The ECAP is now in full swing. It´s an event on an impressive scale, with long days comprising for the most part multiply parallel sessions. It´s also pretty warm in Lisbon right now, and many of the rooms have no air conditioning. This (together with the fact that the university is located under the flight path of the city´s airport) has been the main downer so far. Philosophically there has been plenty to entertain and to challenge. I´ll try and get comments on various papers up here eventually, but since I´m pushed for time now I´ll just briefly describe some material presented yesterday by David Papineau and this afternoon´s talk by Kit Fine.
Papineau was arguing that epistemologists and methodological philosophers of science once had a similar range of interests, but that recently (since Gettier, as far as I could tell) epistemologists have been moving away from methodological concerns, and focussing on other matters (the examples given were tracking, disjunctivism and contextualism). For a while I wondered whether Papineau was going to say that the methodologists were out of date, but it turned out the fault lay with the epistemologists, since Papineau could find little reason to be interested in the concept of knowledge except insofar as knowledge is a means to true beliefs, i.e. insofar as one is interested in the methodology of belief formation.
A few thoughts about this:
1. Even supposing there is a real difference of focus between epistemologists and methodological philosophers of science, I would prefer to think in terms of a division of labour than a competition as to whose project is more worthy.
2. Even if we are inclined to agree that we need a reason to be interested in knowledge which appeals to our prior interest in something else, there seem to be some which aren´t simply that our having knowledge is a means to our having true beliefs. For instance, there is Edward Craig´s idea that we are interested in knowledge because we are interested in the notion of a good informant. There´s still a focus on true belief here, in some sense, but for one thing the shift to the third-person perspective which is (at least sometimes) reasonable when we´re thinking about good informants seems to put issues like contextualism back on the menu. (When I spoke to Papineau after the talk he said he was already thinking about this, and also mentioned the Williamsonian idea of knowledge as the norm of assertion.)
3. It´s not even obvious to me that the only methodological reason for being interested in knowledge is that one is interested in securing true beliefs. Before we have a clear grasp of what knowledge is, gleaned from a thorough exploration of the concept of knowledge of the kind Papineau considers disreputable, how can we say whether methodologists should focus on finding out which belief-forming policies lead to true scientific beliefs, as opposed to saying that methodologists should focus on finding out which policies lead to scientific knowledge?
Kit Fine gave a very interesting paper (of which I´d heard an earlier version in St Andrews in June), in which he proposes a new approach to the notion of class. Rather than building a ZF-like hierarchy by starting with a grasp of the membership relation and using it to explain which sets there are (first the set with no members, then the set with the null set as its only member ... etc.), we would start off with all the classes and any urelemente as given, and then explain membership by saying which of those things the relation held between. He described this as a sort of Copernican Revolution.
In the question session I queried whether one could understand which classes there are without understanding what membership is. It´s not as if classes can be pointed out to us like boxes: to think about a particular class, we have to describe it, and presumably we will most often describe classes using descriptions of the form ´the class whose members are ...´. Fine initially proposed that we associate classes with certain conditions (e.g. the null class with the condition x is not identical to x) which, although they may contain a limited membership relation, do not contain the full notion. But since these are the conditions for membership of the class we are interested in, that doesn´t seem to help - understanding the relation between the condition and the class is understanding that the condition tells you which members the class has.
If something like this is right, then at most I think Fine might be able to claim that, instead of the traditional explanatory asymmetry between the membership relation and the notion of class, we have an interesting interdependence between the two. I don´t think he could say that the asymmetry was to be reversed in the way suggested by the phrase ´Copernican Revolution´.
Fine made a suggestion in reply, which was that we might associate conditions with the objects which would turn out to be the classes in some other way than by saying that the conditions specify the classes´ members. I´m still wondering what to think about this (comments welcome, obviously!), though an initial feeling is that we can´t really get an idea of which classes there are by this means. We would get the idea that there are these objects, but would we have enough information to understand that they were classes if we didn´t understand what membership was?
Monday, August 29, 2005
Thursday, August 25, 2005
Lisbon
I will be away at the European Congress for Analytic Philosophy in Lisbon until Friday 2 September, so there will (probably) be no more posts here until then.
Tuesday, August 23, 2005
Rationality More Generally
Rationality seems to come in different stripes - familiarly, there are epistemic and practical notions of rationality. Maybe there are other (more specific?) kinds as well.
It would be nice to have a general notion of rationality that would cover all the cases. How about something like this:
R: An act’s rationality-of-kind-K is determined by the extent to which it promotes the aims which that act has in virtue of being a (certain type of) act of kind K.
For example, we might say that:
RE: A belief's epistemic rationality is determined by the extent to which it promotes the aims which that act has in virtue of being an epistemic act (or perhaps, more specifically, a belief-like epistemic act).
To get an idea of what I mean, suppose you think that the sole constitutive aim of an epistemic act is to do what will probably get you to the truth about the matter under consideration (so that any act that lacks this aim just isn't a belief). Then you'll think that a belief's epistemic rationality is determined by the extent to which adopting that belief is the (a) thing that will probably get you to the truth about the matter under consideration.
I take it RE would explain why it doesn't seem right to assess non-epistemic acts for epistemic rationality.
It would be nice to have a general notion of rationality that would cover all the cases. How about something like this:
R: An act’s rationality-of-kind-K is determined by the extent to which it promotes the aims which that act has in virtue of being a (certain type of) act of kind K.
For example, we might say that:
RE: A belief's epistemic rationality is determined by the extent to which it promotes the aims which that act has in virtue of being an epistemic act (or perhaps, more specifically, a belief-like epistemic act).
To get an idea of what I mean, suppose you think that the sole constitutive aim of an epistemic act is to do what will probably get you to the truth about the matter under consideration (so that any act that lacks this aim just isn't a belief). Then you'll think that a belief's epistemic rationality is determined by the extent to which adopting that belief is the (a) thing that will probably get you to the truth about the matter under consideration.
I take it RE would explain why it doesn't seem right to assess non-epistemic acts for epistemic rationality.
Sunday, August 21, 2005
Epistemic Rationality
I've been thinking today about how something's being epistemically rational doesn't match up with that thing's being, epistemically speaking, the best thing (or one of a number of optimal things) to do overall.
Suppose you think that withholding judgement as to whether or not the physical world exists would be crippling, in almost all ways, including epistemically. People who withhold judgement about whether there is a physical world are making a big mistake, insofar as they want to do well epistemically - they are pursuing a course of action which is epistemically hopeless. In order to do well epistemically, believing in the external world is the thing to do. It enables us to get on with all sorts of other important epistemic projects. Many of these are, of course, projects which depend on our assuming that the physical world exists (e.g. projects involving visual inspection). But I want to ignore those for now (for reasons that should become clear below). Let's focus instead on the projects which don't actually depend on that assumption, but are just such that we wouldn't ever get round to them if we were too busy worrying about whether the physical world existed or not.
If it's right that withholding judgement about the physical world would prevent our undertaking these projects, then believing in the physical world is, epistemically speaking, a good thing to do, insofar as it enables us to get on with all these projects.
But there could be a drawback: suppose belief in the external world is in fact not supported by evidence (or suppose that it has some other status you would normally take to suffice for irrationality). Then, epistemically speaking, believing in the external world has drawbacks as well as advantages - it enables us to get on with those other epistemic projects, but it requires us to do something that we would normally regard as epistemically dodgy. (NB: this would also mean that any projects which depended on the assumption that there is an external world could not really be counted as epistemic bonuses for the believer - they would share the epistemic dodginess of the assumption on which they depended.)
But suppose that we were eventually going to stop believing in the physical world, but only after we've got around to pursuing a good number of these other (independent) projects. Then, it seems, we would eventually end up in an epistemic situation which had the advantages of belief in the physical world but not the disadvantages.
Perhaps this would mean that believing in the external world was, epistemically speaking, the best thing to do overall. Imagine, furthermore, that it's even known by the subject to be epistemically speaking the best thing to do overall. Could we infer that it was epistemically rational?
That would seem very strange to me. I'd be interested to hear how others' intuitions go on this case, but mine is that the epistemic rationality of a belief in p at a time t is to be evaluated just with regard to the subject's epistemic state at t with regard to p. Considerations about one's future epistemic state with regard to other propostions shouldn't enter into it.
Suppose you think that withholding judgement as to whether or not the physical world exists would be crippling, in almost all ways, including epistemically. People who withhold judgement about whether there is a physical world are making a big mistake, insofar as they want to do well epistemically - they are pursuing a course of action which is epistemically hopeless. In order to do well epistemically, believing in the external world is the thing to do. It enables us to get on with all sorts of other important epistemic projects. Many of these are, of course, projects which depend on our assuming that the physical world exists (e.g. projects involving visual inspection). But I want to ignore those for now (for reasons that should become clear below). Let's focus instead on the projects which don't actually depend on that assumption, but are just such that we wouldn't ever get round to them if we were too busy worrying about whether the physical world existed or not.
If it's right that withholding judgement about the physical world would prevent our undertaking these projects, then believing in the physical world is, epistemically speaking, a good thing to do, insofar as it enables us to get on with all these projects.
But there could be a drawback: suppose belief in the external world is in fact not supported by evidence (or suppose that it has some other status you would normally take to suffice for irrationality). Then, epistemically speaking, believing in the external world has drawbacks as well as advantages - it enables us to get on with those other epistemic projects, but it requires us to do something that we would normally regard as epistemically dodgy. (NB: this would also mean that any projects which depended on the assumption that there is an external world could not really be counted as epistemic bonuses for the believer - they would share the epistemic dodginess of the assumption on which they depended.)
But suppose that we were eventually going to stop believing in the physical world, but only after we've got around to pursuing a good number of these other (independent) projects. Then, it seems, we would eventually end up in an epistemic situation which had the advantages of belief in the physical world but not the disadvantages.
Perhaps this would mean that believing in the external world was, epistemically speaking, the best thing to do overall. Imagine, furthermore, that it's even known by the subject to be epistemically speaking the best thing to do overall. Could we infer that it was epistemically rational?
That would seem very strange to me. I'd be interested to hear how others' intuitions go on this case, but mine is that the epistemic rationality of a belief in p at a time t is to be evaluated just with regard to the subject's epistemic state at t with regard to p. Considerations about one's future epistemic state with regard to other propostions shouldn't enter into it.
Friday, August 19, 2005
Contemporary Debates in Epistemology
I've just got my copy of this collection through from Amazon, and skipped straight to chapter 4 on the a priori. I was interested to notice Michael Devitt (pp. 107-8) discussing one of the questions I asked in my most commented post so far, namely why we should assume that experience only tells us what is the case, rather than what must be the case. (Devitt, unsurprisingly, is in favour of a holistic, web-of-belief account of how it can.)
Even more interestingly, BonJour (p. 100) argues that the way to solve a certain kind of regress problem ('the application of a propositional insight concerning the cogency of ... an inference would require either a further inference of the very sort in question or one equally fundamental') is to claim that a priori rational insight cannot be always (perhaps cannot be ever) 'propositional in form'. Instead, an a priori insight must (often) be 'a direct grasping of the way in which the conclusion is related to the premises and validly flows from them'. This raises several questions, including the question of how best to make sense of how grasping 'the way in which ...' could amount to something other than the grasping of a proposition, or how, even if it is different, it could amount to grasping something which does not itself (by BonJour's - internalist - lights) stand in need of justification like a proposition does. I always suspected the solution to this kind of problem was to reject the (famously regress-generating) internalist premise.
Another interesting question the suggestion raises (which as far as I can tell BonJour does not address) is whether, if non-propositional a priori insight is possible, there could also be empirical grounding for these non-propositional things, whatever they are. It's hard to see an obvious reason why there could not, though I think if there could that would undermine this argument of BonJour's for the existence of a priori insight.
Even more interestingly, BonJour (p. 100) argues that the way to solve a certain kind of regress problem ('the application of a propositional insight concerning the cogency of ... an inference would require either a further inference of the very sort in question or one equally fundamental') is to claim that a priori rational insight cannot be always (perhaps cannot be ever) 'propositional in form'. Instead, an a priori insight must (often) be 'a direct grasping of the way in which the conclusion is related to the premises and validly flows from them'. This raises several questions, including the question of how best to make sense of how grasping 'the way in which ...' could amount to something other than the grasping of a proposition, or how, even if it is different, it could amount to grasping something which does not itself (by BonJour's - internalist - lights) stand in need of justification like a proposition does. I always suspected the solution to this kind of problem was to reject the (famously regress-generating) internalist premise.
Another interesting question the suggestion raises (which as far as I can tell BonJour does not address) is whether, if non-propositional a priori insight is possible, there could also be empirical grounding for these non-propositional things, whatever they are. It's hard to see an obvious reason why there could not, though I think if there could that would undermine this argument of BonJour's for the existence of a priori insight.
Wednesday, August 17, 2005
Vague Existence Gets Murkier
I was talking vague existence over lunch today with Katherine Hawley and Daniel Nolan.
Daniel suggested that in order correctly and exhaustively to represent an ontically vague world, a world (let's say) where it is an ontically vague matter whether an F exists, our best theory BT must be such that it is a vague matter whether or not BT is committed to Fs. It wouldn't be enough for the theory to include a sentence which says that it's a vague matter whether Fs exist.
This would, I think, be a way to respond to my suggestion that ontic vagueness creates tension with the Quinean criterion for ontological commitment. The Nolan line (I use that description without intending to suggest that Daniel endorses the view) would seem to be that although BT is not committed to Fs just by dint of containing a sentence which says that it's vague whether Fs exist, BT is vaguely committed to Fs (or at least, it becomes problematic to say that it is not committed) because it is a vague matter whether or not BT says that Fs exist.
One interesting feature of this proposal is that it seems to imply that ontic vagueness cannot be limited to Fs alone. If it's vague whether there are Fs, it's also vague whether BT includes 'There are Fs'. And to say the latter vagueness is merely linguistic would seem somewhat strange under the circs. How could two different things be responsible for the vagueness of reality and the vagueness of BT, when the latter kind of vagueness exists merely because BT has to be an exhaustive representation a reality which exhibits the former kind?
That aside, though, I'm not sure I can yet see what independent motivation there is for taking this sort of line. It must be that in this situation BT leaves something out (or more cautiously, does not determinately capture everything) if it attempts to say all there is to say on the matter of the existence of Fs just by including the sentence 'It's vague whether there are Fs'. To do its job properly, it must also vaguely include the sentence 'There are Fs'. But why think that? What's been left out exactly?
One motivating thought Daniel mentioned: suppose we take exhaustive representation of the universe to be possible by theories that are not such that it's vague whether they include certain sentences. That skirts close to a bivalence assumption: we might like to think that (best theories are ideally good enough for it to be the case that) the true sentences are the ones in the theory, and it's determinate which ones those are, and all the others are false. Defenders of ontic vagueness who refuse to accept bivalence should therefore be equally unhappy with the idea that correct and exhaustive representation is possible by theories which are not vague in the aforementioned way.
But as far as I can see there is no need to say that the sentences not included in the best theory are false. All we want is for our best theory to include all the sentences that we think are true. So if we think 'It's vague whether there are Fs' is true, that should be in BT. And if we think it's a vague matter which of 'There are Fs' and 'There are no Fs' is true, then we don't think 'There are Fs' is true and we don't think 'There are no Fs' is true. (Which is not to say that we think either of them is untrue. We aren't committed either way.) So BT needn't include either of these sentences. But that's not to say that (either actually, or according to BT) these sentences are false. And if it were we'd have bigger trouble on our hands than a commitment to bivalence ...
BT of course needs to include the information that it's a vague matter which of the two sentences is true, but it does this, not by vaguely including them both, but by including 'It's vague whether there are Fs'.
Daniel suggested that in order correctly and exhaustively to represent an ontically vague world, a world (let's say) where it is an ontically vague matter whether an F exists, our best theory BT must be such that it is a vague matter whether or not BT is committed to Fs. It wouldn't be enough for the theory to include a sentence which says that it's a vague matter whether Fs exist.
This would, I think, be a way to respond to my suggestion that ontic vagueness creates tension with the Quinean criterion for ontological commitment. The Nolan line (I use that description without intending to suggest that Daniel endorses the view) would seem to be that although BT is not committed to Fs just by dint of containing a sentence which says that it's vague whether Fs exist, BT is vaguely committed to Fs (or at least, it becomes problematic to say that it is not committed) because it is a vague matter whether or not BT says that Fs exist.
One interesting feature of this proposal is that it seems to imply that ontic vagueness cannot be limited to Fs alone. If it's vague whether there are Fs, it's also vague whether BT includes 'There are Fs'. And to say the latter vagueness is merely linguistic would seem somewhat strange under the circs. How could two different things be responsible for the vagueness of reality and the vagueness of BT, when the latter kind of vagueness exists merely because BT has to be an exhaustive representation a reality which exhibits the former kind?
That aside, though, I'm not sure I can yet see what independent motivation there is for taking this sort of line. It must be that in this situation BT leaves something out (or more cautiously, does not determinately capture everything) if it attempts to say all there is to say on the matter of the existence of Fs just by including the sentence 'It's vague whether there are Fs'. To do its job properly, it must also vaguely include the sentence 'There are Fs'. But why think that? What's been left out exactly?
One motivating thought Daniel mentioned: suppose we take exhaustive representation of the universe to be possible by theories that are not such that it's vague whether they include certain sentences. That skirts close to a bivalence assumption: we might like to think that (best theories are ideally good enough for it to be the case that) the true sentences are the ones in the theory, and it's determinate which ones those are, and all the others are false. Defenders of ontic vagueness who refuse to accept bivalence should therefore be equally unhappy with the idea that correct and exhaustive representation is possible by theories which are not vague in the aforementioned way.
But as far as I can see there is no need to say that the sentences not included in the best theory are false. All we want is for our best theory to include all the sentences that we think are true. So if we think 'It's vague whether there are Fs' is true, that should be in BT. And if we think it's a vague matter which of 'There are Fs' and 'There are no Fs' is true, then we don't think 'There are Fs' is true and we don't think 'There are no Fs' is true. (Which is not to say that we think either of them is untrue. We aren't committed either way.) So BT needn't include either of these sentences. But that's not to say that (either actually, or according to BT) these sentences are false. And if it were we'd have bigger trouble on our hands than a commitment to bivalence ...
BT of course needs to include the information that it's a vague matter which of the two sentences is true, but it does this, not by vaguely including them both, but by including 'It's vague whether there are Fs'.
Monday, August 15, 2005
Recognizing Necessity
Tonight's post is (even) more of a ramble than usual - a question I'm just starting to get interested in and would like to know (and think) more about.
Say there are some a priori contingent truths (e.g. The metre bar is one metre long). If that's so, how do we recognise necessity when we see it? It can't just be that, when we realize we have special a priori access to some truth, we thereby (gain all the information we need in order to) realize that the truth in question in necessary.
Here's a quick answer: suppose that coming to know a proposition a priori is a matter of realizing that a certain kind of relation holds between the concepts involved. Then there doesn't seem to be any obvious reason why it should always be the case that, when the right sort of relation holds between the concepts in p, that sort of relation also holds between the concepts in Necessarily p. We come to know p a priori by recognizing something about one set of concepts, and we come to know a priori that Necessarily p by recognizing something about a different set of concepts.
I like this sort of answer in principle, though it can't be quite the whole story. One thing it doesn't do is explain why there is so often a connection between realizing that you have a priori knowledge that p and realizing that p is necessary. Apart from that, though, I wonder whether people are inclined to think it is lacking in some other way (and/or to have views as to what should we say to address the fact that there is usually a connection between a prioricity and necessity)?
Say there are some a priori contingent truths (e.g. The metre bar is one metre long). If that's so, how do we recognise necessity when we see it? It can't just be that, when we realize we have special a priori access to some truth, we thereby (gain all the information we need in order to) realize that the truth in question in necessary.
Here's a quick answer: suppose that coming to know a proposition a priori is a matter of realizing that a certain kind of relation holds between the concepts involved. Then there doesn't seem to be any obvious reason why it should always be the case that, when the right sort of relation holds between the concepts in p, that sort of relation also holds between the concepts in Necessarily p. We come to know p a priori by recognizing something about one set of concepts, and we come to know a priori that Necessarily p by recognizing something about a different set of concepts.
I like this sort of answer in principle, though it can't be quite the whole story. One thing it doesn't do is explain why there is so often a connection between realizing that you have a priori knowledge that p and realizing that p is necessary. Apart from that, though, I wonder whether people are inclined to think it is lacking in some other way (and/or to have views as to what should we say to address the fact that there is usually a connection between a prioricity and necessity)?
Thursday, August 11, 2005
Finkish Fitchish Dispositions
I had a great time talking about Fitch this afternoon with some members of the NAMICONA group. I got some very interesting comments and I want to make a note of some of them before I forget - though this post follows a couple of post-talk drinks so apologies if it falls below even my usual standards of clarity ...
One intriguing suggestion, made by Lars Gundersen: maybe saying that p is knowable-if-true is not a matter of asserting 'p --> possibly-Kp', but rather a matter of attributing some sort of dispositional property to p, which might be finkish. To take the conditional to capture this property would be to commit (something close to) the conditional fallacy. (NB: the rest of this post consists in reflections on things Lars and others said in the session - they take no blame for any nonsense in what follows.)
Compare: killer yellow is visible, even though if one were to look at it one would not see it but would in fact perish. It would be a mistake to assume that the dispositional property of visibility is captured by any counterfactual of the form 'if you were to look at it then you would see it'.
To get closer to the Fitch case, consider super-killer-yellow, which is visible, even though necessarily all who look upon it instantly perish. To get even closer again, consider super-suicidal-yellow, which necessarily disappears when someone looks at it. The visibility of super-suicidal-yellow (one might think) is a finkish dispositional property.
But note that we are still some distance from the conditional that generates the Fitch argument, since that conditional is material and so far we're still talking about counterfactuals. But if being knowable-if-true is indeed a dispositional property, perhaps the first step in rejecting its analysis as (p --> possibly-Kp) will be to argue that if any conditional captures it at all it won't be a material one. (The next step will presumably be to argue that if any strightforward counterfactual captures it then what goes on the left hand side of that counterfactual is not 'p' but some description of the stimulus - investigation presumably - which typically triggers the response of becoming known-if-true. And what goes on the right hand side is a description of this response.)
And note that we are getting close to what we want insofar as we've established that the visibility of super-suicidal-yellow is not threatened by the falsity of 'super-suicidal-yellow is possibly seen'. Maybe we can argue by analogy that the knowability-if-true of (p and not-Kp) is not threatened by the falsity of '(p and not-Kp) is possibly true and known'.
Assuming something like a Lewisian analysis of dispositions (for the sake of argument), we might try something like the following:
A proposition p is knowable-if-true at time t (i.e. disposed at time t to give response r - becoming known-if-true - to stimulus s - being sufficiently investigated) if and only if, for some property B that p has at t, for some time t’ after t, if p were to undergo stimulus s at time t and retain property B until t’, s and p’s having of B would jointly cause p’s giving response r.
('Sufficient investigation' = investigation sufficient to produce knowledge of p if p is true and knowledge of not-p if p is false.)
One thing about treating Fitch cases (and any others where the appearance of s necessarily prevents the retention of B) this way, though, at least if we also assume a Lewisian analysis of counterfactuals, is that the counterfactual involved in the analysis will be trivially true in the interesting cases, since it is impossible for any true proposition of the form (p and not-Kp) to retain it's truth-value (which I would imagine must be part of B) while being sufficiently investigated. So I guess we would need to plug in some other analysis of the counterfactual, or else demand that the counterfactual be assertible as well as trivially true, or something of that kind.
There might, of course, also be more promising non-Lewisian analyses of the relevant dispositional properties that don't involve counterfactuals at all.
[Aside: It could be that on some ways of developing this thought, it might end up quite close to some of the things I think about Fitch. Ascribing the relevant dispositional property might depend on (what I would descibe as) the thought that the state of affairs (if any) which makes p true is recognizable. The base property might be a matter of p's relation to that state of affairs (if any). Another extrinsically-based disposition, perhaps!]
One intriguing suggestion, made by Lars Gundersen: maybe saying that p is knowable-if-true is not a matter of asserting 'p --> possibly-Kp', but rather a matter of attributing some sort of dispositional property to p, which might be finkish. To take the conditional to capture this property would be to commit (something close to) the conditional fallacy. (NB: the rest of this post consists in reflections on things Lars and others said in the session - they take no blame for any nonsense in what follows.)
Compare: killer yellow is visible, even though if one were to look at it one would not see it but would in fact perish. It would be a mistake to assume that the dispositional property of visibility is captured by any counterfactual of the form 'if you were to look at it then you would see it'.
To get closer to the Fitch case, consider super-killer-yellow, which is visible, even though necessarily all who look upon it instantly perish. To get even closer again, consider super-suicidal-yellow, which necessarily disappears when someone looks at it. The visibility of super-suicidal-yellow (one might think) is a finkish dispositional property.
But note that we are still some distance from the conditional that generates the Fitch argument, since that conditional is material and so far we're still talking about counterfactuals. But if being knowable-if-true is indeed a dispositional property, perhaps the first step in rejecting its analysis as (p --> possibly-Kp) will be to argue that if any conditional captures it at all it won't be a material one. (The next step will presumably be to argue that if any strightforward counterfactual captures it then what goes on the left hand side of that counterfactual is not 'p' but some description of the stimulus - investigation presumably - which typically triggers the response of becoming known-if-true. And what goes on the right hand side is a description of this response.)
And note that we are getting close to what we want insofar as we've established that the visibility of super-suicidal-yellow is not threatened by the falsity of 'super-suicidal-yellow is possibly seen'. Maybe we can argue by analogy that the knowability-if-true of (p and not-Kp) is not threatened by the falsity of '(p and not-Kp) is possibly true and known'.
Assuming something like a Lewisian analysis of dispositions (for the sake of argument), we might try something like the following:
A proposition p is knowable-if-true at time t (i.e. disposed at time t to give response r - becoming known-if-true - to stimulus s - being sufficiently investigated) if and only if, for some property B that p has at t, for some time t’ after t, if p were to undergo stimulus s at time t and retain property B until t’, s and p’s having of B would jointly cause p’s giving response r.
('Sufficient investigation' = investigation sufficient to produce knowledge of p if p is true and knowledge of not-p if p is false.)
One thing about treating Fitch cases (and any others where the appearance of s necessarily prevents the retention of B) this way, though, at least if we also assume a Lewisian analysis of counterfactuals, is that the counterfactual involved in the analysis will be trivially true in the interesting cases, since it is impossible for any true proposition of the form (p and not-Kp) to retain it's truth-value (which I would imagine must be part of B) while being sufficiently investigated. So I guess we would need to plug in some other analysis of the counterfactual, or else demand that the counterfactual be assertible as well as trivially true, or something of that kind.
There might, of course, also be more promising non-Lewisian analyses of the relevant dispositional properties that don't involve counterfactuals at all.
[Aside: It could be that on some ways of developing this thought, it might end up quite close to some of the things I think about Fitch. Ascribing the relevant dispositional property might depend on (what I would descibe as) the thought that the state of affairs (if any) which makes p true is recognizable. The base property might be a matter of p's relation to that state of affairs (if any). Another extrinsically-based disposition, perhaps!]
Wednesday, August 10, 2005
Word Meaning and Sentence Meaning
Reading a draft chapter of Philip Ebert's PhD thesis today reminded me of a thought I've been batting about for a while concerning Frege's context principle.
Interpretations of the context principle usually seem to take it to be a claim to the effect that (certain) whole sentences in which a word occurs have some kind of semantic priority over the words themselves. But I've never been able to see exactly why a semantic priority claim is what's needed.
Suppose, for instance, that you think that what the context principle does is reveal that it suffices for epistemic access to the referents of mathematical singular terms if we have knowledge of (the propositions expressed by) the whole sentences in which these terms occur. Wouldn't it be enough to support that conclusion if we said that word meaning and sentence meaning are interdependent, so that understanding (certain) sentences in which a term occurs is always sufficient for understanding the term itself? With this principle in place we can argue that understanding the relevant sentences suffices for a grasp of the putative referent of a mathematical term, and that this together with knowledge that the sentences are true suffices for knowledge that the referent exists. (There are other assumptions at work here, of course, but only ones that are needed anyway.)
At most, we might feel pressured to say that our knowledge of the meaning of the sentences is prior to our grasp of the putative referent of the term (e.g. if we wanted an explanation of our grasp of the putative referent that was clearly naturalistically acceptable - didn't rely on intuition of abstract objects). But that's a matter of epistemological priority about semantics, not semantic priority. It doesn't imply that the fact that the term means what it does depends in any interesting (asymmetrical) way on the fact that the sentence means what it does.
In the background to all this is a lurking intuition that it is obvious that neither word nor sentence is semantically prior to the other - that word meaning and sentence meaning are clearly interdependent in such a way as to make claims of asymmetric semantic dependence implausible. I'd be interested, though, if anyone can set me straight as to why a full-on semantic priority claim will buy us more of what we want.
Interpretations of the context principle usually seem to take it to be a claim to the effect that (certain) whole sentences in which a word occurs have some kind of semantic priority over the words themselves. But I've never been able to see exactly why a semantic priority claim is what's needed.
Suppose, for instance, that you think that what the context principle does is reveal that it suffices for epistemic access to the referents of mathematical singular terms if we have knowledge of (the propositions expressed by) the whole sentences in which these terms occur. Wouldn't it be enough to support that conclusion if we said that word meaning and sentence meaning are interdependent, so that understanding (certain) sentences in which a term occurs is always sufficient for understanding the term itself? With this principle in place we can argue that understanding the relevant sentences suffices for a grasp of the putative referent of a mathematical term, and that this together with knowledge that the sentences are true suffices for knowledge that the referent exists. (There are other assumptions at work here, of course, but only ones that are needed anyway.)
At most, we might feel pressured to say that our knowledge of the meaning of the sentences is prior to our grasp of the putative referent of the term (e.g. if we wanted an explanation of our grasp of the putative referent that was clearly naturalistically acceptable - didn't rely on intuition of abstract objects). But that's a matter of epistemological priority about semantics, not semantic priority. It doesn't imply that the fact that the term means what it does depends in any interesting (asymmetrical) way on the fact that the sentence means what it does.
In the background to all this is a lurking intuition that it is obvious that neither word nor sentence is semantically prior to the other - that word meaning and sentence meaning are clearly interdependent in such a way as to make claims of asymmetric semantic dependence implausible. I'd be interested, though, if anyone can set me straight as to why a full-on semantic priority claim will buy us more of what we want.
Monday, August 08, 2005
Muriel and Schmuriel
I've been trying to work out why the area around Billund and Aarhus feels familiar in an unsettling way. I think it's that it combines the climate and long days of my current home county, Fife, with the flat landscapes and wide skies of my previous home county, Cambridgeshire. The effect is somewhat like that of meeting a friend wearing another friend's clothes in a context where you weren't expecting to see either of them.
The NAMICONA centre is pretty quiet at the moment but seems very friendly. I'll be giving a seminar on Fitch on Thursday afternoon to earn my passage out here, so there may be more to follow on that topic. Meanwhile, over dinner last night I discovered that Lars Gundersen shares my interest in the intrinsicness or otherwise of dispositions, and Eline Busck reminded me about this paper by Jennifer McKitrick on the topic (Ingenta access is required for this link).
I thought it might be illuminating to reformulate my 'friend of Muriel' example (originally described here as an example of a disposition with an extrinsic base) in conformity with McKitrick's pattern for examples of extrinsic dispositions. (This ought to work if the original does, since I guess that dispositions with extrinsic bases are extrinsic dispositions, although it would be more controversial to suppose that the converse holds.)
So consider person x and person y, who are perfect duplicates. They each have a friend whom they like very much and call by the name ‘Muriel’, but neither of them has ever met the other's friend. Let us refer to x’s friend as ‘Muriel’, and y’s friend as ‘Schmuriel’. Now we have the following argument:
1. x and y are perfect duplicates.
2. x is disposed to get upset when someone is rotten to Muriel.
3. y is not disposed to get upset when someone is rotten to Muriel.
4. Therefore, perfect duplicates do not necessarily share this dispositional property.
5. Therefore this dispositional property is extrinsic.
As far as I can tell, this example has an advantage over McKitrick's, in that there is no possible interference from relevant context-sensitivity in ‘gets upset when someone is rotten to Muriel’, of the kind that an objector might think was operative in the phrases that appear in McKitrick’s examples (‘weight’, ‘the contents of my pocket’, ‘recognizable’, etc.) and which the objector could use to motivate the ‘objection from relationally specified properties’ (see p. 163ff.).
The NAMICONA centre is pretty quiet at the moment but seems very friendly. I'll be giving a seminar on Fitch on Thursday afternoon to earn my passage out here, so there may be more to follow on that topic. Meanwhile, over dinner last night I discovered that Lars Gundersen shares my interest in the intrinsicness or otherwise of dispositions, and Eline Busck reminded me about this paper by Jennifer McKitrick on the topic (Ingenta access is required for this link).
I thought it might be illuminating to reformulate my 'friend of Muriel' example (originally described here as an example of a disposition with an extrinsic base) in conformity with McKitrick's pattern for examples of extrinsic dispositions. (This ought to work if the original does, since I guess that dispositions with extrinsic bases are extrinsic dispositions, although it would be more controversial to suppose that the converse holds.)
So consider person x and person y, who are perfect duplicates. They each have a friend whom they like very much and call by the name ‘Muriel’, but neither of them has ever met the other's friend. Let us refer to x’s friend as ‘Muriel’, and y’s friend as ‘Schmuriel’. Now we have the following argument:
1. x and y are perfect duplicates.
2. x is disposed to get upset when someone is rotten to Muriel.
3. y is not disposed to get upset when someone is rotten to Muriel.
4. Therefore, perfect duplicates do not necessarily share this dispositional property.
5. Therefore this dispositional property is extrinsic.
As far as I can tell, this example has an advantage over McKitrick's, in that there is no possible interference from relevant context-sensitivity in ‘gets upset when someone is rotten to Muriel’, of the kind that an objector might think was operative in the phrases that appear in McKitrick’s examples (‘weight’, ‘the contents of my pocket’, ‘recognizable’, etc.) and which the objector could use to motivate the ‘objection from relationally specified properties’ (see p. 163ff.).
Saturday, August 06, 2005
Aarhus
I'll be visiting the NAMICONA centre at Aarhus University until Monday 15 August. I hope I'll be able to get a couple of posts up while I'm there but things will be quieter than usual.
Friday, August 05, 2005
Disappearing Diamonds and Disappearing Disjunctions
(I'm using '-->' to represent the material conditional in this post.)
Kvanvig argues (here) that it is surprising (in some deep way) when Fitch's paradox shows us that 'p --> possibly Kp' is equivalent to 'p --> Kp'. It's surprising, he says, because it looks like we're collapsing a distinction between its being possible that Kp and (what is strictly stronger) its actually being the case that Kp.
But if that's the sole source of the puzzlement, why aren't we similarly surprised that '¬A --> (AvB)' is equivalent to '¬A --> B'? Here it looks like we're collapsing a distinction between the truth of a disjunction and (what is strictly stronger) the truth of one of its disjuncts. (Or at least, it looks as much like we're doing that as it looks like we're collapsing a modal distinction in the original case).
I suspect that, if there is something deeply surprising about the Fitch proof that stands in need of explanation, there must be more to it than this.
Kvanvig argues (here) that it is surprising (in some deep way) when Fitch's paradox shows us that 'p --> possibly Kp' is equivalent to 'p --> Kp'. It's surprising, he says, because it looks like we're collapsing a distinction between its being possible that Kp and (what is strictly stronger) its actually being the case that Kp.
But if that's the sole source of the puzzlement, why aren't we similarly surprised that '¬A --> (AvB)' is equivalent to '¬A --> B'? Here it looks like we're collapsing a distinction between the truth of a disjunction and (what is strictly stronger) the truth of one of its disjuncts. (Or at least, it looks as much like we're doing that as it looks like we're collapsing a modal distinction in the original case).
I suspect that, if there is something deeply surprising about the Fitch proof that stands in need of explanation, there must be more to it than this.
Thursday, August 04, 2005
Classify Me
Keith DeRose pointed out a while ago on Certain Doubts that the titles of the essays in this collection form a series of yes/no questions that we can use as a little diagnostic test to put epistemologists into boxes. So for what it's worth I'm going to follow Clayton Littlejohn's example and list my answers here.
1. Is Knowledge Closed under Known Entailment?
Nope.
2. Is Knowledge Contextual?
Probably, in at least one of the senses that could be intended.
3. Can Skepticism Be Refuted?
Nope, but that's not a problem.
4. Is There A Priori Knowledge?
I expect so, but if so it'll be empirically grounded - and no, 'a priori' doesn't mean 'non-empirical' :)
5. Is Infinitism the Solution to the Regress Problem?
Nope.
6. Can Beliefs Be Justified through Coherence Alone?
Nope.
7. Is There Immediate Justification?
Probably, though we'll have to be really careful spelling out what that means.
8. Does Perceptual Experience Have Conceptual Content?
Is it structured in a way that is mirrored by our concepts? Yes. Does it have content which is actually shaped by concepts (i.e. is it conceptualized): some does, but not all of it.
9. Is Justification Internal?
Nope.
10. Is Truth the Primary Epistemic Goal?
Sure.
11. Is Justified Belief Responsible Belief?
If I'm going to borrow terminology from action-talk, I'd rather say 'appropriate' than 'responsible'.
1. Is Knowledge Closed under Known Entailment?
Nope.
2. Is Knowledge Contextual?
Probably, in at least one of the senses that could be intended.
3. Can Skepticism Be Refuted?
Nope, but that's not a problem.
4. Is There A Priori Knowledge?
I expect so, but if so it'll be empirically grounded - and no, 'a priori' doesn't mean 'non-empirical' :)
5. Is Infinitism the Solution to the Regress Problem?
Nope.
6. Can Beliefs Be Justified through Coherence Alone?
Nope.
7. Is There Immediate Justification?
Probably, though we'll have to be really careful spelling out what that means.
8. Does Perceptual Experience Have Conceptual Content?
Is it structured in a way that is mirrored by our concepts? Yes. Does it have content which is actually shaped by concepts (i.e. is it conceptualized): some does, but not all of it.
9. Is Justification Internal?
Nope.
10. Is Truth the Primary Epistemic Goal?
Sure.
11. Is Justified Belief Responsible Belief?
If I'm going to borrow terminology from action-talk, I'd rather say 'appropriate' than 'responsible'.
Wednesday, August 03, 2005
Experiencing Modalities
Why do many philosophers seem to have accepted without argument that experience can only give us epistemic access to how things are, not to how things must be or how they could be? As far as I can tell, Plato, Kant and Hume were all convinced of the truth of (some version of) this claim, and it also has later advocates (I can think of relevant passages in Whewell and Chisholm).
But even if we thought that all modal truths were knowable a priori (and we had not yet appreciated that a priori knowledge may be empirically grounded), what would be the grounds for denying that experience can provide some (a posteriori) form of epistemic access to modal truths?
Granted, we never see modalities or bump into them. But we never see or bump into quarks or dark matter or magnetic fields either. We (or rather, those experts to whom we delegate such things) infer to their existence as the best explanation of what is observed. This is a perfectly respectable way for experience to provide epistemic access to some swathe of reality.
Is it perhaps assumed that modal truths cannot serve as explanations of the things we observe? Or is it that some other, non-modal explanation will always be better?
Alternatively, is the assumption that experience cannot provide us with epistemic access to modal truths just outdated? Has our epistemology moved on, with the realization that we can have empirical grounding for believing in something without actually bumping into it, and left this old-fashioned assumption behind?
But even if we thought that all modal truths were knowable a priori (and we had not yet appreciated that a priori knowledge may be empirically grounded), what would be the grounds for denying that experience can provide some (a posteriori) form of epistemic access to modal truths?
Granted, we never see modalities or bump into them. But we never see or bump into quarks or dark matter or magnetic fields either. We (or rather, those experts to whom we delegate such things) infer to their existence as the best explanation of what is observed. This is a perfectly respectable way for experience to provide epistemic access to some swathe of reality.
Is it perhaps assumed that modal truths cannot serve as explanations of the things we observe? Or is it that some other, non-modal explanation will always be better?
Alternatively, is the assumption that experience cannot provide us with epistemic access to modal truths just outdated? Has our epistemology moved on, with the realization that we can have empirical grounding for believing in something without actually bumping into it, and left this old-fashioned assumption behind?
Tuesday, August 02, 2005
Lynch's Role-Functionalism About Truth
Michael Lynch visited Arche recently and gave two great seminars on alethic pluralism, defending the view that truth is "both many and one" in the sense that truth is a multiply realizable functional property. This post is an attempt to record some of the thoughts I had in the discussion period about one of the arguments we looked at (which can also be found on p.15 of this online manuscript).
Michael proposes that '[i]n general, a real distinction between a property and a concept is merited whenever there are features relevant to something's being F which go beyond what can be known just by reflecting on our concept of Fs.' He also notes that '... according to alethic functionalism, a proposition is a member of the truth kind in virtue of its having the supervenient role property of truth.' But the nature of the realizing property, and whether a proposition has it, 'go beyond' the concept of truth, in that 'mere reflection on the concept of truth does not reveal them'. Therefore, Michael concludes, the property of truth is not a 'mere construction out of the concept'.
In our seminar I raised the concern that two readings of the intial claim are available, only one of which is plausible, although the other seems to be relied upon during the course of the argument. The two readings are:
1. Property and concept are distinct if there are features relevant to something's being F such that whether they are relevant to something's being F is not knowable just through reflection on the concept of truth.
2. Property and concept are distinct if there are features relevant to something's being F such that whether something has those features or not is not knowable just through reflection on the concept of truth.
One thing to note about whatever reading we settle on (this point was made by Crispin Wright during the seminar) is that we must be careful with the notion of 'relevance' here. We don't mean causal or explanatory relevance, for instance. (Any property F, even one which is just a reflection of our concept, could be such that part of the explanation of why a particular thing is F appeals to features of that thing which 'go beyond' - in either sense - reflection on the concept of F.) Something more like constitutive relevance seems to be needed. ('Constitutive' relevance needn't entail any kind of knowability through conceptual reflection - compare e.g. the kind of relevance that the feature of being H2O has to the property of being water.)
Suppose we can settle on an appropriate notion of relevance. Still, even if 1 is plausible, 2 surely isn't. 2, however, seems to be what's at work when it's claimed that it is significant that whether a proposition has some realizer property is not knowable just by reflection on the concept of truth.
Nonetheless, might it be significant that the nature of the realizing properties is not knowable through reflection on the concept of truth? I'm not sure. To convince me that it is, Michael needs to argue that the 'relevance' of the realizer properties to the property of truth is not comparable to causal or explanatory relevance, but is such as to make the realizer properties constitutively relevant to the role property.
But I think there may be a dilemma lurking here. If something about the realizer properties were constitutively relevant to the role property, such that this relevance wasn't knowable just through reflection on the role property, wouldn't that mean the role property was no longer purely functional in nature?
Compare: the Twin Earth thought experiment convinces us that being H2O is (although this fact is not knowable by conceptual reflection) constitutively relevant to being water. But at the same time it convinces us that being water isn't just a matter of being the colourless liquid that flows in our rivers etc.. Similarly, if something convinces us that (say) some fact about the nature of correspondance or coherence is a posteriori constitutively relevant to the property of truth, won't that simultaneously convince us that being true is not just a matter of having a property which fulfils the truth-platitudes that Michael wants to use to characterize truth's functional role?
Michael proposes that '[i]n general, a real distinction between a property and a concept is merited whenever there are features relevant to something's being F which go beyond what can be known just by reflecting on our concept of Fs.' He also notes that '... according to alethic functionalism, a proposition is a member of the truth kind in virtue of its having the supervenient role property of truth.' But the nature of the realizing property, and whether a proposition has it, 'go beyond' the concept of truth, in that 'mere reflection on the concept of truth does not reveal them'. Therefore, Michael concludes, the property of truth is not a 'mere construction out of the concept'.
In our seminar I raised the concern that two readings of the intial claim are available, only one of which is plausible, although the other seems to be relied upon during the course of the argument. The two readings are:
1. Property and concept are distinct if there are features relevant to something's being F such that whether they are relevant to something's being F is not knowable just through reflection on the concept of truth.
2. Property and concept are distinct if there are features relevant to something's being F such that whether something has those features or not is not knowable just through reflection on the concept of truth.
One thing to note about whatever reading we settle on (this point was made by Crispin Wright during the seminar) is that we must be careful with the notion of 'relevance' here. We don't mean causal or explanatory relevance, for instance. (Any property F, even one which is just a reflection of our concept, could be such that part of the explanation of why a particular thing is F appeals to features of that thing which 'go beyond' - in either sense - reflection on the concept of F.) Something more like constitutive relevance seems to be needed. ('Constitutive' relevance needn't entail any kind of knowability through conceptual reflection - compare e.g. the kind of relevance that the feature of being H2O has to the property of being water.)
Suppose we can settle on an appropriate notion of relevance. Still, even if 1 is plausible, 2 surely isn't. 2, however, seems to be what's at work when it's claimed that it is significant that whether a proposition has some realizer property is not knowable just by reflection on the concept of truth.
Nonetheless, might it be significant that the nature of the realizing properties is not knowable through reflection on the concept of truth? I'm not sure. To convince me that it is, Michael needs to argue that the 'relevance' of the realizer properties to the property of truth is not comparable to causal or explanatory relevance, but is such as to make the realizer properties constitutively relevant to the role property.
But I think there may be a dilemma lurking here. If something about the realizer properties were constitutively relevant to the role property, such that this relevance wasn't knowable just through reflection on the role property, wouldn't that mean the role property was no longer purely functional in nature?
Compare: the Twin Earth thought experiment convinces us that being H2O is (although this fact is not knowable by conceptual reflection) constitutively relevant to being water. But at the same time it convinces us that being water isn't just a matter of being the colourless liquid that flows in our rivers etc.. Similarly, if something convinces us that (say) some fact about the nature of correspondance or coherence is a posteriori constitutively relevant to the property of truth, won't that simultaneously convince us that being true is not just a matter of having a property which fulfils the truth-platitudes that Michael wants to use to characterize truth's functional role?
Monday, August 01, 2005
More on Vague Existence
Here's a more concise (and otherwise improved) version of a worry I was playing about with in my post a few days ago, and a look at a couple of manouevres that might be made in response.
There is a tension between the following three claims:
1. One is committed to Fs iff there are Fs among the range of the quantifiers appearing in one's best theory.
2. According to best theory, it is an ontically vague matter whether an F exists.
3. Someone whose best theory (correctly) asserts that it is a vague matter whether an F exists isn’t committed to saying that an F exists, nor is she committed to saying that one does not exist.
By 3, if 2 is true then we are not committed to the existence of an F. By 1, therefore, no F is among the range of the quantifiers appearing in our best theory. Hence our best theory can also truly contain the sentence ‘Nothing is an F’. But how can it be that our best theory can truly assert both that it is a vague matter whether or not there is an F and that nothing is an F? If nothing is an F, then it is not a vague matter whether or not there is an F: it is settled that there isn’t one.
Short of ditching 1 altogether, there seem to be two possible lines of response which a defender of 2 could appeal to. One is to argue (contra 3) that it is a vague matter whether the defender of vague existence is committed to Fs. The other is to revise 1 so that it reads: one is committed to Fs iff, determinately, there are Fs among the range of the quantifiers appearing in one's best theory.
I don’t find the first response appealing; acknowledging ontic vagueness seems to me to be a paradigmatic way of remaining decidedly non-committal. The second, though, may be thought more promising. Given that the defender of vague existence for Fs is not committed to Fs, the revised version of 1 will only deliver that it is not determinately true that there are Fs among the range of the quantifiers appearing in her best theory. This won’t entail that her best theory can truly say ‘Nothing is an F’.
However, some independent motivation for the revision is needed if it is not to appear ad hoc. And I'm not sure what form that motivation might take. There doesn’t seem (for all that’s been said here) to be anything wrong with the original 1 except that it makes claims of vague existence problematic. But until we are persuaded that vague existence is actually unproblematic, why should we regard that as a reason to revise 1?
There is a tension between the following three claims:
1. One is committed to Fs iff there are Fs among the range of the quantifiers appearing in one's best theory.
2. According to best theory, it is an ontically vague matter whether an F exists.
3. Someone whose best theory (correctly) asserts that it is a vague matter whether an F exists isn’t committed to saying that an F exists, nor is she committed to saying that one does not exist.
By 3, if 2 is true then we are not committed to the existence of an F. By 1, therefore, no F is among the range of the quantifiers appearing in our best theory. Hence our best theory can also truly contain the sentence ‘Nothing is an F’. But how can it be that our best theory can truly assert both that it is a vague matter whether or not there is an F and that nothing is an F? If nothing is an F, then it is not a vague matter whether or not there is an F: it is settled that there isn’t one.
Short of ditching 1 altogether, there seem to be two possible lines of response which a defender of 2 could appeal to. One is to argue (contra 3) that it is a vague matter whether the defender of vague existence is committed to Fs. The other is to revise 1 so that it reads: one is committed to Fs iff, determinately, there are Fs among the range of the quantifiers appearing in one's best theory.
I don’t find the first response appealing; acknowledging ontic vagueness seems to me to be a paradigmatic way of remaining decidedly non-committal. The second, though, may be thought more promising. Given that the defender of vague existence for Fs is not committed to Fs, the revised version of 1 will only deliver that it is not determinately true that there are Fs among the range of the quantifiers appearing in her best theory. This won’t entail that her best theory can truly say ‘Nothing is an F’.
However, some independent motivation for the revision is needed if it is not to appear ad hoc. And I'm not sure what form that motivation might take. There doesn’t seem (for all that’s been said here) to be anything wrong with the original 1 except that it makes claims of vague existence problematic. But until we are persuaded that vague existence is actually unproblematic, why should we regard that as a reason to revise 1?
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