An Argument for Counterpart Theory

[I have no idea if the following is at all novel or plausible.  Any feedback would be sweet!]

Here’s a puzzle.  David Lewis (1986) has argued for the following thesis:

L. Self-identity is not constituted, even in part, by having certain qualities.

Kit Fine (1994) argued for the following thesis:

F. An essential property of an object is any property that, in part, constitutes what it is to be that object.

Combining these two theses would seem to imply the following somewhat troubling thesis:

T. Objects do not have any qualities essentially.

I say that this thesis is troubling because, after all, it would seem to be part of, say, my essence that I have the quality of being human.[1] But how can it be both that I have no essential qualities and that being human is part of my essence? Let’s assume for the moment that we don’t want to reject either Lewis’s thesis or Fine’s thesis (I for one have been convinced by both authors). How then might we get out of trouble?

Against Structured Propositions

Here’s a view about propositions:

A proposition P is a set of ordered pairs <A,G> where the first object is an individual and the second a property. These propositions are generally expressed by declarative statements such as my utterance of the sentence `Alvin is Green’. Call this `Structured Propositions’.

Here’s an argument against this view of propositions.

P1) If propositions are structured then one must either: a) become Meinongian, or b) accept gappy propositions.
P2) According to Russell, Meinongianism entails contradictions, so it’s unacceptable.
P3) Gappy propositions cannot explain informative speech acts where true negative existential are asserted. Such speech acts cannot express gappy propositions. So, gappy propositions are unacceptable.
P4) From P2 and P3, it follows that we should neither be Meinongian nor gappy proposition theorists.
C) Propositions are not structured.

Newcomb as a Betting Game

I.
Imagine that you are invited to play a betting game.

(I will use “bet” in a loose sense since you won’t risk any of your own money. Worst case scenario, you gain nothing.)

The game works like this:
You can bet that A or you can bet that B.
If you bet that A, you get $1,000,000 if you win and $0 if you lose.
If you bet that B, you get $1,001,000 if you win and $1,000 if you lose.
You are informed that there’s a 99.9% chance that A and a 0.1% chance that B.

Given this information, and assuming that you’d like to win as much money as you can get, how do you think it is reasonable to bet? I trust that we’ll all agree that the reasonable thing to do is to bet that A.

The Newcomb Problem has the exact structure of this betting game.

A: The predictor made a true prediction about how you’ll bet.
B: The predictor made a false prediction about how you’ll bet.

To bet that A, you take only the closed box.
To bet that B, you take both boxes.
Taking one or both boxes is how you place your bet.

I realize that this talk of placing your bet by taking boxes may sound like trickery, but it isn’t. To see this, we can proceed through a series of variations, from a simple betting game (where the earnings are delivered by a third party) to the standard Newcomb situation. If it is rational to bet that A in (1), I hope it will be conceded that it is equally rational to bet that A in (5). (For ease of reading, I will italicize modifications as they arise.)

Necessarily coextensive, yet distinct?

So here’s an Aristotelian puzzle that I do not know how to sort out. It has apparently been reinstated, or a version of it, by Fine. I believe he did not even present it as a puzzle. Anyway, take a look at it, and help me solve it. Otherwise, I’m lost (and so is my paper).

Suppose you believe that properties are the set of their instances. Suppose, furthermore, that you are a modal realist. Aristotle was not, but he does believe in potential and actual bearers of properties, and he does think these are within the extension of a property [Meta, V.26].

In any case, there is a familiar problem with this view: coextensive properties. ‘renate’ and ‘chordate’ have the same actual extension, yet they are different properties. The solution is easy and well known: ‘renate’ and ‘chordate’ are not coextensive because they have different extensions in other possible worlds. Aristotle’s reply would be similar: ‘renate’ and ‘chordate’ are not coextensive because they have different potential instances.

The problem comes with a twisted version of this objection. Suppose you have necessarily coextensive properties, and yet distinct ones. (This is what Fine presents in his ‘famous’ paper against modal accounts of ‘essence’, where he claims ‘essential property’ is not synoymous with ‘necessary property’, I think, however, that Aristotle’s example is better). Aristotle talks about ‘Grammarian’ and ‘Human’. According to Aristotle, this much is true:x is human iff x is a grammarian (or has knowledge of grammar). Yet, ‘Human’ reveals the essence of its instances, and ‘grammarian’ does not.

My question is this: is there any way in which one can sort this case out, and still be extensionalist about properties? Do you know of any extensionalist reply to this? Or should we simply claim that ‘grammarian’ and ‘human’ have the same meaning?

How to Be an Instrumentally Rational One-Boxer

I’ve been thinking about Newcomb’s Paradox lately and find myself strongly inclined towards one-boxing. Because there are so many interesting and complicated issues looming in the background, perhaps I’ll change my mind at some point. In any case, my goal in this post is not to convince anyone to be a one-boxer but only to defend the claim that one can indeed be an instrumentally rational one-boxer. The defense, I should warn, is exceedingly simple. But simplicity has things to be said for it.

The Defense

Finding myself in the Newcomb room and in a greedy state of mind, I would recognize that I occupy one of the following four worlds (provided that I play the game, that the game is as it was described to me, and so forth), which are ordered according to my preferences:

(W₁) Predicted 1; Taken 2; Payoff $1,001,000
(W₂) Predicted 1; Taken 1; Payoff $1,000,000
(W₃) Predicted 2; Taken 2; Payoff $1,000
(W₄) Predicted 2; Taken 1; Payoff $0

The Road to Ramseyan Humility

I’ve mentioned to a few of you around here that I think it is Lewis’ solution to “Putnam’s Paradox” that lands him in “Ramseyan Humility”. Here’s a sketch of why. I apologize for assuming some background familiarity with both “Putnam’s Paradox” and “Ramseyan Humility”, but I’m trying to keep things punchy.

Consider Lewis’ argument for Humility. Lewis’ assumes that T is realized by fundamental properties, which (because fundamental properties are plausibly wholly distinct from the roles they realize) allows Lewis to run the permutation argument to establish multiple possible realizations of T. But why does Lewis assume that T is realized by fundamental properties? There are actually several questions here. First, why does Lewis think that T is even prima face the sort of thing that is realized—that is, why does Lewis think that the Ramsey sentence approach to the content of T is the right one? Second, why does Lewis think that T is realized (rather than holding a non-representational interpretation of the Ramsey sentence as Sklar does)? Third, assuming that T is realized by something, why does Lewis think that T is realized by (metaphysically robust) natural properties [rather than, say, (metaphysically thin) classes]? And, finally, fourth, assuming that T is realized by natural properties, why does Lewis think that T is realized by completely natural properties, i.e., fundamental properties (rather than, say, natural “enough” properties).

Although there are four questions here, I think Lewis’ answer to the first three will be roughly the same: realism. His answer to the fourth question, however, can be found in RH where he makes a particular observation about scientific progress. Let’s take these questions in order.

An “At-At” Theory of Causal Influence

Salmon, in Causality and Explanation, suggests that causal processes are demarcated from pseudo-processes by their ability to transmit marks - causal processes can transmit marks; pseudo-processes can’t. About mark transmission: “A mark that has been introduced into a process by means of a single intervention at a point A is transmitted to point B if and only if it occurs at B and at all stages of the process between A and B without additional interventions.” (CaE, p. 197)

Here’s a simple example: There’s a rotating spotlight in the center of a circular room which casts a spot of light on the wall. The light ray traveling from the spotlight to the wall is a causal process; interpose a red filter in the beam near its source and the spot on the wall will be red. The spot of light moving around the wall is a pseudo-process; no interposing of a red filter (or intervention of any sort) can make the spot maintain its redness (or retain a mark of any sort) as it moves on.

We can ask this question, though: How does the process make the mark appear elsewhere within it? (CaE, p. 197) Salmon thinks the answer is ‘astonishingly simple’: it doesn’t (not in any deep sense, anyway). The transmission of a mark from point A in a causal process to point B in the same process just is the fact that it appears at each point between A and B without further interactions.(CaE, p. 197)

I don’t think this is right. It doesn’t get mark transmission right in close by possible worlds (maybe even in our world). Consider a world w. In w there’s a particle a. a can have properties P, Q, and R. Choose any time t. The probability that a will be P at t is 1/3. Likewise for Q and R. There’s another particle b in w. If b strikes a, a will be P, but only during the strike. Suppose b strikes a at t1. b then ricochets and barrells into space. a, then, is P at t1. Suppose also that, by chance, a is P at t2 and at all times between t1 and t2. It seems that, by Salmon’s criteria, a mark (i.e. P) is transmitted from t1 to t2 along the a’s-travels-process. But clearly it’s not. Mark transmission seems to not be as simple as Salmon takes it to be.