Wednesday, January 20, 2021

I can jump 100 feet up in the air

Consider a possible world w1 which is just like the actual world, except in one respect. In w1, in exactly a minute, I jump up with all my strength. And then consider a possible world w2 which is just like w1, but where moments after I leave the ground, a quantum fluctuation causes 99% of the earth’s mass to quantum tunnel far away. As a result, my jump takes me 100 feet in the air. (Then I start floating down, and eventually I die of lack of oxygen as the earth’s atmosphere seeps away.)

Here is something I do in w2: I jump 100 feet in the air.

Now, from my actually doing something it follows that I was able to do it. Thus, in w2, I have the ability to jump 100 feet in the air.

When do I have this ability? Presumably at the moment at which I am pushing myself off from the ground. For that is when I am acting. Once I leave the ground, the rest of the jump is up to air friction and gravity. So my ability to jump 100 feet in the air is something I have in w2 prior to the catastrophic quantum fluctuation.

But w1 is just like w2 prior to that fluctuation. So, in w1 I have the ability to jump 100 feet in the air. But whatever ability to jump I have in w1 at the moment of jumping is one that I already had before I decided to jump. And before the decision to jump, world w1 is just like the actual world. So in the actual world, I have the ability to jump 100 feet in the air.

Of course, my success in jumping 100 feet depends on quantum events turning out a certain way. But so does my success in jumping one foot in the air, and I would surely say that I have the ability to jump one foot. The only principled difference is that in the one foot case the quantum events are very likely to turn out to be cooperative.

The conclusion is paradoxical. What are we to make of it? I think it’s this. In ordinary language, if something is really unlikely, we say it’s impossible. Thus, we say that it’s impossible for me to beat Kasparov at chess. Strictly speaking, however, it’s quite possible, just very unlikely: there is enough randomness in my very poor chess play that I could easily make the kinds of moves Deep Blue made when it beat him. Similarly, when my ability to do something has extremely low reliability, we simply say that I do not have the ability.

One might think that the question of whether one is able to do something is really important for questions of moral responsibility. But if I am right in the above, then it’s not. Imagine that I could avert some tragedy only by jumping 100 feet in the air. I am no more responsible for failing to avert that tragedy than if the only way to avert it would be by squaring a circle. Yet I can jump 100 feet in the air, while no one can square a circle.

It seems, thus, that what matters for moral responsibility is not so much the answer to the question of whether one can do something, but rather answers to questions like:

  1. How reliably can one do it?

  2. How reliably does one think (or justifiably think or know) one can do it?

  3. What would be the cost of doing it?


Chris said...

I have a question, and maybe, I'll just use this example in the case of God's existence.

Does religious context really play in thinking that the event is miraculous?

Suppose I prayed to God that I will jump 100 feet up in the air, and there is an audience who saw me and heard me praying. And, let's say that it really happened.

Would the audience probably think that God caused the miracle? If yes or no, how does that differ when someone jumped 100 feet up in the air without praying?

Michael Gonzalez said...

Pruss: Respectfully, I think there is a rather glaring mistake at the heart of this reasoning. From the fact that I jump, and the ground recedes to 100ft below me, it does not follow that I jumped 100ft or that I ever could do so. The statement "I can jump X feet" refers to my capacity to propel myself a certain distance, not my broader capacity to make it the case that things are farther away (say, by strapping rockets to them or praying for a miracle...). Moreover, in your example, it is explicitly not anything in my capacity that makes the Earth recede 100ft. But, even if it were, that would not be what is captured by the claim "I can jumping 100 ft".

So I don't think there's any paradox here, and I don't think it has to do with it being very improbable, rather than impossible. In the Kasparov case, it is impossible for you to play better chess than him; but that has nothing to do with the possibility that you might randomly move pieces in exactly the way that they need to be to beat him (to replicate a Deep Blue moveset, as in your example). It's ludicrously improbable; but, even if you did it, that would not count as playing better chess any more than randomly stepping at the same times as a drum beats counts as having rhythm.

Alexander R Pruss said...

I wasn't thinking of the earth receding. I was thinking of its mass decreasing. Imagine that it turns into a giant sponge while maintaining overall shape.
I did not say I could play better chess than K. I just said that I could win.

Alexander R Pruss said...

Definitely. Prayer would be evidence that an unlikely event is a miracle rather than a fluke.

Michael Gonzalez said...
This comment has been removed by the author.
Michael Gonzalez said...

But isn't it evident that being able to get 100ft up because the Earth miraculously changes density does not tell us the physical capacities of the one jumping? What we mean by "I can X" is not captured in such an example. Likewise, I don't think anyone would call it "winning" if ending up in a checkmate position was due to the pieces changing place via quantum effects.

I think the inferences about moral responsibility and reliability are good and very interesting. I just don't think the earlier part of the argument can work, since that's not at all what we mean by "I can X". It's not within our power to change the density of the Earth so that jumping on it is like jumping on some tiny satellite. And what matters to responsibility is that the relevant instantiation of states of affairs is within your power.

As an example:

1) I could have saved the drowning man if I could swim downward much more quickly than I actually can.
2) I could have made it downward quickly enough if someone had strapped weights onto me.
3) So, I am morally responsible for saving him, because it was possible to get to him as long as someone else did something that I have no control over....

I think what we want to say is that the person who could have put weights on you to help you get to him fast enough has some responsibility; but not you. Am I missing something?

Alexander R Pruss said...

My argument has these premises:

1. In w2, I jump 100 feet in the air.
2. In any world where I jump 100 feet in the air, just prior to the jump it's true that I *can* jump 100 feet in the air.
3. If in w2 prior to the jump I can jump 100 feet in the air, then in w1 at the same time I can jump 100 feet in the air.
4. If in w1 at that time I can jump 100 feet in the air, then in the actual world I can also do so.

Which premise are you denying?

Michael Gonzalez said...

I deny P2. I'm intuitively inclined to deny it quite vehemently (though, I could be quite mistaken).

"I can jump 100 feet" carries with it the assumption that I mean without changing other circumstances, especially ones that are manifestly not under my control, like the density of the Earth. The "I can" part means the success of the attempt cannot depend on things outside of my control. And the "jump" part means the success of the attempt has to be grounded in the act of jumping; not in some other act (like praying for a miracle or setting off my hidden jetpack or performing a Copenhagen miracle and "observing" the density change into being!).

Prior to the change in density, it simply was not in my power to jump 100ft from the surface of the Earth.

Alexander R Pruss said...


I used to think things that committed me to the denial of P2, but then I realized that it seems absurd to say: "I did something that I couldn't do."

Michael Gonzalez said...

Pruss: I agree that it is absurd to say "I did something that I couldn't do", I just deny that it is right to say "I did something" when the relevant factors for success were actually out of my control. For example: Is it right to say that Moses was able to split the Red Sea or that Peter was able to walk on water?

Alexander R Pruss said...

Peter *did* walk on water. So it seems right to say that he could walk on water. Which, I agree, sounds wrong.

I think I now have an idea of what's going on linguistically. I think "can" sentences usually involve a greater degree of generality, while "do" sentences are more particular. A sufficient condition for Peter to *walk* on water is that there be some quantity of liquid water and for Peter to walk on its surface. But it seems to me that when we say that Peter *can* walk on water, we usually mean something a bit more robust than that: we mean that Peter can walk on the surfaces of typical quantities of liquid water. Peter can walk on water in miraculous circumstances--but then so can you and I. (For definiteness, we might assume that the surface tension was miraculously increased.)

Similarly, someone who does a backfloat on the water of the Dead Sea need not count as being able to do a backfloat on water.

Likewise, if I beat Kasparov at chess while he was completely drunk, then it's still quite true that I beat Kasparov. But if I say I *can* beat him at chess, I mean that I can beat him in the typical circumstances for playing chess with someone, which is false.

If this is right, then the principle "If you did A, you could do A" is correct, but you have to watch out for de dicto / de re confusion, and a shift in the quantification over cirucmstances in the _de re_ case.

When the "something" and "it" are read as _de re_, the principle is unqualifiedly correct: if you performed a token action A, then you were capable of performing a token action A.

But if you try to apply the principle with A being some description of a type of action, like "jumping 100 feet" or "walking on water" or "beating Kasparov at chess" (with the grammar cleaned up), then you have a problem, because "you did A" means "you performaed at least one instance of A" while "you could do A" normally means something like "you could perform A in any of the typical situations for performing A".

If A is a general description, then the correct principle is: "If you did A, then you were able to do A in at least one set of logically possible circumstances."

So, my post was wrong. I can jump 100 feet in the air under some circumstances, but it does not follow that I can jump 100 feet in the air.