Saturday, July 28, 2007

Assignment Part 3

Sorry I know this is long, and repeats a number of things, but I wanted to address both Dan and Adam's comments point by point.

Both Dan and Adam noted that my reconstruction of Salmon's irrelevance objection, as it is presented in Divers (8.1), was invalid. Which I do agree with. So first, I reconstructed the argument, which appears as follows:

Irrelevance objection from Salmon (via Divers) made valid:
  1. If an ordinary possibility sentence of modal English is about a counterpart (i.e. facts about an individual y having a certain feature F, at possible world, w), then that counterpart is relevant to the truth of a sentence of ordinary modal English which is about an individual x, which shares the same feature F, as y, at another world.
  2. Nothing is a counterpart of anything else in its world (P5).
  3. Anything in a world is a counterpart of itself (P6).
  4. (2) & (3)
  5. If (4), then the relevant modal truth about an individual, x, is its own counterpart in its own world (i.e. not another counterpart, y, having a certain feature F, at possible world, w).
  6. So, the relevant modal truth about an individual, x, is its own counterpart in its own world (i.e. not another counterpart, y, having a certain feature F, at possible world, w).
  7. Therefore, it is not the case that an ordinary possibility sentence of modal English is about a counterpart (i.e. facts about an individual y having a certain feature F, at possible world, w).

I'll first deal with Dan's, then Adam's objections to my reconstruction of the irrelevance argument presented above, then rewrite the above argument to better reflect their suggestions.
Dan on Chelsey, on Divers, on Salmon:

As Dan notes in his evaluation, there are two significant changes that he would make to the irrelevance argument which he reconstructs as follows:

  1. If ordinary possibility sentences of modal English are about counterparts (i.e. facts about an individual y having a certain feature F, at possible world W) then entailment relations that hold in CT will hold in ordinary modal English.
  2. (P5)
  3. (P6)
  4. (2)&(3)
  5. If (4) then there is some entailment relation that holds in CT but not in ordinary modal English.
  6. There is some entailment relation that holds in CT but not in ordinary modal English.
  7. It is not the case that ordinary modal sentences are about counterparts.

First, Dan argues that Salmon would not accept premise (5) and (6) in the above argument. There are two ways this can be taken, either Dan thinks that I am being unfaithful in reconstructing the argument presented in Divers, or my reconstruction is faithful to Divers but Divers is unfaithful to Salmon. In either case he thinks (5) and (6) should be changed in order to deliver a better argument. His justification for this is as follows:

“I do not think that Salmon would accept premise (5). Salmon’s argument involves a dis-analogy between the semantics of GR and that of English. That is, he asserts that “there may have been a Humphrey counterpart who won” entails “Humphrey might have won” in GR, but it does not in English. This lack of analogy is meant to support the claim that concerns about our counterparts are different from, and irrelevant to, concerns about our modal properties. Salmon would agree that premise (5) holds for certain individuals & propositions meant to produce counter-examples, but I do not think he would have it be a fully general rule. He would reject (6) on the same grounds.”

Second, Dan suggests that (2) to (5) are superfluous:

“Indeed, the argument may be better without them. (P5) and (P6) need not be true for the argument to go through, they merely need to be true according to GR. If we hold them true simpliciter, then the argument entails things about counterparts. However, it’s best if an argument against counter part theory does not entail things about counterparts. So, simply put, the argument can be reconstructed like so:

9. If ordinary possibility sentences of modal English are about counterparts (i.e. facts about an individual y having a certain feature F, at possible world W) then entailment relations that hold in GR will hold in ordinary modal English.

10. There is some entailment relation that holds in GR but not in ordinary modal English

11. It is not the case that ordinary modal sentences are about counterparts.”

Here, Dan makes two particular points about the argument's construction which I will address in turn.

First, I think Dan is jumping the gun a bit with Salmon's argument. As it is presented in Divers, it is meant as an irrelevance objection, that is, counterparts are irrelevant to the truth of an ordinary possibility sentence of modal English. In other words, that counterparts are irrelevant, for certain purposes. As it is presented, it is not an argument against counterparts, it is simply to show that they suck in a particular way. So, incorporating counterparts by way of premises (2) to (5), that is to hold them true simpliciter is required. This may just be a preference on my part, but I think stripping Salmon's argument of premises (2) to (5) is to eliminate one of the awesome characteristics that it has as an argument type. Essentially what Salmon's irrelevance argument is saying to the genuine realist is this, okay fine I'll accept your counterpart theory, and even better I'll accept the identity fixing postulates that you give which accompany it, but even when I play your game by your rules, counterparts are still useless at doing what it is that you want them to do. To Dan's credit, I do believe that he is correct, in that this argument lends to the further argument against CT and GR. In which case, it would be best if the argument does not entail things about counterparts, but that would be an additional argument, which would require additional premises, and not that present in Divers as Salmon's irrelevance objection.

The second point is that for the reconstruction, (8) to (10), that Dan offers, he has essentially chosen to eliminate the premises (2) to (5) because they are plainly superfluous. But as he notes later, the justification for (9) will require invoking the postulates (P5) and (P6) when asserting which entailment relations hold under GR. So, I suppose (and Chris your input on this particular point would be appreciated), should the postulates (P5) and (P6) be written as explicit premises within the argument's reconstruction, or taken as the implicit justification for premise (9)? In either case they are still being used, as it were, by and in the argument. Personally, I would prefer to keep them as explicit premises. It seems only fair to have them as individual premises, so that if an objector to the argument wishes to deny either (for what it is worth denying either postulate, in the hopes of denying the conclusion, seems like an untenable and misguided way to object to this argument) they can do so.

Adam on Chelsey, on Divers, on Salmon:

Adam makes one main recommendation for the reconstruction of my Divers on Salmon (other then making it valid). He thinks a more faithful reconstruction would look something like this:

C: The non-modal (metalinguistic) truth-conditions specified by (CT) for ordinary (object language) sentences of modal English correctly represent our pre-theoretical modal intuitions.
R: The non-modal (metalinguistic) truth-conditions specified by (CT) for ordinary (object language) sentences of modal English are relevant to the modal truth of the individuals they are about.
M: An (object language) sentence of modal English about a counterpart of an individual a is intuitively weaker than a sentence of modal English about a itself.
U: The (CT) truth-conditions specified for a modal English sentence about a counterpart of an individual a logically entail the (CT) truth-conditions specified for a modal English sentence about a itself.

  1. ~C → ~R
  2. M
  3. M → (U → ~C)
  4. (U → ~C) (2,3)
  5. U
  6. ~C (4,5)
  7. ~R (1,6)

Adam argues that the conclusion, that it is therefore not the case that an ordinary possibility sentence of modal English is about a counterpart, in my reconstruction is unfaithful to that presented in Divers. In Adam's reconstruction the conclusion states that, it is not the case that the non-modal (metalinguistic) truth-conditions specified by (CT) for ordinary (object language) sentences of modal English are relevant to the modal truth of the individuals they are about. I both agree and disagree with Adam on this point (as is my usual m.o.). I agree that my previous reformulation does not quite capture faithfully the conclusion intended by the irrelevance argument. The problem does not lie with English not being about couterparts, which is the conclusion that my reconstruction delivers. But, I disagree that his reformulation is any better. For the argument to be faithful to one presented in Divers, it must be the case that the individuals (or counterparts) are doing the work. That is, that the roles expressed in the conclusion of his reconstruction need to be reversed and reformulated as such:

7. It is not the case that the modal truth of the individuals are relevant to the non-modal (metalinguistic) truth-conditions specified by (CT) for ordinary (object language) sentences of modal English, in which they are about.

Adam also suggests that the argument can be shortened to the following:

P: An ordinary sentence of modal English is about a counterpart.
Q: A counterpart is relevant to the truth of an ordinary modal English sentence.
R: Nothing is a counterpart of anything else in this world.
S: Anything in a world is a counterpart of itself.

I believe this could be shortened to the following and still remain valid:

  1. R
  2. S
  3. (R&S)
  4. (R&S) →~Q
  5. ~Q →~P
  6. ~P (1-3 HS)

I must admit, I'm a little confused here. Premises (1) to (3) cannot derive the conclusion in (6) using hypothetical syllogism. (4) and (5) can because they are conditionals. But, then the conclusion in (6) would read ~P → (R&S). Which is not the conclusion that is needed for the irrelevance argument. If I am mistaken here please let me know.

The other points that are brought up by Adam pertain to the fact that the argument as it is presented in Divers is not faithful to Salmon. I think he is correct in this analysis. Unfortunately, for the present purposes of this assignment I am unsure where my loyalties are supposed to lay. Am I supposed to reconstruct the argument as faithfully to Divers' text, or should I be going to the original source and be faithful to that presented by Salmon?

Sticking with the Divers text and taking the previously mentioned, new and hopefully more faithful conclusion, the irrelevance argument can be reformulated once again as follows:

Irrelevance objection from Salmon (via Divers) made valid:

  1. If the modal truth of a counterpart (i.e. facts about an individual y having a certain feature F, at possible world, w) are relevant to the non-modal (metalinguistic) truth-conditions specified by (CT) for ordinary (object language) sentences of modal English, in which they are about, then that counterpart is relevant to the truth of a sentence of ordinary modal English which is about an individual x, which shares the same feature F, as y, at another world.
  2. Nothing is a counterpart of anything else in its world (P5).
  3. Anything in a world is a counterpart of itself (P6).
  4. (2) & (3)
  5. If (4), then it is not the case that that counterpart is relevant to the truth of a sentence of ordinary modal English which is about an individual x, which shares the same feature F, as y, at another world. (i.e. not another counterpart, y, having a certain feature F, at possible world, w).
  6. So, it is not the case that that counterpart is relevant to the truth of a sentence of ordinary modal English which is about an individual x, which shares the same feature F, as y, at another world. (i.e. not another counterpart, y, having a certain feature F, at possible world, w).
  7. Therefore, it is not the case that the modal truth of a counterpart (i.e. facts about an individual y having a certain feature F, at possible world, w) are relevant to the non-modal (metalinguistic) truth-conditions specified by (CT) for ordinary (object language) sentences of modal English, in which they are about.

Sorry for the wordiness, but hopefully it's v.f.a. (valid, faithful and awesome).

3 comments:

Adam said...

I thought I would reply to a couple of points you make in your last post. You said:

“I must admit, I'm a little confused here. Premises (1) to (3) cannot derive the conclusion in (6) using hypothetical syllogism. (4) and (5) can because they are conditionals. But, then the conclusion in (6) would read ~P → (R&S). Which is not the conclusion that is needed for the irrelevance argument. If I am mistaken here please let me know.”

You’re absolutely right about the first bit. Sorry I didn’t notice that before I had submitted it. It should read (3-5 HS). However, the conclusion (in this case, ~P), follows from (3-5).
Second, you wrote that:

“But, I disagree that his reformulation is any better. For the argument to be faithful to one presented in Divers, it must be the case that the individuals (or counterparts) are doing the work. That is, that the roles expressed in the conclusion of his reconstruction need to be reversed and reformulated as such:
7. It is not the case that the modal truth of the individuals are relevant to the non-modal (metalinguistic) truth-conditions specified by (CT) for ordinary (object language) sentences of modal English, in which they are about.”

I’m not sure I get what’s going on here. The “modal truth” about an individual is supposed to BE some fact about a counterpart of that individual, if GR is right. It’s not the other way around. This is why Divers says on 124 that “the most fundamental and persistent objection of principle to Lewis’s use of CT is that facts about the counterparts of an individual are, in general, irrelevant to the modal truth about that individual.” Your proposed (7) above reverses this. So, two questions: what is it for the counterparts to “do the work” in the argument, and how is it that counterparts do not “do the work” in the version presented by me?
Third, I think you’re right that it would be a different task altogether than the one assigned to present and assess the original argument given by Salmon. I mentioned it only because (i) the version in Divers is not faithful to that given by Salmon, (ii) the version given by Divers is not capable of providing the intended conclusion (since there is a ready counterexample, as I pointed out in the comment) and (ii) because the original Salmon argument is not vulnerable to the same counterexample, since he derives his version from different sorts of claims/premises than those presented by Divers.

Chelsey said...

Ummmm... still not seeing where HS can be used anywhere. Premises (3) to (5) of your reconstruction which derive (6) the conclusion are:

(3) (R & S)
(4) (R & S) → ~Q
(5) ~Q → ~P
(6) ~P (3-5 HS)

This is what you are suggesting?

First, you can't use three premises in HS because it follows the form:

P → Q
Q → R
Therefore, P → R

Second, HS derives a conditional, which, ~P, is not.
And third, the above would be invalid no matter what inference rule you use, if the premise ~Q is missing.

So, I really don't see how the argument can be completed in less then seven steps (or using HS), while maintaining validity. So the argument must be as I presented it:

(1) P → Q
(2) R
(3) S
(4) R & S (2,3) CONJ
(5)(R & S) → ~Q
(6) ~Q (5,4) MP
(7) ~P (1,6) MT

The only other option would be to formalize it as:

(1) R
(2) S
(3) R & S (1,2) CONJ
(4)(R & S) → ~Q
(5) ~Q (3,4) MP
(6) ~Q → ~P
(7) ~P (6,5) MP

But really, because they amount to the same thing. Where premise (6) in the former, is simply the negation of (1) in the latter. So, MP is used instead of MT.

Anyhow ~P is derived, which is what the first part of your second comment is about. And ummmm... I can't quite remember why I flipped things around, but there has to be reason, which I think has to do with the second part of this second question, which I'll have to post up later after I sort some things out... sorry...

Adam said...

Again, that seems absolutely right. So why not just drop the 'HS'? Still seems like, whatever rule is bing applied, that ~P is going to follow from 3-5. Call it extended modus ponens or something.
Any better?