I'm organizing an Arché workshop on Basic Knowledge, which will take place on 24-25 November 2006. Speakers will include Jason Stanley, Duncan Pritchard, Jessica Brown and Timothy Williamson. There will be a slot for a graduate student paper. Graduate students, and those who obtained their PhDs within the last twelve months, are invited to submit papers of not more than 5000 words. Please send me submissions as email attachments in Word or similar format (no pdf files please). Suitable topics include: Sceptical Paradox, Transmission and/or Closure, Non-Evidential Warrant, Internalism and Externalism, and A Priori Knowledge. Particularly welcome are papers which open up new areas of enquiry within these fields, and/or highlight directions in which further research is needed. Travel and subsistence will be covered by Arche for the author of the selected paper. The deadline for submissions is 31 August 2006.
ADDENDUM: Submissions should be prepared for blind review.
Tuesday, March 28, 2006
Wednesday, March 15, 2006
Counterfactuals and Ontic Vagueness
Following on from the idea I floated in this post, I'm posting a draft of a note on why you shouldn't use counterfactuals to characterize commitment to ontic vagueness (which won't surprise those who know that I tend to think you probably shouldn't use counterfactuals to characterize anything metaphysically interesting ...). Comments very welcome, as always.
Tuesday, March 07, 2006
Saturday, March 04, 2006
Weighing Implausibilities
Here's something I was wondering about during Tim Williamson's talk at the Arché Vagueness Workshop yesterday.
Suppose you want to keep bivalence, and you also think that the only way for something to be an aspect of a predicate's meaning is for our use of the predicate to determine that it is (both Williamsonian thoughts, I gather). But you also think it is at least prima facie implausible that usage determines an exact cut-off point for all the vague predicates (a thought pressed against Williamson by McGee and McLaughlin).
We seem to have at least two options.
1: Accept the implausible-sounding claim (with Williamson), or
2: Argue that many of the things we think are vague predicates ('red', 'bald' etc.) are in fact not predicates at all. By bivalence, in order for them to be predicates we would need there to be cut-off points for their application. But it is implausible that our use of these terms determines such cut-off points. And there is nothing else which can do this sort of meaning-constituting work.
It's initially implausible, sure, that words like 'red', 'bald' and so on are not predicates. But my question is: by what sorts of methodological considerations do we weigh this implausibility against that of the claim that usage determines cut-off points for all such terms?
(Incidentally, Williamson mentioned that he talks about Option 2 in his book on vagueness, which I haven't had a chance to look at yet. He obviously has reasons for preferring Option 1, which I will be interested to read.)
Suppose you want to keep bivalence, and you also think that the only way for something to be an aspect of a predicate's meaning is for our use of the predicate to determine that it is (both Williamsonian thoughts, I gather). But you also think it is at least prima facie implausible that usage determines an exact cut-off point for all the vague predicates (a thought pressed against Williamson by McGee and McLaughlin).
We seem to have at least two options.
1: Accept the implausible-sounding claim (with Williamson), or
2: Argue that many of the things we think are vague predicates ('red', 'bald' etc.) are in fact not predicates at all. By bivalence, in order for them to be predicates we would need there to be cut-off points for their application. But it is implausible that our use of these terms determines such cut-off points. And there is nothing else which can do this sort of meaning-constituting work.
It's initially implausible, sure, that words like 'red', 'bald' and so on are not predicates. But my question is: by what sorts of methodological considerations do we weigh this implausibility against that of the claim that usage determines cut-off points for all such terms?
(Incidentally, Williamson mentioned that he talks about Option 2 in his book on vagueness, which I haven't had a chance to look at yet. He obviously has reasons for preferring Option 1, which I will be interested to read.)
Friday, March 03, 2006
Lewis/Blackburn Note
I wrote up some thoughts relating to my previous post as a short note. Comments welcome!
Thursday, February 23, 2006
Quasi-Realism No Fictionalism (But Not Quite For Blackburn's Reasons)
I've just been leading the MRG on the Lewis/Blackburn exchange in this collection concerning whether quasi-realism is fictionalism (Blackburn's half of which is online here).
It seems to me that Lewis's claim that quasi-realism is a version of fictionalism is mistaken, but not for a reason that comes through in Blackburn's response.
Lewis's argument, in essentials, is that the quasi-realist wants to say everything the realist does, so must either be a realist or be making believe that realism is true. But he is not a realist, therefore he is making believe that realism is true, i.e. he's a fictionalist.
I think we can show what's wrong with that argument in a few lines. The sense in which the quasi-realist 'says everything the realist does' is not the one which enforces either being or pretending to be a realist. This would be enforced if the quasi-realist was making the same assertions as the realist, but he isn't (indeed, the paradigm quasi-realist isn't making assertions at all). The quasi-realist says things which sound like what the realist says, but they are to be interpreted differently - in the moral case, as expressions of attitudes, rather than as committing to moral properties. Expressing an attitude requires neither belief in moral properties (realism) or pretense that moral properties exist (making believe that realism is true).
So here's why quasi-realism is not fictionalism:
The fictionalist differs from the realist in adopting the realist account of the meaning of the target sentences but dissenting from those sentences (same content, different attitude) whereas the quasi-realist differs from the realist in adopting a different account of the meaning while continuing to accept those sentences (different content, same - or at least similar - attitude).
It seems to me that Lewis's claim that quasi-realism is a version of fictionalism is mistaken, but not for a reason that comes through in Blackburn's response.
Lewis's argument, in essentials, is that the quasi-realist wants to say everything the realist does, so must either be a realist or be making believe that realism is true. But he is not a realist, therefore he is making believe that realism is true, i.e. he's a fictionalist.
I think we can show what's wrong with that argument in a few lines. The sense in which the quasi-realist 'says everything the realist does' is not the one which enforces either being or pretending to be a realist. This would be enforced if the quasi-realist was making the same assertions as the realist, but he isn't (indeed, the paradigm quasi-realist isn't making assertions at all). The quasi-realist says things which sound like what the realist says, but they are to be interpreted differently - in the moral case, as expressions of attitudes, rather than as committing to moral properties. Expressing an attitude requires neither belief in moral properties (realism) or pretense that moral properties exist (making believe that realism is true).
So here's why quasi-realism is not fictionalism:
The fictionalist differs from the realist in adopting the realist account of the meaning of the target sentences but dissenting from those sentences (same content, different attitude) whereas the quasi-realist differs from the realist in adopting a different account of the meaning while continuing to accept those sentences (different content, same - or at least similar - attitude).
Wednesday, February 15, 2006
Entitlement and Rationality
My paper on Crispin Wright's notion of Entitlement is now also up - though NB still in draft form - on my home page. Comments welcome on this too!
Tuesday, February 14, 2006
Knowability Again
I've just posted the final draft of my knowability paper on my home page. Comments are still welcome!
Wednesday, February 08, 2006
New Arche Blog
Tuesday, February 07, 2006
Cook on Unknowability
Roy Cook has just argued that there are some unknowable propositions provided it is possible for the following situation to obtain. Ava, Brigitte and Dorothy are all inhabitants of Smullyan’s (1978) island occupied solely by knights and knaves. Knights are people who always speak truly, knaves are people who always speak falsely. Simultaneously, they utter the following:
Ava: What Brigitte is now saying cannot be known to be true
Brigitte: What Dorothy is now saying cannot be known to be true
Dorothy: What Ava is now saying cannot be known to be true
Cook shows that if this happens then at least two of Ava, Brigitte and Dorothy must be knights (see his p. 12), and goes on to show as a consequence of this that at least one of them – we do not know which one – has uttered a true but unknowable proposition. He assumes classical logic and certain facts about the behaviour of the knowability operator in order to get this result, all of which we can grant here for the sake of argument.
Cook stresses that his argument relies on the thought that the scenario he describes is free from ‘any paradox, failure of reference, or other pathology’ (p. 14). It seems to me, however, that the anti-realist who accepts the principle p --> Kp will think Cook’s scenario is paradoxical, because it presents a version of the paradox raised by what Cook would call the semantic open triple (sorry, no corner quotes):
p: ¬Tq
q: ¬Tr
r: ¬Tp
(where T is the truth predicate). No assignment of (classical) truth values to these three propositions is consistent.
Anti-realists for Cook’s purposes are those who accept that if p then p is knowable, which Cook represents as p --> Kp, the contrapositive of which is ¬Kp --> ¬p. By this and the contrapositive of disquotation for the truth predicate, ¬p --> ¬Tp, these anti-realists will also accept that ¬Kp implies ¬Tp. Hence the three characters in Cook’s story are uttering claims which are either stronger than or identical in strength to the paradox-creating claims of the semantic open triple. In fact, anti-realists will presumably think the claims are identical in strength; for they are happy to accept ¬Kp --> ¬Tp, and ¬Tp --> ¬Kp is trivial.
One might respond that this is to beg the question; the only reason that is being offered for thinking that Cook’s situation is paradoxical is adherence to p --> Kp, which, of course, one does not accept unless one is an anti-realist.
But we need to be clear about where the burden of proof lies. Cook is (tentatively) offering an argument that should be capable of persuading anti-realists that there could be an unknown truth. To do this, as he acknowledges, the situation he describes should not be paradoxical. But the anti-realist will think it generates a Liar-like paradox, namely the semantic open triple. Therefore Cook’s argument will not be persuasive to an anti-realist.
Ava: What Brigitte is now saying cannot be known to be true
Brigitte: What Dorothy is now saying cannot be known to be true
Dorothy: What Ava is now saying cannot be known to be true
Cook shows that if this happens then at least two of Ava, Brigitte and Dorothy must be knights (see his p. 12), and goes on to show as a consequence of this that at least one of them – we do not know which one – has uttered a true but unknowable proposition. He assumes classical logic and certain facts about the behaviour of the knowability operator in order to get this result, all of which we can grant here for the sake of argument.
Cook stresses that his argument relies on the thought that the scenario he describes is free from ‘any paradox, failure of reference, or other pathology’ (p. 14). It seems to me, however, that the anti-realist who accepts the principle p --> Kp will think Cook’s scenario is paradoxical, because it presents a version of the paradox raised by what Cook would call the semantic open triple (sorry, no corner quotes):
p: ¬Tq
q: ¬Tr
r: ¬Tp
(where T is the truth predicate). No assignment of (classical) truth values to these three propositions is consistent.
Anti-realists for Cook’s purposes are those who accept that if p then p is knowable, which Cook represents as p --> Kp, the contrapositive of which is ¬Kp --> ¬p. By this and the contrapositive of disquotation for the truth predicate, ¬p --> ¬Tp, these anti-realists will also accept that ¬Kp implies ¬Tp. Hence the three characters in Cook’s story are uttering claims which are either stronger than or identical in strength to the paradox-creating claims of the semantic open triple. In fact, anti-realists will presumably think the claims are identical in strength; for they are happy to accept ¬Kp --> ¬Tp, and ¬Tp --> ¬Kp is trivial.
One might respond that this is to beg the question; the only reason that is being offered for thinking that Cook’s situation is paradoxical is adherence to p --> Kp, which, of course, one does not accept unless one is an anti-realist.
But we need to be clear about where the burden of proof lies. Cook is (tentatively) offering an argument that should be capable of persuading anti-realists that there could be an unknown truth. To do this, as he acknowledges, the situation he describes should not be paradoxical. But the anti-realist will think it generates a Liar-like paradox, namely the semantic open triple. Therefore Cook’s argument will not be persuasive to an anti-realist.
Friday, January 27, 2006
I Wanna Have Control
Here's a point that came up recently following a talk by Arché visitor Dean Zimmerman on Molinism.
It can't be sufficient, to count as having control over someone else's actions, that their actions vary counterfactually with yours - that were you to F they would F, and were you to G they would G, etc.. For if this were the case we could have symmetric control. It might also be that were they to F you would F too, and so on. (Suppose that, necessarily, you F iff they do.) But you can't each be controlling the actions of the other - control is an asymmetric relation.
So what do we need in order to explicate the notion of control? It doesn't help to specify that exactly one of them is aware of the counterfactual relationship between his actions and the other guy's, and say the controller is the one who's aware. For one can perfectly well be aware that one's actions are being controlled by someone else (who is not aware of the fact).
Unsurprisingly, I think what we need to appeal to here is probably explanation. What matters is whose actions explain those of the other. You are in control just in case your actions explain the other guy's. Explanation brings with it the right kind of asymmetry, as well as making sense of the feeling that the controllee's actions depend upon the controller's.
It can't be sufficient, to count as having control over someone else's actions, that their actions vary counterfactually with yours - that were you to F they would F, and were you to G they would G, etc.. For if this were the case we could have symmetric control. It might also be that were they to F you would F too, and so on. (Suppose that, necessarily, you F iff they do.) But you can't each be controlling the actions of the other - control is an asymmetric relation.
So what do we need in order to explicate the notion of control? It doesn't help to specify that exactly one of them is aware of the counterfactual relationship between his actions and the other guy's, and say the controller is the one who's aware. For one can perfectly well be aware that one's actions are being controlled by someone else (who is not aware of the fact).
Unsurprisingly, I think what we need to appeal to here is probably explanation. What matters is whose actions explain those of the other. You are in control just in case your actions explain the other guy's. Explanation brings with it the right kind of asymmetry, as well as making sense of the feeling that the controllee's actions depend upon the controller's.
Monday, January 16, 2006
Knowability
I'm just about to start work on the final draft of my new paper on Fitch's Knowability argument, so I'm posting the current draft here to invite comments. The earlier Fitch paper of mine which I refer to can be found here and the forthcoming Kvanvig paper I talk about is online here.
Saturday, December 31, 2005
What I'm Doing On My Holidays
I'm writing a paper on modal knowledge over this Christmas/New Year break. In it I'm trying to argue that we can answer two questions simultaneously:
1. How can experience be a guide to modal truth?
2. How can conceivability be a guide to modal truth?
by proposing that experience grounds our concepts (that is, makes them knowledge-conducive guides to the structure of the world), and that what we can conceive of is constrained by what our concepts are like in such a way that the information about the world's structure which is in encoded in the structure of our concepts is recoverable through the activity we call 'attempting to conceive'.
What's all that got to do with knowledge of what's possible and necessary? Well, things are easy if you think that modal facts are , or metaphysically depend upon, structural facts about the actual world. Because the latter are the kinds of facts that 'attempts to conceive' put us in touch with.
What I'm looking at now are ways in which people who don't like that metaphysical idea might also get in on my epistemological act. Ways, that is, in which you might think that information about actual-world structure can be an epistemic guide to modal facts even though these facts do not depend metaphysically on facts about actual-world structure.
One option is to believe in metaphysical dependence in the other direction: that is, to think that actual-world structural facts depend on modal facts. But that option doesn't have much prima facie plausibility (at least, not to me).
Alternatively you might think both actual-world structural facts and modal facts depend on some other class of facts in a way which explains the correlation between the two. (But what sort of facts would they be?)
There's always the option of brute correlation, but we'll need a damn good story about why we should take the correlation to be brute, to tell to those who think that it's actually evidence of metaphysical dependence in one direction or the other.
Finally, I thought, perhaps you might think there is some satisfying explanation of the correlation which does not appeal to metaphysical dependence at all. (But what would it look like?)
As always, any comments/suggestions/further possibilities are very welcome here.
Happy New Year!
1. How can experience be a guide to modal truth?
2. How can conceivability be a guide to modal truth?
by proposing that experience grounds our concepts (that is, makes them knowledge-conducive guides to the structure of the world), and that what we can conceive of is constrained by what our concepts are like in such a way that the information about the world's structure which is in encoded in the structure of our concepts is recoverable through the activity we call 'attempting to conceive'.
What's all that got to do with knowledge of what's possible and necessary? Well, things are easy if you think that modal facts are , or metaphysically depend upon, structural facts about the actual world. Because the latter are the kinds of facts that 'attempts to conceive' put us in touch with.
What I'm looking at now are ways in which people who don't like that metaphysical idea might also get in on my epistemological act. Ways, that is, in which you might think that information about actual-world structure can be an epistemic guide to modal facts even though these facts do not depend metaphysically on facts about actual-world structure.
One option is to believe in metaphysical dependence in the other direction: that is, to think that actual-world structural facts depend on modal facts. But that option doesn't have much prima facie plausibility (at least, not to me).
Alternatively you might think both actual-world structural facts and modal facts depend on some other class of facts in a way which explains the correlation between the two. (But what sort of facts would they be?)
There's always the option of brute correlation, but we'll need a damn good story about why we should take the correlation to be brute, to tell to those who think that it's actually evidence of metaphysical dependence in one direction or the other.
Finally, I thought, perhaps you might think there is some satisfying explanation of the correlation which does not appeal to metaphysical dependence at all. (But what would it look like?)
As always, any comments/suggestions/further possibilities are very welcome here.
Happy New Year!
Sunday, December 18, 2005
Chalmers, Carnap and Lightweight Existential Quantification
I clicked through to David Chalmers's powerpoint slides on Ontological Indeterminacy yesterday, wondering if I might get a discussion of ontic vagueness. In fact I found something else equally interesting: a discussion of 'deflationary' (=, roughly, Carnapian) views about certain existential questions.
I have a few comments (though NB I have not heard the full talk, so maybe some of these points are addressed there):
1. I'm not sure whether the kind of 'relativism' Chalmers describes should count as deflationary. To say that there are many equally good answers to a question (which I think is the core of the proposed 'relativism') is prima facie different from saying that there is *no* substantial answer to the question (deflationism). To get the latter from the former we seem to need to assume that relativism about answers to a question is incompatible with the thought that the question and its answers are metaphysically substantial.
2. I think substantial ontological existence claims can be what Chalmers calls 'lightweight', i.e. a priori knowable or analytic or something in that area. Which is to say, in effect, that I don't think 'lightweight' (a priori knowable) existential claims need be genuinely lightweight. The envisaged connection between 'lightweightness' and real , metaphysical, lightweightness is, I guess, supposed to be effected by the thought that a priori reflection can only address what Carnap would call 'internal' questions, while genuinely heavyweight ontological questions must be 'external'. But personally (for what it's worth), I think concept-led a priori reflection might well lead to knowledge of substantial conclusions, including existential conclusions. Once we acknowledge that concepts can be grounded - i.e. sensitive to the way the world is in such a way as to make them good epistemic guides to reality - we can think (in Carnapian terms) of frameworks as being selected on more-than-pragmatic grounds, that is, selected for their fit with the world. And then there is no reason to doubt that a priori reflection on concepts within a framework can give us epistemically respectable answers to (what Carnap would have called) external questions.
I have a few comments (though NB I have not heard the full talk, so maybe some of these points are addressed there):
1. I'm not sure whether the kind of 'relativism' Chalmers describes should count as deflationary. To say that there are many equally good answers to a question (which I think is the core of the proposed 'relativism') is prima facie different from saying that there is *no* substantial answer to the question (deflationism). To get the latter from the former we seem to need to assume that relativism about answers to a question is incompatible with the thought that the question and its answers are metaphysically substantial.
2. I think substantial ontological existence claims can be what Chalmers calls 'lightweight', i.e. a priori knowable or analytic or something in that area. Which is to say, in effect, that I don't think 'lightweight' (a priori knowable) existential claims need be genuinely lightweight. The envisaged connection between 'lightweightness' and real , metaphysical, lightweightness is, I guess, supposed to be effected by the thought that a priori reflection can only address what Carnap would call 'internal' questions, while genuinely heavyweight ontological questions must be 'external'. But personally (for what it's worth), I think concept-led a priori reflection might well lead to knowledge of substantial conclusions, including existential conclusions. Once we acknowledge that concepts can be grounded - i.e. sensitive to the way the world is in such a way as to make them good epistemic guides to reality - we can think (in Carnapian terms) of frameworks as being selected on more-than-pragmatic grounds, that is, selected for their fit with the world. And then there is no reason to doubt that a priori reflection on concepts within a framework can give us epistemically respectable answers to (what Carnap would have called) external questions.
Friday, December 09, 2005
Non-trivial Counterpossibles
A reflection that was triggered by hearing Timothy Williamson give a paper here last weekend at the last ever Arché Modality Workshop.
Some people (classically, Lewis) think any counterfactual with an impossible antecedent is trivially true, and I'm prima facie inclined to agree. But we should be able to distinguish between ones where there appears to be something non-trivial going on, such as:
1. If the square root of 2 were rational, it could be represented as n/m with n, m integers
and ones which don't seem to have this feature, such as:
2. If the square root of 2 were rational, there would be lemonade rivers.
Two options are:
A: to say that the difference between trivial and non-trivial counterpossibles is one of assertability (1 is assertable in many contexts where 2 is not),
B: to say that this difference is a matter of epistemic accessibility (you can know 1 is true without knowing it has an impossible antecedent, whereas this looks doubtful for 2).
But I'm currently wondering whether, in some cases at least, neither assertability nor epistemic access gives the deepest or most insightful characterization of the difference - they may rather be symptoms. For instance, you might think that in some cases it is the existence of some metaphysically interesting connection between states of affairs described in 'A' and 'B' that really explains why a counterpossible conditional 'A []--> B' is non-trivially true. You would then expect this conditional to exhibit the pattern of assertability and epistemic accessibility usually associated with non-trivial counterpossibles, although that behaviour is not what its non-triviality amounts to but rather a sign of it.
(PS For the record, I don't assume there will be the same story to tell in every case about what sort of factor underlies the assertability and accessibility symptoms.)
(PPS I will - hopefully - get round to replying to the interesting comments on my previous post soon ...)
Some people (classically, Lewis) think any counterfactual with an impossible antecedent is trivially true, and I'm prima facie inclined to agree. But we should be able to distinguish between ones where there appears to be something non-trivial going on, such as:
1. If the square root of 2 were rational, it could be represented as n/m with n, m integers
and ones which don't seem to have this feature, such as:
2. If the square root of 2 were rational, there would be lemonade rivers.
Two options are:
A: to say that the difference between trivial and non-trivial counterpossibles is one of assertability (1 is assertable in many contexts where 2 is not),
B: to say that this difference is a matter of epistemic accessibility (you can know 1 is true without knowing it has an impossible antecedent, whereas this looks doubtful for 2).
But I'm currently wondering whether, in some cases at least, neither assertability nor epistemic access gives the deepest or most insightful characterization of the difference - they may rather be symptoms. For instance, you might think that in some cases it is the existence of some metaphysically interesting connection between states of affairs described in 'A' and 'B' that really explains why a counterpossible conditional 'A []--> B' is non-trivially true. You would then expect this conditional to exhibit the pattern of assertability and epistemic accessibility usually associated with non-trivial counterpossibles, although that behaviour is not what its non-triviality amounts to but rather a sign of it.
(PS For the record, I don't assume there will be the same story to tell in every case about what sort of factor underlies the assertability and accessibility symptoms.)
(PPS I will - hopefully - get round to replying to the interesting comments on my previous post soon ...)
Saturday, December 03, 2005
Language-Dependence
Here's a common claim schema:
If ... is dependent on our language, then were our language to be different in relevant respects then so would ... be.
E.g.:
(1) If vagueness depends on our language, then were all semantic vagueness to be eliminated then there would be no vagueness.
A worry about this is that it seems a semantic theorist of vagueness (someone who thinks vagueness is entirely due to semantic features of our language, and has nothing to do with how the world is independently of our linguistic representations of it) might sensibly reject (1), and instead assert:
(2) Although vagueness depends on our language, if all semantic vagueness were eliminated, this apple would still be borderline red.
For the consequent of the counterfactual is couched in the very language which is supposed to be suitable for creating vagueness. Asserting (2) therefore does nothing to undermine the thought that it is the semantic features of our actual word 'red' language which are responsible for the borderlineness, in other worlds, of the apple's redness.
What do people think?
If ... is dependent on our language, then were our language to be different in relevant respects then so would ... be.
E.g.:
(1) If vagueness depends on our language, then were all semantic vagueness to be eliminated then there would be no vagueness.
A worry about this is that it seems a semantic theorist of vagueness (someone who thinks vagueness is entirely due to semantic features of our language, and has nothing to do with how the world is independently of our linguistic representations of it) might sensibly reject (1), and instead assert:
(2) Although vagueness depends on our language, if all semantic vagueness were eliminated, this apple would still be borderline red.
For the consequent of the counterfactual is couched in the very language which is supposed to be suitable for creating vagueness. Asserting (2) therefore does nothing to undermine the thought that it is the semantic features of our actual word 'red' language which are responsible for the borderlineness, in other worlds, of the apple's redness.
What do people think?
Friday, November 25, 2005
Counting Vaguely Identical Objects
Dominic Hyde gave three talks on vagueness during his recent visit here, the most recent of which focussed on an argument from Pinillos against vague identity (NB you need a subscription to Mind to get to the full text from this link).
Suppose a ship (b) leaves port and two ships (a and c) dock, but (for the usual reasons having to do with the replacement of bits) we want to say it is indeterminate whether a=c, and indeterminate whether b=c, yet determinately not the case that a=c. Pinillos argues this cannot be right, and a key premise of his argument is that the set of ships which left port - {b} - is distinct from the set of ships which docked - {a,c} - because these two sets have different cardinalities. (This leads him to conclude that there must be something in one set which is not in the other - so that there is some pair consisting of one member from each set such that it is (determinately) the case that the two things in that pair are not identical - contradicting the assumption that all the relevant identity claims are indeterminate.)
I won't go into the details of Dominic's response to the Pinillos argument, since (as far as I know) it's not yet publicly available. But my own reaction (different from Dominic's) was to wonder whether the defender of this sort of vague identity should accept that the two sets are distinct. Maybe she should say that it's indeterminate whether the set of ships which left port is identical to the set of ships which docked.
Sure, there is a strong intuition that something is wrong with '{b} = {a,c}', but perhaps this could be explained as an intuition to the effect that, because of the difference in cardinality between the sets, this identity claim is necessarily not true, which does not (for people - like Dominic - who are into three-valued logics) entail that it is false. (By analogy, a claim Dominic argued for in one of his other talks here is that although we have a strong intution that claims like 'Patch p is red and non-red' are not true, we should not therefore regard them as false when p is a borderline case.)
In fact, is the defender of vague identity even compelled to accept the claim that the sets have distinct cardinalities? If it really is indeterminate whether a=b and indeterminate whether b=c, then the set of ships which left port contains b, and it is indeterminate whether it contains a and indeterminate whether it contains c. And the set of ships which docked contains a and c, and it is indeterminate whether it contains b. Maybe, therefore, we should say that the cardinality of each set is indeterminate, in such a way that it is not determinately the case that the two sets have distinct cardinalities.
Suppose a ship (b) leaves port and two ships (a and c) dock, but (for the usual reasons having to do with the replacement of bits) we want to say it is indeterminate whether a=c, and indeterminate whether b=c, yet determinately not the case that a=c. Pinillos argues this cannot be right, and a key premise of his argument is that the set of ships which left port - {b} - is distinct from the set of ships which docked - {a,c} - because these two sets have different cardinalities. (This leads him to conclude that there must be something in one set which is not in the other - so that there is some pair consisting of one member from each set such that it is (determinately) the case that the two things in that pair are not identical - contradicting the assumption that all the relevant identity claims are indeterminate.)
I won't go into the details of Dominic's response to the Pinillos argument, since (as far as I know) it's not yet publicly available. But my own reaction (different from Dominic's) was to wonder whether the defender of this sort of vague identity should accept that the two sets are distinct. Maybe she should say that it's indeterminate whether the set of ships which left port is identical to the set of ships which docked.
Sure, there is a strong intuition that something is wrong with '{b} = {a,c}', but perhaps this could be explained as an intuition to the effect that, because of the difference in cardinality between the sets, this identity claim is necessarily not true, which does not (for people - like Dominic - who are into three-valued logics) entail that it is false. (By analogy, a claim Dominic argued for in one of his other talks here is that although we have a strong intution that claims like 'Patch p is red and non-red' are not true, we should not therefore regard them as false when p is a borderline case.)
In fact, is the defender of vague identity even compelled to accept the claim that the sets have distinct cardinalities? If it really is indeterminate whether a=b and indeterminate whether b=c, then the set of ships which left port contains b, and it is indeterminate whether it contains a and indeterminate whether it contains c. And the set of ships which docked contains a and c, and it is indeterminate whether it contains b. Maybe, therefore, we should say that the cardinality of each set is indeterminate, in such a way that it is not determinately the case that the two sets have distinct cardinalities.
Sunday, November 20, 2005
More Paradox
Here's the promised conclusion to my last post. (Thanks to Robbie for a helpful discussion of this stuff over dinner last night).
The reason I'm uneasy about Field's project is simply that I need to hear more about why the notion of truth that we end up with is (the) one that we're interested in when we get worried about semantic paradox. We are to understand truth as the thing governed by Schema (T), and we are to understand (T) by understanding its logical constants, and we are to understand its logical constants by understanding which arguments are valid. (The notion of validity which is used to give us a grip on the logical constants in Schema (T) - and hence on the truth-predicate - will render the paradox-generating argument invalid - specifically, by rendering unrestricted LEM invalid).
But what reason is there to think the kind of truth we were concerned with when we started out is so definable? Maybe Field's project is just to show that a predicate obeying (T) can be used consistently. But even this claim presents difficulties: if how we understand (T) depends on how we understand the constants it contains (undeniable), and if how we understand of those concepts is governed by which arguments we take to be valid (Field's claim), then we have first to agree with Field about which arguments are valid in order even to accept that the (thing which looks like a) T-schema that he ends up preserving is the same as the one we wanted to preserve. Otherwise, he may have preserved the truth of the sentence 'T(< A >) iff A' but only at the expense of making it mean something else.
In addition, traditional worries about implicit definition seem relevant to the claim that we can understand logical constants by understanding which arguments are valid, and the claim that we can understand (T) once we understand the constants involved. (To illustrate with the first case, suppose you have a bunch of arguments involving '&' which you're told are valid. If you're meant to be able to tell from that what '&' means, you're presumably supposed to do this by noting that the intended interpretation of '&' is (the) one which will make all these arguments come out valid. But what guarantees that there is such an interpretation, and exactly one of them?)
The reason I'm uneasy about Field's project is simply that I need to hear more about why the notion of truth that we end up with is (the) one that we're interested in when we get worried about semantic paradox. We are to understand truth as the thing governed by Schema (T), and we are to understand (T) by understanding its logical constants, and we are to understand its logical constants by understanding which arguments are valid. (The notion of validity which is used to give us a grip on the logical constants in Schema (T) - and hence on the truth-predicate - will render the paradox-generating argument invalid - specifically, by rendering unrestricted LEM invalid).
But what reason is there to think the kind of truth we were concerned with when we started out is so definable? Maybe Field's project is just to show that a predicate obeying (T) can be used consistently. But even this claim presents difficulties: if how we understand (T) depends on how we understand the constants it contains (undeniable), and if how we understand of those concepts is governed by which arguments we take to be valid (Field's claim), then we have first to agree with Field about which arguments are valid in order even to accept that the (thing which looks like a) T-schema that he ends up preserving is the same as the one we wanted to preserve. Otherwise, he may have preserved the truth of the sentence 'T(< A >) iff A' but only at the expense of making it mean something else.
In addition, traditional worries about implicit definition seem relevant to the claim that we can understand logical constants by understanding which arguments are valid, and the claim that we can understand (T) once we understand the constants involved. (To illustrate with the first case, suppose you have a bunch of arguments involving '&' which you're told are valid. If you're meant to be able to tell from that what '&' means, you're presumably supposed to do this by noting that the intended interpretation of '&' is (the) one which will make all these arguments come out valid. But what guarantees that there is such an interpretation, and exactly one of them?)
Thursday, November 17, 2005
Paradox Workshop
Yesterday's workshop on Semantic Paradox was enjoyable. Here is a nice photo of the workshop participants taken by Simon Prosser.
One of the many interesting questions that came up concerned "model-theoretic revenge" for approaches like Hartry Field's. I was interested by some of the stuff which appears around p. 23 of the written version of Field's paper. Here Field claims that his model theory 'plays at best a very indirect role in explaining truth. Rather, truth is directly explained by Schema (T), and model theory enters only in helping us understand more fully the logical connectives that occur in instances of Schema (T)'. Validity is not necessary truth-preservation, but is (co-extensive with) preservation of designation in all models. Apparent 'revenge' sentences of the form of:
(Q*) Q* is not designated in model M
(see p. 27) are supposed to be unproblematic precisely because designation in M is not truth but merely a model-relative notion, which means that Q* can consistently be either designated or undesignated in M.
I'm uneasy, but reasons why will have to wait till my next post, as I'm dashing off now to the Vagueness workshop ...
One of the many interesting questions that came up concerned "model-theoretic revenge" for approaches like Hartry Field's. I was interested by some of the stuff which appears around p. 23 of the written version of Field's paper. Here Field claims that his model theory 'plays at best a very indirect role in explaining truth. Rather, truth is directly explained by Schema (T), and model theory enters only in helping us understand more fully the logical connectives that occur in instances of Schema (T)'. Validity is not necessary truth-preservation, but is (co-extensive with) preservation of designation in all models. Apparent 'revenge' sentences of the form of:
(Q*) Q* is not designated in model M
(see p. 27) are supposed to be unproblematic precisely because designation in M is not truth but merely a model-relative notion, which means that Q* can consistently be either designated or undesignated in M.
I'm uneasy, but reasons why will have to wait till my next post, as I'm dashing off now to the Vagueness workshop ...
Monday, November 14, 2005
Novemberfest and Conventionalism
A busy couple of weeks at Arche, with two workshops (on semantic paradox and vagueness respectively), and talks by (among others) Greg Restall, JC Beall, Hartry Field, Diana Raffman, Achille Varzi and Dominic Hyde (with many others in town - e.g. Steve Yablo, Richard Heck, Graham Priest). I'll try and post some paper reports here as the fortnight progresses.
In the meantime, does anyone think the following is a way to rescue conventionalism about necessary/a priori/analytic truth from one obvious type of objection to it?
Here's the objection (as expressed by BonJour):
[w]hat convention might be adopted that would make it possible for something to be red and green all over at the same time? It is, of course, obvious that new conventions could change the meaning ... of the words ‘red’ and ‘green’, but there is no plausibility at all to the idea that such changes would result in the falsity of ... the proposition that nothing can be red and green all over at the same time, as opposed to merely altering the way in which [that proposition is] expressed.
(From In Defence of Pure Reason, p. 53.)
Mightn’t the conventionalist try and distinguish two ways of understanding the claim that had our conventions been different it would have been possible for something to be red and green all over? On one of these, the relevant counterfactual worlds are being assessed by us, and therefore our own conventions are in play. So we deny that these worlds where our conventions are different are worlds and something can be red and green all over (because our actual-world conventions fix that nothing can be red and green all over in any world, including these ones). On the other approach we consider, not what is true at those worlds considered as worlds governed by our actual conventions, but what is true at those worlds considered as worlds governed by the conventions we have at the worlds in question. So on this second approach we accept that there are some worlds where it is possible for something to be red and green all over at the same time.
Maybe the conventionalist could argue that our intuition that changing our conventions wouldn’t change the facts (the intuition driving BonJour's objection) is well-enough preserved by the result we get on the first approach. But on the second approach there are worlds where the proposition is made false by the fact that we have different conventions at those worlds. And this (she might say) is enough to rescue the thought that we could have had different conventions which would have made it false that nothing is red and green all over - i.e. enough to rescue conventionalism from the objection.
In the meantime, does anyone think the following is a way to rescue conventionalism about necessary/a priori/analytic truth from one obvious type of objection to it?
Here's the objection (as expressed by BonJour):
[w]hat convention might be adopted that would make it possible for something to be red and green all over at the same time? It is, of course, obvious that new conventions could change the meaning ... of the words ‘red’ and ‘green’, but there is no plausibility at all to the idea that such changes would result in the falsity of ... the proposition that nothing can be red and green all over at the same time, as opposed to merely altering the way in which [that proposition is] expressed.
(From In Defence of Pure Reason, p. 53.)
Mightn’t the conventionalist try and distinguish two ways of understanding the claim that had our conventions been different it would have been possible for something to be red and green all over? On one of these, the relevant counterfactual worlds are being assessed by us, and therefore our own conventions are in play. So we deny that these worlds where our conventions are different are worlds and something can be red and green all over (because our actual-world conventions fix that nothing can be red and green all over in any world, including these ones). On the other approach we consider, not what is true at those worlds considered as worlds governed by our actual conventions, but what is true at those worlds considered as worlds governed by the conventions we have at the worlds in question. So on this second approach we accept that there are some worlds where it is possible for something to be red and green all over at the same time.
Maybe the conventionalist could argue that our intuition that changing our conventions wouldn’t change the facts (the intuition driving BonJour's objection) is well-enough preserved by the result we get on the first approach. But on the second approach there are worlds where the proposition is made false by the fact that we have different conventions at those worlds. And this (she might say) is enough to rescue the thought that we could have had different conventions which would have made it false that nothing is red and green all over - i.e. enough to rescue conventionalism from the objection.
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