Sunday, May 06, 2007
Anti-Realism: Decidability and Detectability
Back in 1983, Crispin Wright wrote:
'It is a common misunderstanding of the thrust of the anti-realist's criticisms of the role assigned to truth in classical semantics that he believes that the central notion in the theory of meaning should be an effectively decidable one.'
Amen. My entire life-span later, and this is still a point which simply has not been absorbed by opponents of anti-realism (a rare exception is Darragh Byrne, but it's hard to think of any others). I'm writing a paper at the moment, tentatively titled 'Anti-Realist DOs and DON'Ts', in which I'll substantiate Crispin's point, and show how doing so enables the anti-realist to avoid most of the objections recently leveled at him. More specifically, it'll be a defense of compatiblist anti-realism; that is, anti-realism which wants to hold on to truth-conditional semantics (the term is Byrne's). It's been claimed that such a view either inflates into realism (Alex Miller) or must deny that truth is undecidable (Williamson), but these criticisms simply make the assumption Wright warned against all those years ago. More on this in the finished paper.
Here, I want to offer a taster. I'll present two very recent arguments against anti-realism which are not major targets of my paper, but which casually overlook the possibility of a compatiblist anti-realism which holds that truth is necessarily detectable, but is not decidable. First up is Michael Loux's piece on the debate in The Oxford Handbook of Metaphysics. On page 656 we get the following passage:
'...Dummett's more particular claim that the assertability theorist should trade in verification conditions (that is, conditions that conclusively justify assertion) must face the objection that the resulting theory of meaning has precisely the difficulties Dummett takes to be the undoing of the truth-conditional theory. The claim is that to know the meaning of a statement is to know what would conclusively warrant its assertion; but statements that are in principle undecidable are such that there neither is nor can be anything that would conclusively justify their assertion or their denial. [My emphasis]. But, then, where is the strategic advantage of the assertibility-conditional theory? As we have seen, Dummett tries to forestall this objection by identifying the apparently epistemic state with a practical, discriminatory ability - the ability to recognize, if presented with it, a condition which would justify assertion. But, of course [sic], that is an ability that is in principle incapable of being exercised. [My emphasis]. And how is the attribution of that sort of ability any improvement on the truth-conditional theorist's attribution of epistemic states that can never can manifested?'
Look carefully at the crucial lines I put in italics, and ask yourself: how does it follow from a statement's undecidability - that is, the lack of a procedure which could be followed in a finite amount of time, and which if correctly implemented would be bound to conclusively verify or falsify that statement - that there could not be anything that would conclusively justify its assertion? Only, I submit, if we run together undecidability and undetectability; we assume that just because there is no such procedure, there can be no evidence which would decide the matter one way or the other (and hence our discriminatory capacities for such statements must be 'in principle incapable of being exercised') . Dummett himself is perfectly explicit that this is a mistake in his most recent book:
'Although we may have no means, even in principle, of putting ourselves into a position in which we can effectively decide whether the proposition expressed by the utterance of a given sentence is or is not true, it does not follow that we may not come to recognize that proposition as true or false; we may sometimes, and indeed often do, decide the truth or falsity of utterances of undecidable sentences, in the sense I gave to this expression.' (58)
So I submit, Loux's objection simply rests on the conflation of decidability and detectability. Now, the problem may be that Loux appears to interpret undecidable statements to be those which are 'verification- or falsification-transcendent' (635). But there's no real justification for such an interpretation, even if a few passages in Dummett may unfortunately encourage it.
A much more striking example of a failure to appreciate this point, and to miss the possibility of a compatiblist anti-realism, comes in Charles McCarthy's 'The Coherence of Anti-Realism'. In the opening line of the abstract, we are told:
'The project of anti-realism is to construct an assertibility semantics on which (1) the truth of statements obeys a recognition condition so that (2) counterexamples are forthcoming to the law of excluded middle and (3) intuitionistic formal predicate logic is provably sound and complete with respect to the associated notion of validity.'
On page 948, we are further told that in order to 'ensure that the recognition condition obtains', the anti-realist assumes that the central notion in the semantics is decidable in the sense that a decision procedure 'is available in principle'. It turns out, McCarthy argues, that this package is incoherent. All the worse for anti-realism so conceived, I say. But we're given no clues that this conception isn't mandated.
This gives you a taste of just how casually critics of anti-realism have been willing to run together the crucial notions of decidability and detectability, despite (and without so much as acknowledgment of) Crispin's explicit disavowal in print over twenty years ago. My paper, when it's done, will leave many important aspects of the debate completely untouched, but I think I'll have achieved something if I manage to start to change people's attitudes on this central issue. Seems unlikely on the face of it, but we'll see.......
'It is a common misunderstanding of the thrust of the anti-realist's criticisms of the role assigned to truth in classical semantics that he believes that the central notion in the theory of meaning should be an effectively decidable one.'
Amen. My entire life-span later, and this is still a point which simply has not been absorbed by opponents of anti-realism (a rare exception is Darragh Byrne, but it's hard to think of any others). I'm writing a paper at the moment, tentatively titled 'Anti-Realist DOs and DON'Ts', in which I'll substantiate Crispin's point, and show how doing so enables the anti-realist to avoid most of the objections recently leveled at him. More specifically, it'll be a defense of compatiblist anti-realism; that is, anti-realism which wants to hold on to truth-conditional semantics (the term is Byrne's). It's been claimed that such a view either inflates into realism (Alex Miller) or must deny that truth is undecidable (Williamson), but these criticisms simply make the assumption Wright warned against all those years ago. More on this in the finished paper.
Here, I want to offer a taster. I'll present two very recent arguments against anti-realism which are not major targets of my paper, but which casually overlook the possibility of a compatiblist anti-realism which holds that truth is necessarily detectable, but is not decidable. First up is Michael Loux's piece on the debate in The Oxford Handbook of Metaphysics. On page 656 we get the following passage:
'...Dummett's more particular claim that the assertability theorist should trade in verification conditions (that is, conditions that conclusively justify assertion) must face the objection that the resulting theory of meaning has precisely the difficulties Dummett takes to be the undoing of the truth-conditional theory. The claim is that to know the meaning of a statement is to know what would conclusively warrant its assertion; but statements that are in principle undecidable are such that there neither is nor can be anything that would conclusively justify their assertion or their denial. [My emphasis]. But, then, where is the strategic advantage of the assertibility-conditional theory? As we have seen, Dummett tries to forestall this objection by identifying the apparently epistemic state with a practical, discriminatory ability - the ability to recognize, if presented with it, a condition which would justify assertion. But, of course [sic], that is an ability that is in principle incapable of being exercised. [My emphasis]. And how is the attribution of that sort of ability any improvement on the truth-conditional theorist's attribution of epistemic states that can never can manifested?'
Look carefully at the crucial lines I put in italics, and ask yourself: how does it follow from a statement's undecidability - that is, the lack of a procedure which could be followed in a finite amount of time, and which if correctly implemented would be bound to conclusively verify or falsify that statement - that there could not be anything that would conclusively justify its assertion? Only, I submit, if we run together undecidability and undetectability; we assume that just because there is no such procedure, there can be no evidence which would decide the matter one way or the other (and hence our discriminatory capacities for such statements must be 'in principle incapable of being exercised') . Dummett himself is perfectly explicit that this is a mistake in his most recent book:
'Although we may have no means, even in principle, of putting ourselves into a position in which we can effectively decide whether the proposition expressed by the utterance of a given sentence is or is not true, it does not follow that we may not come to recognize that proposition as true or false; we may sometimes, and indeed often do, decide the truth or falsity of utterances of undecidable sentences, in the sense I gave to this expression.' (58)
So I submit, Loux's objection simply rests on the conflation of decidability and detectability. Now, the problem may be that Loux appears to interpret undecidable statements to be those which are 'verification- or falsification-transcendent' (635). But there's no real justification for such an interpretation, even if a few passages in Dummett may unfortunately encourage it.
A much more striking example of a failure to appreciate this point, and to miss the possibility of a compatiblist anti-realism, comes in Charles McCarthy's 'The Coherence of Anti-Realism'. In the opening line of the abstract, we are told:
'The project of anti-realism is to construct an assertibility semantics on which (1) the truth of statements obeys a recognition condition so that (2) counterexamples are forthcoming to the law of excluded middle and (3) intuitionistic formal predicate logic is provably sound and complete with respect to the associated notion of validity.'
On page 948, we are further told that in order to 'ensure that the recognition condition obtains', the anti-realist assumes that the central notion in the semantics is decidable in the sense that a decision procedure 'is available in principle'. It turns out, McCarthy argues, that this package is incoherent. All the worse for anti-realism so conceived, I say. But we're given no clues that this conception isn't mandated.
This gives you a taste of just how casually critics of anti-realism have been willing to run together the crucial notions of decidability and detectability, despite (and without so much as acknowledgment of) Crispin's explicit disavowal in print over twenty years ago. My paper, when it's done, will leave many important aspects of the debate completely untouched, but I think I'll have achieved something if I manage to start to change people's attitudes on this central issue. Seems unlikely on the face of it, but we'll see.......
Labels: Anti-Realism, Crispin Wright, Dummett, Tim Williamson
# posted by Aidan @ 12:39 PM 
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Hi Aidan,
Interesting post, we've talked about this before, but I thought I'd post a comment.
I tend to see something like the following argument as central to Dummett-style anti-realism.
(1) One must know the meaning theory in order to understand a language.
(2) This knowledge cannot be explicit and so must consist in an the implicit ability to recognize that a condition obtains when it in fact does.
(3) The realist, who offers a truth conditional meaning theory associates each expression with a condition that might not be recognizable when it obtains.
Therefore, the central notion in the theory of meaning should not be truth conditional.
A plausible consequence: the central notion in the theory of meaning should an assertability condition. The notion of truth should be defined in terms of assertability.
I've been using 'recognize', which is one of the terms that gets thrown around in this debate. As I see it, the important question at this point is: What kind of recognitional capacity can plausibly be counted as implicit knowledge of a language? Most of the opponents of anti-realism tend to equate recognizable with what you call 'decidability'. And, to be fair, Dummett can be seen as waffling back and forth. I think it's more useful, though, to see him as trying to open up debate about what sorts of recognitional capacities can ground our understanding of the language (for example, in "Wang's Paradox"). I would then tend to view 'decectability' as a stand in for whatever fills this role.
But, I think it's a bit unfair to the realist to criticize him for confusing these. It's up to the anti-realist to offer up a notion of detectability that makes the assertability condition differ from the realist's truth conditions. After all, there is a sense in which even the Goedel sentence is detectable, should we have sufficient power to survey the whole of the natural numbers. But I haven't read much from Wright on this stuff, so maybe he has offered up an account.
As an aside, this debate reminds me a lot of the discussion between Carnap and Neurath about whether the protocol sentences were "autopsychological" or objective.
Interesting post, we've talked about this before, but I thought I'd post a comment.
I tend to see something like the following argument as central to Dummett-style anti-realism.
(1) One must know the meaning theory in order to understand a language.
(2) This knowledge cannot be explicit and so must consist in an the implicit ability to recognize that a condition obtains when it in fact does.
(3) The realist, who offers a truth conditional meaning theory associates each expression with a condition that might not be recognizable when it obtains.
Therefore, the central notion in the theory of meaning should not be truth conditional.
A plausible consequence: the central notion in the theory of meaning should an assertability condition. The notion of truth should be defined in terms of assertability.
I've been using 'recognize', which is one of the terms that gets thrown around in this debate. As I see it, the important question at this point is: What kind of recognitional capacity can plausibly be counted as implicit knowledge of a language? Most of the opponents of anti-realism tend to equate recognizable with what you call 'decidability'. And, to be fair, Dummett can be seen as waffling back and forth. I think it's more useful, though, to see him as trying to open up debate about what sorts of recognitional capacities can ground our understanding of the language (for example, in "Wang's Paradox"). I would then tend to view 'decectability' as a stand in for whatever fills this role.
But, I think it's a bit unfair to the realist to criticize him for confusing these. It's up to the anti-realist to offer up a notion of detectability that makes the assertability condition differ from the realist's truth conditions. After all, there is a sense in which even the Goedel sentence is detectable, should we have sufficient power to survey the whole of the natural numbers. But I haven't read much from Wright on this stuff, so maybe he has offered up an account.
As an aside, this debate reminds me a lot of the discussion between Carnap and Neurath about whether the protocol sentences were "autopsychological" or objective.
# posted by 
: 5/10/2007 1:58 PM
: 5/10/2007 1:58 PM
Sorry Bryan, the email which should have informed me there was a comment that needed moderating seems to have gone AWOL, hence the delay in your comment appearing.
I agree it's up to the anti-realist to give us the notion of detectability which distinguishes it from decidability, and which marks a realist/anti-realist watershed. I'll spend some time making some steps towards that in the paper. But Crispin's own proposal has been in the literature for as long as I've been alive. It may not work, but realists have just simply ignored it. Why isn't that grounds for criticism?
I'm going to just deny that argument you offer as 'central to Dummett-style anti-realism' really is central. Dummett himself changed his mind repeatedly on the issue of whether to endorse compatiblism, or whether to reject truth-conditional semantics in favor of something like assertibility-conditional semantics. That suggests we're already outside of the domain of what's essential to the position. And compatiblism is just a much more plausible, less revisionary version of the view. I don't see anything in Dummett's arguments which close it off. The immediate consequence of those arguments is that the central notion in our theory of meaning shouldn't be a recognition-transcendent one. As Dummett realized, it's a further step to conclude that we must abandon truth-conditional semantics - that only follows on the assumption that truth can be recognition-transcendent. But this is precisely what's at issue between the compatiblist and the semantic realist, so the compatiblist is hardly going to concede that assumption.
PS. Congratulations!
I agree it's up to the anti-realist to give us the notion of detectability which distinguishes it from decidability, and which marks a realist/anti-realist watershed. I'll spend some time making some steps towards that in the paper. But Crispin's own proposal has been in the literature for as long as I've been alive. It may not work, but realists have just simply ignored it. Why isn't that grounds for criticism?
I'm going to just deny that argument you offer as 'central to Dummett-style anti-realism' really is central. Dummett himself changed his mind repeatedly on the issue of whether to endorse compatiblism, or whether to reject truth-conditional semantics in favor of something like assertibility-conditional semantics. That suggests we're already outside of the domain of what's essential to the position. And compatiblism is just a much more plausible, less revisionary version of the view. I don't see anything in Dummett's arguments which close it off. The immediate consequence of those arguments is that the central notion in our theory of meaning shouldn't be a recognition-transcendent one. As Dummett realized, it's a further step to conclude that we must abandon truth-conditional semantics - that only follows on the assumption that truth can be recognition-transcendent. But this is precisely what's at issue between the compatiblist and the semantic realist, so the compatiblist is hardly going to concede that assumption.
PS. Congratulations!
Anyone who understands that mathematical intuitionism is Dummett's paradigm, and who understands mathematical intuitionism, will understand that the Dummettian claim involves, not decidability, but verifiability (a.k.a. positive semi-decidability, recognizability as true when true).
But anyone who understands that mathematical intuitionism is Dummett's paradigm will understand that, even if it is granted that grasp of verification-transcendent truth-conditions does not constitute grasp of meaning, still what does constitute grasp of meaning cannot be grasp of verification-conditions, either, since if meaning were verification-conditional, usage would be radically different from what it is. The "plausible conclusion" therefore is that (assuming grasp of meaning is what guides usage) grasp of meaning simply is not grasp of truth-conditions, whether verification-transcendent or verificationist.
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But anyone who understands that mathematical intuitionism is Dummett's paradigm will understand that, even if it is granted that grasp of verification-transcendent truth-conditions does not constitute grasp of meaning, still what does constitute grasp of meaning cannot be grasp of verification-conditions, either, since if meaning were verification-conditional, usage would be radically different from what it is. The "plausible conclusion" therefore is that (assuming grasp of meaning is what guides usage) grasp of meaning simply is not grasp of truth-conditions, whether verification-transcendent or verificationist.
# posted by : 10/17/2008 12:55 PM
: 10/17/2008 12:55 PM << Home
