### Is looking the same as transitive?

Is the following thesis true?:

Many philosophers have denied this thesis. However, the following argument appears to be a compelling argument in its favor:

1. Let w, x, y, and z be arbitary individuals and suppose that x looks the same as y to w and y looks the same as z to w.

2. For all x, y, and z, x looks the same as y to z iff the way x looks to z is the same as the way y looks to z.

3. For all x, y, and z, the way x looks to z is the same as the way y looks to z iff the way x looks to z=the way y looks to z.

4. The way x looks to w=the way y looks to w and the way y looks to w=the way z looks to w. [From (1),( 2), and (3)]

5. For all x, y, and z, if x=y and y=z, then x=z.

6. The way x looks to w=the way z looks to w. [From (4) and (5)]

7. x looks the same as z to w. [From (2), (3), and (6)]

8. For all w, x, y, and z, if x looks the same as y to w and y looks the same as z to w, then x looks the same as z to w. [(1)-(7), conditional proof]

What, if anything, should one say to this argument in favor of the Transitivity of Looking the Same As? Should we accept its conclusion? Deny one of its premises? If deny one of its premises, which one?

[Delia Graff Fara seems to present such an argument in her "Phenomenal Continua and the Sorites", available at http://www.princeton.edu/~graff/papers/mindcontinua.pdf]

**Transitivity of Looking the Same As**: For all w, x, y, and z, if x looks the same as y to w and y looks the same as z to w, then x looks the same as z to w.Many philosophers have denied this thesis. However, the following argument appears to be a compelling argument in its favor:

1. Let w, x, y, and z be arbitary individuals and suppose that x looks the same as y to w and y looks the same as z to w.

2. For all x, y, and z, x looks the same as y to z iff the way x looks to z is the same as the way y looks to z.

3. For all x, y, and z, the way x looks to z is the same as the way y looks to z iff the way x looks to z=the way y looks to z.

4. The way x looks to w=the way y looks to w and the way y looks to w=the way z looks to w. [From (1),( 2), and (3)]

5. For all x, y, and z, if x=y and y=z, then x=z.

6. The way x looks to w=the way z looks to w. [From (4) and (5)]

7. x looks the same as z to w. [From (2), (3), and (6)]

8. For all w, x, y, and z, if x looks the same as y to w and y looks the same as z to w, then x looks the same as z to w. [(1)-(7), conditional proof]

What, if anything, should one say to this argument in favor of the Transitivity of Looking the Same As? Should we accept its conclusion? Deny one of its premises? If deny one of its premises, which one?

[Delia Graff Fara seems to present such an argument in her "Phenomenal Continua and the Sorites", available at http://www.princeton.edu/~graff/papers/mindcontinua.pdf]

## 2 Comments:

I like this argument. But, I am not sure what I think about it yet. I guess I am inclined to deny (2). But, I am a little puzzled by the linguistic function of the definite article in sentences of the form 'x looks the same as y to z'. This makes me think worry that my objection to (2) is no good. But, let me first spell out that objection and then talk a little bit about my worry.

Consider premise (2).

2. For all x, y, and z, x looks the same as y to z iff the way x looks to z is the same as the way y looks to z.

Presumably, there is some x y and z such that x looks the same as y to z. (Let's just assume that for now and worry about it a little bit later.) Now, given a Russellian-like view fo definite descriptions, premise (2) entails that there is one and only one way that x looks to z (if x looks the same as y to x). But presumably there are many ways that an arbitary individual will look to any particular person. This suggests that (2) is false.

We might replace (2) with somethinglike the following:

2*. For all x, y, and z, x looks the same as y to z iff

away x looks to z is the same asaway y looks to z.But if we do that, then the resulting argument is invalid. Moreover, I don't see a plausible way to make it valid.

That is my best objection to this argument. Now for my slight worry involving the definite article in phrases of the form 'x looks the same as y to x'. One might argue that the linguistic function of that article precludes there being multiple ways that a thing looks to a particular person. In other words, it might make (2) very plausible. If that were the case, then I would be inclined to say the arguemnt is sound but that it is never the case that anything looks the same as anything else to any particular person.

I guess the gross implausibility of saying that there is no true instance of (1) inclines me to say that any linguistic theory on which the definite article in question precludes there being multiple ways that a thing looks to a particular person is false. Since i am inclined to think that such linguistic theories are false, I am inclined to stand by my original objection above.

It strikes me that the argument can be tidied up to avoid Joshua's objection, if we turn 2. into:

2*. For all x, y, and z, x looks the same as y to z under aspect a iff the way x looks to z under aspect a is the same as the way y looks to z under aspect a.

This allows that things might look multiple ways, under different aspects.

I think the right thing to do is to reject 3. as involving an illicit move from talking about "looks the same as", which is a judgment relating objects, to "ways things look", which is supposed to capture some properties in virtue of which that judgment is made. I deny the existence of these properties, whether they be supposed to inhere in the objects, or in properties of perceptual experiences.

The right person to argue about all this with is Wylie Breckenridge, who is going to be at Cornell soon, and who recently wrote a thesis called "The Meaning of ‘Look’". I went to a talk by Wylie in Sydney last year where he defended the transitivity of "looks the same as" to much general incredulity, including mine. (That probably says as much about Sydney as it does about Wylie, whose work I think is very interesting).

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