral realist (which I try to be, or at least I do on Mondays, Wednesdays, alternate Tuesdays and maybe on Yom Kippur even when it falls on one of the other days), I take it for graned that it is never true that one is morally obliged to do P & ~P. (On Thursdays-through-Sundays, I'm even more sure of it!) So, programmatically, my sympathies are entirely with Rawls here.
What I find interesting, though, is that he makes no arguments, none whatsoever, to tell us *why* to think this should be the case. In what is, at least to me, one of the most interesting lines in the whole of the ToJ, Rawls attacks intuitionism by saying that if we don't have a knowable principle for deciding between conflicting prima facie obligations, "the means for rational discussion come to an end."
So....why? Let's put it this way. There are at least three options when dealing with a prima facie obligation to do P and a prima facie obligation to do ~P.
(1) Use some principle to decide between P & ~P, as Rawls and his utilitarian opponents both do.
(2) Admit, as Rawls castigates the inuitionist for doing, that there's no way to decide, that you just have to go with your gut on a case-by-case basis, but take it as a given that of course the conjunction of an action and its negation can't be obligatory.
(3) Say, as Graham Priest does in his chapter on Philosophy of Law in "In Contradiction," that there is no general reason to assume that contradictory prima facie obligations need always to be merely prima facie.
Now, perhaps Rawls is right that there's nothing much to discuss given (2)--it's hard not to think of Stephen Colbert's inspired White House Correspondents dinner riff on knowledge based on the gut rather than on the head--but Rawls takes it as a given that (2) being unpalatable, we must go with (1). Why?
Well, if we assume that the underlying logic of this rational discussion need be classical, it's certainly the case that in standard classical logic extended with deontic operators, you can conclude ~O(P) from O(~P), and hence [O(P) & ~O(P)] from O(P & ~P). This could be seen as problematic due to the alleged explosiveness of contradictions--that is to say, on the assumption that the underlying logic of Rawls' "rational discussion" is classical, and [O(P) & ~O(P)] is sometimes true, then any randomly chosen O(Q) would also be true. Hence, if in a lifeboat situation, you were morally obliged to save your sister and your mother from drowning, and it was impossible to do both, then it would follow that you were morally obliged to go around killing puppies. The strong moral intuition that we are not in fact so obliged might be considered, on an intuition-reliant reflective-equilibrium sort of model of moral reasoning, to be taken to be pretty good evidence that we never have inconsistent obligations.
So far, so good. By why should the means of rational discusison about morality have to be based on classical logic? It seems fairly clear that--since, as we've seen in earlier posts, the Duns Scotus proof follows from logical rules that only make sense if we assume that the Law of Non-Contradiction is universally true--if there are indeed inconsistent obligations, then the underlying logic of rational moral discussion had best be paraconsistent.
So, given that, why should we rule out (3)?
A moral philosopher could leave the refutation of dialetheism to the logician and assume that, since dialetheism is false, there are no moral dialetheias, but if inconsistent obligations are taken to be part of the motivating evidence for dialetheism, the burden is distributed the other way around. (Indeed, when Graham Priest came to Miami last spring, he told me that inconsistent obligations are the most compelling cases of true contradictions. While his primary focus in this work is on the philosophy of law, he's very clear in the chapter on this in "In Contradiction" that any normative system is likely to give rise to similar examples.) As such, the logician needs the moral philosopher to do his part for the refutation of dialetheism by giving us independent grounds for supposing moral obligations to be necessarily consistent.
The obvious move is to say that "ought implies can," and we can't engage in contradictory actions. You can't both save your mother and (by saving your sister on the other end of the lifeboat) not save your mother. Even Graham Priest, who has a detailed argument in "Doubt Truth to Be a Liar" that there are no contradictions in the "observable world," would grant this much. (As a side note, I think that his argument for the consistency of the observable world is extremely dubious, and that if the Law of Non-Contradiction is not universally and necessarily true--which of course I think it is--there are no particularly good reasons to believe the observable world to be consistent. BUT that would get us well off-track from the present discussion, so for the moment, I'm happy to grant Priest the point.) But why should we suppose that ought does indeed imply can?
After all, in contemporary work on moral responsibility, that principle is less secure than ever. Frankfurt in particular has given us some extremely compelling thought experiments that pump our intuitions in the opposite direction. In his cases, we do in fact morally judge people even when they could not to otherwise, and statistical evidence from experimental philosophers have shown that most people's pre-philosophical intuitions lie with Frankfurt.
So what's a moral realist anti-dialetheist who takes Frankfurt's examples seriously to do? There may be a way of reconstructing "ought implies can" that freely admits that "can" need not be an actual physical possibility for a given agent as required in libertarian (or even traditional compatibilist) conceptions of free will, but that is still carefully enough construed to rule out things that are never physically possible for any agent under any circumstances, but caution and independent grounding would be sorely required here to avoid making this completely ad hoc and question-begging.
Anyone have any ideas?
Rawls, in his "Theory of Justice," makes it clear that his primary enemy is utilitarianism. His grand project is to come up with a plausible more or less Kantishly-flavored alternative to it. Despite this, he praises utilitarianism for giving us a single consistent principle of justice, thereby ruling out the possibility of conflicting obligations. He admits that this would be best, but since he doesn't find their one principle defensible, he thinks the next best thing is to postulate a lexical ordering of obligations, such that when obligations stemming from Principle A conflict with alleged obligations rooted in Principle B, the A-obligations always win and so on down the line.
Now, to the extent that I'm a moral realist (which I try to be, or at least I do on Mondays, Wednesdays, alternate Tuesdays and maybe on Yom Kippur even when it falls on one of the other days), I take it for graned that it is never true that one is morally obliged to do P & ~P. (On Thursdays-through-Sundays, I'm even more sure of it!) So, programmatically, my sympathies are entirely with Rawls here.
What I find interesting, though, is that he makes no arguments, none whatsoever, to tell us *why* to think this should be the case. In what is, at least to me, one of the most interesting lines in the whole of the ToJ, Rawls attacks intuitionism by saying that if we don't have a knowable principle for deciding between conflicting prima facie obligations, "the means for rational discussion come to an end."
So....why? Let's put it this way. There are at least three options when dealing with a prima facie obligation to do P and a prima facie obligation to do ~P.
(1) Use some principle to decide between P & ~P, as Rawls and his utilitarian opponents both do.
(2) Admit, as Rawls castigates the inuitionist for doing, that there's no way to decide, that you just have to go with your gut on a case-by-case basis, but take it as a given that of course the conjunction of an action and its negation can't be obligatory.
(3) Say, as Graham Priest does in his chapter on Philosophy of Law in "In Contradiction," that there is no general reason to assume that contradictory prima facie obligations need always to be merely prima facie.
Now, perhaps Rawls is right that there's nothing much to discuss given (2)--it's hard not to think of Stephen Colbert's inspired White House Correspondents dinner riff on knowledge based on the gut rather than on the head--but Rawls takes it as a given that (2) being unpalatable, we must go with (1). Why?
Well, if we assume that the underlying logic of this rational discussion need be classical, it's certainly the case that in standard classical logic extended with deontic operators, you can conclude ~O(P) from O(~P), and hence [O(P) & ~O(P)] from O(P & ~P). This could be seen as problematic due to the alleged explosiveness of contradictions--that is to say, on the assumption that the underlying logic of Rawls' "rational discussion" is classical, and [O(P) & ~O(P)] is sometimes true, then any randomly chosen O(Q) would also be true. Hence, if in a lifeboat situation, you were morally obliged to save your sister and your mother from drowning, and it was impossible to do both, then it would follow that you were morally obliged to go around killing puppies. The strong moral intuition that we are not in fact so obliged might be considered, on an intuition-reliant reflective-equilibrium sort of model of moral reasoning, to be taken to be pretty good evidence that we never have inconsistent obligations.
So far, so good. By why should the means of rational discusison about morality have to be based on classical logic? It seems fairly clear that--since, as we've seen in earlier posts, the Duns Scotus proof follows from logical rules that only make sense if we assume that the Law of Non-Contradiction is universally true--if there are indeed inconsistent obligations, then the underlying logic of rational moral discussion had best be paraconsistent.
So, given that, why should we rule out (3)?
A moral philosopher could leave the refutation of dialetheism to the logician and assume that, since dialetheism is false, there are no moral dialetheias, but if inconsistent obligations are taken to be part of the motivating evidence for dialetheism, the burden is distributed the other way around. (Indeed, when Graham Priest came to Miami last spring, he told me that inconsistent obligations are the most compelling cases of true contradictions. While his primary focus in this work is on the philosophy of law, he's very clear in the chapter on this in "In Contradiction" that any normative system is likely to give rise to similar examples.) As such, the logician needs the moral philosopher to do his part for the refutation of dialetheism by giving us independent grounds for supposing moral obligations to be necessarily consistent.
The obvious move is to say that "ought implies can," and we can't engage in contradictory actions. You can't both save your mother and (by saving your sister on the other end of the lifeboat) not save your mother. Even Graham Priest, who has a detailed argument in "Doubt Truth to Be a Liar" that there are no contradictions in the "observable world," would grant this much. (As a side note, I think that his argument for the consistency of the observable world is extremely dubious, and that if the Law of Non-Contradiction is not universally and necessarily true--which of course I think it is--there are no particularly good reasons to believe the observable world to be consistent. BUT that would get us well off-track from the present discussion, so for the moment, I'm happy to grant Priest the point.) But why should we suppose that ought does indeed imply can?
After all, in contemporary work on moral responsibility, that principle is less secure than ever. Frankfurt in particular has given us some extremely compelling thought experiments that pump our intuitions in the opposite direction. In his cases, we do in fact morally judge people even when they could not to otherwise, and statistical evidence from experimental philosophers have shown that most people's pre-philosophical intuitions lie with Frankfurt.
So what's a moral realist anti-dialetheist who takes Frankfurt's examples seriously to do? There may be a way of reconstructing "ought implies can" that freely admits that "can" need not be an actual physical possibility for a given agent as required in libertarian (or even traditional compatibilist) conceptions of free will, but that is still carefully enough construed to rule out things that are never physically possible for any agent under any circumstances, but caution and independent grounding would be sorely required here to avoid making this completely ad hoc and question-begging.
Anyone have any ideas?
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