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.
Friday, November 25, 2005
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.
Monday, November 07, 2005
Accidental Representation
Here's a bunch of interesting questions.
1. Does the involvement of (certain kinds of) luck interfere with representation? Suppose, for instance, that I have a drawing in front of me which, considered as a road map of a small town in Wales, would serve as an accurate guide. But suppose it is purely coincidental that the drawing has this feature - it was produced as a circuit diagram. Does the drawing represent the road layout of this small Welsh town?
2. If accidental representation is not possible, is the kind of accident that prevents representation from occuring analogous to the kind of accident which prevents some true beliefs from being knowledge?
3. If accidental representation is possible, what (if any) are the conditions on representation which prevent it being the case that (e.g.) any two resembling things represent each other?
1. Does the involvement of (certain kinds of) luck interfere with representation? Suppose, for instance, that I have a drawing in front of me which, considered as a road map of a small town in Wales, would serve as an accurate guide. But suppose it is purely coincidental that the drawing has this feature - it was produced as a circuit diagram. Does the drawing represent the road layout of this small Welsh town?
2. If accidental representation is not possible, is the kind of accident that prevents representation from occuring analogous to the kind of accident which prevents some true beliefs from being knowledge?
3. If accidental representation is possible, what (if any) are the conditions on representation which prevent it being the case that (e.g.) any two resembling things represent each other?
Tuesday, November 01, 2005
Epistemic Twin Earth
(Nod to Daniel for starting me thinking about this topic this morning.)
Suppose that epistemically normative claims are made true by the same facts as certain natural-sounding claims (even though the former do not necessarily 'mean the same' as the latter in any other sense).
And suppose that, on Epistemic Twin Earth, people's use of (what sound like, and are treated like) epistemically normative terms is regulated by natural properties distinct from those which regulate our use of these terms. Perhaps we agree to the sentence: "One epistemically ought not to have beliefs that one knows to be contradictory", and the Twin Earthers dissent from a sentence which sounds exactly like this. Do the people on Epistemic Twin Earth disagree with us about what epistemic norms there are?
If the view described above is right, it might seem that they don't, since (presumably) the Twin Earthlings' normative-sounding claims are made true by different natural facts to ours. Hence the appearance of disagreement is illusory, and (for all that's been said so far, anyway) we might both be right.
Two questions:
1. If this is right, should we be worried (as, according to Horgan and Timmons, we should be worried by an analogous result in the ethical case)?
2. Is it right? Nothing is being claimed, on the view under discussion, about the sense-meaning of our terms of epistemic evaluation or how their reference gets fixed. If we have the intuition that people on Epistemic Twin Earth are disagreeing with us in such a way that we could not both be right, then could we allow that their terms of epistemic evaluation pick out the same properties that ours do, despite the fact that their use of these terms is regulated by some other property? It is plausible that the reference of 'water' is fixed in such a way that Twin Earthlings' term 'water' refers to XYZ, not H20. But is a similar claim plausible for terms of epistemic evaluation?
Suppose that epistemically normative claims are made true by the same facts as certain natural-sounding claims (even though the former do not necessarily 'mean the same' as the latter in any other sense).
And suppose that, on Epistemic Twin Earth, people's use of (what sound like, and are treated like) epistemically normative terms is regulated by natural properties distinct from those which regulate our use of these terms. Perhaps we agree to the sentence: "One epistemically ought not to have beliefs that one knows to be contradictory", and the Twin Earthers dissent from a sentence which sounds exactly like this. Do the people on Epistemic Twin Earth disagree with us about what epistemic norms there are?
If the view described above is right, it might seem that they don't, since (presumably) the Twin Earthlings' normative-sounding claims are made true by different natural facts to ours. Hence the appearance of disagreement is illusory, and (for all that's been said so far, anyway) we might both be right.
Two questions:
1. If this is right, should we be worried (as, according to Horgan and Timmons, we should be worried by an analogous result in the ethical case)?
2. Is it right? Nothing is being claimed, on the view under discussion, about the sense-meaning of our terms of epistemic evaluation or how their reference gets fixed. If we have the intuition that people on Epistemic Twin Earth are disagreeing with us in such a way that we could not both be right, then could we allow that their terms of epistemic evaluation pick out the same properties that ours do, despite the fact that their use of these terms is regulated by some other property? It is plausible that the reference of 'water' is fixed in such a way that Twin Earthlings' term 'water' refers to XYZ, not H20. But is a similar claim plausible for terms of epistemic evaluation?
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