The last thought

Entertain this thought:

1. There is a unique last thought that anyone ever thinks and it’s not true.

Or, more briefly:

2. The last thought is not true.

There are, of course, possible worlds where there is no last thought, because (temporal) thoughts go on forever, and worlds where there is a tie for last thought, and worlds where the last thought is “I screwed up” and is true. But, plausibly, there are also worlds where there is a unique last thought and it’s not true—say, a world where the last thought is “I see how to defuse the bomb now.”

In other words, (1) seems to be a perfectly fine, albeit depressing, contingent thought.

Is there a world where (1) is the last thought? You might think so. After all, it surely could be the case that someone entertains (1) and then a bomb goes off and annihilates everyone. But supposing that (1) is the last thought in w, then (1) either is or is not true in w. If it is true in w, then it is not, and if it is not true, then it is true. Now that’s a paradoxical last thought!

Over the last week, I’ve been thinking of a paradox about thoughts and worlds, inspired by an argument of Rasmussen and Bailey. I eventually came to realize that the paradox (apparently unlike their argument) seems to be just a version of the Liar Paradox, essentially the one that I gave above.

But we shouldn’t stop thinking just because we have hit upon a Liar. (You don’t want your last thought to be that you hit upon a Liar!) Let’s see what more we can say. First, the version of the Liar in (1) is the Contingent Liar: we only get paradoxicality in worlds where the last thought is (1) or something logically equivalent to (1).

Now, consider that (1) has unproblematic truth value in our world. For in our world, there is no last thought, given eternal life. And even if there were no eternal life, and there was a last thought, likely it would be something that is straightforwardly true or false, without any paradox. Now an unproblematic thought that has truth value has a proposition as a content. Let that proposition be p. Then we can see that neither p nor anything logically equivalent to it can be the content of the last thought in any world.

This is very strange. If you followed my directions, as you read this blog post, you began your reading by entertaining a thought with content p. It surely could have happened that at that exact time, t, no one else thought anything else. But since a thought with content p cannot be the last thought, it seems that some mysterious force would be compelling people to think something after t. Granted, Judaism, Christianity and Islam, there is such a mysterious force, namely God: God has promised eternal life to human beings, and this eternal life is a life that includes thinking. But we could imagine someone thinking a thought with content p at a time when no one else is thinking in a world where God has made no such promises.

So what explains the constraint that neither p nor anything logically equivalent to it can be the content of the last thought in a possible world? After all, we want to maintain some kind of a reasonable rearrangement or mosaic principle and it’s hard to think of one that would let one require that a world where a thought with content p happens at a time t when no one else is thinking, then a thought must occur later. Yet classical logic requires us to say this.

I think what we have to say is this. Take a world w₁ without any relevant divine promises or the like, where after a number of other thoughts, Alice finally thinks a thought with content p at a time when no one else is engaging in any mental activity, and then she permanently dies at t before anyone else can get to thinking anything else. Then at w₁ there will be other thoughts after Alice’s death. Now take a world w₂ that is intrinsically just like w₁ up to and including t, and then there is no thought. I think it’s hard to avoid saying that worlds like w₁ and w₂ are possible. This requires us to say that at w₂, Alice does not think a thought with content p before death, even though w₂ is intrinsically just like w₁ up to and including the time of her death.

What follows is that whether the content of Alice’s thought is p depends on what happens after her (permanent) death. In other words, we have a particularly controversial version of semantic externalism on which facts about the content of mental activity depend on the future, even in cases like p where the proposition does not depend on the identities of any objects or natural kinds other than perhaps ones (is thought a natural kind?) that have already been instantiated. Semantic externalism extends far!

The lastness in (1) and (2) functions to pick out a unique thought in some worlds without regard for its content. There are other ways of doing so:

• the most commonly thought thought

• the least favorite thought of anybody

• the one and only thought that someone accepts with credence π/4.

Each of these leads to a similar argument for a very far-reaching semantic externalism.

A weird escape from the Knowledge Argument?

Take Jackson’s story about Mary who grows up in a black-and-white room, but learns all the science there is, including the physics and neuroscience of color perception. One day she sees a red tomato. The point of the story is that in seeing the red tomato, she has learned something, even though she already knew all the science, so the science is not all the truth there is, and hence physicalism is false.

This story is generally told in the context of the philosophy of mind, and the conclusion drawn is that physicalism about the mind is false. But that does not actually follow without further assumptions. As far as the argument goes, perhaps Mary didn’t learn anything about herself that she didn’t already know, but has learned something about tomatoes, and so we should conclude that physicalism about tomatoes is false.

Let’s explore that possibility and see if this hole in the argument can be filled. I will assume (though I am suspicious of it) that indeed the kind of knowledge gap that Jackson identifies would imply an ontological gap. Thus, I will accept that Mary has learned what it is like to see the red of a tomato, and that the knowledge of what it is like to see the red of a tomato is not a knowledge of physical fact.

Can one say this and yet accept physicalism about the mind? The one story I can think of that would allow that is a version of Dretske’s qualia externalism: just as most of us think that the content of our thoughts is partly constituted by external facts, so too the qualitative character of our perceptions is partly constituted by external facts. But in fact for the story to work as a way of blocking the inference to non-physicalism about the mind, the qualia (understood as that in the experience that cannot be known by Mary by mere book-learning) would need to be entirely constituted by extra-mental facts.

I think this kind of qualia externalism is not all that crazy. Divine simplicity requires that all of God’s knowledge of contingent fact be partly constituted by states of affairs outside God. But it is plausible that God has something like contingent qualia: that were God to contemplate a world with unicorns, it would “look” different to God than our world. On divine simplicity, we would need to have externalism about these qualia.

That said, the above affords no escape from literal anti-physicalism about the mind. If physicalism about the mind is true, then minds are brains. But if we accept that colored things have a nonphysical component that partly constitutes the perceiver’s qualia, then brains have a nonphysical component, since brains are colored things, namely pinkish (here is a description of their color in vivo, though I cannot vouch for its accuracy).

Maybe, though, this misses the point in the debate. The typical dualist thinks that there is something different about minds and other physical things. If it turns out that minds are just brains, but that they are not physical simply because their pinkness is not entirely a physical property, that’s really not what the dualist was after. The dualist’s intuition is that there is something radically different in the human brain, something not found in a pink sunset cloud (unless it turns out that panpsychism is true!).

Maybe this works to save a more robust dualist conclusion: Plausibly, one doesn’t need a tomato to make Mary have a red sensation. All one needs is to do is to induce in her brain’s visual centers the same electrical activity as normally would result from her seeing a red tomato. And the equipment inducing that electrical activity need not be red at all.

Semantic externalism and time

Here is a curious thing. Suppose that I’ve been lying in bed trying to fall asleep for a while. I’ve lost track of time. At t₁, I know: “I haven’t fallen asleep yet.” At a later time t₂, I know: “I haven’t fallen asleep yet.” It seems quite possible that my internal mental state at t₁ and at t₂ is exactly the same. Yet what I know at t₂ is logically stronger than what I knew at t₁: for that I haven’t yet fallen asleep by the later time entails that I hadn’t fallen asleep by the earlier time.

So it seems that I gained some information, without any change in my internal mental state. This means is that we need to have some semantic externalism with respect to time.

An argument for semantic externalism

I am not actually convinced by this argument. But let's go.

1. If it is possible that whether an utterance expresses a proposition depends on what happens at the same time in distant places in the universe, then semantic externalism is true.
2. It is possible that whether an utterance expresses a proposition depends on what happens at the same time in distant places in the universe.
3. Therefore, semantic externalism is true.

I am not going to defend (1). It's fairly plausible, though I think it's actually a weak point. I want to defend (2). Suppose Fred and Janine are in distant places in the universe, and speak simultaneously. Fred says:

4. The sentence Janine is now uttering is true.

Janine says:

5. The sentence Fred is now uttering is not true.

It cannot be that both of Janine's and Fred's utterances succeed in expressing a proposition. For if they do, then if what Janine says is true, it is not true, and if what Janine says is not true, it is true, which is a contradiction. But in a world where Fred instead says:

6. 2+2=5.

and Janine still says (5), what Janine utters does express a proposition—indeed, a true one. And in a world where Fred still says (4) but Janine says (6), Fred's utterance expresses a false proposition. So it must be that whether Janine's utterance expresses a proposition depends on what Fred says far away, or that whether Fred's utterance expresses a proposition depends on what Janine says far away. Either option is sufficient to yield (1).