Friday, November 14, 2014

Possibility, Aristotelian propositions and an open future

Aristotelians think that tensed sentences like "It is sunny" expressed "tensed propositions" capable of changing in truth value between true and false as the facts alter. The proposition that it is sunny is false today but was true two days ago. Anti-Aristotelians, on the other hand, roughly say that the sentence "It is sunny" expresses the proposition that it is sunny at t0, where t0 is the time of utterance, a proposition whose truth value does not vary between true and false as the facts alter.

Most presentists are Aristotelians about propositions, and most open futurists these days seem to be presentists. I will argue, however, that an open futurist should not be an Aristotelian about propositions. I think this means that an open futurist should not be a presentist.

Consider the sentence

1. I will freely put on a pink shirt in one day.
Let p be the proposition expressed by this. Clearly:
1. p is possible.
(Also, the negation of p is possible.)

According to the anti-Aristotelian open futurist, p is the proposition that I will put on a pink shirt on day d0+1, where d0 is November 14, 2014. The anti-Aristotelian open futurist holds that on November 14, p is not true, but that on November 14 it may become true. So the anti-Aristotelian open futurist has a nice way of accounting for (2). While it's impossible that today p is true, it is possible that p be true tomorrow, and that's enough to make p possible.

But the Aristotelian open futurist is in trouble. For on her view, on November 15, p doesn't tell us about how things are on November 15, but about how things are on November 16: it's a tensed proposition that on any day says how things will be on the next. But on no day is it true that on the next day I will freely put on a pink shirt, if open futurism is true. And open futurism isn't just a contingent thesis. So given open futurism:

1. It is impossible that p ever be true.
(And what cannot ever be true cannot become true either, since if something were to become true, it would then be true.) But surely:
1. If it is impossible that p ever be true, then p is not possible.

Alexander R Pruss said...

The anti-Aristotelian faces the same problem with a different proposition. Clearly it's possible that I will freely sing "Joy to the world" on infinitely many days (say, in heaven). The anti-Aristotelian says that this proposition says that after t0, there are infinitely many days on which I freely sing "Joy to the world". But the proposition that there are infinitely many such days always depends on the future, and so can never be true on open future views.

Mike Almeida said...

But that proposition p can be expressed with at least two linguistic vehicles. The proposition express by 'it will rain tomorrow' (uttered on the 14th) expresses the same proposition as 'it will rain today', uttered on the 15th. If p is that proposition, then though it is never true as expressed in the first sentence, it is true as uttered in the second sentence.

Mike Almeida said...
This comment has been removed by the author.
Mike Almeida said...

What might be a worry is that the very same proposition p is expressed by one sentence on the 14th and by another on the 15th. But that proposition has different properties on the 14th and the 15th (true on the 15th, not true on the 14th). So, the proposition, expressed on the 14th and the 15th, cannot be the same one. Otherwise we have a violation of LL.

Alexander R Pruss said...

I don't see the violation. The Aristotelian says: the proposition is true on the 14th and false on the 15th, say. This is no more a violation of LL than my being sleepy on the 14th and wakeful on the 15th.

Mike Almeida said...

Right, except that that's not what the proposition says. It say that it will rain 'the day after tomorrow' (or, something like that). So, assume an open future, and consider (1) and (2),

(1) It will rain the day after tomorrow.

(2) It will rain today.

These two vehicles express the same proposition when (1) is uttered two days before (2) is uttered. But that can't be right, since the proposition expressed by (2) (on the day of the event) has properties different from the proposition uttered by (1). One takes a truth value of true or false, the other is neither true nor false. If the sentences were indexed to specific times or days (at t or on the 14th, etc.) then I agree there would be no problem with LL. But as it is, there does seem to be a problem.

Alexander R Pruss said...

Mike:

The Aristotelian denies that the same proposition is expressed.

Mike Almeida said...

That seems absurd. If I promised yesterday that (1).

1. I will give you the book tomorrow.

And it is false today that (2)

2. I will give you the book today,

Then don't I break a promise? Isn't what I promised yesterday expressed in (2) uttered today? 'Today' and 'tomorrow' have precisely the same referent in (1) and (2) when they're expressed, and that is the only difference in the sentences.So, it's hard to see how they could fail to express the same proposition.

Alexander R Pruss said...

No disagreement. It's not my theory. :-)

Alexander R Pruss said...

Notice, too, that on the Aristotelian theory you have to keep on changing your mind. I believe it's evening now. In 10 hours, I will need to deny that very proposition.

Michael Gonzalez said...

Wait a minute! Isn't the possibility of p, on your own theory of alethic modality (here I go again with the "ad hominem" responses!), entirely contained in the current causal powers of the person making the statement?? That means that (2) is true just because I currently have the causal capacity to accomplish p.

Anyway, regardless of that, it seems to me that a presentist (and any layperson with common sense) will think of p as expressing {I will put on a pink shirt in one day... and now begin the countdown, such that, at every moment from now until 24 hours hence, p is altered by the relevant amount of time remaining.} The "in one day" phrase sets a marker on the moment I utter it, and then the statement is altered appropriately as time goes on. Think about it: If someone were to ask me "hey, what did you promise 12 hours ago?", I could properly say "that I will put on a shirt in another 12 hours". Now, those aren't the words I said, but it is common sense that I should adapt the statement to wherever I am in the countdown. Isn't it?

Michael Gonzalez said...

As to your other example, you say Clearly it's possible that I will freely sing "Joy to the world" on infinitely many days (say, in heaven).

My immediate response is, NOPE! Lol. No matter how many days go by, you will never get to a point where it is true that you have sung "Joy to the World" infinitely many times. So, right there, we're right back at the fundamental disconnect between presentism and your view. And, as I've said before, I don't see how a statement with the present-tense term "is" can be true of all these future points. And that isn't just a semantic nit-pick. Your anti-Aristotelian is genuinely saying that all these infinite days co-exist, and have (another present-tense term) a song in them. "Now" becomes utterly indexical, which, for me, causes similar problems to the way that Lewis' EMR takes the "actual" world to be a mere indexical. In our experience, one of the most relevant things is whether something is actual, or merely potential (just as it is equally important that something is actual rather than merely possible). So relegating this to an indexical truth just seems wrong to me. Take the matter of the problem of evil. I genuinely think it matters that the suffering of innocent people actually ceases at some point. Saying "they are not suffering at this location, they are only suffering at that one" doesn't help anything. It is still always true that they are suffering there (at x1, y1, z1, and t1... at that spatiotemporal location).

Heath White said...

Notice, too, that on the Aristotelian theory you have to keep on changing your mind. I believe it's evening now. In 10 hours, I will need to deny that very proposition.

Without prejudice to the overall question....I can see a reply to this argument that goes, "When the facts change, I change my mind. What do you do, sir?"

Alexander R Pruss said...

Michael:

My official theory of modality doesn't require the possibilities to be within the power of the person making the possibility claim. It's rather more complicated than that.

BUT nonetheless I am extremely valuable to you for pointing me towards truth here. For although the official theory is more complicated, I think my freely singing infinitely often is still a counterexample to my theory of possibility.

I am now trying to figure out how to fix my theory of possibility.

Alexander R Pruss said...

Heath:

Yeah, it's not a huge cost.

It would be an interesting challenge to fit this into, say, Bayesian update theories, but mainly just a technical challenge.

Michael Gonzalez said...

Pruss: I agree that your theory is more complicated than one merely predicated on the person making the claim. It appeals more to the actual existence of things which can initiate causal chains leading to the possibility in question. What I meant was that whether or not it is possible for my promise to come true is a fact right now just if there exist the right states of affairs such that a causal chain can be initiated leading to that point. And I brought it up because this possibility has nothing to do with the future actually containing any truth value. The possibility exists right now, that I will initiate and sustain a causal chain leading to the pink shirt.

I do not think your theory of modality needs fixing; I think the idea of freely singing infinitely often is incoherent. That's what needs fixing, in my humble opinion. If you accepted temporal becoming, then you wouldn't think you could ever actually accumulate an infinite number of instances where you sing Joy to the World. It's only the ludicrous B-theory and its affirmation of future-tense truths as though they were (right now) true, which leads to this absurdity (again, that's my humble, and uneducated opinion).