Infinitely Harry

I’m grading papers, and wanting distraction, I thought of this puzzle:

Jones voted for Bush. Black was ready to intervene and ensure, had the ensurance been necessary, that Jones so vote, but it wasn’t necessary. It may seem that Jones could not have refrained from voting for Bush.

But, in fact, White was ready to intervene and ensure, had the ensurance been necessary, that Black not intervene with Jones, but it wasn’t necessary. Now it may seem that Jones could have refrained from voting for Bush.

But, in fact, Gray was ready to intervene and ensure, had the ensurance been necessary, that White not intervene with Black, but it wasn’t necessary. Now it may seem that Jones could not have refrained from voting for Bush.

But, in fact, the sequence of would-be interveners is infinite. Could Jones have refrained from voting for Bush?

Comments

[Patricia Greenspan]

Hi Randy. I have lots of distractions currently, but why not add this to the list. If the chain of hypothetical interveners-with-interveners is infinite, it seems as though no one could have intervened. So assuming that Jones could have refrained if there were no hypothetical interveners, he could have refrained in this case too -- don't you think?

[Mark Smeltzer]

I'm still trying to get my head around what an actually infinite set of numbers would look like... so, I'll have to defer commenting on this until I've got that more rudimentary puzzle figured out ;)

[Mike]

Suppose he attempted to vote against Bush. It would then have been the case that he neither voted for Bush nor against him. Does that count as refraining? Imagine the same situation with a light switch. Were Jones to attempt to flip the switch off, Black would interfere to ensure that he flipped it on, and White would then interfere to ensure that it is not flipped on, and Gray to ensure that it is flipped on, and so on. The sequence of interference ensures that it is neither flipped on nor off. I'm not sure if that counts as refraining from flipping it on.

[Tamler Sommers]

Maybe this explains Kerry's position on the Iraq war in 2004.

[John Fischer]

Hi Randy,

Interesting!! You've got me thinking (for a change, some would no doubt say). Patricia Greenspan says:

"If the chain of hypothetical interveners-with-interveners is infinite, it seems as though no one could have intervened. So assuming that Jones could have refrained if there were no hypothetical interveners, he could have refrained in this case too -- don't you think?"

But my puzzle about this is, "Where to start?", as it were. So I grant that what Patricia Greenspan says is plausible. But why not say the following:

"Given Black's presence and dispositions, Jones could not have done otherwise than vote for Bush. And given that there are an infinitely large number of interveners posed to stop the Whites of the world from intervening to block Black's efforts, it seems that Jones could not have done otherwise."

So, my question is: why is Greenspan's point any more valid than this one?

[John Fischer]

Of course, in my previous post, I should have said something like:

"Given just Black, and no further interveners, it seems that Jones could not have done otherwise. Now, given additionally that there is an infinitely large number of interveners poised to support Black's efforts..."

[Mike]

I think the result a contradiction. The question is whether Jones can R (refrain), isn't it? And we have a familiar series of counterfactuals, letting I1 be the first interference and I2 the second, I3 the third and so on to infinity. It looks like this,

1. I1 []-> ~R

2. (I1 & I2) []-> R

3. (I1 & I2 & I3) []-> ~R

4. (I1 & I2 & I3 & I4) []-> R

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.
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oo

He can R only if the antecedent includes an even number of interferences and he can ~R only if it contains an odd number. Since the antecedent contains neither, it is not possible that he refrains or does not. But ~<>(R v ~R) is a contradiction. Since anything follows, he can refrain.

[Patricia Greenspan]

Hi John. Your first message relies on reference to Black's "dispositions," as if they were unaltered from what they would be without the further chain of interveners. But doesn't that deserve question, if "dispositions" means, not what Black is inclined to do, but what he actually *would* do, *if* Jones attempted to refrain?

[Mike]

Oops. I neglected to note that a contradiction follows if Jones tries to refrain. So he can't so much as try.

[Randy Clarke]

On the one hand, Jones and Black are alike in having above them an infinite series of would-be interveners. So it seems we should say the same thing about ability to do otherwise in both of their cases.

On the other hand, it seems that if Black can intervene, then Jones can't refrain.

Speaking of dispositions and Frankfurt cases, the upcoming discussion on GFP of Kadri Vihvelin's paper will include some attention to that.

[Alan]

Isn't it the case that the counterfactually countercancelling infinite series of interveners are relevant here iff there is some well-defined and real sense that the actual world Jones can/may refrain from voting for Bush in the first place? (In the series of interveners this issue arises first with White--so I thought it appropriate I raise the issue! :-) One could argue that an actual world Jones who is subject to absolute determinism could not have refrained from voting for Bush, and thus the question becomes moot. Can this question be clearly resolved with a free-floating sense of "refraining"?

[Mike]

Jones and Black are alike in having above them an infinite series of would-be interveners. So it seems we should say the same thing about ability to do otherwise in both of their cases.

Randy, that's a nice observation. Generalizing the argument, we get that Jones cannot refrain, Black cannot interfere, White cannot interfere . . .and so on upward. From which it follows that since Black cannot interfere, White cannot interfere...all the way up, that Jones can refrain. Conclusion: Jones cannot refrain iff. he can AND Black cannot interfere iff. he can...and so on upward.

[Cihan Baran]

Speaking of dispositions and Frankfurt cases, the upcoming discussion on GFP of Kadri Vihvelin's paper will include some attention to that.

Okay, so I was really excited to read that paper because it is quite innovative and resourceful. (In fact I am so interested I am jumping at the merest opportunity to poke a question about that paper...) I really found it a fascinating reading - it made me want to read about Lewis... BUT...

Did anyone else think that the paper was disappointing in that it didn't really deal with origination/sourcehood worries? I wonder what kind of a response Vihvelin would have to Mele's Zygote Argument. Or any other manipulation argument..

Okay, this may be a little premature - so feel free to ignore this message and warn me to wait for another week or so...

[Patricia Greenspan]

Randy: What does "doing otherwise" amount to in the case of Black or other *hypothetical* interveners? Are you taking it as *not* intervening? But what Black in fact does -- in the original Frankfurt scenario OR if he's restrained by other interveners -- is exactly that. So unless we should substitute a denial of the hypothetical that's assumed to be true of Black (even though that's not a "doing"), doing otherwise would mean intervening. But if it means intervening, and he can't, then there's no barrier to Jones's refraining. And the same thing would seem to follow if we deny the hypothetical. So again, Jones can refrain -- assuming, of course (to satisfy Alan), that the ordinary claim that Jones can refrain is acceptable.

Let me also suggest, in answer to Mike, that deriving a contradiction from the case would mean that it's impossible, not that Jones or the other agents in it are REALLY REALLY hamstrung. If the infinite chain of hypothetical interveners yields a contradiction, then Jones is able to refrain -- assuming, once again, that he'd be able to refrain without any hypothetical interveners.

[Patricia Greenspan]

On further reflection, I should retract my answer to Mike just above. If the case is impossible, I had been assuming that just got rid of the chain of interveners, leaving Jones as he would be otherwise (as in Mike's first formulation of the contradiction argument). But another response might be to deny that the chain of interveners can be infinite. Whether or not Jones can refrain depends on where the chain stops (who's set to intervene with whose intervention, etc.), though, and there's no way of settling that. So is the point just that Frankfurt cases need to specify an end-point in the chain of hypothetical interventions?

[Randy Clarke]

Let's stipulate that, in the absence of would-be interveners, Jones would be able to refrain from voting for Bush. Likewise, in the absence of further would-be interveners, Black would be able to intervene with Jones. And so on.

Black does not in fact intervene with Jones. The relevant doing otherwise for Black would be intervening with Jones. And similarly for White, Gray, etc.

It would be curious if the case were impossible. I don't know whether there are actually infinitely many beings, but it certainly seems that there could be (infinitely many electrons, or stars, or Toyotas). A lot of beings could be lined up as would-be intereveners. Why not infinitely many of them? I don't assume that, in every sort of matter, if there can be a lot of things doing something, there can be infinitely many doing it. I just don't see why there can't be in this case.

[Joe]

Chihan,

That might be a good question to ask Kadri once the discussion starts!

[Peter Brian Barry]

Randy,

Would you need an infinite number of counterfactual interveners? A finite number of recycled interveners might do the trick. Perhaps Black stands in the CFI relation to Jones, Gray to Black, White to Gray... and later in the sequence Black again stands in the CFI relation to someone else, Gray to Black again, White to Gray again, and so forth ad nauseum.

[Cihan Baran]

Hey Joe,

I know it would be a good point to press. I just wanted to be the first - who knows, that may be the only substantial thing I may be able to say about that paper. (Hence my eagerness.)

Hey everyone,

I have a rather "sketchy" solution for this - one that's mathematical in nature and one that won't convince anyone, not even me... However, I just thought it would at least be amusing.

1- If the number of interveners is odd, then Jones couldn't have done otherwise, as in the original Frankfurt case. If the number of interveners is even, then Jones could have done otherwise - as the interveners would cancel each other out.

2- Infinity (i.e. the countable kind) is, by definition, divisible by every integer, including two. Therefore, infinity is an even number.

(Conclusion) Hence, Jones could have done otherwise.

I know it's really "sketchy" but I think the solution of the puzzle turns around the question of whether infinity (countable) is an even number. To me, this seems like a meaningless question, as it is meaningless to look for properties like evenness, oddness in an unusual number like infinity.

[Joe]

Am I correct to think that, on Kadri's account, Randy's problem is no problem at all -- and neither is Frankfurt's?

According to Kadri, Franfurt examples are examples of 'finks': dispositions “which would vanish immediately, on being put to the test.” She advocates a revised conditional analysis of dispositions, inspired by Lewis. On her view, (1) Jones could have done otherwise iff Jones was disposed to do so and (2) such dispositions are not undermined by Frankfurt examples, for (3) the revised conditional analysis of dispositions is the right analysis. Since (4) Jones had the relevant disposition, (5) Jones could have done otherwise dispite the efforts of White, Black, Grey, etc.

It is worth noting that Frankfurt-style examples always involve finks (or masks) and that most philosophers working on dispositions believe that agents/objects have the relevant dispositions in cases of finks and masks.

Perhaps Kadri is wrong about (3) -- that the revised conditional analysis of dispositions is correct (an analysis that I've defended). However, that is irrelevant to the main issues lurking behind Frankfurt-style examples. The main claim is (1), which with (4) yields (5). Frankfurt-style examples (as well as Randy's example) are entirely mute unless one adopts a radical view of dispositions.

Or so it seems to me.