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Parity and Ambiguity
By S. Matthew Liao

1. Chang’s Argument for Parity
The Trichotomy Thesis says that there are three and only three positive value relations: ‘better than,’ ‘worse than,’ and ‘equal to.’ Incomparability, which is not a positive value relations, follows, if none of these three relations holds between two things being compared. In “The Possibility of Parity,” Ruth Chang argues for a fourth positive relation, what she calls ‘on a par.’ To do this, Chang gives an argument based on comparing the creative genius of Mozart and Michaelangelo, which can be put as follows:

1. Mozart is neither better nor worse than Michaelangelo, with respect to Creative Genius (CG).
2. A Mozart who has some small improvement that bears on CG (Mozart+) is better than Mozart, with respect to CG.
3. Mozart+ is not better than Michaelangelo, with respect to CG.
4. Therefore, Mozart and Michaelangelo are not related by any of the standard trichotomy of relations, with respect to CG. (This is the Small Improvement Argument)

5. Mozart is better than Talentlessi, a very bad music composer, with respect to CG.
6. Michaelangelo is also better than Talentlessi, with respect to CG.
7. Therefore, Mozart and Michaelangelo are comparable, with respect to CG. (This is the Chaining Argument)

8. Given 4 and 7, there must be a fourth comparative relation; Chang calls it the parity relation. (This is the Parity Conclusion)

I shall argue that Chang’s argument for the parity relation appears to work because it contains ambiguities. Once disambiguated, I argue that her argument fails. In particular, I shall claim that a) on one understanding of CG, the Small Improvement Argument would fail; b) on a different understanding of CG that would allow the Small Improvement Argument to succeed, the Chaining Argument would fail; and c) on an understanding of CG that would allow the Chaining Argument to succeed, the Small Improvement had already been shown to fail. To show this, I shall begin by presenting an analogous example of comparing an apple and an orange. I shall then apply the lessons from this example to Chang’s example of Mozart and Michaelangelo.

2. Comparing an Apple and an Orange

9. Suppose an Apple is neither better nor worse than an Orange, with respect to Taste.
10. Suppose an Apple with some small improvement that bears on Taste (Apple+) is better than the Apple, with respect to Taste.
11. Apple+ is not better than the Orange, with respect to Taste.
12. Therefore, the Apple and the Orange are not related by any of the standard trichotomy of relations, with respect to Taste. (This is the Small Improvement Argument)

13. The Apple is better than a Rotten Apple, with respect to Taste.
14. The Orange is also better than the Rotten Apple, with respect to Taste.
15. Therefore, the Apple and the Orange are comparable, with respect to Taste. (This is the Chaining Argument)

16. Given 12 and 15, there must be a fourth comparative relation, namely, the parity relation. (This is the Parity Conclusion)

This Apple/Orange example should be analogous to Chang’s Mozart/Michaelangelo example.

It should be clear that the notion of Taste is ambiguous here, as it can have many meanings. To keep things simple, let us stipulate that there are just two factors that affect the taste of apples: a) sweetness and b) crunchiness. Let us also stipulate that there are just two factors that affect the taste of oranges: c) sweetness; and d) the softness of the pulp. Sweetness is chosen as a factor because it seems to be a factor that apples and oranges can share. Crunchiness for apples is chosen because it seems to be a factor that oranges cannot share; and similarly, the softness of the pulp for oranges is chosen because it seems to be a factor that apples cannot share.

Suppose by Taste, we mean sweetness. Then the Small Improvement Argument would look like the following:

17. Suppose an Apple is neither better nor worse than an Orange, with respect to sweetness.
18. Suppose an Apple with some small improvement that bears on sweetness (Apple+) is better than the Apple, with respect to sweetness.
19. Apple+ is not better than the Orange, with respect to sweetness.
20. Therefore, the Apple and the Orange are not related by any of the standard trichotomy of relations, with respect to sweetness.

But on the understanding that Taste means sweetness, it is not obvious that 19 would be true. If 17 and 18 were really true, then conceivably, Apple+ could be better than the Orange with respect to sweetness.

Suppose by Taste, we mean instead sweetness and crunchiness. Then the Small Improvement Argument would look like the following:

21. Suppose an Apple is neither better nor worse than an Orange, with respect to sweetness and crunchiness.
22. Suppose an Apple with some small improvement that bears on sweetness and crunchiness (Apple+) is better than the Apple, with respect to sweetness and crunchiness.
23. Apple+ is not better than the Orange, with respect to sweetness and crunchiness.
24. Therefore, the Apple and the Orange are not related by any of the standard trichotomy of relations, with respect to sweetness and crunchiness.

In this case, the Small Improvement Argument would be valid. But now consider the Chaining Argument on an understanding of Taste that takes it to mean sweetness and crunchiness:

25. The Apple is better than a Rotten Apple, with respect to sweetness and crunchiness
26. The Orange is also better than the Rotten Apple, with respect to sweetness and crunchiness.
27. Therefore, the Apple and the Orange are comparable, with respect to sweetness and crunchiness.

As one can see, 26 would be false, since the Orange cannot be crunchy. Therefore, the Chaining Argument would not be valid. If so, the Parity Conclusion would also not follow.
None of this means that the Chaining Argument can never be valid. It can be valid if the attributes to be compared are shared by the two things being compared. In the case of comparing the Apple with the Orange, comparing their sweetness would allow the Chaining Argument to be valid. For example,

28. The Apple is better than a Rotten Apple, with respect to sweetness.
29. The Orange is also better than the Rotten Apple, with respect to sweetness.
30. Therefore, the Apple and the Orange are comparable, with respect to sweetness.

The Chaining Argument would be valid here. However, this does not mean that the Parity Conclusion would follow. In fact, as we have already seen, if Taste were understood as just sweetness, then the Small Improvement Argument would fail. If so, the Parity Conclusion would not follow.

3. Chang’s Mozart and Michaelangelo Reconsidered
I shall now apply the lessons above to Chang’s example of Mozart and Michaelangelo.

First, like Taste, the notion of Creative Genius is also ambiguous. To keep things simple, let us stipulate that there are just two factors that affect its attribution to a composer’s work: a) imaginativeness; and b) interesting contrasts in the music. Let us also stipulate that there are just two factors that affect the attribution of CG to a sculptor’s work: c) imaginativeness; and d) expressiveness of the sculpture. Imaginativeness is chosen as a factor because it seems to be one that a composer and a sculptor can share with respect to CG. Interesting contrasts in the music for composers is chosen because it seems to be a factor that a sculptor cannot share; and similarly, expressiveness of the sculpture is chosen because it seems to be a factor that a composer cannot share.

Suppose by CG, we mean imaginativeness. Then the Small Improvement Argument would look like the following:

31. Mozart is neither better nor worse than Michaelangelo, with respect to imaginativeness.
32. A Mozart who has some small improvement that bears on CG, namely, he shows a bit more imaginativeness in his compositions, (Mozart+) is better than Mozart, with respect to imaginativeness.
33. Mozart+ is not better than Michaelangelo, with respect to imaginativeness.
34. Therefore, Mozart and Michaelangelo are not related by any of the standard trichotomy of relations, with respect to CG. (This is the Small Improvement Argument)

But on the understanding that CG means imaginativeness, it is not clear that 33 would be true. That is, if 31 and 32 were really true, then conceivably, Mozart+ could be better than Michaelangelo with respect to imaginativeness.

Suppose by CG, we mean instead imaginativeness and interesting contrasts in the music. Then the Small Improvement Argument would look like the following:

35. Mozart is neither better nor worse than Michaelangelo, with respect to imaginativeness and interesting contrasts in the music.
36. A Mozart who has some small improvement that bears on CG, namely, he shows a bit more imaginativeness and interesting contrasts in his compositions, (Mozart+) is better than Mozart, with respect to imaginativeness and interesting contrasts in the music.
37. Mozart+ is not better than Michaelangelo, with respect to imaginativeness and interesting contrasts in the music.
38. Therefore, Mozart and Michaelangelo are not related by any of the standard trichotomy of relations, with respect to imaginativeness and interesting contrasts in the music. (This is the Small Improvement Argument)

In this case, the Small Improvement Argument would be valid. But now consider the Chaining Argument on an understanding of CG that takes it to mean imaginativeness and interesting contrasts in the music:

39. Mozart is better than Talentlessi, a very bad music composer, with respect to imaginativeness and interesting contrasts in the music.
40. Michaelangelo is also better than Talentlessi, with respect to imaginativeness and interesting contrasts in the music.
41. Therefore, Mozart and Michaelangelo are comparable, with respect to imaginativeness and interesting contrasts in the music.

As one can see, 40 would be false, since one cannot attribute ‘interesting contrasts in the music’ to Michaelangelo. Therefore, the Chaining Argument would not be valid. If so, the Parity Conclusion would also not follow.

Again, this does not mean that the Chaining Argument can never be valid in the Mozart/Michaelangelo example. For example, comparing the imaginativeness of their works would allow the Chaining Argument to be valid.

42. Mozart is better than Talentlessi, a very bad music composer, with respect to imaginativeness.
43. Michaelangelo is also better than Talentlessi, with respect to imaginativeness.
44. Therefore, Mozart and Michaelangelo are comparable, with respect to imaginativeness.

The Chaining Argument would be valid here. Still, as we have already seen, if CG were understood as just imaginativeness, then the Small Improvement Argument would fail. If so, the Parity Conclusion would still not follow.

4. Conclusion
Chang’s argument for parity appears to work because it contains ambiguities. Properly disambiguated, her argument fails. The parity relation may or may not exist. But Chang’s argument fails to show that it does.


Comments

  1. 1. Posted by Guy Kahane | June 1, 2007 3:50 pm

    Matthew,

    Let me start the discussion by asking for a clarification. Your argument against parity can be understood in two distinct way. On the first, your claim is that the value concepts ‘taste’ and ‘creative genius’ ARE ambiguous. Chang and others reach mistaken conclusions because they fail to notice this ambiguity. On the second, your claim is that these concepts MIGHT be ambiguous. If they are, we’d get the same pattern of argument that seems to support the parity view, but we’d be wrong to conclude it does unless we can rule out the possibility of ambiguity.

    Your remarks suggest you take the first, stronger view. You write “It should be clear that the notion of Taste is ambiguous here, as it can have many meanings,” and “like Taste, the notion of Creative Genius is also ambiguous.” But this are just assertions, and so far as I can see not supported by what you say in the post. You go on to STIPULATE a simple ambiguity, to ‘keep things simple’. This is more in line with my second, weaker reading. In order to support the stronger reading, you’ll need to SHOW that there’s an ambiguity, even if later it would be legitimate for you to simplify things to keep the argument simpler.

    Let me now issue two worries. The first is precisely about ‘keeping things simple’. This suggests that the ambiguity is actually far more extensive. And for your argument to go through, these multiple ambiguities should be one we often fail to detect. But this is implausible. It would imply that in much talk and debate about, say, creative genius people are just talking past each other. They are talking about lots of different things, and can’t themselves keep track of what they’re talking about from one moment to the next.

    More worryingly, to my mind, is that your version of argument requires that people unwittingly shift between the different senses in a very particular way. This is especially true of your reading of the Chaining Argument. But this seems to me implausible. If the term is ambiguous, then different people should be using the two (or more) different senses in ALL contexts, and thus many would have to disagree with Chang’s conclusion. But so far as I can see, this empirical prediction is incorrect. This supports Chang’s conclusion.

    No doubt there are different features upon which valuations of taste or creative genius supervene in the different contexts. But these could be said to be ‘creative genius-making’ features, not different meanings or even contained in the meaning of ‘creative genius’. Ascriptions of creative genius would involve holistic responses to patterns of such features in each case. And it seems to me certainly conceivable, and fairly probable, that there will be cases where we can compare the creative genius of X and Y although neither share a particular creative genius-making feature.

  2. 2. Posted by S. Matthew Liao | June 2, 2007 1:03 am

    Guy,

    First of all, many thanks for those excellents remarks. Secondly, let me comment on your remarks first. I shall then make some general remarks.

    You said:

    Your argument against parity can be understood in two distinct way. On the first, your claim is that the value concepts ‘taste’ and ‘creative genius’ ARE ambiguous. . . On the second, your claim is that these concepts MIGHT be ambiguous.

    I do intend to make the first claim.

    You said:

    Your remarks suggest you take the first, stronger view. You write “It should be clear that the notion of Taste is ambiguous here, as it can have many meanings,” and “like Taste, the notion of Creative Genius is also ambiguous.” But this are just assertions, and so far as I can see not supported by what you say in the post. You go on to STIPULATE a simple ambiguity, to ‘keep things simple’. This is more in line with my second, weaker reading. In order to support the stronger reading, you’ll need to SHOW that there’s an ambiguity, even if later it would be legitimate for you to simplify things to keep the argument simpler.

    I think there is a misunderstanding here. I think that the notions of Taste and Creative Genius are ambiguous in at least those two ways. At least I have that intuition. In fact, I believe that there are even more senses of Taste and Creative Genius. What I am stipulating therefore is the number of ambiguities we should be considering, and not the idea that there is an ambiguity.

    You said:

    Let me now issue two worries. The first is precisely about ‘keeping things simple’. This suggests that the ambiguity is actually far more extensive. And for your argument to go through, these multiple ambiguities should be one we often fail to detect. But this is implausible. It would imply that in much talk and debate about, say, creative genius people are just talking past each other. They are talking about lots of different things, and can’t themselves keep track of what they’re talking about from one moment to the next.

    In fact, I think they are. When people discuss whether Roger Federer is better than Tiger Woods, I think that often they are just talking past each other. Sometimes they are talking about their dominance of a sport. Sometimes they are referring to their athletic abilities. And so on. I feel that when they talk about ‘better than,’ if they specified ‘with respect to what,’ then they would be able to come to some agreement.

    You said:

    your version of argument requires that people unwittingly shift between the different senses in a very particular way. . . But this seems to me implausible. If the term is ambiguous, then different people should be using the two (or more) different senses in ALL contexts, and thus many would have to disagree with Chang’s conclusion. But so far as I can see, this empirical prediction is incorrect.

    My particular stipulations of the notions of Taste and Creative Genius are meant just to be examples. So I am certainly not claiming that Chang or others are ambiguating in exactly those ways. I am claiming though that they are ambiguating in some ways. See above my remarks about Federer and Woods. People may not be disagreeing with Chang yet because they have not noticed that there are ambiguities in these terms. That’s at least what I am trying to point out.

    Your said:

    No doubt there are different features upon which valuations of taste or creative genius supervene in the different contexts. But these could be said to be ‘creative genius-making’ features, not different meanings or even contained in the meaning of ‘creative genius’. Ascriptions of creative genius would involve holistic responses to patterns of such features in each case. And it seems to me certainly conceivable, and fairly probable, that there will be cases where we can compare the creative genius of X and Y although neither share a particular creative genius-making feature.

    I am sceptical about your claim that we can compare the creative genius of X and Y though neither share a particular creative genius-making feature.

    Though it may not have been clear, it may be worth pointing out that I have considered the scenarios in which the notions of Taste and Creative Genius are understood in the same way throughout the argument, in particular, as sweetness and as imaginativeness. However, I have argued that understood in these ways, the argument for parity still does not go through.

    A few general remarks, which hopefully will clarify my position:

    1. Obviously I am not claiming that every concept contains ambiguities. However, I do believe that as a matter of fact, the notions of Taste and Creative Genius are ambiguous in at least the two ways I have specified.

    2. I am not claiming that more specific concepts such as sweetness and crunchiness could not be aggregated (or combined in a holistic way, to use your term) to form a more general concept such as Taste. However, to continue with this example, suppose that one also aggregates sweetness and the softness of the pulp, then I believe that one should understand that this notion of Taste is different from a notion of Taste that involves the aggregation of sweetness and crunchiness.

    3. My argument is meant to be a negative argument against Chang’s argument. It’s not meant to be a general argument against parity. So I am open to the possibility that someone can come up with an example that does not contain the kind of ambiguities that I think Chang’s example has, and that allows the Parity Conclusion to obtain. But I’d have to see that example first.

  3. 3. Posted by Guy Kahane | June 4, 2007 8:11 pm

    Thanks for the clarification. Let me just issue a quick reply to the reply. I may have more to say if I think about this further.

    I did understand that the examples of ambiguity you used in your post were meant to be examples of possibly wider ambiguities. One thing I worried about was that your ambiguity claim nevertheless did amount to a stipulation. A semantic argument is needed to show that these notions are ambiguous, whereas the weaker argument just needs the claim that they might be.

    We should hope that there are independent semantic criteria for the presence of ambiguity that we could appeal to decide the truth of this claim, otherwise it would seem simply question-begging to your opponents. I worry, for example, about the way you dismiss many common disagreements about e.g. creative genius as due to confusion about ambiguity. The semantics of such ordinary terms presumably must supervene on their use, or their standard use, or their correct use, and if you need to commit yourself to the claim that this use is itself founded on error, your challenge to Chang seems significantly weaker.

  4. 4. Posted by Richard Chappell | July 15, 2007 1:36 am

    Matthew, let’s simply form an holistic aggregate Taste* (or CG*) of all the components you allege “Taste” (“CG”) to be ambiguous between. Then the parity argument should work, right?

  5. 5. Posted by S. Matthew Liao | July 15, 2007 8:31 pm

    Richard, it depends on what is in the aggregate. If the aggregate contains components that are shared by the things being compared, then I think the Small Improvement would not work. If the aggregate contains components not shared by the things being compared, then I think the Chaining Argument would not work.

    It might be helpful to say here that I’m not against aggregating the various components. What I am claiming though is that for a particular comparision, the metrics of comparison has to be consistent across the things being compared. Otherwise, one should not be surprised to find strange results. So, in effect, I am claiming that Chang has not been consistent with respect to her metrics of comparison, and that once one is consistent, it is not obvious (at least to me) that there is such a thing as a parity relation.

  6. 6. Posted by Richard Chappell | July 16, 2007 12:28 am

    If the aggregate contains components not shared by the things being compared, then I think the Chaining Argument would not work.

    I expect that Chang would deny this. It just seems plainly true that “Michaelangelo is better than Talentlessi” with respect to the holistic totalities of their creative genius, even if their is no non-holistic scale against which to compare them. We have the holistic scale, and it generally works just fine. However, because there’s some degree of vagueness as to how much each individual component contributes to the whole, we need the “parity” relation (or vague equality) in addition to the relations of strict equality and inequality.

    At least, that’s how I’d understand Chang’s claims. I can see how you’re proposing an alternative conception of things. But I can’t see that you’ve shown anything wrong with this one. (It seems more like you’re smuggling in premises that simply presuppose the holistic picture to be mistaken — e.g. assuming that you can reduce taste to its individual components.)

  7. 7. Posted by Richard Chappell | July 16, 2007 12:30 am

    sorry, typo: “even if there is no…”

  8. 8. Posted by S. Matthew Liao | July 16, 2007 2:14 am

    Richard, thanks for the rejoinder. See if this helps. Notice that the Chaining Argument has two premises, not just one:

    5. Mozart is better than Talentlessi, a very bad music composer, with respect to CG.
    6. Michaelangelo is also better than Talentlessi, with respect to CG.
    7. Therefore, Mozart and Michaelangelo are comparable, with respect to CG. (This is the Chaining Argument)

    So this is my claim: Use whatever holistic metric you like. The metrics of comparison for the two premises must be the same. That means that their components must be the same. If you use metric (x,y,z) for one premise, and metric (x,y,w) for the other, you shouldn’t be surprised that the Chaining Argument does not go through.

    I don’t see how assuming that “their components must be the same” means that I am presupposing the holistic picture to be mistaken. Metrics (x,y,z) and (x,y,w) are both holistic.

    Also, I’m not objecting to vagueness. Metrics (x,y,z) or (x,y,w) may each be vague in its own way. What I am objecting to is the inconsistent use of metrics for a particular comparison.

  9. 9. Posted by Richard Chappell | July 16, 2007 5:32 am

    Now I’m confused. I thought we had agreed to use the same complete, totalizing metric Taste* (say: x,y,z AND w) throughout. Now you’re back to talking about incomplete metrics that each leave out various components. That is simply to ignore my earlier suggestion!

  10. 10. Posted by S. Matthew Liao | July 16, 2007 11:15 am

    I was responding to your #6, which appears to challenge my claims about the Chaining Argument. Let’s take stock then. Say you use metric (x, y, z and w). Either this metric is applicable to all the relevant premises or it is not. If it is (by this, I mean that x,y,z,and w are components shared by the premises), the Small Improvement Argument will not work. Recall that the Small Improvement Argument is

    1. Mozart is neither better nor worse than Michaelangelo, with respect to Creative Genius (CG).
    2. A Mozart who has some small improvement that bears on CG (Mozart+) is better than Mozart, with respect to CG.
    3. Mozart+ is not better than Michaelangelo, with respect to CG.
    4. Therefore, Mozart and Michaelangelo are not related by any of the standard trichotomy of relations, with respect to CG. (This is the Small Improvement Argument)

    3, I claim, will not be true.

    On the other hand,if one or more of the components (e.g. w) is not applicable in one premise, and another or more of the components (e.g. z) is not applicable in the other premise, then the Chaining Argument will not work. This is because although initially it looks like one is using the same metric, in fact, one is not. One is instead doing what I said in #8.

    Note that I’m still not denying one can use holistic metrics nor am I denying that these metrics can be vague. I think that vagueness is not the problem here, as a number of people have thought; rather, it is ambiguities.

  11. 11. Posted by Richard Chappell | July 17, 2007 1:15 am

    Consider the following case: Mozart is worth 100w, and Michelangelo is worth 100z, and Mozart+ is worth 101w. Let CG be a scale holistically combining w and z, but such that there is some vagueness in their relative weightings (i.e. whether a unit of w can outweigh a unit of z, or vice versa).

    The following claims are then consistent:

    1. Mozart is neither better nor worse than Michaelangelo, with respect to CG. (Because it is not determinate that each unit of w or z outweighs the other.)

    2. Mozart+ is better than Mozart, with respect to CG. (Because 101w determinately outweighs 100w.)

    3. Mozart+ is not better than Michaelangelo, with respect to CG. (Because it is not determinate that 101w outweighs 100z.)

    So the small improvement argument works. Now add in ‘Talentlessi’, who is much worse than Mozart, being worth only 5w. Then the chaining argument also works:

    6. Michaelangelo is also better than Talentlessi, with respect to CG. (Because 100z determinately outweighs a mere 5w.)

    I have used the same holistic scale (CG) throughout. Which claim do you think is false?

  12. 12. Posted by S. Matthew Liao | July 17, 2007 2:37 am

    Your appeal to vagueness actually undermines Chang’s argument that there is the parity relation, because the parity relation is supposed to be a determinate relation. For this reason, Chang argues extensively in her paper against vagueness.

    More specifically, 1 is false on a vagueness account. If it is vague as to whether Mozart is better or worse than Michaelangelo or equally good, then, it is not true that Mozart *is* neither better nor worse than Michaelangelo or equally good. On the usual account of vagueness, what one should say instead is that Mozart is indeterminately better (or worse or equally good) than Michaelangelo. On Williamson’s account, it is a determinate matter whether Mozart is better (or worse or equally good) than Michaelangelo; we just don’t know where the line is. Compare: if it is vague as to whether John is bald or not, then it is not true that John is neither bald nor not bald. On the usual account of vagueness, what is true is that John is indeterminately bald. On Williamson’s account, it is a determinate matter whether John is bald or not; we just don’t know where the line is.

    If 1 is false, then (a few other premises are false and) 4 does not follow. And the Parity Conclusion does not obtain.

  13. 13. Posted by Richard Chappell | July 17, 2007 5:35 am

    Much depends on where we locate the vagueness. Note in particular that I never claimed that “it is vague as to whether Mozart is better or worse than Michaelangelo or equally good.” That is, I never claimed that one’s position on the CG scale is vague. Rather, what’s vague is how much of a contribution each sub-component makes to the holistic aggregate. We can avoid ultimate vagueness simply by adding the ‘DET’ operator as a final step in the internal process, before producing the “CG” outcome.

    To clarify, consider the following definitional principle:

    (BETTER) X is better than Y with respect to CG iff X’s subcomponents determinately outweigh Y’s subcomponents.

    This renders CG relations perfectly determinate, despite internal vagueness (at the level of weighing subcomponents). In particular, it is perfectly determinate that premise (1) is true on this account. Mozart is determinately not better than Michelangelo, in virtue of his component skills failing to determinately outweigh the latter’s within CG’s internal calculus.

    That’s one possible formalization of Chang’s intuitive ideas, anyway. (My main aim was simply to show that a charitable interpretation of her argument can easily avoid imputing “ambiguity”. It’s another question whether it can avoid problematic vagueness. I think it can on my model. But even if not, we’ve seen no general reason to think that this must be a problem for any interpretation of her argument that avoids ambiguity.)

  14. 14. Posted by S. Matthew Liao | July 17, 2007 12:39 pm

    I’m afraid I don’t understand your response. But let me have a go at it. As I understand your presentation, the comparative relations (that is, the comparative relations between the subcomponents) in 1 and 3 are vague but comparable. You said:

    Let CG be a scale holistically combining w and z, but such that there is some vagueness in their relative weightings (i.e. whether a unit of w can outweigh a unit of z, or vice versa).

    So, first of all, I have assumed that you take it that w and z are subcomponents that are shared by all the premises.

    Secondly, as I have said, 1 and 3 are false on such a vagueness interpretation (to keep things simple, I’ll just use Williamson’s account of vagueness), because on such an interpreation there is a fact of a matter as to whether one is better than the other or that they are equally good; even if epistemically speaking, we may not know it.

    Put it differently, You said:

    (BETTER) X is better than Y with respect to CG iff X’s subcomponents determinately outweigh Y’s subcomponents.

    From this, I take it that you also believe this (otherwise, I don’t know what you mean by ‘it is not determinate.’ Actually this is one reason why I’m not sure if I understood your response. So perhaps you can clarify):

    (NOT BETTER OR WORSE OR EQUALLY GOOD) X is not better or worse or equally good than Y with respect to CG iff it is not determinate whether X’s subcomponents outweighs Y’s subcomponents.

    This is false on a vagueness reading of ‘it is not determinate.’ On such a reading, there is a fact of the matter as to whether the subcomponents of X is better or worse or equally good than the subcomponents of Y with respect to CG. We may just epistemically not know it. In other words, your talk of ‘internal calculus’ just shifts the vagueness problem a level down, but does not solve it.

    So rather than being charitable to Chang’s argument, I think your response undermines it.

    Since Chang has rejected vagueness, I have therefore also assumed for the purpose of my analysis that we are not dealing with vagueness. It is in this context that ambiguities are relevant.

  15. 15. Posted by Richard Chappell | July 17, 2007 1:52 pm

    Right, I endorse the (NOT BETTER OR WORSE OR EQUALLY GOOD) [but certainly a mouthful!] principle. I’ll abbreviate this to “(PARITY)”

    Granting an epistemic account of vagueness, (PARITY) is false iff we understand a CG value to be the raw sum of its subcomponents (w + z). But I instead recommend an alternative, more complex construction. In particular, I meant for (BETTER) and similar principles to be understood as stipulative. They are built into the definition of holistic values.

    I thus propose to construct a value CG from subcomponents (w,z) according to the following definitions:
    (i) X is better than Y with respect to CG =df X’s subcomponents determinately outweigh Y’s subcomponents.
    (ii) X is worse than Y with respect to CG =df X’s subcomponents are determinately outweighed by Y’s subcomponents.
    (iii) X is equal to Y with respect to CG = df X’s subcomponents are determinately equal in weight to Y’s subcomponents.

    (PARITY) straightforwardly follows from these definitions.

    To generalize: we define a standard ordering relation to hold “with respect to CG” iff that ordering relation holds determinately over the relevant subcomponents. CG is thus a two-step construction: first aggregate to form a “proto-CG” value, then apply the DET operator to any ordering relations (where DET p is true iff p is determinately true). You interpreted me as stopping as the “proto-CG” stage; in fact I’m proposing a further step, which removes the vagueness.

    To illustrate: it is vague/indeterminate whether Mozart’s proto-CG value (100w + 0z) outweighs Michelangelo’s (0w + 100z). So it is false that Mozart’s proto-CG determinately outweighs Michelangelo’s. Thus, by definition (i), it is simply false that Mozart is better than Michelangelo with respect to CG.

    (He might be indeterminately better with respect to proto-CG. But that’s different.)

    Is that any clearer?

  16. 16. Posted by S. Matthew Liao | July 17, 2007 4:25 pm

    Three comments. First, you said:

    (PARITY) straightforwardly follows from these definitions.

    I don’t think it does. If one subcomponent (w) is not better or worse than (z) or equally good as (z), it could be the case that the two are just incommensurate, by which I mean that the two cannot be compared.

    Secondly and relatedly, if PARITY were true as a matter of stipulation, then Chang’s argument would become circular. That is, PARITY shouldn’t feature as a premise in an argument that results in the Parity Conclusion. Chang’s argument purports to work instead by exclusion.

    Thirdly, you said:

    To illustrate: it is vague/indeterminate whether Mozart’s proto-CG value (100w + 0z) outweighs Michelangelo’s (0w + 100z). So it is false that Mozart’s proto-CG determinately outweighs Michelangelo’s.

    On the vagueness interpretation, it is not false that there is a fact of the matter whether Mozart’s proto-CG outweighs Michaelangelo’s; whether we know this or not is a separate question.

    You go on to say:

    Thus, by definition (i), it is simply false that Mozart is better than Michelangelo with respect to CG.(He might be indeterminately better with respect to proto-CG. But that’s different.)

    Given what I have just said, on the vagueness interpretation, there is a fact of the matter whether Mozart is better than Michaelangelo; whether we know this or not is a separate matter. So 1 and 3 are both false.

    As I noted in the my previous comment, I think your talk of ‘internal calculus’ just shifts the vagueness problem down a level down, but does not solve it.

  17. 17. Posted by Richard Chappell | July 18, 2007 12:20 am

    Well, I mean for (PARITY) to be a basic axiom of my formal model. There’s always the further question of whether it’s a good model, i.e. whether it yields intuitive outcomes. That’s where Chang’s argument comes in. If her premises were implausible, then so would be my model. But my formalization illustrates one way that we could understand the values being appealed to, in such a way as to make Chang’s argument valid. So I don’t see anything circular about this. (In particular, my formalization doesn’t assume her premises are true. It simply provides one interpretation of what their truth would consist in.)

    Anyway, the third issue you raise is the key one. You deny the inference from
    (a) it is vague/indeterminate whether X outweighs Y.
    to
    (b) it is false that X determinately outweighs Y.

    Frankly, I’m baffled. There’s no room for dispute here: (b) is simply a rewording of (a). For a fact to determinately obtain is simply for it to obtain as a non-borderline (i.e. non-vague) instance.

    You say:

    On the vagueness interpretation, it is not false that there is a fact of the matter whether Mozart’s proto-CG outweighs Michaelangelo’s; whether we know this or not is a separate question.

    This is irrelevant, as I never made any claim to the contrary. I claimed that it is false that there is a DETERMINATE fact of the matter. You can’t just ignore my use of the DET operator, it’s absolutely central to my case! And fairly standard too, I believe — cf. the Stanford encyclopedia (1998):

    The object language can be extended to include an operator `It is determinate (or definite) that …’ (`Det’) appropriate to the expression of vagueness in the object language. The vagueness of expressions like `heap’ is characterised by their possessing border cases; this can now be expressed as the existence of cases which are neither determinately heaps nor determinately non-heaps.

  18. 18. Posted by S. Matthew Liao | July 18, 2007 2:16 am

    You’ve misunderstood my point. You said,

    You deny the inference from
    (a) it is vague/indeterminate whether X outweighs Y.
    to
    (b) it is false that X determinately outweighs Y.

    I’m not denying this inference nor your use of the DET operator. As you said,”(b) is simply a rewording of (a).”

    My point is that (a) and (b) can both be true, and yet it is not false that there is a fact of the matter whether Mozart’s proto-CG outweighs Michaelangelo’s.

    You seem to accept this point too since you said “I never made any claim to the contrary.”

    But from the fact that “there is a fact of the matter whether Mozart’s proto-CG outweighs Michaelangelo’s,” a point which you do not deny, it follows that there is a fact of the matter whether Mozart is better than Michaelangelo; whether we know this or not is a separate matter.

  19. 19. Posted by Richard Chappell | July 18, 2007 5:08 am

    Okay, in that case we are back at the problem I noted in comment #15: you are stopping at proto-CG, and ignoring my further step. You’ve merely shown that there is a fact of the matter whether Mozart is better than Michelangelo with respect to proto-CG. But no-one cares about “proto-CG”, it’s just a meaningless internal variable employed by my model for purely technical purposes.

    What we care about is the true value, CG: the final output of the model. And with respect to CG, your final paragraph is simply a non-sequitur. The only way to move from facts about proto-CG to facts about CG itself is via the definitions (i)-(iii). And if you do that, we get the desired result: Mozart is not better than Michelangelo with respect to CG. (And note that this fact holds determinately.)

  20. 20. Posted by S. Matthew Liao | July 18, 2007 11:56 am

    I think we have a real disagreement here because if it could be true that Mozart is better than Michaelangelo with respect to CG, and on a vagueness account, I don’t see that you have shown otherwise, then it’s false to claim that Mozart is not better than Michaelangelo with respect to CG.

    You need a fourth definition, namely PARITY, to get the conclusion you want, and I have said that PARITY doesn’t follow from (i)-(iii). While (i)-(iii) may be true, PARITY is not.

  21. 21. Posted by Richard Chappell | July 19, 2007 12:05 am

    Technically, that can’t be right: it could be that Michelangelo never created any art at all, in which case Mozart was easily better than him with respect to Creative Genius. But nothing of interest follows from this distant possibility. (In particular, it doesn’t follow that “it’s false to claim that Mozart is not better than Michaelangelo with respect to CG.”)

    I guess what you mean to suggest is that even holding fixed the base facts (in particular, that it is vague whether one’s subcomponents or proto-CG value outweighs the other’s), on my model it could still “be true that Mozart is better than Michaelangelo with respect to CG.” But this is false, and betrays a misunderstanding of my model.

    One last time, here is my argument:

    [axiom] (i) X is better than Y with respect to CG =df X is determinately better than Y with respect to proto-CG.

    [premise] (a) it is vague/indeterminate whether X is better than Y with respect to proto-CG

    Thus [from a] (b) it is false that X is determinately better than Y with respect to proto-CG.

    Thus [from i, b] (c) it is false that X is better than Y with respect to CG.

    This argument is logically valid. (i) is an axiom of my model, and you have already granted the premise (a) [and the inference to (b)]. Together, these straightforwardly entail the conclusion (c).

  22. 22. Posted by Richard Chappell | July 19, 2007 2:56 am

    Okay, I’ve unified my scattered argument and presented it more clearly, in a new post: Parity of Value: a formal model.

    Thanks for all the help in getting me to iron out the kinks!

  23. 23. Posted by S. Matthew Liao | July 19, 2007 12:15 pm

    I’ll have a go one last time too. Your formalization of (i)-(iii) is irrelevant for the purpose of this debate. What is relevant is how to understand the idea ‘not better than or worse than or equal to.’ If that idea is understood in terms of vagueness, it will already have undermined Chang’s argument (Chang is very explicit about this. See Chang’s own arguments against vagueness).

    More specifically, following your rationale, you subscribe to

    (iv) (NOT BETTER OR WORSE OR EQUALLY GOOD) X is not better or worse or equally good than Y with respect to CG iff it is not determinate whether X’s subcomponents outweighs Y’s subcomponents.

    As I have said, (iv) is false on a vagueness reading of ‘it is not determinate.’ On such a reading, there is a fact of the matter as to whether the subcomponents of X is better or worse or equally good than the subcomponents of Y with respect to CG.

    Since (iv) is false, it doesn’t matter if it follows from (i)-(iii) or not. As it happens, I don’t think it follows from (i)-(iii). It’s just false simpliciter.

    And since (iv) is false, this affects the whole of Chang’s argument. It affects premise 1. And a result it also affects premise 3, and so on.

    It is no good to show that premise 3 can be interpreted in terms of (i), because, as I said, what is relevant is (iv). Since (iv) is false, (c) in #21 is a nonsequitur.

  24. 24. Posted by Ruth Chang | July 19, 2007 7:23 pm

    Thanks to Richard for alerting me to these postings. I’m a blog newbie so forgive any conventions I might flout.

    I read through the whole shebang quickly and thought I’d throw in the following two cents about Matthew’s nice argument (thanks!) against my argument for the possibility of parity.

    First cent. Matthew’s argument seems to be that if the covering concept (CC) with respect to which comparisons are made is disambiguated and one fixes on a single unambiguous concept as one’s CC, one can’t get both the small improvement argument (SIA) and the Chaining Argument to work. But his argument for this conclusion seemed to turn on two mistaken assumptions.
    Forgetting about Mozart and Michelangelo and sticking with fruit, essentially Matthew’s argument is that if we attempt to compare and apple and an orange with respect to tastiness, we can’t fix on a single disambiguated notion of tastiness according to which both the SIA and Chaining Argument would work.
    Let’s just grant that the word ‘tastiness’ covers two quite distinct concepts, one sweetness and the other some function of sweetness and crunchiness.
    Here’s what Matthew says:

    “Suppose by Taste[iness], we mean sweetness. Then the Small Improvement Argument would look like the following:
    17. Suppose an Apple is neither better nor worse than an Orange, with respect to sweetness.
    18. Suppose an Apple with some small improvement that bears on sweetness (Apple+) is better than the Apple, with respect to sweetness.
    19. Apple+ is not better than the Orange, with respect to sweetness.
    20. Therefore, the Apple and the Orange are not related by any of the standard trichotomy of relations, with respect to sweetness.
    But on the understanding that Taste means sweetness, it is not obvious that 19 would be true. If 17 and 18 were really true, then conceivably, Apple+ could be better than the Orange with respect to sweetness.”

    Matthew wants to conclude that the SIA doesn’t work if the CC is ‘sweetness’. But this is to misunderstand the SIA. The claim is not that there are no apples and oranges for which 17-20 are false. It is rather that there are some apples and oranges for which 17-20 are true. It is of course true that “conceivably, Apple+ could be better than the Orange with respect to sweetness.”

    I agree with this claim. My point instead is that there could be some Apple+ for which 19 is true. The point of the SIA is that there are some cases in which you can have premises 17 and 18 satisfied wrt a CC and yet 19 hold. The SIA does not say it is inconceivable that if 17 and 18 hold that 19 not hold. It seems plausible that there is an apple neither sweeter nor less sweet than an orange such that if the apple were improved in sweetness a touch, it would nonetheless till be neither sweeter nor less sweet than the orange. So the SIA works if ‘tastiness’ is understood as sweetness.
    What about the Chaining Arg? Strictly, we need to fix on those apples, apples+ and oranges for which 17-20 is true. The Chaining Argument is supposed to hold for at least some of the cases in with the SIA holds. (It may not hold for all b/c of what I called the Aristotelian and Hegelian provisos).

    By Matthew’s lights the Chaining argument for sweetness is valid. He writes:

    “In the case of comparing the Apple with the Orange, comparing their sweetness would allow the Chaining Argument to be valid. For example,
    28. The Apple is better than a Rotten Apple, with respect to sweetness.
    29. The Orange is also better than the Rotten Apple, with respect to sweetness.
    30. Therefore, the Apple and the Orange are comparable, with respect to sweetness.
    The Chaining Argument would be valid here.”

    I agree. So we now have an example involving apples, oranges and sweetness that supports parity.
    That is enough to show that the argument against parity Mathew suggests doesn’t work. But Matthew’s argument has a second part that raises important issues about the unity of concepts and ‘noncomparability’, so I’d like to say something about that part too.
    Matthew goes on to suggest that if we take ‘tastiness’ to mean some function of ‘sweetness and crunchiness’ then the SIA works but not the Chaining Arg. Let’s grant, as Matthew does, that the SIA involving apples, oranges, and the CC that is some function of ‘sweetness and crunchiness’ goes through. Now the question is whether the Chaining Arg works for at least some of these cases.
    Here’s Matthew’s arg about this:

    “…now consider the Chaining Argument on an understanding of Taste that takes it to mean sweetness and crunchiness:
    25. The Apple is better than a Rotten Apple, with respect to sweetness and crunchiness
    26. The Orange is also better than the Rotten Apple, with respect to sweetness and crunchiness.
    27. Therefore, the Apple and the Orange are comparable, with respect to sweetness and crunchiness.
    As one can see, 26 would be false, since the Orange cannot be crunchy. (Hmmm. I note that Matthew lives in Oxford – I’ve had many a distastefully crunchy so-called orange there…) Therefore, the Chaining Argument would not be valid. If so, the Parity Conclusion would also not follow.”

    Why should we think that 26 is false? There are two relevant possibilities here. 1) either (the function of) ‘sweetness and crunchiness’ must be understood as a mere conjunction of two evaluative dimensions, or 2) the function is not mere conjunction but some ‘holistic’ function of these components that involves some normative relations between them.

    Take the first possibility. If we are attempting to compare an apple and orange with respect to a mere conjunction of CCs not all of which ‘cover’ both items, I myself have suggested that it won’t be determinately true that a positive comparative relation holds between them wrt that conjunction of CC. The cases I focused on were ones in which the predicate associated with one of the concepts didn’t have within its domain of application the one of the items being compared. So I thought it wasn’t true that fried eggs are better than the number nine with respect to tastiness. Similarly, it wouldn’t be true that fried eggs are better than the number nine with respect to the mere conjunction of tastiness and beauty as an abstract number. So if we take ‘sweetness and crunchiness’ as a mere conjunction of two evaluative dimensions, at least one of which does not ‘apply’ to one of the items being compared, I would agree with Matthew that 26 is not determinately true. (Whether it’s false is another matter).

    But I take it – and I think this is essentially Richard’s point – that the cases of interest aren’t like this. If there is indeed a concept parading under the label ‘tastiness’ that is some function of sweetness and crunchiness and not a mere conjunction of those qualities, then once we, arguendo, disambiguate it from other concepts that parade under the same label, it still seems pretty plausible that that very concept applies to apples and oranges. Suppose we have a deliciously sweet and super-crunchy MacIntosh and are wondering whether it is tastier than a rather insipid orange. The notion of ‘tastiness’ we have in mind here is some ‘holistic’ function (not a mere conjunction) of sweetness and crunchiness. According to this notion, it seems pretty clear that the MacIntosh is tastier. Most of the evaluative CCs of interest are unified concepts whose contributory components stand in certain normative relations with one another – they aren’t simply conjunctions of a bunch of separate evaluative dimensions. Beauty, justice, tastiness, to name a few. I’ve rabbited on about this elsewhere.

    To insist that it can never be true that x is not better than y wrt V if x bears only some but not all of the same contributory components of V as y does is to deny, as I think Richard pointed out, a great many things we are pretty sure we should be able to say. We could, for instance, pretty much never say that one person was a better philosopher than another – that e.g. Kant is a better philosopher than Fichte – because the various components of ‘philosophical talent’ each bore was not exactly the same. The revision required goes on and on and quite deep. We’d be equivocating all over the place.

    On the second possibility, then, 26 is plausibly true. This is the understanding of the CC I had in mind when I put forward both the SIA and the Chaining Argument.

    So again, even taking ‘tastiness’ to be a function of ‘sweetness and crunchiness’, the example supports parity.

    My second cent has to do with Guy’s remark that an argument needs to be given to show that the sorts of CC at issue are ones that are ambiguous. This seems to be exactly right. Even if Matthew’s arguments worked, we’d need to show that there not only could be but IS ambiguity in the relevant CCs. This is not an easy thing to do. You have to get into messy and difficult issues about concept individuation and probably invoke a substantive theory of meaning that an opponent might reject. And there would be a lot of linguistic data that would undermine the conclusion that there is ambiguity rather than something else (could we, as Guy points out, really be so confused?). This leads me to my second cent. I myself think the right thing to say here is not that these evaluative terms are ambiguous but that there is some indeterminacy in how their contributory components relate. This is Richard’s suggestion and I think right on the money. Unlike Richard, however, I don’t think the indeterminacy is semantic, and in particular a matter of vagueness, for reasons I try to give at the end of my paper and elsewhere.

    In any case, as I’ve suggested, even if we grant that the CCs I use are ambiguous, the very same arguments can be run on each of the putatively disambiguated CCs. The two mistaken assumptions of Matthews argument seem to me to be these. First, that the SIA claims that it is inconceivable that any x and y that satisfy premises 17 and 18 not also satisfy premise 19. Second, that the CCs at issue are mere conjunctions of qualities rather than genuine evaluative concepts that give in some unified way the relations among their contributory components. So, I hope, the possibility of parity is left intact.

  25. 25. Posted by Jeff Huggins | July 20, 2007 12:46 am

    Please allow me to interrupt, briefly, to ask a quick question, the answer to which will help me understand the various arguments in this thread: Do the various parties in the discussion here believe that one or the other of the following statements is true in some absolute sense?: i.e., that EITHER it is true that there are three and only three positive value relations (‘better than,’ ‘worse than,’ and ‘equal to’) and that ‘incomparability’ (not a positive value relation) follows if none of these three relationships hold between two things being compared; OR it is true that a fourth positive relation, ‘on a par’, can describe a valid relationship between two items being compared (and thus that are not ‘incomparable’ in this sense anyhow) that cannot be described as ‘better than,’ ‘worse than,’ or ‘equal to’?

    Brief context to explain what I mean: Picture a world without humans. Imagine an apple and a rock. (Or, imagine a relatively creative chimp, and a whale with particularly harmonious vocalizations.) There are, of course, many similarities between each of the two items in these two sets, as well as many differences, in ‘kind’ and in ‘degree.’ But, without humans, there are no human words with which to make and characterize comparisons. Now add humans. Nothing much has changed in terms of the actual myriad similarities and differences between apples and rocks, or between creative chimps and harmonious whales. But, we humans invent nouns and adjectives as well as the means of stringing them together to describe the relationships we see between apples and rocks, or between chimps and whales. So, in this sense, my question above amounts to this: Is the discussion in this thread about A) Two differing views regarding the actual similarities/differences and comparisons that can possibly be made between two items, or B) The internal consistency of human terms and phrases so that our human ways of describing and comparing items among ourselves (including the terms and the principles used to relate the terms) are internally consistent? If “B”, isn’t it true that either view being discussed in the thread could be correct, and indeed is/are correct, as long as the terms used are defined and understood consistent with each view?

    Sorry for the digression and question.

  26. 26. Posted by Ruth Chang | July 22, 2007 12:08 am

    I can’t speak for others, but I take myself to be saying something about the way things are, not about our words or even our concepts. The most natural way to ‘get at’ reality, of course, is to examine what we believe and the reasons we have for those beliefs. And beliefs involve concepts, and the expression of beliefs involves words.

    You may not be willing to believe that in reality one thing can be better than another wrt V but insist instead e.g. that it’s a convenient fiction for us to maintain. Similarly you may not be willing to believe that in reality two things can be on a par wrt V but instead think e.g. that our concepts such as ‘comparability’ are simply consistent with other concepts like ‘betterness’ and ‘parity’. Most of us, I think, aim to say something about the way the world is. Whether we succeed, of course, is another matter!

  27. 27. Posted by Jeff Huggins | July 22, 2007 1:25 am

    Ruth, thank you for your helpful response. I understand most of it, but please allow me to clarify what I was getting at and, based on that, ask one or two more clarifying questions so that I can understand your position:

    Regarding your second paragraph, I do believe that, in reality, one thing can move faster from point “A” to “B” (for example) than another thing that also starts at point “A” at the same time. So, we can accurately call the one thing ‘faster’ than the other (in that race anyhow). No problem there. And, I believe that, in reality, one thing can emit sound waves at two different frequencies that are fairly far apart while another thing may emit sound waves at five different frequencies that are scrunched together. Thus, one of those things (the first) can sound more harmonious to us humans than the second thing sounds to us humans. So, I don’t doubt at all that one thing can have a different ‘quality’ wrt characteristic V (speed, or harmony, or etc.) and that we humans can validly, from our perspective, judge one ‘better than’ the other, or ‘greater than’ the other, from that standpoint. I don’t think of any of those things, or our characterizations or comparisons of them, as mere ‘fictions’ that we maintain, as long as we consider them for what they are. I definitely aim to understand and say things about the way the world is. (And I agree with you that, whether and to what degree we succeed is another matter.)

    Instead, what I was getting at is this: In attempting to say something about the way the world is (and here I mean everything in and about the world, including the things or other people being compared, as well as their qualities, but not including the third parties trying to do the particular comparison or communicate it to another third party), can’t both approaches being argued earlier in the thread work, as long as we understand each one correctly? In other words, as long as each approach defines its terms and possible relationships (one allowing three relationships; the other four) to be internally consistent with each other (that is, each approach is internally consistent with itself), then both approaches can be correct, yes?

    In saying this, I don’t mean that things don’t exist. Nor do I mean that they don’t have qualities. Nor do I mean that we humans are merely ‘fictionalizing’ when we hear or see, and try to categorize and compare, those qualities. I am simply suggesting that your approach (which includes ‘on a par with’) and the other approach (which doesn’t) can be and are both correct (as long as terms are defined accordingly). Or, at least that it is possible that they are both correct. The problem arises if you and the other party in the argument share precisely the same definitions of all other terms being used, but you argue that four comparisons are possible and he argues only three. Then, of course, one of you must be incorrect, I would think. But, if you two have ever-so-slightly-different views of what the other terms mean, then each of your approaches might be correct given your own definitions, right?

    If I’m communicating myself clearly, does this make sense, and do you agree? Or, am I missing something?

    Thanks.

  28. 28. Posted by Ruth Chang | July 22, 2007 2:19 am

    Thanks for the clarification, Jeff. I hope I’ve got your point now. The trichotomist and I, I think, aren’t just stipulating different meanings for words we use in common. If we were doing that, both of our views could be correct — most obviously, when the trichotomist says ‘incomparability’, I mean by that term ‘on a par with’.

    We are having a genuine disagreement about the nature of comparability. The trichotomist says, if you look at the ‘positive’ space of comparability that exists between two alternatives wrt V, that space is exhausted by the relations ‘better than’, ‘worse than’, and ‘equally good’. I say, no the very same positive space you’re looking at actually contains four, not three positive relations that together exhaust the space of comparability. We’re not stipulating different meanings for ‘the space of comparability’ – we’re talking about the same space and offering different substantive views about it. In my Poss of Parity paper, I ask the reader to imagine a ‘dichotomist’ who looks at the space of comparability between two items and insists that there are only two relations that exhaust that space. Such a person aims to talk about the same space of comparability as the trichotomist, only — as we all think — he’s made a substantive mistake about it. Similarly, my suggestion is that as trichotomists we’ve all made a substantive mistake about the space of comparability. The reason this seems so incredible is that we are gripped by models of evaluation from science and mathematics – but I wonder why we should be so confident that those translate nicely into the domain of normative evaluation.

  29. 29. Posted by Jeff Huggins | July 22, 2007 6:15 pm

    Ruth, thanks very much for your time and clarification. Very helpful. Given where my understanding now is (much better but still incomplete), I have another question. I apologize that I’m asking these questions without having read your paper, but for now I’m just trying to get an initial grasp of what is being argued.

    My question is this: To which of the following ‘types’ of judgments and comparisons does the current argument apply? (In other words, to which of the following types of comparisons can we apply ‘better than’, ‘worse than’, ‘equally good’, and (on your view) ‘on a par with’ as they relate to the current debate?)

    A) Comparisons of simple physical properties or phenomena between two objects. For example, if one object moves between point X and point Y faster than another object (which starts at the same point X and at the same time), we can say that the one object is faster than the other object (at least in that race) and, if we have reason (between the two people discussing the matter) to value greater speed, then we can also say that the one object is ‘better than’ the other object, with respect to speed. Does the argument apply to these types of comparisons? Are you saying that there is such a thing as ‘on a par with’ regarding comparisons of simple matters such as velocity?

    B) Aesthetic and related comparisons. This is, of course, where we are comparing Mozart’s creativity or brilliance with Leonardo da Vinci’s creativity or brilliance. I can certainly see, intuitively, that ‘on a par with’ can or might apply in these types of comparisons.

    C) Moral/ethical judgments and comparisons. For example, is it your position that one might compare, say, someone who tortures and cripples 50 people with someone else who knowingly watches (but omits to act) while 10 people are being murdered, and then possibly conclude as follows: That the first person’s act was not ‘better than’, ‘worse than’, or ‘equally good’ (morally speaking) relative to the second person’s act, but that nevertheless the two acts are comparable (rather than incomparable) and that the two acts were ‘on a par with’ each other from a moral standpoint? (In using this example, which might not be a very good one, I’m not trying to see if you agree with this as a specific moral assessment: Instead, I’m simply trying to understand whether the argument of this thread is meant to apply in the realm of moral comparisons.)

    In sum, does the trichotomist vs. ‘on a par with’ disagreement apply to all three of these realms of possible comparison, i.e., to A, B, and C? Or, does it mainly regard one or two of them? If so, which ones?

    (Of course, the list here is not meant to include all possible realms of comparison.)

    FYI, although I am very interested in art and aesthetics (i.e., “B”), and I have a scientific background (and am interested in matters “A”), I am mainly interested in understanding morality (i.e., “C”). Thus, if your argument is meant to apply to moral-ethical assessments and comparisons (“C”), then I’m especially interested and would like to read the paper itself.

    Thanks again Ruth.

  30. 30. Posted by S. Matthew Liao | July 22, 2007 11:53 pm

    Welcome Ruth! And thank you very much for your very helpful responses. I’m very delighted to have the opportunity to sharpen up my arguments in light of them. I should also thank Richard for his comments and for alerting you about this post.

    To respond to your comments, I shall go over how I see the dialectic of this debate. Along the way, I shall comment on your specific points.

    As I see the debate, the “status quo” is that there are only three positive value relations, and incomparability follows if none of these three relations hold.

    You then give a (very nice) case (Mozart/Michaelangelo) in which it seems intuitively plausible that the three positive value relations do not hold. Then you give an argument that purports to show that nevertheless a positive value relation holds in such a case. You call this positive value relation the parity relation.

    My strategy is to present a trilemma for your argument.

    To set up the trilemma, I point out that it is possible to interpret your case in different ways. In particular, I suggest that when people think that they are making ‘holistic with-respect-to’ claims in the case you have identified, they either are sliding/ambiguating between different, specific, ‘with-respect-to’ claims that involve comparing subcomponents that are not shared by the two items OR they are not. (I thank Guy for helping me to get clear on what I want to claim).

    First horn of the trilemma (Think of a genetically mutated bull with three horns). Suppose they are not ambiguating, then I claim that SIA would fail, based on 17-20.

    In defense of your argument, you said:

    Matthew wants to conclude that the SIA doesn’t work if the CC is ‘sweetness’. But this is to misunderstand the SIA. The claim is not that there are no apples and oranges for which 17-20 are false. It is rather that there are some apples and oranges for which 17-20 are true. It is of course true that “conceivably, Apple+ could be better than the Orange with respect to sweetness. . . My point instead is that there could be some Apple+ for which 19 is true.

    To support this possibility, you give the following example:

    It seems plausible that there is an apple neither sweeter nor less sweet than an orange such that if the apple were improved in sweetness a touch, it would nonetheless still be neither sweeter nor less sweet than the orange. So the SIA works if ‘tastiness’ is understood as sweetness.

    First, it is worthwhile noting here that your accepting that Apple+ could be better than Orange with respect to sweetness causes SIA to lose some intuitive appeal. By this, I mean that whereas previously you seem to have offered a clear case that supports your claim, now the case is no longer as clear.

    Secondly, I think the plausibility of your example depends on whether vagueness is at issue or not. If vagueness is not at issue, and you have ruled out vagueness, I have to admit that I don’t seem to have your intuition. In other words, I said that “it is not obvious that 19 would be true” because I think that 17 could be vague. If 17 is not vague, then my intuition is that 19 would be false. So, for me at least, SIA doesn’t seem to work with this example. If so, then if people are not ambiguating and vagueness is not at issue, then I think SIA would not be sound.

    Second horn of the trilemma. Suppose they are ambiguating and they are using different, specific, ‘with-respect-to’ claims that involve comparing subcomponents that are not shared by the two items. In such a case, I have said that I can see how SIA would go through. But I then claim that the Chaining Argument would fail. For example, 26 would be false.

    The reason I think this is pretty much the same reason why you think that it wouldn’t be true that fried eggs are better than the number nine with respect to the conjunction of tastiness and beauty as an abstract number, namely, they involve the conjunction of different subcomponents that are not shared by the two items.

    You seem to agree with this, but you think that “interesting cases” such as your case or the case of comparing apples and oranges are not like this.

    So, I’ll move on to the third horn of the trilemma.

    Third horn of the trilemma. Some people might think that they are using different, specific, ‘with-respect-to’ claims that involve comparing subcomponents that are not shared by the two items, but they might claim that at the same time they are making holistic ‘with-respect-to’ claims. I think that this kind holistic claim is what you have in mind when you said that “interesting cases” such as your case or the case of comparing apples and oranges are not like this.

    First, it may be worth noting that the idioms ‘comparing apples and oranges’ and ‘don’t add apples and oranges’ are typically used to indicate that two items or groups of items are incomparable. So maybe some interesting cases are like this after all. In fact, this is why I chose the example of comparing apples and oranges.

    Secondly, I would deny that this kind of holistic claim is possible. There is a stronger and a weaker version to my contention.

    Strong version: It is not possible to make ‘holistic with-respect-to’ claims regarding two items, if these claims involve comparing subcomponents that are not shared by the two items.

    Weak version: It needs to be shown that it is possible to make ‘holistic with-respect-to’ claims regarding two items, if these claims involve comparing subcomponents that are not shared by the two items.

    I think that both versions are plausible, firstly, because while people sometimes claim that such holistic claims are possible, I don’t know of any demonstration of it.

    Secondly, this kind of holistic claims looks very similar to “mere conjunction” claims discussed earlier. Given what we have said about “mere conjunction” claims, this casts serious doubt on such holistic claims. It certainly puts pressure on those who think that this kind of holistic claims is possible to show that it in fact is possible.

    You go on to say:

    To insist that it can never be true that x is not better than y wrt V if x bears only some but not all of the same contributory components of V as y does is to deny, as I think Richard pointed out, a great many things we are pretty sure we should be able to say. We could, for instance, pretty much never say that one person was a better philosopher than another – that e.g. Kant is a better philosopher than Fichte – because the various components of ‘philosophical talent’ each bore was not exactly the same. The revision required goes on and on and quite deep. We’d be equivocating all over the place.

    But on the view I have in mind, we can say that one person is a better philosopher than another, if the comparative subcomponents are shared by both. For example, if Kant was more prolific and opened up more fields of inquiry than Fichte, and suppose both comparisons are applicable to Fichte as well as Kant, then one can say that Kant is a better philosopher than Fichte in these respects. So I would deny that my contention entails that we can never compare talent, justice, beauty, etc. We can as long as the comparative subcomponents are shared by both items being compared.

    Also, while it is an empirical matter, personally, I do think that there are a lot of apparent, verbal, disagreements. So I would not find it surprising or counterintuitive to learn that we in fact equivocate a lot.

    Here you might ask, why should you incur the argumentative burden to show that such holistic claims are possible?

    The reason is partly because of the status quo. In particular, given my contention, there are two possible ways one can proceed: 1) One can deny that people are equivocating all over the place and accept a fourth positive relation. Or, 2) one can accept that people are equivocating all over the place and deny that there is a fourth positive relation. Although 2) incurs the cost of holding the view that people are making mistakes of which they might not be aware, it also has the advantage of not introducing a whole new value relation, about which people also did not know until recently.

    If I am right that this third option is not available, then 26 would remain false.

    You said further:

    My second cent has to do with Guy’s remark that an argument needs to be given to show that the sorts of CC at issue are ones that are ambiguous.

    I think I wasn’t very clear when I responded to Guy, but I hope that it is clearer now that I am presenting a trilemma. If Guy is right, and there is no ambiguity in the sorts of CC at issue, then I would appeal to the first horn of the trilemma.

    In conclusion, I’m still not persuaded that the parity conclusion obtains, but I am definitely open to further arguments.

  31. 31. Posted by Ruth Chang | July 27, 2007 4:27 am

    Thanks for your replies/queries Matthew & Jeff.

    1) First horn of ‘trilemma’.

    Here is your original argument:
    “Suppose by Taste, we mean sweetness. Then the Small Improvement Argument would look like the following:
    17. Suppose an Apple is neither better nor worse than an Orange, with respect to sweetness.
    18. Suppose an Apple with some small improvement that bears on sweetness (Apple+) is better than the Apple, with respect to sweetness.
    19. Apple+ is not better than the Orange, with respect to sweetness.
    20. Therefore, the Apple and the Orange are not related by any of the standard trichotomy of relations, with respect to sweetness.
    But on the understanding that Taste means sweetness, it is not obvious that 19 would be true. If 17 and 18 were really true, then conceivably, Apple+ could be better than the Orange with respect to sweetness.”
    Your argument is that since it’s *conceivable* that there is some Apple+ (a slightly sweeter apple than Apple) that is sweeter than the orange, the SIA doesn’t work wrt sweetness. But this isn’t how the SIA works. It holds that there is SOME OR OTHER apple that is slightly sweeter than Apple that is nevertheless neither sweeter nor less sweet than Orange. That’s all one needs for the SIA to work for sweetness. It doesn’t say FOR EVERY apple that is slightly sweeter than Apple, it is neither sweeter nor less sweet than Orange. If you showed that it is *inconceivable* [let’s bracket the relation b/t conceivability and possibility here] that there is any apple that is slightly sweeter than Apple that is not also sweeter than Orange, then the SIA would fail. I say in response: can you imagine ANY Apple+ that is slightly sweeter than Apple and nonetheless is neither sweeter nor less sweet than Orange? I can – I’m doing it right now. You can do this apples and oranges and with coffees and teas. Your first horn does not show that SIA fails; it misinterprets the argument.
    In your reply you introduce a new claim, saying that you think the plausibility of the SIA turns on whether vagueness is involved. I try to address this concern at the end of the paper and won’t repeat what I say here.
    2) Second horn of the trilemma:
    We seem to be agreed that if the cases of interest are like the ones I think of as cases of noncomparability, then we shouldn’t think of these cases as cases of parity. So it seems to me that the real issue you are raising is whether we should think of the interesting cases as ones in which we’ve got something different from noncomparability, that is, cases in which we are attempting to compare items with respect to a mere conjunction of disparate evaluative notions, not both of which apply to each of the items being compared.
    This leads us to your ‘third’ horn of what you call your ‘trilemma’. If I might say as an aside, I think the heart of your worry about parity is, as I said, over the issue of whether the cases I think of as cases of parity aren’t simply cases of what I call noncomparability. Since, if I’m right above, you have misinterpreted the SIA, there is no ‘trilemma’ or even a dilemma. Ambiguity isn’t the issue – the issue is whether the cases I think of as cases of parity –e.g., comparisons between Mozart and Michelangelo wrt creative genius – are really cases of noncomparability – like e.g. comparisons of fried eggs and the number nine wrt tastiness.
    You may have a separate worry about vagueness, but that would be a separate worry and I don’t really want to get into that since I haven’t got anything more to say than what I said in my paper.
    3) Third horn of the trilemma:
    So are comparisons between fried eggs and the number nine wrt tastiness, on the one hand, relevantly like comparisons between Apple and Orange with respect to tastiness on the other? You seem to assume that if an item doesn’t ‘bear’ a contributory component of the covering value then the case is automatically like trying to compare fried eggs and the number nine wrt tastiness. As I tried to argue in the introduction to that volume on incommensurability, we have to distinguish such cases of noncomparability from ones like the ones of interest to practical reason. We compare things that don’t ‘share’ exactly the same contributory components of a covering value all the time and we shouldn’t conflate such cases with cases of noncomparability. Again, it would take me way too long to repeat what I say about this in that introduction. Part of the issue here is to say precisely what one means by ‘share’ a contributory component.
    But there is a general issue that you go on to raise, putting parity to one side now. You want to defend the idea that we can never compare two items wrt V, where that V has ‘subcomponents’ v1, v2, v3, not all of which are ‘shared’ by both items.
    “Strong version: It is not possible to make ‘holistic with-respect-to’ claims regarding two items, if these claims involve comparing subcomponents that are not shared by the two items.”
    The strong version seems to me patently false. Do you want to deny that we can compare the philosophical talent of Kant and, say, a typical first grader? Suppose some of the subcomponents of philosophical talent are originality, insightfulness, clarity of thought, and historical sensitivity. Our first grader has never studied philosophy so has no historical sensitivity. She doesn’t ‘share’ the subcomponent of historical sensitivity. Kant has historical sensitivity but she doesn’t. So according to the strong version, we can’t make ‘holistic wrt’ comparative claims about the philosophical talents of Kant and the first grader. But this seems absurd. We couldn’t reason practically; we couldn’t make the evaluations we do – we’re talking major revision of our normative practices generally.
    Now here’s the weak version:
    “Weak version: It needs to be shown that it is possible to make ‘holistic with-respect-to’ claims regarding two items, if these claims involve comparing subcomponents that are not shared by the two items.”
    The weak version is I think an interesting claim which I think it would be great if someone did some serious work defending. While it’s pretty clear we can make these ‘holistic wrt’ comparisons, how is it that we can? What explains how different subcomponents are ‘put together’? I have my own pet sketch of a view. But maybe every such view crashes and burns. So the fruitless search for an account may lend support to the strong version.
    So Matthew’s worry taken at its broadest is a deep, revisionist attack not on parity, but on the whole idea of being able to make – as you put it – ‘holistic wrt’ comparisons. Forget about parity – if you’re right, we should worry about the bread and butter comparisons we make in everyday life.
    A final word generally about attempts (not so much yours, really) to reduce parity to some function of the usual trichotomy of relations. You nicely raise the point that opponents of parity have the
    “advantage of not introducing a whole new value relation, about which people…did not know until recently.”
    If I might use this comment as an occasion to clarify what I think philosophers are up to when they introduce a new concept. I’m not saying – hardly any philosopher who introduces a new notion is – hey here’s this funky new thing people have failed to notice. People who introduce new concepts are usually attempting to systematize familiar ways of going on in a way that attempts to shake us from our passive acceptance of the usual ways of thinking about things in the hope that this reconceptualization might lead to some insight. Here’s an example from science that I borrow from Christopher Peacocke. Newton was working with the concept of a limit of a series – he didn’t know it as such, but if you look at the kind of mathematics he was doing, the concept was implicit in his work. When someone came along later and introduced the concept of a limit, he wasn’t saying – here’s this funky new thing everyone missed. Instead, the concept of a limit was introduced to make sense of perfectly familiar mathematical practices including those of Newton. Similarly, when I introduce the idea of parity, I’m just trying to systematize and make sense of our ordinary practices of making comparative judgments. In Peacockian terms, we’ve got an ‘implicit conception’ of parity. That’s why I rely a lot on our intuitive judgments about what comparisons are or are not possible. Both the SIA and the Chaining Argument rely very heavily on what might be called the ‘practice data’. Of course, there’s always cost in reconceptualizing things and, by implication, understanding reality differently.
    On Jeff’s comment. I say the arguments for parity work for your B and C (and others too) but I don’t argue that it extends to matters A (though I actually think it does).
    I hope that helps to clarify things. Thanks again to Matthew, Guy, Richard, and Jeff for your comments. I welcome any further comments, apologize in advance for any misunderstandings on my part, and really don’t mean to give myself the last word, but please don’t be annoyed if I disappear from the blog. I can now die happy knowing that I’ve blogged once in my life. Thanks for the experience!

  32. 32. Posted by S. Matthew Liao | July 27, 2007 1:42 pm

    Thanks for your replies, Ruth.

    Here is a way to think about why ambiguities might be at issue. If the Parity Conclusion can be defended by using ‘with-respect-to’ claims that involve comparing subcomponents that are shared by the two items, why bother trying to defend the use of ‘holistic with-respect-to’ claims that involve comparing subcomponents that are not shared by the two items, which is much more controversial? My suggestion is that SIA is much more plausible when one uses the latter rather than the former, but the Chaining Argument works better on the former rather than the latter. For that reason, I think there are ambiguities at issue.

    On SIA and sweetness, you may have misunderstood my reply. My problem is not with vagueness. Instead, I was trying to explain why I initially only made the weaker claim that ‘it is conceivable’ that Apple+ could be better than the Orange with respect to sweetness.’ The reason is that I was thinking that 17 could be vague. But I should have just assumed that 17 is not vague, given that I have granted you that vagueness is not at issue. Given that, I said that I would hold the stronger view that Apple+ would always be better than the Orange with respect to sweetness. So, the issue here is that you and I have different intuitions about this matter.

    By the way, though I don’t challenge your argument against vagueness, I have a question about it. If I understood your argument correctly, your claim is that the resolution of hard cases such as Mozart and Michaelangelo can be a matter of arbitrary stipulation on a vagueness account, but the resolution of these cases cannot be a matter of arbitrary stipulation, and therefore, the vagueness account cannot explain these hard cases. I think that an epistemicist such as Williamson would deny that vagueness implies that the resolution of these cases can be done as a matter of arbitrary stipulation. He would say that there is a fact of the matter in these cases; we just make mistakes when we try to resolve them because of our epistemic limitations.

    On your replies to the second and the third horns of the dilemma, I want to note what you say in your paper:

    the assumption that there is always a covering consideration should be understood in an innocuous way; a covering consideration might be nothing more than a stipulated consideration that is a bare conjunction or list of all the considerations relevant to the comparison . . . Thus “overall” and “all things considered” are placeholders for a covering consideration which in turn might be nothing more than a list of all the things to be considered. (p. 667).

    So, in fact, at least in your paper, you seem to endorse only comparisons formed by “bare conjunctions” where the subcomponents are shared by the items being compared, and you do not seem to appeal to holistic wrt comparisons involving subcomponents that are not shared by the items being compared, which I think would not be an “innocuous” assumption. If so, then I think the second horn of the trilemma would kick in.

    On your point about Kant and the first grader, denying that we couldn’t compare Kant and the first grader with respect to historical sensitivity is not the same thing as denying that we couldn’t say that Kant is a better philosopher than the first grader. Kant is a better philosopher than the first grader just in case Kant could provide plausible answers to certain philosophical problems when asked at time t and the first grader could not. Is Kant more original as a philosopher than a 2 year old if the 2 year old was J.S. Mill? It seems that we cannot compare the two, since the 2 year old has not yet begun to do philosophy. As you said, part of the issue here is to say precisely what one means by ‘sharing’ a contributory component.

  33. 33. Posted by Jeff Huggins | July 27, 2007 5:02 pm

    Dr. Liao / Matthew, I would be very interested in your answer to the question in my Post #29 (July 22), in which I seek to understand what realms of thought or phenomena (the physical, the aesthetic, the moral, etc.) the disagreement in this thread is thought to apply to. In her recent Post #31, (referring to the definitions and examples of A, B, and C that I used in my Post #29), Ruth answered that she believes that her parity argument applies to “B” and “C” but that she doesn’t argue that it applies to “A” (although she thinks it does). Regarding the original Trichotomy Thesis and your argument in defense of it, which of “A”, “B”, and “C” do you argue that they apply to, or perhaps all of them?

    As I mentioned in my Post #29, I am particularly interested in matters and comparisons having to do with morality/ethics (designated “C” in this particular classification).

    Thank you.

  34. 34. Posted by S. Matthew Liao | July 27, 2007 5:44 pm

    Jeff, thanks for your note. Please do call me Matthew. I think that the Trichotomy Thesis, as it is typically understood, applies to all three. This said, when applied to C, one may want to distinguish between axiological and deontic evaluations. It is possible that X is better than Y, from an axiological point of view, and yet one *ought* not, deontically speaking, bring about X. So, for example, it may be that a state of affair in which five people live is a better than a state of affair in which one person lives. And yet, one ought not to bring about the former, if this means taking the organs of the one healthy person without his consent in order to save the five. I hope this helps.

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