Monday, March 29, 2010
Wednesday, March 24, 2010
Glenn Greenwald and Informal Fallacies
Anyone whose read this blog in the past when the subject matter has wandered onto political territory should be unsurprised to hear that I find Ann Coulter's frequently expressed views about Muslims and Arabs to be fairly loathsome. That said, free speech protections only applying to views that you like (or that are close enough to views that you like to be in your sphere of "the bounds of civilized discussion") isn't worth much, so I find the attempts of a Canadian university administrator to use that country's "hate speech" laws to stifle the free expression of Coulter's vile opinions to be pretty vile in its own way.
All of this, however, is mostly by way of preamble. What I find more interesting is that if you read the comment thread on the Glenn Greenwald article I just linked to, you find a really weird sort of confusion about the difference between fallacious slippery slope arguments against those laws and substantive objections to the laws based on fairly banally familiar sorts of social contract considerations.
The former go like this:
"It starts with the criminalization of hate speech. Then, before you know it, we're criminalizing all kinds of categories of speech, and sooner or later, Big Brother is monitoring and censoring every word that comes out of your mouth and telling you exactly what to think about every conceivable subject. We need to stop this progression before it's too late!"
This is a very silly kind of argument, for very familiar reasons. Contrast it with the following argument:
"'Hatred' is a tricky notion, and which political opinions count as expressions of hatred and which don't depends on where you're sitting. If you criminalize views you find offensive, then you might be acting against your own long-term self-interest by setting a precedent which could be used against you, if your political enemies ever take power and they find your views offensive. Really, it's in everyone's interests for society to be ordered in such a way that the expression of all views is equally and automatically protected."
Now, reasonable people can disagree about whether the second argument goes through, and it could be no doubt be objected to in all sorts of ways, but it certainly doesn't commit the glaringly obvious slippery slope fallacy at the heart of the first argument, right?
Well, in his article, Greenwald talks about how he will "never understand people's failure to realize that endorsing this power will, one day, very likely result in their own views being criminalized when their political enemies (rather than allies) are empowered." I think the "very likely" is over-reach, but still, what he's saying seems to be, very clearly, an instance of the second argument rather than anything even close to the first. Yet the comment thread is absolutely filled with people responding to Greenwald as if he'd made the first argument, going on about how Canada is hardly an Orwellian nightmare, and it's still a functioning democracy, and making snarky little comments about how Greenwald should be careful about getting a midnight knock on his door from the Mounties come to stifle his free speech and so on and so forth.
So, really, maybe I've just been doing philosophy for too long and I've lost touch with the way people argue out there in the real world, but....really? Is the distinction between those two sorts of arguments really too subtle for casual readers on Salon to sort out?
All of this, however, is mostly by way of preamble. What I find more interesting is that if you read the comment thread on the Glenn Greenwald article I just linked to, you find a really weird sort of confusion about the difference between fallacious slippery slope arguments against those laws and substantive objections to the laws based on fairly banally familiar sorts of social contract considerations.
The former go like this:
"It starts with the criminalization of hate speech. Then, before you know it, we're criminalizing all kinds of categories of speech, and sooner or later, Big Brother is monitoring and censoring every word that comes out of your mouth and telling you exactly what to think about every conceivable subject. We need to stop this progression before it's too late!"
This is a very silly kind of argument, for very familiar reasons. Contrast it with the following argument:
"'Hatred' is a tricky notion, and which political opinions count as expressions of hatred and which don't depends on where you're sitting. If you criminalize views you find offensive, then you might be acting against your own long-term self-interest by setting a precedent which could be used against you, if your political enemies ever take power and they find your views offensive. Really, it's in everyone's interests for society to be ordered in such a way that the expression of all views is equally and automatically protected."
Now, reasonable people can disagree about whether the second argument goes through, and it could be no doubt be objected to in all sorts of ways, but it certainly doesn't commit the glaringly obvious slippery slope fallacy at the heart of the first argument, right?
Well, in his article, Greenwald talks about how he will "never understand people's failure to realize that endorsing this power will, one day, very likely result in their own views being criminalized when their political enemies (rather than allies) are empowered." I think the "very likely" is over-reach, but still, what he's saying seems to be, very clearly, an instance of the second argument rather than anything even close to the first. Yet the comment thread is absolutely filled with people responding to Greenwald as if he'd made the first argument, going on about how Canada is hardly an Orwellian nightmare, and it's still a functioning democracy, and making snarky little comments about how Greenwald should be careful about getting a midnight knock on his door from the Mounties come to stifle his free speech and so on and so forth.
So, really, maybe I've just been doing philosophy for too long and I've lost touch with the way people argue out there in the real world, but....really? Is the distinction between those two sorts of arguments really too subtle for casual readers on Salon to sort out?
Monday, March 22, 2010
Generality Problems in Biology and Epistemology
Reliabilist definitions of knowledge tend to go something like this:
R: "S knows that P iff S has a true belief in P that was generated by a generally reliable belief-forming mechanism."*
A traditional objection to this is the so-called "generality problem," which goes something like this:
I want to know what time it is, so I pull my cell phone out of my pocket, flip it open and look at the screen. Now, assuming that my phone is working properly, I now have a true belief about what time it is**, etc., we'd want to call my belief about what time it is a case of knowledge, and the reliabilist would point to the process by which I arrived at that belief--checking my phone--as a generally reliable one.
But wait! What level of generality are we talking about? The process of *me* checking *this particular* phone? The process of anyone checking the time on any phone? The process of anyone checking the time on any time-telling device? Depending on what level we're talking about, the statistical (hypothetical limiting) frequency with which the process in question generates true beliefs will vary all over the damned place. Moreover, there seems to be no non-ad hoc way to decide which level is the important one. Ergo, reliabilism is just a hopeless epistemic theory.
Hold that thought for a moment while we switch our attention to evolutionary biology. Whatever one thinks of generation by "generally reliable belief-forming processes" as a condition that makes true belief knowledge, no reasonable person would deny that the claim that "natural selection" is the primary engine of evolution is a respectable, informative, and well-understood bit of biological theory, or indeed that it's extraordinarily well-confirmed by the evidence. Right?
Well...
Jerry Fodor has recently attacked natural selection, claiming that, when it comes to pairs of correlated traits, (a) there's no fact of the matter about which trait is "selected for" and which is the free-riding spandrel, or at least that (b) there's no way for us to have epistemic access to which is which, and at any rate that (c) standard evolutionary biology's problems with sorting out which trait is which in a plausible, principled way, whatever exactly the standard for plausibility and principledness is taken to be in this context (which is far from obvious) constitute a huge problem for the theory of evolution by natural selection, indeed a reason to reject theory. (Many of Fodor's formulations--e.g. that the distinction between selected-for traits and spandrels is "invisible to natural selection"--are frustratingly hard to pin down, but fortunately, the distinction between the more radical reading of Fodor in (a) and the more moderate reading (b) isn't central to the point at hand. For our purposes, (c) is what really matters.) This may cause some head-scratching in readers who know enough contemporary biological theory to know something about how biologists investigate and sort out spandrels from selection.
In a review of Fodor's book by Ned Block and Philip Kitcher, they put the issue like this:
"Consider the famous case of industrially induced melanism in the peppered moth. Supposedly, in landscapes where pollution has destroyed the lichens on the trunks of trees, melanic (black) variants of the moth are better camouflaged when they rest on tree trunks than their lighter, speckled relatives. With improved camouflage, birds and other predators are less likely to pick the moths off the tree trunks. In polluted environments, then, melanic moths are more likely to survive, and hence to leave descendants in later generations. So far, so familiar.
"Enter Gould and Lewontin. Maybe moth coloration is a spandrel, and some other property of the moths is both relevant to their proliferation and correlated with their color. For example, evolutionary biologists have observed that moths usually rest by day on the undersides of branches rather than on the trunks of trees. So is the familiar black-as-camouflage story really true? Perhaps a characteristic of the larvae of melanic moths makes them more likely to survive. Or perhaps melanic moths have a tendency to move around less at night, which makes them less vulnerable to being eaten by bats (who care nothing for color). These are interesting alternatives to the familiar story, and the causal hypotheses they introduce can be tested in obvious ways: by examining the rates of larvae survival or by investigating nocturnal motions of moths. And this is what biologists have done. Concerned that an apparent adaptation (a camouflaging color) may be a side effect, they have looked for correlated traits that might figure in some alternative process that would culminate in greater representation of the melanic moths. Despite some controversy in the 1990s, the traditional story seems to be standing up well.
"If Fodor and [his co-author] Piattelli-Palmarini acknowledge the evidence that favors the camouflaging-color hypothesis over the moth-larvae and moth-mobility hypotheses, they will have to say that the biologists have not been imaginative enough—that they have overlooked some other correlated trait for which there could be no fact of the matter about whether it, or the black coloration, caused the reproductive success.
"What exactly could this trait be? One possibility, suggested by remarks in some of Fodor’s previous writings, would be that there are two different properties: being black, on the one hand, and matching the environment on the other. Is there a fact of the matter as to which of these causes the reproductive success?....
...[Fodor and Piattelli-Palmarini] envisage a vast space of properties and expect proponents of natural selection to discriminate among all the rivals. Not only is there a property of being-a-melanic-moth, there is also a property of being-a-melanic-moth-and-smaller-than-Manhattan."
Now, I'm not particularly interested in the Fodor-exegesis question here. Perhaps Block and Kitcher have captured Fodor's position and perhaps they haven't. However, in terms of Fodor as Block and Kitcher understand him, two points seem worth making here:
(1) This doesn't seem to be a particularly good objection to standard biological theory,
...and...
(2) It's strikingly similar to the generality problem for reliabilism.
In fact, it seems reasonable to call Fodor's-objection-interpreted-this-way a sort of generality problem for biology, where instead of worrying about how to cut up reliable processes, we're worrying about how to cut up causally-efficacious traits.
So, if we don't take the difficulty in determining whether being-a-black-moth or being-a-black-moth-smaller-than-Manhattan or being-a-moth-smaller-than-Manhattan-that-blends-into-the-color-of-its-background is relevant level of analysis for natural-selection-talk to be much of a problem for evolutionary biology, should we regard the difficulty in determining whether me-consulting-my-cell-phone, me-consulting-any-cell-phone or anyone-consulting-any-time-telling-device is the right level of analysis for reliable-process-talk to be a serious problem for reliabilism? Alternately, should we regard the fact that, for the sake of argument, the latter is clearly a troubling problem to be a good reason to take the generality worry about evolutionary biology seriously? Or are the two cases just so clearly and importantly disanalogous that our reaction to the generality problem for biology and our reaction to the generality problem in epistemology should properly be utterly independent of one another?
These questions aren't rhetorical. I'm open to the possibility that the generality problem really is a deep problem for reliabilism, although its biological analogue is an easily-dismissed problem for natural selection. The only positive claim I'm making here is a relatively narrow, wussy sort of claim:
There's an interesting, suggestive analogy between the two cases, and if one shares my strong intuition that the generality problem for evolutionary biology is a non-problem, this should, at the very least, give us a good reason to pause and take a harder look at the generality problem for reliabilism, and why exactly we take it to be such a problem.
*A note of caution here: Not everyone whose epistemic views would be characterized as reliabilist would put it quite like that, some would add substantial extra conditions and some epistemologists, while emphasizing reliability considerations enough to deserve the "reliabilist" label, might regard the project of trying to precisely formulate necessary and sufficient conditions for knowledge as a fool's errand. For present purposes, though, R should be good enough to capture the aspect of the position I'm interested in.
**"Etc." here papers over, among other things, Gettier-style problems....what do we say about a case where my phone somehow froze exactly twenty four hours ago and I didn't notice? Is that a reliably-caused true belief? This is an interesting question, but it's one that I suspect many people likely to read this are beyond sick of hearing about, and one which I don't have much of anything new to say about in any case.
R: "S knows that P iff S has a true belief in P that was generated by a generally reliable belief-forming mechanism."*
A traditional objection to this is the so-called "generality problem," which goes something like this:
I want to know what time it is, so I pull my cell phone out of my pocket, flip it open and look at the screen. Now, assuming that my phone is working properly, I now have a true belief about what time it is**, etc., we'd want to call my belief about what time it is a case of knowledge, and the reliabilist would point to the process by which I arrived at that belief--checking my phone--as a generally reliable one.
But wait! What level of generality are we talking about? The process of *me* checking *this particular* phone? The process of anyone checking the time on any phone? The process of anyone checking the time on any time-telling device? Depending on what level we're talking about, the statistical (hypothetical limiting) frequency with which the process in question generates true beliefs will vary all over the damned place. Moreover, there seems to be no non-ad hoc way to decide which level is the important one. Ergo, reliabilism is just a hopeless epistemic theory.
Hold that thought for a moment while we switch our attention to evolutionary biology. Whatever one thinks of generation by "generally reliable belief-forming processes" as a condition that makes true belief knowledge, no reasonable person would deny that the claim that "natural selection" is the primary engine of evolution is a respectable, informative, and well-understood bit of biological theory, or indeed that it's extraordinarily well-confirmed by the evidence. Right?
Well...
Jerry Fodor has recently attacked natural selection, claiming that, when it comes to pairs of correlated traits, (a) there's no fact of the matter about which trait is "selected for" and which is the free-riding spandrel, or at least that (b) there's no way for us to have epistemic access to which is which, and at any rate that (c) standard evolutionary biology's problems with sorting out which trait is which in a plausible, principled way, whatever exactly the standard for plausibility and principledness is taken to be in this context (which is far from obvious) constitute a huge problem for the theory of evolution by natural selection, indeed a reason to reject theory. (Many of Fodor's formulations--e.g. that the distinction between selected-for traits and spandrels is "invisible to natural selection"--are frustratingly hard to pin down, but fortunately, the distinction between the more radical reading of Fodor in (a) and the more moderate reading (b) isn't central to the point at hand. For our purposes, (c) is what really matters.) This may cause some head-scratching in readers who know enough contemporary biological theory to know something about how biologists investigate and sort out spandrels from selection.
In a review of Fodor's book by Ned Block and Philip Kitcher, they put the issue like this:
"Consider the famous case of industrially induced melanism in the peppered moth. Supposedly, in landscapes where pollution has destroyed the lichens on the trunks of trees, melanic (black) variants of the moth are better camouflaged when they rest on tree trunks than their lighter, speckled relatives. With improved camouflage, birds and other predators are less likely to pick the moths off the tree trunks. In polluted environments, then, melanic moths are more likely to survive, and hence to leave descendants in later generations. So far, so familiar.
"Enter Gould and Lewontin. Maybe moth coloration is a spandrel, and some other property of the moths is both relevant to their proliferation and correlated with their color. For example, evolutionary biologists have observed that moths usually rest by day on the undersides of branches rather than on the trunks of trees. So is the familiar black-as-camouflage story really true? Perhaps a characteristic of the larvae of melanic moths makes them more likely to survive. Or perhaps melanic moths have a tendency to move around less at night, which makes them less vulnerable to being eaten by bats (who care nothing for color). These are interesting alternatives to the familiar story, and the causal hypotheses they introduce can be tested in obvious ways: by examining the rates of larvae survival or by investigating nocturnal motions of moths. And this is what biologists have done. Concerned that an apparent adaptation (a camouflaging color) may be a side effect, they have looked for correlated traits that might figure in some alternative process that would culminate in greater representation of the melanic moths. Despite some controversy in the 1990s, the traditional story seems to be standing up well.
"If Fodor and [his co-author] Piattelli-Palmarini acknowledge the evidence that favors the camouflaging-color hypothesis over the moth-larvae and moth-mobility hypotheses, they will have to say that the biologists have not been imaginative enough—that they have overlooked some other correlated trait for which there could be no fact of the matter about whether it, or the black coloration, caused the reproductive success.
"What exactly could this trait be? One possibility, suggested by remarks in some of Fodor’s previous writings, would be that there are two different properties: being black, on the one hand, and matching the environment on the other. Is there a fact of the matter as to which of these causes the reproductive success?....
...[Fodor and Piattelli-Palmarini] envisage a vast space of properties and expect proponents of natural selection to discriminate among all the rivals. Not only is there a property of being-a-melanic-moth, there is also a property of being-a-melanic-moth-and-smaller-than-Manhattan."
Now, I'm not particularly interested in the Fodor-exegesis question here. Perhaps Block and Kitcher have captured Fodor's position and perhaps they haven't. However, in terms of Fodor as Block and Kitcher understand him, two points seem worth making here:
(1) This doesn't seem to be a particularly good objection to standard biological theory,
...and...
(2) It's strikingly similar to the generality problem for reliabilism.
In fact, it seems reasonable to call Fodor's-objection-interpreted-this-way a sort of generality problem for biology, where instead of worrying about how to cut up reliable processes, we're worrying about how to cut up causally-efficacious traits.
So, if we don't take the difficulty in determining whether being-a-black-moth or being-a-black-moth-smaller-than-Manhattan or being-a-moth-smaller-than-Manhattan-that-blends-into-the-color-of-its-background is relevant level of analysis for natural-selection-talk to be much of a problem for evolutionary biology, should we regard the difficulty in determining whether me-consulting-my-cell-phone, me-consulting-any-cell-phone or anyone-consulting-any-time-telling-device is the right level of analysis for reliable-process-talk to be a serious problem for reliabilism? Alternately, should we regard the fact that, for the sake of argument, the latter is clearly a troubling problem to be a good reason to take the generality worry about evolutionary biology seriously? Or are the two cases just so clearly and importantly disanalogous that our reaction to the generality problem for biology and our reaction to the generality problem in epistemology should properly be utterly independent of one another?
These questions aren't rhetorical. I'm open to the possibility that the generality problem really is a deep problem for reliabilism, although its biological analogue is an easily-dismissed problem for natural selection. The only positive claim I'm making here is a relatively narrow, wussy sort of claim:
There's an interesting, suggestive analogy between the two cases, and if one shares my strong intuition that the generality problem for evolutionary biology is a non-problem, this should, at the very least, give us a good reason to pause and take a harder look at the generality problem for reliabilism, and why exactly we take it to be such a problem.
*A note of caution here: Not everyone whose epistemic views would be characterized as reliabilist would put it quite like that, some would add substantial extra conditions and some epistemologists, while emphasizing reliability considerations enough to deserve the "reliabilist" label, might regard the project of trying to precisely formulate necessary and sufficient conditions for knowledge as a fool's errand. For present purposes, though, R should be good enough to capture the aspect of the position I'm interested in.
**"Etc." here papers over, among other things, Gettier-style problems....what do we say about a case where my phone somehow froze exactly twenty four hours ago and I didn't notice? Is that a reliably-caused true belief? This is an interesting question, but it's one that I suspect many people likely to read this are beyond sick of hearing about, and one which I don't have much of anything new to say about in any case.
Monday, March 15, 2010
Flickers of Freedom
If you miss the Garden of Forking Paths as much as I do, you'll be delighted to find out about the new phil of action/free will blog Flickers Of Freedom, and the list of people involved in the project--Thomas Nadelhoffer, Neil Levy, Tamler Sommers, Dan Speak, Eddy Nahmias, Manuel Vargas, Michael McKenna, & Daniel Cohen--pretty well guarantees that it should be consistently worth reading. The announcement of its formation is here and the first real post is here.
Wednesday, March 10, 2010
Omniscience and Dialetheism
(Thanks to M.C. for showing me the article.)
So in a 2007 article in Analysis*, Peter Milne suggests that omniscient beings would have to be dialetheists, given sentence S, below:
Sentence S: No omniscient being knows that which sentence S expresses.
His reasoning is that, if no omniscient beings exist, sentence S is "quite straightforwardly true." If an omniscient being exists, however, that being would have to both know and not know that which sentence S expresses. Thus, Milne seems to be suggesting, we have to choose between atheism and dialetheism.
Now, I am, to a slightly obnoxious degree, convinced of the deep irrationality of theism, but this particular argument doesn't strike me as a good one. Here's why: if this should force theists to accept true contradictions, then very mundanely familiar parallel arguments should force atheists to accept true contradictions as well. Whatever one thinks about the rationality of believing inconsistencies, the theist doesn't seem to be in any worse a boat than the rest of us.
Why, after all, should we think that an omniscient being would both know and not know the content of S? Because, presumably, if an omniscient being existed and didn't know the content of S, then S would be true, which would mean that omniscient beings would know it.
Why, however, does that last step--that "which would mean"--go through? Presumably because "some being is omniscient" simply means "some being knows the content of all true sentences."
Given this, on the assumption that an omniscient being exists, the claim that no omniscient being knows the content of S reduces to the claim that S isn't true. Put differently, it looks like S is the negation of the conjunction of the claim that there is an omniscient being and the claim that S is true...and is, thus, a pretty straightforward Contingent Liar. Presumably, if Liar sentences in general are problematic in some way--ungrounded, non-truth-evaluable, meaningless, whatever one's story may be--then S is problematic in exactly the same way. The fact that this particular Liar is rigged so as to have its paradoxicality not "kick in" unless an omniscient being exists changes nothing, just as, presumably, any plausible story about what makes Liars problematic should also apply to resolutely non-paradoxical cousins of the Liar like the Truth-Teller sentence ("This sentence is true.")
Thoughts?
*"Omniscient Beings Are Dialetheists," Analysis 67.3, July 2007, pp. 250–51.
So in a 2007 article in Analysis*, Peter Milne suggests that omniscient beings would have to be dialetheists, given sentence S, below:
Sentence S: No omniscient being knows that which sentence S expresses.
His reasoning is that, if no omniscient beings exist, sentence S is "quite straightforwardly true." If an omniscient being exists, however, that being would have to both know and not know that which sentence S expresses. Thus, Milne seems to be suggesting, we have to choose between atheism and dialetheism.
Now, I am, to a slightly obnoxious degree, convinced of the deep irrationality of theism, but this particular argument doesn't strike me as a good one. Here's why: if this should force theists to accept true contradictions, then very mundanely familiar parallel arguments should force atheists to accept true contradictions as well. Whatever one thinks about the rationality of believing inconsistencies, the theist doesn't seem to be in any worse a boat than the rest of us.
Why, after all, should we think that an omniscient being would both know and not know the content of S? Because, presumably, if an omniscient being existed and didn't know the content of S, then S would be true, which would mean that omniscient beings would know it.
Why, however, does that last step--that "which would mean"--go through? Presumably because "some being is omniscient" simply means "some being knows the content of all true sentences."
Given this, on the assumption that an omniscient being exists, the claim that no omniscient being knows the content of S reduces to the claim that S isn't true. Put differently, it looks like S is the negation of the conjunction of the claim that there is an omniscient being and the claim that S is true...and is, thus, a pretty straightforward Contingent Liar. Presumably, if Liar sentences in general are problematic in some way--ungrounded, non-truth-evaluable, meaningless, whatever one's story may be--then S is problematic in exactly the same way. The fact that this particular Liar is rigged so as to have its paradoxicality not "kick in" unless an omniscient being exists changes nothing, just as, presumably, any plausible story about what makes Liars problematic should also apply to resolutely non-paradoxical cousins of the Liar like the Truth-Teller sentence ("This sentence is true.")
Thoughts?
*"Omniscient Beings Are Dialetheists," Analysis 67.3, July 2007, pp. 250–51.
Monday, March 8, 2010
Wednesday, March 3, 2010
Room's Reserved And Everything
Monday, March 8th
3:00 PM
University of Miami
Ashe Building, Room 733
Ben Burgis
Dissertation Defense--"Truth Is A One-Player Game: A Defense Of Monaletheism And Classical Logic"
3:00 PM
University of Miami
Ashe Building, Room 733
Ben Burgis
Dissertation Defense--"Truth Is A One-Player Game: A Defense Of Monaletheism And Classical Logic"
Monday, March 1, 2010
The Rejection-Liar: A Revenge Paradox For Paradox-Solvers Who Make A Big Deal About Rejection
In recent literature about the semantic paradoxes, a big deal is made in certain quarters about the distinction between negation and rejection. For example, for reasons of revenge-paradox-avoidance, paracomplete theorists scrupulously speak of "rejecting" the claim that the Liar sentence is true and "rejecting" the claim that it is false, rather than asserting the negation of those claims, or asserting them to be neither true nor false or what have you.
In "Spandrels of Truth," JC Beall grants that "just true" can't express any information that "true" doesn't--"'just true' is just 'true'"--but suggests that saying of certain statements that they're "just true" (while technically devoid of any information about whether they're also false) signals, in a conversational implicature sort of way, the speaker's intention to reject the claim that the statements are false.
Now, all of this acceptance/rejection talk crucially trades on the assumption that--whatever one thinks about the relationship between truth and falsity--as a matter of psychological fact, it's impossible for an agent to simultaneously accept and reject a claim. Whatever one thinks about that claim, however, I think that the sort of use to which its put in literature about paradox only makes sense if one takes the point of acceptance/rejection talk not to be mere self-reports about the actual psychological states of the paradox-solver making the claim, but a normative claim. For a paracomplete logician, claims about the truth of paradoxical sentences are the kinds of things that, rationally, we should reject. For the non-trivialist dialetheist struggling with the difficulties with "just true," the point is that sentences like "it's not true that 'grass is green'" are the sorts of things that one should reject.
When, in "Saving Truth From Paradox," Hartry Field talks about rejecting infinite chains of Excluded Middle instances originating in problematic sentences, he presumably shouldn't be taken as self-reporting his psychological atittudes towards each and every member of the infinite series. Even as a dispositional thing, it seems ludicrously implausible on that level. He couldn't hear a complicated, not-obviously-a-member member of that infinite series and be tricked or slip up and take the wrong atittude? What about members too long to be processed by human brains?
So, if I'm right about the exegetical issue (at least as a matter of charitable interpretation), the dominant assumption of those who throw around acceptance/rejection talk to help them navigate their way around paradoxes is that there's not just not overlap between the claims one does accept and the claims one does reject (at a given time), but also no overlap between the claims one should accept and the claims one should reject.
Presumably, everyone thinks that we should accept claims that are (just) true, and dialetheists think we should also accept claims that are both true and false. (We should accept, for example, that the Russell Set is a member of itself.) Everyone thinks we should reject claims that are (just) false, and paracomplete theorists thinks we should also reject claims that...well, the subject of puzzling out exactly what we can say about the claims they go into the "to be rejected" slot on their account is an immensely complicated one, but let's just say that there are some claims about which assert that they're false (although they'd certainly put their truth-value at less than 1) that they want to reject, and leave it at that.
Taking all that into account, I suggest the following as a revenge problem for paradox-solvers who take (correct) acceptance and (correct) rejection to be mutually exclusive. Provided that they take Liar sentences to be meaningful, standard Liar reasoning to be correct, etc., I'm hard-pressed to see what a defender of the mutual-exclusivity claim could say about this.
#
Let’s call the following sentence the Rejection-Liar:
“This sentence would be rejected by someone who accepts all true sentences, who rejects all sentences he doesn’t accept, and who doesn’t act on any rules mandating acceptance or rejection except for the ones listed in this sentence.”
If the Rejection-Liar is true, then it’s both true and a sentence that would be rejected by someone who accepts all true sentences, hence it’s a sentence that would both be rejected and accepted by someone with absolutely perfectly rational acceptance/rejection behavior.
If the Rejection-Liar is both true and false, then it’s both true and a sentence that would be rejected by someone who accepts all true sentences, hence it’s a sentence that would both be rejected and accepted by someone with absolutely perfectly rational acceptance/rejection behavior.
If the Rejection-Liar is (just) false, then it would be rejected by someone who accepts all true sentences, who rejects all sentences he doesn’t accept, and who doesn’t act on any rules mandating acceptance or rejection except for those two, which is exactly what the Rejection-Liar says, so it’s true, hence it’s a sentence that would both be rejected and accepted by someone with absolutely perfectly rational acceptance/rejection behavior.
If the Rejection-Liar is neither true nor false, then it would be rejected by someone who accepts all true sentences, who rejects all sentences he doesn’t accept, and who doesn’t act on any rules mandating acceptance or rejection except for those two, which is exactly what it says, so it’s true, hence it’s a sentence that would both be rejected and accepted by someone with absolutely perfectly rational acceptance/rejection behavior.
In "Spandrels of Truth," JC Beall grants that "just true" can't express any information that "true" doesn't--"'just true' is just 'true'"--but suggests that saying of certain statements that they're "just true" (while technically devoid of any information about whether they're also false) signals, in a conversational implicature sort of way, the speaker's intention to reject the claim that the statements are false.
Now, all of this acceptance/rejection talk crucially trades on the assumption that--whatever one thinks about the relationship between truth and falsity--as a matter of psychological fact, it's impossible for an agent to simultaneously accept and reject a claim. Whatever one thinks about that claim, however, I think that the sort of use to which its put in literature about paradox only makes sense if one takes the point of acceptance/rejection talk not to be mere self-reports about the actual psychological states of the paradox-solver making the claim, but a normative claim. For a paracomplete logician, claims about the truth of paradoxical sentences are the kinds of things that, rationally, we should reject. For the non-trivialist dialetheist struggling with the difficulties with "just true," the point is that sentences like "it's not true that 'grass is green'" are the sorts of things that one should reject.
When, in "Saving Truth From Paradox," Hartry Field talks about rejecting infinite chains of Excluded Middle instances originating in problematic sentences, he presumably shouldn't be taken as self-reporting his psychological atittudes towards each and every member of the infinite series. Even as a dispositional thing, it seems ludicrously implausible on that level. He couldn't hear a complicated, not-obviously-a-member member of that infinite series and be tricked or slip up and take the wrong atittude? What about members too long to be processed by human brains?
So, if I'm right about the exegetical issue (at least as a matter of charitable interpretation), the dominant assumption of those who throw around acceptance/rejection talk to help them navigate their way around paradoxes is that there's not just not overlap between the claims one does accept and the claims one does reject (at a given time), but also no overlap between the claims one should accept and the claims one should reject.
Presumably, everyone thinks that we should accept claims that are (just) true, and dialetheists think we should also accept claims that are both true and false. (We should accept, for example, that the Russell Set is a member of itself.) Everyone thinks we should reject claims that are (just) false, and paracomplete theorists thinks we should also reject claims that...well, the subject of puzzling out exactly what we can say about the claims they go into the "to be rejected" slot on their account is an immensely complicated one, but let's just say that there are some claims about which assert that they're false (although they'd certainly put their truth-value at less than 1) that they want to reject, and leave it at that.
Taking all that into account, I suggest the following as a revenge problem for paradox-solvers who take (correct) acceptance and (correct) rejection to be mutually exclusive. Provided that they take Liar sentences to be meaningful, standard Liar reasoning to be correct, etc., I'm hard-pressed to see what a defender of the mutual-exclusivity claim could say about this.
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Let’s call the following sentence the Rejection-Liar:
“This sentence would be rejected by someone who accepts all true sentences, who rejects all sentences he doesn’t accept, and who doesn’t act on any rules mandating acceptance or rejection except for the ones listed in this sentence.”
If the Rejection-Liar is true, then it’s both true and a sentence that would be rejected by someone who accepts all true sentences, hence it’s a sentence that would both be rejected and accepted by someone with absolutely perfectly rational acceptance/rejection behavior.
If the Rejection-Liar is both true and false, then it’s both true and a sentence that would be rejected by someone who accepts all true sentences, hence it’s a sentence that would both be rejected and accepted by someone with absolutely perfectly rational acceptance/rejection behavior.
If the Rejection-Liar is (just) false, then it would be rejected by someone who accepts all true sentences, who rejects all sentences he doesn’t accept, and who doesn’t act on any rules mandating acceptance or rejection except for those two, which is exactly what the Rejection-Liar says, so it’s true, hence it’s a sentence that would both be rejected and accepted by someone with absolutely perfectly rational acceptance/rejection behavior.
If the Rejection-Liar is neither true nor false, then it would be rejected by someone who accepts all true sentences, who rejects all sentences he doesn’t accept, and who doesn’t act on any rules mandating acceptance or rejection except for those two, which is exactly what it says, so it’s true, hence it’s a sentence that would both be rejected and accepted by someone with absolutely perfectly rational acceptance/rejection behavior.
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