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.