Friday, July 15, 2022

Necessity and the open future

Suppose the future is open. Then it is not true that tomorrow Jones will freely mow the lawn. Moreover, it is necessarily not true that Jones will freely mow the lawn, since on open future views it is impossible for an open claim about future free actions to be true. But what is necessarily not true is impossible. Hence it is impossible that Jones will freely mow the lawn. But that seems precisely the kind of thing the open futurist wishes to avoid saying.

10 comments:

ASBB said...

What's impossible is the proposition 'WILL(Jones freely mows thee lawn)'. This is consistent with the truth of 'Jones freely mows the lawn'. The former proposition (like all propositions) is about how the world is right now, not about what's happening at some future moment (at least on presentism, where most of the open futurists reside). p is not logically equivalent to WAS(WILL(p)).

ASBB said...

Me again. It just occurred to me that another way to capture the difference is to focus on the relative scope of the POSSIBLE and WILL operators. So the presentist open futurist should insist that ~POSSIBLE(WILL(Jones freely mows)) whilst also maintaining WILL(POSSIBLE(Jones freely mows lawn)). I think you take it that former entails the negation of the latter? (or even entails simply that ~POSSIBLE(Jones freely mows) ?). But this neglects the different scopes at play.

Zsolt Nagy said...

Okay. I suppose the future to be open as you said, that in your first sentence "Suppose the future to be open.".
So then possibly Jones will freely mow the lawn tomorrow as possibly Jones will freely not mow the lawn tomorrow, if we also suppose there being "free will".
Now it's not necessarily the case, that Jones will freely mow the lawn tomorrow, if and only if it is possibly the case, that Jones will not freely mow the lawn tomorrow: ~□(proposition P) ⇔ ◇(~P).
Also it's necessarily not the case, that Jones will freely mow the lawn tomorrow, if and only if it is not possibly the case, that Jones will freely mow the lawn tomorrow: □(~P) ⇔ ~◇(P).
But since we supposed to suppose the future to be open [◇(P) Λ ◇(~P)], then how are we supposed to suppose, that ~◇(P) or □(~P) could ever be the case?!?
So then what are you, Alexander, talking about again?
EITHER I don't understand the notion of "open future" or we understand different things under the notion of "open future" OR the "inconsistent narrator" is at it's best again producing an inconsistent narration - you unreasonably twisting logic itself - not properly making a quantifier shift or mish mashing different quantifiers with each other.("Necessity □" and "possibilty ◇" are just modal logical quantifiers - logically working similarly to the usual quantifiers all/any ∀ and "some ∃".)

Tom said...

This would prove too much as it would prove that a denial of Molinism is false.

Suppose there are no true subjunctive conditionals. Then it is not true that Jones would freely mow the lawn (in some hypothetical scenario S). Moreover, it is necessarily not true that Jones would free mow the lawn, since on a non-Molinism view, it is impossible for conditionals regarding free actions to be true. But what is necessarily not true is impossible. Hence it is impossible that Jones would freely mow the lawn in S. But that is precisely the kind of thing that any libertarian would want to avoid saying.

I think the way out of your problem and my parody is to say that the modal operator modifies the entire statement. In my case, it modifies the conditional and in yours it modifies the future. For example, it is impossible that Jones would freely mow the lawn in S. But not because wouldn't mow the lawn in S, but rather, because any statement about what he would do in S is an impossible statement. There is no such thing. Likewise, for open future views, the claim that Jones will mow the lawn is necessarily false. Not because he will in fact mow the lawn, but because any proposition about future free conditionals is necessarily false.

Alexander R Pruss said...

Zsolt:

What people generally mean by open future is that there are no facts about what will contingently happen: i.e., ~WILL(p) and ~WILL(~p).

Alexander R Pruss said...

ASBB:

That's one option for the open futurist. But ~POSSIBLE(WILL(Jones mows the lawn)) still sounds wrong. Mowing the lawn differs relevantly from squaring the circle.

Zsolt Nagy said...

If there are no facts about what will contingently happen, then it's not, that ~WILL(p) AND ~WILL(~p).
If there are no current facts about what will contingently happen, then WILL(p OR ~p) = WILL(p) OR WILL(~p) = WILL(p) OR ~WILL(p).

~WILL(p) AND ~WILL(~p) = WILL(~p AND p) = WILL(logical contradiction).
I still think very much so, that you are simply logically inconsistent here.

Zsolt Nagy said...

Well, to be more precise I guess, that these are the logical implications/biconditionals, which are satisfied by the predicate "WILL":
(I) For any proposition p: ~WILL(p) ↔ WILL(~p)
(II) For any proposition p and q: WILL(p AND q) ↔ (WILL(p) AND WILL(q))

(corollary) For any proposition p and q: WILL(p OR q) ↔ (WILL(p) OR WILL(q))
Proof:
1.0) ~(WILL(p OR q) ↔ (WILL(p) OR WILL(q))) (indirect proof assumption)
1.1) (~WILL(p OR q) AND (WILL(p) OR WILL(q))) OR (WILL(p OR q) AND ~(WILL(p) OR WILL(q))) (1.0, by logical equivalence)
1.2) (WILL(~(p OR q)) AND (WILL(p) OR WILL(q))) OR (WILL(p OR q) AND (~WILL(p) AND ~WILL(q))) (1.1, by I and De Morgan's law)


1.3) (WILL(~p AND ~q) AND (WILL(p) OR WILL(q))) OR (WILL(p OR q) AND (WILL(~p) AND WILL(~q))) (1.2, by De Morgan's law and I)
1.4) ((WILL(~p AND ~q) AND WILL(p)) OR (WILL(~p AND ~q) AND WILL(q))) OR (WILL(p OR q) AND WILL(~p AND ~q)) (1.3, by AND dirstribution over OR and II)
1.5) (WILL((~p AND ~q) AND p) OR WILL((~p AND ~q) AND q)) OR WILL((p OR q) AND (~p AND ~q)) (1.4, by II)
2) WILL(p OR q) ↔ (WILL(p) OR WILL(q)) (1.0-1.5, by indirect proof)

How on earth and by which logic does the assumption of an "open future" supposed to entail, that ~WILL(p) AND ~WILL(~p)?!? I still don't get it, what's the matter here.

Alexander R Pruss said...

Zsolt:

The "open future" view says basically that in the case of a future contingent, WILL(p) is not true. Thus, it is not true that Jones will mow the lawn, since "Jones will mow the lawn" would be a future contingent. Similarly, it is not true that Jones will not mow the lawn.

There are two main versions of the view:
1. WILL(p) is neither true nor false
2. WILL(p) is false.
(But both agree that WILL(p) is not true.)

Additionally, there is disagreement as to whether
3. WILL(p) iff True(WILL(p)).

Zsolt Nagy said...

Yeah, I guess, that's supposed ot be the notion "open future".

But why? That's just illogical - literally disrespecting the logical Law of excluded middle.

In my opinion "open future" can and still should mean, that there is no basis, no current fact CurF in the present, which might imply any future contingent fact FutConF to be true:
There is no CurF for any FutConF, such that CurF → FutConF.
Or in other words, for any CurF there is some true FutConF, such that ~(CurF → FutConF) = (CurF AND ~FutConF).
A "closed future" would mean the opposite/negation of that:
There are some CurF for any FutConF, such that CurF → FutConF.

So philosophers are wasting their time with these illogical and therefore irrelevant things in these days. What a shame? And what a waste of time?
Hm, and what a waste of the future?!?
Hm. I guess then, that the future is not that “open” after all, if one can predict the future from the current state of affairs with such ease.