Thursday, November 09, 2006
Analyticity and the Sorites
For a long time I've been a pretty big fan of treating analyticity as a purely epistemic notion. That is, I've agreed with Boghossian that no refinement of the basic thought that analytic truths are truth in virtue of meaning alone is likely to work (where 'in virtue of' is read metaphysically). Instead we should adopt an epistemic notion of analyticity; something like analytic truths are statements which one is justified in believing merely in virtue of understanding (as Boghossian puts it in 'Analyticity', mere grasp of S's meaning by T suffices for T's being justified in holding S true).
Recently Andreas has been working to persuade people that the reasons Boghossian offers in favour of epistemic rather than metaphysical analyticity don't really support that conclusion at all. I haven't had a chance to really get to catch up on his stuff yet, but I have been wondering whether there isn't serious pressure put on the epistemic conception from other quarters.
In particular, I've been wondering if the analytic sorites paradox creates trouble for this account of analyticity. Here's an example (adapted from Sorensen's Vagueness and Contradiction: 117-8):
1. 1 second after noon is noonish
2. For all n, if n seconds after noon is noonish, then n+1 seconds after noon is noonish
3. 10000 seconds after noon is not noonish
Premises 1 and 3 are supposed to be analytically true, and that strikes me as plausible. Sorensen holds (if I remember his view correctly) that all but one of the instances of 2 are analytically true (the exception being analytically false). Now, take any of the true instances of 2, where n seconds and n+1 seconds are borderline for noonish. Does S's understanding that instance suffice for S to be justified in believing it to be true? Surely not.
This way of putting the objection rests on the epistemicist thesis that Sorites premises like 2 have exactly one false instance, but that we can never knowledgably identify which instance that is. I'm not sure how things go on other theories of vagueness, but it seems likely that some of them will have the consequence that there's at least one true instance of 2 (for n and n+1 borderline). If it is plausible that this true instance is analytically true, then it looks again like the epistemic conception of analyticity is in trouble. In any case, it would be surprising to discover that which account of analyticity is correct turns on what the correct solution to the Sorites is.
Any thoughts? And have I missed any discussions of this topic in the literature?
Update: I should be more explicit. Obviously the argument sketched above against the epistemic conception of analyticity takes as an assumption that Sorensen is right to suggest that some instances of 2 are appropriately regarded as analytic. That's very questionable here, and it's open to the proponent of the epistemic conception to deny the assumption. But I'm taking it there are costs to taking this route, for example, we now need some alternative account of the special status these statements have (or alternatively some explanation of why many philosophers have - mistakenly, according to this proposal - thought they possessed some special status). So basically, I'd like to put the objection to the epistemic conception as a dilemma; either there are analytic statements for which understanding doesn't suffice for justified belief, or there are statements which we intuitively take to be analytic truths, but which fall outside of the proposal on offer (thus requiring some alternative account of their (putative) special status, having debarred ourselves from regarding them as analytic).
Recently Andreas has been working to persuade people that the reasons Boghossian offers in favour of epistemic rather than metaphysical analyticity don't really support that conclusion at all. I haven't had a chance to really get to catch up on his stuff yet, but I have been wondering whether there isn't serious pressure put on the epistemic conception from other quarters.
In particular, I've been wondering if the analytic sorites paradox creates trouble for this account of analyticity. Here's an example (adapted from Sorensen's Vagueness and Contradiction: 117-8):
1. 1 second after noon is noonish
2. For all n, if n seconds after noon is noonish, then n+1 seconds after noon is noonish
3. 10000 seconds after noon is not noonish
Premises 1 and 3 are supposed to be analytically true, and that strikes me as plausible. Sorensen holds (if I remember his view correctly) that all but one of the instances of 2 are analytically true (the exception being analytically false). Now, take any of the true instances of 2, where n seconds and n+1 seconds are borderline for noonish. Does S's understanding that instance suffice for S to be justified in believing it to be true? Surely not.
This way of putting the objection rests on the epistemicist thesis that Sorites premises like 2 have exactly one false instance, but that we can never knowledgably identify which instance that is. I'm not sure how things go on other theories of vagueness, but it seems likely that some of them will have the consequence that there's at least one true instance of 2 (for n and n+1 borderline). If it is plausible that this true instance is analytically true, then it looks again like the epistemic conception of analyticity is in trouble. In any case, it would be surprising to discover that which account of analyticity is correct turns on what the correct solution to the Sorites is.
Any thoughts? And have I missed any discussions of this topic in the literature?
Update: I should be more explicit. Obviously the argument sketched above against the epistemic conception of analyticity takes as an assumption that Sorensen is right to suggest that some instances of 2 are appropriately regarded as analytic. That's very questionable here, and it's open to the proponent of the epistemic conception to deny the assumption. But I'm taking it there are costs to taking this route, for example, we now need some alternative account of the special status these statements have (or alternatively some explanation of why many philosophers have - mistakenly, according to this proposal - thought they possessed some special status). So basically, I'd like to put the objection to the epistemic conception as a dilemma; either there are analytic statements for which understanding doesn't suffice for justified belief, or there are statements which we intuitively take to be analytic truths, but which fall outside of the proposal on offer (thus requiring some alternative account of their (putative) special status, having debarred ourselves from regarding them as analytic).
Labels: Epistemology, Vagueness
# posted by Aidan @ 7:11 PM 
Comments:
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You say, "Does S's understanding that instance suffice for S to be justified in believing it to be true? Surely not."
I have to say that at least this comment strikes me as pretty plausible, whatever the soundness of the rest of the argument. I'd like to hear a bit more about your reasons for the "surely not," but my comment here is entirely friendly. Do you think that the argument would be even stronger against a conception of analyticity in terms of knowledge -- after all, there will be all sorts of Gettier worries about knowledge of these cases. So, we surely don't have knowledge in virtue of understanding even if, implausibly, we have justification in virtue of understanding.
On the other hand, perhaps the mere fact that we know we can be so easily misled in these cases means that we won't even be justified. Is this something like your reasoning?
I have to say that at least this comment strikes me as pretty plausible, whatever the soundness of the rest of the argument. I'd like to hear a bit more about your reasons for the "surely not," but my comment here is entirely friendly. Do you think that the argument would be even stronger against a conception of analyticity in terms of knowledge -- after all, there will be all sorts of Gettier worries about knowledge of these cases. So, we surely don't have knowledge in virtue of understanding even if, implausibly, we have justification in virtue of understanding.
On the other hand, perhaps the mere fact that we know we can be so easily misled in these cases means that we won't even be justified. Is this something like your reasoning?
# posted by 
: 11/10/2006 2:47 PM
: 11/10/2006 2:47 PM
Thanks for your comment. I'm now worried that I wasn't sufficiently sensitive to the differences between a justification based approach, and a knowledge based one. So let me tease those two approaches apart more here.
Starting with the knowlege bases approach, it's usually taken as a datum of the vagueness debate that we can't knowledgably identify the false instance of my universally quanified premise 2 (because there is no single such false instance; because which instance is the false one shifts with context or other factors; because a belief of this form would not be appropriately safe to count as knowledge; because the borderline region gives rise to truth-maker gaps; etc). So without taking a stance here on what explains that sort of ignorance, my thought was just that even understanding each of the instances of 2, one's knowledge in borderline cases would still be impeded.
Justification based approaches are trickier. There's at least some pull on certain views of vagueness to say that you are justified in accepting at least some of the instances of 2. If for example there is only one false instance, and the Sorites series is sufficiently long, you might think you're justified in accepting lots of the instances (just as you might be justified in believing of lots of tickets in a sufficiently big lottery that they'll lose, even if you don't think you can know that they're losers). In fact, I think Sorensen in effect suggests you're justified in accepting all the instances of 2, despite that on his view one of them is an analytic falsehood.
But the justification based approach seemed to me to require something much stronger - for each (true?) instance of 2 which we understand, we're justified in believing that instance. Even if you think that you're justified in believing *some* of the instances of 2 involving borderline cases, this stronger demand of the justification based approach struck me as very implausible.
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Starting with the knowlege bases approach, it's usually taken as a datum of the vagueness debate that we can't knowledgably identify the false instance of my universally quanified premise 2 (because there is no single such false instance; because which instance is the false one shifts with context or other factors; because a belief of this form would not be appropriately safe to count as knowledge; because the borderline region gives rise to truth-maker gaps; etc). So without taking a stance here on what explains that sort of ignorance, my thought was just that even understanding each of the instances of 2, one's knowledge in borderline cases would still be impeded.
Justification based approaches are trickier. There's at least some pull on certain views of vagueness to say that you are justified in accepting at least some of the instances of 2. If for example there is only one false instance, and the Sorites series is sufficiently long, you might think you're justified in accepting lots of the instances (just as you might be justified in believing of lots of tickets in a sufficiently big lottery that they'll lose, even if you don't think you can know that they're losers). In fact, I think Sorensen in effect suggests you're justified in accepting all the instances of 2, despite that on his view one of them is an analytic falsehood.
But the justification based approach seemed to me to require something much stronger - for each (true?) instance of 2 which we understand, we're justified in believing that instance. Even if you think that you're justified in believing *some* of the instances of 2 involving borderline cases, this stronger demand of the justification based approach struck me as very implausible.
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