A Recent Objection to the Alethic Openness of the Future
The future is 'alethically' open at time T with respect to possible state of affairs X and future time T* > T if and only if neither "X will obtain at T*" nor "X will not obtain at T*" is true at T.
I believe that the future is alethically open with respect to future contingent states of affairs. Thus, if the present state of the world is indeterministic with respect to whether a sea battle occurs tomorrow (i.e., if that's a future contingent), then on my view neither "A sea battle will occur tomorrow" nor "A sea battle will not occur tomorrow" is now true. Indeed, I submit that both propositions are now false.
There's an interesting challenge to my view that has recently been proposed by Alex Pruss of Baylor Univ. His argument is encumbered with the technical trappings of probability theory, but the basic objection can be stated quite simply as follows:
- On the open future view that I espouse, there are no “will” or “will not” truths about future contingents.
- But we have excellent (inductive) reasons for believing that there are “will” or “will not” truths about future contingents (e.g., “S will not win the lottery” - assume, e.g., a standard lotto and that S has only one lotto ticket).
- Therefore, we have excellent reasons for believing that the open future view is false.
In the first place, it is essential to get as clear as we can on exactly what proposition is expressed by the sentence "S will not win the lottery". This is important because linguistic expressions do not wear their meaning on the sleeve, so to speak. We have to interpret them as best we can in light of whatever contextual clues are available. Due to factors like vagueness, ambiguity, lack of information about the context, and so forth, interpretation is often difficult and frequently inconclusive.
In the second place, there is an important distinction that we have to make between modally inflected uses of "will" and "will not" and amodal uses. Interpreted in the former sense, "S will not win the lottery" may be read as saying something like "S will probably not win the lottery". Here the word "probably" attributes an objective probability to the event S's not winning the lottery. Different objective probabilities can be captured with different qualifiers (e.g., "will definitely", "will possibly", or, more generally, "will, with probability p"). Interpreted in the amodal sense, "S will not win the lottery" should be read as saying something like "Subsequently, S does not win the lottery". This says nothing about what it's objective probability is, other than implying that it is non-zero. Probabilities applied to this proposition have be read as epistemic probabilities, which qualify the attitude that a subject has toward a proposition without entering in the meaning of the proposition. The contrast, then, is between a modal, objective probability reading "S will probably not win the lottery" and an amodal reading "Subsequently, S does not win the lottery".
In the third place, there is a potential ambiguity in the scope of the word "not" in "S will not win the lottery". Does it apply just to the predicate alone or to the rest of the proposition in its entirety? On the first reading, "S will not win the lottery" means "S will not-(win the lottery)". On the second reading, "S will not win the lottery" means "Not-(S will win the lottery)". These readings are distinct since the former entails the latter, but not vice-versa. It is possible, after all, for "Not-(S will win the lottery)" to be true without "S will not-(win the lottery)" being true - for example, when S does not exist.
Crossing the above distinctions gives us four basic readings of "S will not win the lottery":
- S will probably not-(win the lottery).
- Not-(S will probably win the lottery).
- Subsequently, S does not-(win the lottery).
- Not-(subsequently, S does win the lottery).
For a proposition to be true, what it represents as being the case must correspond to reality, to what is the case. Likewise, for a proposition to be true now, what it represents as being the case must correspond to present reality, to what is the case now. Now, (c) clearly represents what is, from our present perspective, a future contingent state of affairs. It represents S's not winning the lottery subsequent to a contextually specified index date. I deny, however, that (c) is true now or that we have good reason for believing it to be true now on the grounds that there is no present reality that it corresponds to. We have good reason for believing that it will probably come to be true, but not for believing that it is true. Thus, after the drawing of the lottery, either S will have won subsequently to the index date or not. At that point, assuming S does not win, (c) will be true. But not until then.
With respect to (d), I grant that it is true now and that we have good reason for believing it to be true now, but I deny that it directly concerns the future. It concerns, rather, a present fact, for it says it that it is not (now) the case that subsequently S does not win the lottery. This is provably correct. Future events do not obtain now.
In summary, I reject premise (2) of the objector's argument on the grounds that (i) the sorts of "will not" propositions about future contingents that we have good reasons for believing to be true now are not the sorts of propositions to which the doctrine of alethic openness applies, and (ii) the sorts of "will not" propositions about future contingents to which alethic openness applies are not the sorts of propositions that we have good reason for believing to be true now.
posted by Alan Rhoda @ 10:41 AM
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15 Comments:
Alan,
Thanks for this blog post. Your writing is always clear and fairly easy to follow, which is always a virtue for philosophical writing!
Regards,
Ross Parker
Hi Alan. Sorry to have been quiet for so long. You say "For a proposition to be true, what it represents as being the case must correspond to reality, to what is the case. Likewise, for a proposition to be true *now*, what it represents as being the case must correspond to present reality, to what is the case now." [my emphasis]
As I have mentioned, I am working on a translation of Scotus' commentary on the Perihermenias. In book I questions 7-9 he discusses the famous 'sea battle' problem posed by Aristotle. Scotus argues against the claim you appear make above, namely that the truth of a proposition about the future must correspond in some way to 'present reality'. He writes:
"It must be understood that a proposition about the future can be understood to signify something in the future in two ways. So that the proposition about the future signifies it to be true now that something in the future will have to be true [verum esse habebit] (for example, that ‘you will be white at a’ signifies it now to be in reality so that at time a you will be white). Or it can be understood that it signifies *now* that you will be white *then*: not that it signifies that it is now such that then you ought to be white, but that it signifies now that then you will be white. For to signify it to be [the case] now that you will be white at a, signifies more than to signify that you will be white at a."
It rather hangs upon what you mean by 'true now'. Scotus argues for something like a redundancy theory of truth. A proposition that says that S *will* be P so is (now) true iff it will be P, and false if it will not be P. If you mean by 'is now true' something like 'something exists now in reality that makes the proposition true' then Scotus would disagree (and so would I). If you mean that 'now' simply indicates the present tense of the 'is' in 'is true', then this is harmless and trivially true.
I think Scotus puts this very neatly, and we do have to take seriously his claim that "to signify it to be [the case] now that you will be white at a, signifies more than to signify that you will be white at a."
Incidentally I am learning Japanese at the moment. This does not have a future tense. You say 'sea battle is tomorrow' or 'sea battle is today'.
Ross,
Good to hear from you. I appreciate the compliment on my writing.
BTW, I see from your profile photo that you've become a daddy. Congrats!
Alan
Ocham,
Good to hear from you and thanks for your comment.
You're right to call attention to my claim that present truth requires a present truthmaker (or, more exactly, that truth-at-t requires a truthmaker-at-t). It is a controversial claim, though quite defensible, I would argue.
Your reference to Scotus is interesting, in particular his claim that "to signify it to be [the case] now that you will be white at a, signifies more than to signify that you will be white at a."
I think I would disagree with him, though. It seems to me that "you will be white at a" minimally signifies your subsequently (i.e., in relation to some indexed "present") being white at a. Otherwise, it doesn't represent your being white at a as future.
Many philosophers have claimed that "E will occur at t" is true at all times prior to t (and hence true "now") iff E occurs when t arrives. I think this is mistaken. "E will occur at t" entails "At t, E occurs", but not vice-versa since the latter omits the notion of futurity conveyed by the future-tense of the former.
Hello Alan,
I can't comment on AP's 'sound argument' (SA) but I think we can say something about your condensation. It seems to have the form
P-->Q
ER(~Q)
------
ER(~P)
where ER(p) means 'there are excellent reasons to believe p'. As a heuristic for forming beliefs this seems acceptable enough but I don't see the connection with truths. Further, propositions P and Q are hardly first order. Q appears to have the form 'proposition q involving the future has no truth value' and P the form 'no proposition involving the future has a truth value'. For clarity, I have taken the liberty of reformulating alethic openness (AO) in terms of lack of truth values at all rather than never being True, as you hold, but this doesn't affect my point about the essential higher-order nature of SA. Which is that it's not clear to me at all what faith we should place in arguments that quantify over propositions, especially those that assert the presence or absence of truth values. Far, far too reflexive to be trustworthy! SA is far from devastating in my view, and I'm mildly surprised that anyone would take it seriously as a counter to AO.
Hi David,
Thanks for your comments. I'm not sure I follow your line of thought, however.
You say, "As a heuristic for forming beliefs this seems acceptable enough but I don't see the connection with truths." Wouldn't you agree, though, that to believe p is to believe p to be true? That looks like a pretty straightforward connection between belief and truth.
The point where I part ways with 'SA', as you call it, is that I want to distinguish between believing that p is true now and believing that p comes to be true in the future. Where p is a modally loaded proposition about the future, I agree that we can have reasons for believing it to be true now. But where p is an amodal proposition about the future I think that we can at most have reasons for believing that it will come to be true. Either way, there's no problem for AO.
Hello Alan,
Thanks for the response. Yes, I agree that to believe p is to believe p to be true, but is p in fact true? I don't see how to make the deductive step from 'I believe p' to 'p'. SA appears to be an argument about reasons to believe p rather than p itself. There have been good reasons to believe that X committed a murder that have been subsequently overthrown by better reasons to believe that M did it, and only X and M were ever in possession of the truth of the matter, namely that X didn't do it and M did.
I'm interested in your remark that "...we can at most have reasons for believing that it will come to be true". Also, that you hold that both 'a sea battle will occur tomorrow' and 'a sea battle will not occur tomorrow' are both false now but may change in truth value tomorrow. This suggests that you see props as somehow evolving in time. Could you expand a little on how you see propositions and what, if any, changes to classical logic are needed to treat them? Is it sufficient to index all arguments to a stated time, say? And do you have any sympathies with the view that arguments quantifying over propositions are not to be trusted?
Greetings David,
I'm still not sure I understand what your objection against SA is. I'm thinking it's something like this: Even if SA is sound, it doesn't entail that OA is false. OA is a thesis about truth, whereas SA is about what we have reason to believe. If that's your point, then I agree with you, but I'm not sure it does me much good. I'd like to think, after all, that I have good reasons for believing OA.
As for my remark that "...we can at most have reasons for believing that it will come to be true", I'm talking here about the semantics of an amodal or Ockhamist use of the future tense. On that usage, "E will occur" means basically "Subsequent to some contextually defined 'present', E occurs." Now, given the plausible (albeit controversial) thesis that a contingent proposition is true at a time iff a truthmaker for that proposition obtains at that time, it follows that "E will occur" on that reading is not true now. It will be true when E occurs, however.
I do believe that propositions can have different truth values at different times. This follows from above stated assumption about the dependence of truth a T on the existence of a truthmaker at T, together with the fact that what exists is changing or non-constant. As things change, new truthmakers come into being, old ones go out of being, and what is true changes accordingly. So, I reject the idea that there is some static or timeless vantage point from which all of history can be fully and truly described.
I don't think that any revisions to classical logic are mandated by the above considerations because I don't believe that 'will' and 'will not' propositions, whether understood in a modally loaded sense or not, are contradictories. In fact, I don't even think it's true of 'is' and 'is not' propositions. Compare Russell's example, "The present king of France is bald". Both 'is' and 'is not' versions of that proposition are false (I claim) if there is no present king of France.
Finally, as for arguments that quantify over propositions, I'm not sure what I think about them. Do you have a good example of such an argument that you think raises suspicious about quantifying over propositions?
Hi Alan. I think Scotus gets over the problem by saying 'signifies now'. I.e. the reference to the indexed present is achieved by 'signifying now'. And what is signified by the 'signifying now' does not contain any content that says anything is the case now (only that something will be the case then And in any case we could restate his challenge as follows:
"For to signify now that it is the case now that you will be white at a, signifies more than to signify now that you will be white at a."
Can't a proposition be expressed, Japanese-style, that something will happen on Wednesday 4 February 2009, namely the very same thing that will be expressed on that date by someone saying (indexically) that 'something is now happening', i.e. the content of the proposition is entirely specific to that date, and the content is the same whenever the proposition is expressed? There is the additional fact that this proposition is being expressed *now* (and not this time next week), but that can be something the hearer is aware of as true, without it being expressed within the proposition. In the same way that the hearer can be aware that the speaker is speaking loudly, or speaking Japanese, without the fact of speaking loudly or Japanese being expressed as part of the proposition.
Hi Ocham,
There's a way in which I can accommodate Scotus' line: "For to signify now that it is the case now that you will be white at A, signifies more than to signify now that you will be white at A."
Suppose we understand "to signify now [at T] that it is the case now [at T] that you will be white at A" as meaning to express at T it's being true at T that you will be white at A. And suppose we understand "to signify now [at T] that you will be white at A" as meaning to express at T that it will be true at A that you are then white. On that reading, I agree with Scotus that the former says something more than the latter. The former says that "you will be white at A" is true at T, which entails that "you are white at A" is true at A. The latter, however, only says that "you are white at A" is true at A; it says nothing about whether "you will be white at A" is true at T.
Of course, I may just be reading my own thoughts into Scotus. At any rate, if the above in not what he means, then I not sure what he does mean.
You ask, "Can't a proposition be expressed, Japanese-style, that something will happen on Wednesday 4 February 2009, namely the very same thing that will be expressed on that date by someone saying (indexically) that 'something is now happening', i.e. the content of the proposition is entirely specific to that date, and the content is the same whenever the proposition is expressed?"
Suppose we have three sentences (1) "It will rain on Tuesday" uttered on Monday, (2) "It is raining today" uttered on Tuesday, and (3) "It rained yesterday" uttered on Wednesday. (1)-(3) all have some content in common; they all imply that "it rains on Tuesday" is true on Tuesday. But they are not identical in meaning. (1) implies that Tuesday's rain is yet to come; (3) implies that Tuesday's rain has already come. These are incompatible since the same rain cannot both be yet to come and have already come.
Hi Alan,
If I have understood aright you see a proposition as rather like a function whose domain is time and whose range is truth values. You speak of a proposition p being true at a time t, say. just as we might say that p is true at some possible world w. When p is already a tensed assertion, 'there will be a sea battle tomorrow', say, this leads us to ask is p true now? But this seems to be introducing a second temporal argument, 'now', in addition to 'tomorrow'. My feeling is that this is getting too complicated. Can we not deal with tensed assertions more simply by including the time directly in the proposition? Instead of 'Queen Victoria dies' is true at 1901 just say 'Queen Victoria dies in 1901' is true. Similarly, rather than concern ourselves whether 'There will be a sea battle tomorrow (Wednesday)' is true today (Tuesday) just ask whether 'A sea battle occurs on Wednesday'. I think this is what Ocham is urging too, though I think you reject the 'timeless vantage point' view. It seems to me that this is either true or false, but that we have to wait til Wednesday to find out. In the meantime we can investigate possible futures by assigning either truth value to this proposition and making deductions. Historians sometimes do this with events in the past, calling their work counter-factual history. For me, this brings out the distinction I tried to make in my earlier comments between states of affairs and knowledge or belief. We can use propositions to describe both. By taking all future contingent propositions to be false or possibly without truth value (so that nothing can be deduced from them) you are modelling our ignorance of the future. This is fine, but is it the same as what the future turns out to be?
For a dicey argument that quantifies over propositions you may remember this.
>>Of course, I may just be reading my own thoughts into Scotus. At any rate, if the above in not what he means, then I not sure what he does mean.
He specifies elsewhere what he means, namely that 'it being the case now [at T] that you will be white at A' means that it ought to (debet) happen, or that it exists 'in its causes'. He repeats the scholastic formula equating truth with being. "You should know that 'true' signifies the being of that which is, 'false' signifies the being of that which is not. But what is actually in the present, has in itself what is true, just as it has being per se". But what is to be does not exist in itself, but in [its] cause, because it is possible in three ways - as something in the cause from which the effect necessarily follows (e.g. as an eclipse follows from the current position and movement of the planets), as something which has 'inclination to cause' but which can be prevented, and 'as what no more stands to being than non-being'.
To return to the argument behind this: events on Wednesday and Thursday can be such that the truths of statements about them can be logically independent, even if the truth about Thursday is uttered on Wednesday (according to me and, I think, Scotus). Your position is that something has to be true on Wednesday, i.e. meaning some fact has to obtain on Wednesday, in order to state a truth concerning Thursday, on Wednesday.
>>>Suppose we have three sentences (1) "It will rain on Tuesday" uttered on Monday, (2) "It is raining today" uttered on Tuesday, and (3) "It rained yesterday" uttered on Wednesday. (1)-(3) all have some content in common; they all imply that "it rains on Tuesday" is true on Tuesday. But they are not identical in meaning. (1) implies that Tuesday's rain is yet to come; (3) implies that Tuesday's rain has already come. These are incompatible since the same rain cannot both be yet to come and have already come.
But as I commented the Japanese would have "Rain on Thursday" uttered on Wednesday, to express the future tense (which the language does not possess). I agree that the English future tense may have a different meaning, but this is because there is an additional statement embedded, namely "it is not yet Thursday". In any case, could we not imagine a language where there is no tense at all, and all statements refer simply to dates? In such a language, the problem of the necessity of future contingents would not arise. For we would have to assert that the truth of 'Rain on Thursday' depends on the truth of a statement of the form 'X on Wednesday'. But there isn't any such X, if truths at different times can be logically independent in the way that you appear to suggest.
David Brightly is making a similar point above, I think.
Hi David,
You pose a fair question:
Can we not deal with tensed assertions more simply by including the time directly in the proposition? ... [R]ather than concern ourselves whether 'There will be a sea battle tomorrow (Wednesday)' is true today (Tuesday) just ask whether 'A sea battle occurs on Wednesday'.
In response, I invoke a distinction between truth at a time and truth simpliciter. The former I take to be grounded in what exists at that time; the latter in what exists simpliciter. In these terms, I take the substance of your question to be why we even need such a category as 'truth at a time'. Why doesn't truth simpliciter suffice?
The short answer is that to jettison 'truth at a time' is to foreclose the possibility of there being transient truths (as opposed to omnitemporal or temporally invariant truths). Nearly all ancient and many medieval philosophers affirm that possibility, as must anyone who holds to an A-theory of time. Disallowing 'truth at a time' is, therefore, neither an historically nor a metaphysically innocent matter.
I should stress that my views on 'truth at a time' are motivated primarily by metaphysical, not epistemological, considerations. I'm not trying to "model ignorance". My position emerges from my commitment to an A-theory of time (specifically presentism), to future contingency, and to the principle that truth supervenes on being.
Hi Ocham,
I accept the idea, as you put it, that
'it being the case now [at T] that you will be white at A' means that it ought to (debet) happen, or that it exists 'in its causes'.
But I think this supports my position, not yours. If for it to be true on Wednesday that a sea battle occurs on Thursday, Thursday's sea battle must be 'present in its causes' on Wednesday, then I agree completely. What I deny is that it can be true on Wednesday if Thursday's sea battle is not present in its causes on Wednesday.
[C]ould we not imagine a language where there is no tense at all, and all statements refer simply to dates?
Perhaps we could imagine such a language, but we couldn't use it for everyday purposes. D.H. Mellor, Arthur Prior, and numerous others have pointed out that for practical decision making it is essential to be able to situate matters in relation to "now", and not just to some date. For example, suppose you know "I have (tenseless) a job interview at T" but you don't know how T stands in relation to "now". In that case you won't know if you've already missed the interview, if you have to rush out the door, or if you have two weeks more to go.
>>But I think this supports my position, not yours.
I don't think so. Scotus is not denying that the causes of some future event (e.g. an eclipse) could be present now. Rather, he is claiming that any such statement about these causes, together with a statement that the effect will happen, say more than the bare 'X will happen'. You countered this with the argument that 'X will happen at t' does say more than 'X is happening' (uttered at t). My reply to this was that we can decompose 'X will happen at t' into the indexical statement 'now is before t' and the tenseless 'X at t' which is a Japanese-like statement combining a reference to an event X, plus a time marker 't'. You haven't really addressed this counter-argument.
(1) X will happen at t = now is before t and X at t
(2) X is happening (at t) = now is t and X at t
(3) X happened at t = now is after t and X at t
I claim that the sentence 'X at t' has exactly the same content in (1)-(3). The difference in content between the tensed statements is merely due to the difference between 'now is before t', 'now is t' &c. If this is correct, there is no truth on now on Wednesday expressed by the statement 'X will happen on Thursday' except perhaps for the trivial fact that now is before Thursday.
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