Excluded middle
September 2, 2009 — 13:46

Author: Alexander Pruss  Category: Open Theism  Comments: 54

Some, but not all, open futurists deny excluded middle for future contingents. Thus, they deny that either there will or there will not be a sea battle tomorrow. Here is an inductive argument to the contrary: A sea battle typically requires a conflict between naval powers that has been brewing for some time.
Such a conflict is probably not brewing right now. Therefore, probably, there will be no sea
battle tomorrow. But if there will be no sea battle tomorrow, then there will or will not be
a sea battle tomorrow (disjunction-introduction). Hence, there will or will not be a sea battle
tomorrow. But if there will or will not be a sea battle tomorrow, views that deny excluded middle for future contingents are false.

Objection: The argument is merely probabilistic, so all that we have
establishes is that probably there will or will not be a sea battle tomorrow.

Response: Indeed. But that there will or will not be a sea battle tomorrow entails (given uncontroversial facts about what is and is not contingent) that excluded middle holds for some future contingents. And hence, probably, the open future view under consideration is false. That is a non-trivial result.

Moreover, we can jack up the probabilities higher. Let p be the proposition that the pattern of the first ten die-pair tosses at Las Vegas over time tomorrow will not be 1-1, 2-2, 1-1, 2-2, 1-1, 2-2, 1-1, 2-2, 1-1, 2-2. Then, P(p) is approximately 1/3610, a very small number. Hence, P(p or not-p) is at least 1-1/3610 which is very close to 1. Hence the probability of the open future view in question is close to zero.

• Alan Rhoda

Hi Alex,
Your argument assumes, incorrectly I think, that corresponding ‘will’ and ‘will not’ propositions are contradictories. Equivalently, it assumes that ‘will not’ = ‘not will’. Obviously, if this is not so then “there will or will not be a sea battle tomorrow” is not an instance of excluded middle.
The difference between ‘will not’ and ‘not will’, as I see it, lies it the scope of ‘not’. In the ‘not will’ case an entire ‘will’ proposition is negated, thereby giving its contradictory. In the ‘will not’ case only a predicate is negated. Case in point: “The present king of France will shave his head tomorrow” vs. “The present king of France will not shave his head tomorrow”. Arguably, both of these are false on account of presupposition failure. Both seem to assume, falsely, that there is a present king of France. If so, then what we have here are contraries, not contradictories.
If you want to maintain that ‘will not’ = ‘not will’, then bear in mind that “It is not the case that there will be a sea battle tomorrow” would be true even if there were no creation at all. Hence it is not equivalent to any proposition which presupposes that there are or have been such things as seas or battles or that there will be times like today and tomorrow.

September 3, 2009 — 10:01
• Alan Rhoda

Hi Alex,
Your argument assumes, incorrectly I think, that corresponding ‘will’ and ‘will not’ propositions are contradictories. Equivalently, it assumes that ‘will not’ = ‘not will’. Obviously, if this is not so then “there will or will not be a sea battle tomorrow” is not an instance of excluded middle.
The difference between ‘will not’ and ‘not will’, as I see it, lies it the scope of ‘not’. In the ‘not will’ case an entire ‘will’ proposition is negated, thereby giving its contradictory. In the ‘will not’ case only a predicate is negated. Case in point: “The present king of France will shave his head tomorrow” vs. “The present king of France will not shave his head tomorrow”. Arguably, both of these are false on account of presupposition failure. Both seem to assume, falsely, that there is a present king of France. If so, then what we have here are contraries, not contradictories.
If you want to maintain that ‘will not’ = ‘not will’, then bear in mind that “It is not the case that there will be a sea battle tomorrow” would be true even if there were no creation at all. Hence it is not equivalent to any proposition which presupposes that there are or have been such things as seas or battles or that there will be times like today and tomorrow.

September 3, 2009 — 10:02
• Alan Rhoda

Oops, sorry for the double post. My reply didn’t appear the first time I submitted it.

September 3, 2009 — 10:09
• Mike Almeida

Hi Alan,
I don’t think your worry addresses the Las Vegas example, which is the more convincing case. That case does use wide-scope negation as Alex formalizes it. That aside, I don’t see how narrow scope negation presupposes anything. If you Russellize the definite description you get an entailment that there is a PKF on the narrow scope reading, not a presupposition. But that’s a good reason not to read it as narrow scope.

September 3, 2009 — 11:49
• Andrew Moon

Alex,
In your response to the objection, I wasn’t clear on how you moved from it is very likely that (pv~p) to it is very likely that open futurism is false. Or is that what you were saying?
To put this another way, I took you to be saying it is very likely that either there will or there will not be a sea battle tomorrow to it is very likely that open futurism is false. Is that what you were saying? If so, then what justification is there for that inference? If not, it’s not clear to me what your response to the objection is. Maybe you can clarify?

September 3, 2009 — 14:26
• Andrew Moon

in the first line of my second paragraph, replace “saying” with “moving from”. replace the second “saying” (in line 3) with “inferring”.

September 3, 2009 — 14:48
• OK, but isn’t a more plausible position for the proponent of the open future view to retain LEM but deny the Principle of Bivalence? On most readings of the text, that’s the position put forward in De Int. 9–it’s not true (or false) that there will be a sea battle tomorrow, nor is it true (or false) that there will not be a sea battle tomorrow, but it is true that either there will or will not be a sea battle tomorrow.

September 3, 2009 — 14:57
• Alan:
By “will not” I did mean “not will”. Thus, your view, on which it is not the case that there will be a sea battle tomorrow is not being criticized.
Andrew:
Let OFNLEM be the open future view I am attacking. OFNLEM says that if p is a future contingent, then (p or ~p) isn’t true. But I’ve given a case where p is a future contingent, and probably (p or ~p). Hence, probably (p is a future contingent and (p or ~p)). Hence, probably (there is a q such that q is a future contingent and (q or ~q)). Hence, probably, ~OFNLEM.
I use the principle that if P evidently entails Q, and P probably holds, then Q probably holds.
Tim:
It’s a toss-up. Personally, I find denial of the Tarski Schema T in non-paradoxical and non-indexical cases to be implausible. But a denial of Schema T is required by the view you suggest. Otherwise, from:
will(p) or ~will(p)
one could derive
True(will(p)) or True(~will(p)).

September 3, 2009 — 15:11
• C

Alex,
This is an interesting argument, but first a question: Which open future view that accepts LEM do you find most plausible? Are there any mandatory readings on the subject?
One way to get out of your argument is to claim that the probability that “there will be a sea battle tomorrow = 0” and that “the probability that there will not be a sea battle tomorrow = 0”. If future contingents are guaranteed to be false, then the probability that they are true = 0. Moreover, for any proposition P, if the probability that P is true = 0, then no evidence raises the probability that P is true. Thus, there are no cogent inductive arguments for propositions about future contingents.
“Therefore, probably, there will be no sea battle tomorrow.”
So, this claim is false. It is not probable that there will be a sea battle tomorrow. The probability that there will be a sea battle tomorrow = 0.

September 3, 2009 — 16:08
• C:
It’s hard to choose, because all these views are so implausible. ๐ Maybe the most plausible open future view that accepts LEM is Keith DeRose’s view that LEM holds but bivalence doesn’t; thus, it is true that either there will be a sea battle or that there will not be a sea, but neither disjunct is true (or false). Or maybe it’s Alan Rhoda’s view that LEM and bivalence hold, but it is both false that there will be a sea battle tomorrow and that there will not be a sea battle tomorrow. On general principles, I think the Rhoda view is better in that instead of forcing one to revise rules of inference regarding the general concept of truth, it forces one to revise rules of inference only in one subject area, namely that of reasoning about the future.
Surely if something has probability zero, it is almost surely false. So, on the view you propose, it is almost surely false that there will be a sea battle tomorrow. But if so, then it is almost surely true that there won’t be one tomorrow. (Unless we adopt the Rhoda semantics for will-not.) But if so, then it is almost surely true that there will or won’t be one tomorrow. And if so, then it is almost surely true that LEM holds for the sea battle.

September 3, 2009 — 16:43
• Andrew Moon

Alex,
ah, thanks, I see. Hmm… interesting argument.

September 3, 2009 — 20:24
• Christian

Alex,
“It’s hard to choose, because all these views are so implausible. :-)”
That’s my impression too. So I’m wondering what I’m missing.
“Or maybe it’s Alan Rhoda’s view that LEM and bivalence hold, but it is both false that there will be a sea battle tomorrow and that there will not be a sea battle tomorrow.”
I don’t see how such a view could work either. How can one maintain that P is false, not-P is false, but also maintain that (P or not-P) is true? Disjunctions are false when their disjuncts are both false, right? Alan, if you’re reading, paper reference?
“Surely if something has probability zero, it is almost surely false.”
I would say it is certainly false.
“So, on the view you propose, it is almost surely false that there will be a sea battle tomorrow.”
Yes, it is certainly false.
“But if so, then it is almost surely true that there won’t be one tomorrow.”
No, on the view (not mine) that I’m offering, it is also certainly false that there will be a sea battle tomorrow (without Rhoda semantics).
“But if so, then it is almost surely true that there will or won’t be one tomorrow.”
On this view, this is false as well. It is certainly false that there will or there won’t be one tomorrow.
“And if so, then it is almost surely true that LEM holds for the sea battle.”
But it’s not so. LEM does not hold for the sea battle.

September 3, 2009 — 21:07
• Joshua Rasmussen

Interesting. I wonder why an open theist would be tempted to give up the LEM, rather than to say merely that all future tensed contingencies are false. Take for example:
(1) WILL
(2) WILL
One might think that (1) and (2) are both false but that LEM is true. LEM commits one to saying that either (1) is true or NOT (1) is true. An open theist who thinks that (1) is false may affirm that NOT (1) is true. What’s crucial is that affirming that NOT (1) is true is not the same as affirming that (2) is true. Thus, one might think that NOT (1) is true while also thinking that (2) is false. (I think this was Alan’s point.)
Now I realize this doesn’t pose a problem for your argument against those open theists who deny LEM. But I am curious if you have any reasons against this verson of open theism. On this view, God could know all true propositions and so be omniscient in the classical sense.
I’m especially curious because PSR + presentism is pushing me through the door of open theism… care to block my next step?

September 4, 2009 — 9:47
• Joshua Rasmussen

The props above should be:
(1) WILL [there is a sea battle]
(2) WILL [there is not a sea battle]

September 4, 2009 — 9:50
• Joshua:
The best way to block the step is to deny presentism. ๐ At this point, I know only one good argument for presentism: if A-theory is true, then presentism is true. And I know only one good argument for the A-theory: it feels like my life is ebbing away and I am approaching death (as I indeed am, unless the Second Coming comes first, and maybe even then if Aquinas is right). It’s not a very strong argument, because I can explain not only my feelings but the normative implications within the B-theory.
On reflection, my argument also works against Alan’s view, in this way: The inductive evidence supports the claim that tomorrow there will be at least one car on I-35. Thus, probably, tomorrow there will be at least one car on I-35. But it is uncontroversially contingent that tomorrow there will be at least one car on I-35. That tomorrow there will be at least one car on I-35 together with uncontroversial claims entails the falsity of Alan’s view. Thus, Alan’s view is probably false, and I should be at least as surprised by its turning out true as by finding I-35 bereft of cars tomorrow. (That might be in a way nice in light of the family plan to drive to Austin. On the other hand, it would probably be really spooky, too spooky to make the drive.)

September 4, 2009 — 11:05
• Just in case anybody reads too much into the first paragraph in my previous comment and worries about me, I should add that to my knowledge I am not suffering from a terminal disease or anything like that, barukh haShem.

September 4, 2009 — 11:07
• Christian:
On Alan Rhoda’s view, “There will not be a sea battle tomorrow” is not the negation of “There will be a sea battle tomorrow.” (He may even be right about that, thus far. For it might be that “There will not be a sea battle tomorrow” entails that there will be a tomorrow, while the negation of “There will be a sea battle tomorrow” is compatible with there being no tomorrow.)

September 4, 2009 — 11:11
• Joshua Rasmussen

Alex,
I thought you might say that–give up presentism. I realize we are straying a bit from the original topic, but a few comments about your comment:
1. On my understanding, the A-theory says that the A-properties are not reducible to tenseless B-properties. But I’m inclined to think that A-properties are reducible to the B-properties (see รขยยPresentism and Grounding,รขยย Noรยปs 41 (2007): 90-109). Ironically, I think a B-theory is only plausible given presentism. But that’s another story…
2. I’ll give you two reasons I favor presentism:
A. I don’t see what it can mean to say that x exists at a time t other than to say that t entails that x’s existence obtains simpliciter. This means that the time at which dinosours roamed the earth doesn’t obtain (otherwise, that would contradict the fact that there are no dinosours). By similar reasoning, no past or future times obtain (without contradicting something that obtains). The ‘present time’ I understand to be whatever time it is that obtains. Thus, only the present time obtains (simpliciter). Another way to this conclusion is to view times as maximal, abstract states of affairs (which I’m prepared to argue for). By virtue of being maximal, only one time can have that special status of obtaining (being present). I’m of course assuming that there is a non-time indexed property of obtaining simpliciter (which strikes me as undeniable).
B. Consider the proposition P that Alex used to be shorter. Now of course one and the same thing cannot be shorter than it is. Therefore, if I reject presentism, I might translate (1) as saying that Alex has the property of being tall-at-t and short-at-t0, where t0 is earlier than t, and t is the time I uttered P (or something like that). But that is a bad translation for two reasons: (i) (P) isn’t nearly that complicated; (ii) although Alex may well have the property of being tall-at-t, he also has the simpler property of being tall; and although Alex may well have the property of being short-at-t0, he also used to have the simpler property of being short. Surely, there are non-time indexed properties, and surely Alex exemplifes some of them. But I do not see how someone who denies presentism can accept that. Someone may try to translate (1) as talking about things distinct from me, like my temporal parts. But then that surely won’t be a translation.
Those two reasons seem to me much more pressing than the feeling that my life is ebbing away.

September 4, 2009 — 12:11
• Joshua Rasmussen

Oops: (1) = P above.

September 4, 2009 — 12:15
• Gordon Knight

Alex: How do you understand the truth of “I am writing this now”

September 4, 2009 — 14:05
• Gordon:
I understand you to say that you were writing that then. ๐
Joshua:
A. Do you understand what it means to say that a person is in London? If so, why not just say whatever you say about that about existence at t? I think a worry arises if the right answer to the spatial question is: “x is in London iff all of x’s parts are in London.” For it might be thought false that all of my parts exist presently–my placenta does not. (I take the view that the placenta is a part of the fetus. If you deny it, then use an amputation case.) For me this isn’t a worry as I don’t believe in proper parts. But there is an independent worry about the “all of x’s parts are in London” answer anyway. It rules out the possibility of (robust) multilocation, and hence of time travel.
B. All sorts of ordinary properties are, in fact, more complex than they seem. Being “short” is surely contextual, for instance (a tall three-year-old is much shorter than most short adults; a short basketball player might be a moderately tall person). We might understand that contextuality in two ways. (1) Being short is a relational property, with the relation being between the short person and a context. (2) “Short” is an impure indexical term: it has different content in different contexts. So, “short” turns out not to be a simple property after all. And so I just say that it is even more complex than even the above reveals.
I like the indexical way out for the temporal case.

September 4, 2009 — 14:26
• Gordon Knight

Alex,
“Then” is a tensed property!

September 4, 2009 — 14:57
• Alan Rhoda

Hi Alex,
I realized that you weren’t directly critiquing my position. I merely wanted to point out that, from my perspective at least, what you offer as an instance of LEM isn’t.
Alex: “The inductive evidence supports the claim that tomorrow there will be at least one car on I-35. Thus, probably, tomorrow there will be at least one car on I-35. But it is uncontroversially contingent that tomorrow there will be at least one car on I-35. That tomorrow there will be at least one car on I-35 together with uncontroversial claims entails the falsity of Alan’s view. Thus, Alan’s view is probably false, and I should be at least as surprised by its turning out true as by finding I-35 bereft of cars tomorrow.”
You won’t be surprised to learn that I don’t think this argument is sound. ๐ Inductive evidence supports the claim that the chance of a car’s being on I-35 tomorrow is very high. By the Principal Principle this grounds a correspondingly high credence in “a car is on I-35 tomorrow”. But this credence is not the degree of belief that the proposition is true (now). Rather, it is the degree of belief that the proposition comes to be true (tomorrow).

September 4, 2009 — 15:49
• Joshua Rasmussen

Alex,
Thanks for those comments. Some replies:
A. x is in London means that x is spatially between some of the many things that jointly exemplify being London. I suppose by analogy, we might say that x is at t means that x is “temporally between” some of the things that jointly instantiate t. But what is this “temporally between”? Should I understand it as a spatial relation, or as something else? If a spatial relation, then why call it temporal? If not a spatial relation, then what relation is this? Whatever it is, it’s such that necessarily, if it is exemplified, then its relata exist (all relations are like that). And if it’s a temporal relation (and not merely spatial), then its relata exist at different times. But unless the relata are necessarily existing things (like abstract times), there will be cases in which the relata don’t all exist unless multiple times obtain, which is impossible if times are maximal states of affairs.
Now someone can reply by saying that times are actually concrete segments, some of which are to the “temporal” left of (earlier than) me and others to my “temporal” right (later than). I suppose I understand what is being said here (in some sense of understand). But the idea that times are really concrete regions to my temporal “left” or “right” seems to me no more plausible than the view that “possibilities” are really causally isolated universes. These views equally invite an incredulous stare. I hope I’m not being too uncharitable. ๐
B. I suppose some properties turn out to be more complex than they initially seem. But I suspect this happens for properties we don’t fully grasp. I also suspect that sometimes we come to analyze certain properties in terms of co-extensive ones that are more complex but also not identical to the properties we originally had in mind. There are probably also times when we start with a determinable property and then come to grasp one of its more complex determinates. Here again the property we grasp later isn’t the same as the original one we had in mind. At any rate, I feel nearly certain that I grasp certain geometric properties sufficiently well to tell that they aren’t time-indexed. I also feel nearly certain that there are (or at least could be) things that change from having one of these geometric properties to having a different incompatible one. I can’t see how to make sense of this if presentism isn’t true (assuming that exemplification isn’t time-indexed either). That’s just me. ๐

September 4, 2009 — 17:12
• Joshua:
A: I don’t see any more need to be committed to times than to places. Maybe George exists during WWII because he is temporally between many of the events that constitute WWII–I rather like that. Temporal betweenness and spatial betweenness are, I think, very similar but not exactly the same. They are both special cases of betweenness. ๐ It’s just that one of the betweenness relations–the temporal one–has a special pattern of interaction with causation, namely that there is a privileged direction to the betweenness such that, in contingent fact, most causal relations go in that direction. This simultaneously explains how temporal betweenness and spatial betweenness differ, and solve the problem (which is of course just as much a problem for the presentist as for everybody else, except the growing block theorist and maybe open futurist) of how the past and the future differ.
B: According to relativity theory, the standard geometric properties of concrete objects (e.g., triangularity) are relative to the reference frame. And this may well turn out to be true. Consider also a different contextuality in geometric properties. When we say that Fred is cubical, using the ordinary concept of cubicality, we do not imply that he has six exactly square sides. In the ordinary sense of the word “cubical”, an object is cubical iff the six sides are approximately square, and what level of approximation is compatible with “cubicity” depends (vaguely?) on the context. In certain contexts, a figure might be said to be “six-sided” while in other contexts it will be said to be “fourteen-sided” (take a cube where each corner is very slightly beveled). Ordinary terms seem to always have this sort of relativity, as Plato noted. ๐ Now it is true that our purified geometric concept of a cube doesn’t have this relativity. But it’s a concept that, in at least contingent fact, has no application in the physical world.

September 5, 2009 — 8:08
• Joshua:
Here is an argument for the possibility of multilocation. Plausibly, while God the Son became incarnate as Jesus Christ, God the Holy Spirit might have become incarnate as a spherical alien. So, the one same God, though not qua God, would be a human and a spherical alien. That’s a kind of multilocation. Moreover, observe that geometric terms would require further disambiguation before we could apply them to God, because we’d have to say with respect to which incarnation we were applying them.
Next, observe that from the standard doctrine of Incarnation we already learn that ordinary geometric terms have some relationality that wasn’t initially plain. Thus, if we say that Christ is x feet tall and has just left Bethlehem, what we mean is that Christ in his human nature is x feet tall and has left Bethlehem, while in fact Christ also remains divine and omnipresent. So, ordinary geometric terms have, as we might not have known apart from divine revelation, a relation to a nature.
According to Aquinas, Christ could have become incarnate as two men. If Aquinas is right, then ordinary geometric terms not only have a relation to a nature, but to a nature and a particular body.

September 5, 2009 — 8:23
• Alan:
‘By the Principal Principle this grounds a correspondingly high credence in “a car is on I-35 tomorrow”. But this credence is not the degree of belief that the proposition is true (now). Rather, it is the degree of belief that the proposition comes to be true (tomorrow).’
So, we have two propositions about cars and I-35.
(1) That there is a car on I-35 tomorrow.
(2) That (1) comes to be true (tomorrow).
Let C(p) be the proposition that p comes to be true at the time that it is a proposition about p.
And it seems that you’ve admitted that C(that a car is on I-35 tomorrow) is very probable–or at least that it’s reasonable to believe it with high credence.
But now I don’t see how you can remain an open theist. If p is probable, then Knows(God,p) is equally probable, since God necessarily knows all truth. Hence, probably, Knows(God, C(that a car is on I-35 tomorrow)). But any metaphysical reasons to worry about Knows(God, that a car is on I-35 tomorrow) are reasons to worry about Knows(God, C(that a car is on I-35 tomorrow)). For all practical purposes, the knowledge C(that a car is on I-35 tomorrow) can substitute for the knowledge that a car is on I-35 tomorrow. Thus, God can issue a prophecy that a car is on I-35 tomorrow, and if C(that a car is on I-35 tomorrow) is true, that prophecy will come true. Etc.
If I am understanding you–and I fear I am not–your theory is not so much a bold theory about the future being open (for it’s not open if it’s already true that it will come to be true that a car is on I-35 tomorrow), as an innovative account of the semantics of the English future tense.

September 5, 2009 — 8:36
• Gordon:
I don’t see how “Then” is tensed.
X: “At 7:00 pm Beijing time today, the prisoner is executed.”
Y: “Then? Are you sure?”
X: “Yes.”
Y: “Has that time come yet? I don’t remember what the time difference with Beijing is.”
If you say that “Then” picks up the tense of the original time reference, then when you say “I am writing this now” and I come to believe “He was writing that then” (by the time I process the speech, I need to use the past tense to express what I’ve learned), I come to believe some nonsense, because I have a tense mismatch between the present in “then” and the past in “was writing”.

September 5, 2009 — 8:41
• Alan Rhoda

Alex:
I don’t follow your definition of C(p). Specifically, I don’t understand the phrase “at the time that it is a proposition about p”. Did you mean to say “at the time proposition p is about”?
At any rate, you claim that “If p is probable, then Knows(God,p) is equally probable, since God necessarily knows all truth.”
You seem to assume that the probability that p equals the probability that p is true and thus equals the probability that God knows p. I disagree with that assumption. Let p be “E occurs tomorrow”. To have a high credence in p is not ipso facto to have a high credence that p is true; rather, it is to have a high credence that “E occurs” comes to be true tomorrow.
Case in point. The weather center has informed me that there is a 30% chance of rain tomorrow. I have no other relevant information. Hence, my credence that it rains tomorrow is 30%. But this is not my credence that it is true now that it rains tomorrow. The chance that any proposition is true now is either zero or one–either it is true or it isn’t. The chance of a proposition’s being true can’t be 30%. So if I’m going to match my credence to my best estimate of the chance (as the Principal Principle urges), then my credence in “it rains tomorrow” has to be my best estimate of the chance that “it rains” comes to be true tomorrow.
In sum, let the chance be 99.99% that, tomorrow, a car is on I-35. It is then true now, and known to God, that the chance of a car’s being on I-35 tomorrow is 99.99%. God also has a corresponding credence that “a car is on I-35” comes to be true tomorrow. But this is not equal to God’s credence that “a car is on I-35 tomorrow” is now true, for the chance of that has got to be either zero or one–either it is now true or it isn’t.

September 5, 2009 — 15:40
• Alan:
I think your earlier remarks had confused me. You wrote: “By the Principal Principle this grounds a correspondingly high credence in ‘a car is on I-35 tomorrow’. But this credence is not the degree of belief that the proposition is true (now). Rather, it is the degree of belief that the proposition comes to be true (tomorrow).”
Now, my C(p) (which does need to be corrected as you indicated) is meant to be the proposition “that the proposition p comes to be true (tomorrow or whatever the relevant time in p is)”. Let p be the proposition that there is a car on I-35 tomorrow. Your above-quoted remarks seem to commit you to:
1. We should not have a high credence in p.
2. We should have a high credence in C(p).
Now, add to (1) and (2) something like the following premises (if you don’t think anything is certain, my argument can still be made to go through as long as you grant that the biconditional in 3 is very likely):
3. For all propositions a, it is certain that necessarily(a iff True(a)).
4. If it is certain that a entails b, then the credence in b should be at least as large as the credence in a.
Then:
5. If it is certain that necessarily(a iff b), then the credence in b should equal the credence in a. (By two applications of 4)
6. For all a, the credence in a should equal the credence in True(a). (By 3 and 5)
7. We should have a high credence in True(C(p)). (By 2 and 6)
But your latest set of remarks seems to affirm 2 but deny 7. If that’s the right reading, you need to deny at least one of 3 and 4, both of which are extremely plausible (though one might worry about 3 in liar cases).

September 7, 2009 — 9:01
• Alan Rhoda

Alex:
I reject 3. I think it’s apparent plausibility stems from conflating “Tp iff p” with an indexed analogue, “T(i)p iff p(i)” (read: “It is true at i that p iff p-at-i.”). The latter is undeniably true, but not sufficient for your argument.
You might, perhaps, suggest that they come to the same thing on the grounds that the actual world, @, contains a complete history and that truth at @ = truth simpliciter. But if you go that route then you beg the question against open futurism. No open futurist will concede that there is an actual world which includes a complete history. Indeed, it is the very essence of open futurism to deny that.

September 7, 2009 — 10:23
• Alan:
I don’t know what p-at-i means, so let me, perhaps lamely, try to restructure my argument.
You wrote: “In sum, let the chance be 99.99% that, tomorrow, a car is on I-35. It is then true now, and known to God, that the chance of a car’s being on I-35 tomorrow is 99.99%. God also has a corresponding credence that ‘a car is on I-35’ comes to be true tomorrow.”
Let p be the proposition that a car will be on I-35 tomorrow. Let i be the actual present.
Now, you accept that:
1. L(T(i)p iff p-at-i).
Given that this is certain, it follows:
2. P(T(i)p) = P(p-at-i).
Now, what is p-at-i? Here is where I get confused. The straightforward reading is “the proposition that a car will be on I-35 tomorrow at i”. But that’s just ungrammatical.
In any case, I am very much tempted to say that p-at-present is equivalent to p:
3. L(p-at-present iff p), and this is certain.
It seems to me that presentists at least ought to accept 3: a proposition’s holding simpliciter is just the same as its presently holding (stipulation: “present” is non-rigid, while “now” is rigid).
Moreover, working with epistemic probabilities, I know with certainty that the present is now (=i). So, by 3,
4. P(p-at-i) = P(P-at-present) = P(p).
Putting this together with 2:
5. P(T(i)p) = P(p).
But this you deny, since on your view P(T(i)p) = 0, while you allow that maybe P(p) = 99.99%.
I take it you need to deny 3. But now I want to hear a bit more about what proposition p-at-i is. You could just identify “p-at-i” with T(i)p. But now you have no non-trivial substitute for L(Tp iff p).

September 8, 2009 — 11:55
• Joshua Rasmussen

Alex,
Just for the record, I’m actually inclined to reject relativity theory (of the metaphysically loaded sort, such as Minkowski’s version) because it seems to require that the standard geometric properties of concrete objects (e.g., triangularity) are relative to a reference frame, which I take to be impossible (absurd even :)). I account for the same scientific data in a different way.
Your remarks on the incarnation are clever. Sometime I hope to discuss them further, but perhaps in person would be easier…
A final note: I suppose I can understand eternalism if I imagine that there’s really just one big time (or state of affairs) that obtains (is ‘present’ in the real sense of present), which is built up out of things that stand in “temporal” relations of the sort you described. (Though now I want to complain that “change” within this state of affairs isn’t genuine.)

September 8, 2009 — 20:22
• Joshua:
So, the change isn’t genuine, by definition, since in your model you don’t have variation of time but only an axis of “time”. However, what matters for our lives is not change, but causation–that we be causes of our lives in significant respects. ๐

September 9, 2009 — 7:40
• Joshua:
You said that PSR and presentism are pushing you to Open Theism. But are PSR and presentism compatible?
Put ourselves back at the time when God is creating. The following then is a contingent truth: God is presently creating. What explains this contingent truth? (Augustine’s variant on the question: Why hadn’t God already created?) Well, we can give the reasons God has for creating, such as to spread his love. But while these reasons explain why God is creating at some time or other, they seem to fail to fully explain why God is presently creating.
We might reasonably say: Well, God is presently creating because five minutes ago he was planning to create in five minutes. But that, plainly, leads to a regress. For, five minutes ago, he was planning to create in five minutes. But now we have two unexplained things. First, why he was planning to create in five minutes rather than at some other time, and, second, why he was then planning to create in five minutes (rather than having that plan earlier or later).
This Leibnizian argument does not really presuppose theism (talking of creation just makes it vivid), and it works (if it works) not just against presentism, but against all A-theories. It also works against non-relational B-theories with infinite past.
Here is a way of making the point in Crisp’s abstract times setting. An abstract time is a maximal consistent (tensed) proposition. An uncentered world then can be thought of as a maximal temporally connected sequence of abstract times, and a temporally centered world is just an abstract time. I think it follows from this that there cannot be two uncentered worlds with the same entities and events, but where everything is shifted over temporally (e.g., Socrates and Napoleon dying a hundred years earlier than in our uncentered world, our Lord and Savior coming a hundred years earlier, etc.) For that would require time-haecceities, and then it is the time-haecceities that would be the right candidate for abstract times. So in Crisp’s setting, one can’t ask–as one can on substantivalist B-theories with eternal past–why history isn’t shifted over temporally.
But one can still ask why it is that, of all the abstract times in our uncentered world, this time is present (I know this asks for a contrastive explanation, and that in my PSR book I worry whether the PSR applies to contrastive explanations. But in the end I think it does), i.e., why it, rather than one of the other times in our uncentered world, is actually true. And I think the only answer available is something that leads to a regress: Because five minutes ago, a certain other time was true, and that other time was such that, necessarily, five minutes after it, the present time would be true.

September 9, 2009 — 9:27
• Joshua Rasmussen

Interesting comment, Alex. I sense there are multiple things to explain, and I may not have in mind all the same items you have in mind. But here’s a stab:
When [God is presently creating] was true, it was explained by [God wants to create a good world, if no good world has been created], which is a necessary truth. The explanation doesn’t entail its explanandum, of course, but I suggest that it’s still a satisfying explanation.
You may ask, “But what explains why God created THEN rather than 5 minutes earlier?” I answer, “Because it was impossible to create 5 minutes earlier, since necessarily, there is no such time as 5 minutes before the first action.”
You may ask, “But what explains why God created THEN rather than 5 minutes later?” I answer, “Either because God had good reasons for his first action to be one of creation, or because there was a series of prior actions (perhaps divine thoughts), such that the latest member of that series, when it obtains, motivates creation, and the earliest member of that series was explained by God’s having good reasons for his first action to be of the relevant sort.”
You may ask, “What explains why, among all the abstract times, any given one is present rather than any of the other ones?” I answer, “t is present because five minutes ago [assuming there was a five minues ago], a certain other time was true, and that other time was such that its being true explains why in five minutes, t would be true. A regress results, but it terminates in the first time which was true in part because of a certain necessary truth concerning God’s desires.”
What else must I explain?

September 10, 2009 — 9:24
• Joshua:
So you take Augustine’s solution–time begins with creation.
That’s fine, but I think it may be inconsistent with the conjunction of presentism and theism. We seem to get an inconsistent triad:
1. To exist = to exist presently. (By presentism)
2. God is eternal. (By theism)
3. Time had a beginning. (St Augustine’s solution)
The conflict comes in when one tries to spell out what the doctrine that God is eternal must mean. Here is one way to see the point. There are two ways of spelling out eternity: temporal and timeless eternity. The temporal eternity (everlastingness) route is not compatible with 3, since then God’s being temporally eternal would be compatible with God’s being, say, 15 billion years old, which is absurd. So, God must be timelessly eternal. But that means that God exists outside of time. But by 1, this means that God presently-exists outside of time. But that appears contradictory.
One solution to take is to qualify 1, saying it only applies to our existence. Then we have presentism for us, but God outside of time. However, then, from the God’s eye point of view, there will be no fact of the matter which time is present. But the God’s eye point of view is correct. Hence, presentism will be false.
Maybe one can try WL Craig’s solution. He thinks that God is outside time and enters into time with creation. So, God has an atemporal and a temporal mode of existence. Now it would be incoherent to say that the atemporal mode of existence ceases with creation. So, we have to admit that God continues to have the atemporal mode of existence in addition to the temporal mode. This is weird: it’s like an Incarnation, in that God ends up having two ways of existing, and two kinds of knowledge. For God qua atemporally existing won’t know which time is present, but God qua temporally existing will. This decreases the specialness of the Incarnation.
Moreover, once one allows atemporal existence as a mode of existence, one’s motivations for presentism are somewhat undercut. For if we admit that atemporal existence is a possible mode of existence, why not likewise admit that past and future existence are possible modes of existence? It seems at this point arbitrary to limit existence to the disjunction of atemporal and present existence.

September 10, 2009 — 11:57
• Joshua Rasmussen

You aren’t going to let me escape easily, are you. ๐ I would define eternal has having no beginning and no end to its existence, and then I would analyze a beginning of x’s existence as a transition from a state of affairs (time) in which x doesn’t exist to one in which x does. You’ve offered me reasons (helpful ones) to not go with this analysis, but you see here my motivation for it… ๐

September 10, 2009 — 14:22
• Joshua Rasmussen

I suppose I do have to say that God, though eternal, is 15 billion years old. I remember when I first told me mom about that–she did find that strange….

September 10, 2009 — 14:26
• Joshua:
That x is eternal surely entails that either (a) x exists timelessly or (b) x will exist tomorrow and existed yesterday, or both (a) and (b). But on your view, that x is eternal only entails the conditional: if there is a tomorrow, x will exist tomorrow; if there is a yesterday, x did exist yesterday.
I do not think anybody in Christian tradition would accept that God’s eternity is consistent with the conjunction of the claims “God will not exist in five minutes”, “God did not exist 20 billion years ago” and “God does not timelessly exist.” Granted, some thinkers may have incautiously said that an eternal being is one that exists, has always existed and will always exist, but I suspect that they would recognize that the compatibility of their claim with the conjunction of these three propositions is a conclusive reason to reject this characterization of eternity.
Consider the promises of eternal life and the warnings against eternal damnation. On your reading of “eternal”, it seems that these promises and warnings are compatible with the hypothesis that all of us have less than an hour of existence left: in half an hour judgment comes (all the of the apocalyptic events could happen really fast!), and then we get half an hour of eternal life or damnation, and then that’s it for time, God and us. The worm dieth not, but if your view of cessation is correct, this is compatible with the worm existing for only half an hour, as long as it happens to exist until the end of time.
What you need is an additional promise, that the future is infinite. I do not recall this promise in Scripture, except as phrased in terms which on your view can be interpreted as compatible with temporal finitude (“without death”, “endless”, “eternal”, “for ever and ever”).
Moreover, on your view, the difference between an eternal and a non-eternal being is extrinsic. The mayfly that lived from May 1, 2008 to May 1, 2009 would have been eternal had there been no time before May 1, 2008 and no time after May 1, 2009.

September 10, 2009 — 15:23
• Joshua Rasmussen

Alex,
Well, maybe my view is unusual. ๐
My thought concerning the prospect of an infinite future has been that as long as there is change, there is time, and furthermore, even if there is no change, there will be time–otherwise, it would be impossible for everything to freeze and then unfreeze again, and it seems to me that that isn’t impossible. So, once time starts, no one can do anything to keep it from continuing forever. But even if time could stop, the thought that God would delete or freeze everything to stop time (“permanently”, of course) seems to me contrary to God’s character.

September 10, 2009 — 18:42
• Joshua Rasmussen

Perhaps I should add that all this (concerning eternity) is more a tentative hypothesis of mine than a committed belief.

September 10, 2009 — 18:47
• Joshua:
Suppose everything ceased to exist. But ex nihilo nihil fit. So if everything ceased, there would no longer be any possibility of change, either.
In terms of the hierarchy of theological problematicalness, my intuition is that your view is more problematic than open theism. ๐ The idea that something of finite age could be as old as God…

September 11, 2009 — 10:34
• Joshua:
I am actually a bit worried whether the beginning of time answer is satisfactory given an A-theory. It’s hard to formulate what exactly doesn’t have an explanation. Maybe the way to put it is this: “Why is it now 15 billion (rather than 14 thousand or 16 trillion) years after the beginning of time?”

September 11, 2009 — 10:42
• Joshua Rasmussen

Hey Alex,
It occurred to me that my view (hypothesis) about eternity may not be quite so “unusual” given a tenseless presentism (where the A-properties are analyzed in terms of tenseless properties; see รขยยPresentism and Grounding,รขยย Noรยปs 41 (2007): 90-109). For then prior to God’s creation, God tenselessly exists. And since I suggested the flow of time is ontologically grounded in God’s act of creation, prior to that act, there is a sense in which we might call God “timeless” prior to creation. And perhaps for that very reason it would be inappropriate to assign God an age–to say he’s as old as the flow of time. I think this puts my view in close proximity with Bill Craig’s.
Perhaps you’ll have various objections to this sort of view, but at least it isn’t wholly unorthodox.

September 12, 2009 — 10:15
• Joshua:
Yes, that’s less unorthodox, though it does seem to posit a change in God as a result of creation. But I am puzzled by this “prior to God’s creation, God tenselessly exists”. How can something be “prior” to time? Maybe “prior” here is explanatory, not temporal, priority?
I am also worried that Crisp has not really given a tenseless account of the A-properties. For, on his view, truth seems to be, in effect, a tensed property–or, more precisely, the predicate “is true” is a tensed predicate. Which abstract time is present? The one that is true. But of course that means: the one that is presently true. To reduce A-properties to present truth is no more of a reduction of A-properties to tenseless properties than to reduce A-properties to age (which works if the age of the universe is necessarily finite; t is present iff t-t0 equals the age of the universe, t is past iff t-t0 is less than the age of the universe, and t is future iff t-t0 is more than the age of the universe; here, t0 is the beginning of the universe; in fact, one doesn’t even need the universe to have finite age for this pseudo-reduction; one just needs one punctiliar event, and the notion of the age of an event–WWII is now 54 years old, and ten years before it started, it was negative 10 years old). But “is of age x” is a tensed predicate.

September 14, 2009 — 11:10
• Joshua Rasmussen

My understanding is that for Crisp a tenseless proposition is one that one can grasp or conceive of without thereby grasping an A-property. And by that account, the proposition that X is true counts as tenseless because one can grasp it without thereby grasping is presently true. My own hypothesis is that when I say X is presently true, what I’m saying is that it is in/entailed by that time which is true simpliciter. So, I analyze ‘presently true’ in terms of just plain ‘is true’.

September 14, 2009 — 18:23
• Yes, if you do things this way then you can have tenseless properties which entail non-trivial things involving A-properties. Being red entails being presently red, being true entails being presently true, and so on. I do not think, however, that this is what “tenseless” normally means. For instance, I think “x exists (tenselessly)” is compatible with “x does not presently exist.” I am not here begging the question against presentism–I am simply reporting what I think is the usual usage of “exists (tenselessly)”. The presentist is welcome to analyze “exists (tenselessly)” as “existed, exists (simpliciter) or will exist”–that is compatible with the usage. But the presentist is not welcome to analyze “exists (tenselessly)” as “exists (simpliciter)”–only the B-theorist can do that.
Here’s a way of seeing this fact about usage. It seems correct to say things like: “Napoleon is (tenseless) defeated at Waterloo.” But if this entails “Napoleon is (simpliciter) defeated at Waterloo”, then presentism is false. I take it that paradigmatic natural language uses of tenseless verbs are precisely in these kinds of historical claims.
A different point. There are untensed languages. Take, e.g., classical Hebrew, which has perfective and imperfective moods (perfective: an action considered as completed by the time under consideration; imperfective: an action considered as not completed by the time under consideration), but no tenses. While there are some pragmatic preferences for using the perfective for the past and the imperfective for the present and future, these are not hard-and-fast, and anyway without context or explicit markers like “today” or “tomorrow”, there is no distinction between present and future. (This is even more evident in Ugaritic.) The correct way to translate a Hebrew verb without sufficient context or markers would thus either be with a present-tense English verb plus a footnote or parenthesis that this is tenseless, or else with a triple disjunction like “jumped, jumps or will jump”.
Now, it seems very plausible to identify the “tenseless” verbs in English with precisely that by which one would translate verbs in languages that have no tense.
Next point. It seems to me (as a regulative ideal) that important philosophical points should be statable in any sophisticated language. In particular, your presentist claims should be statable in a language that has no tenses. But I don’t think they are. Consider the claim: “p is true” = “p is now true”. The translation of this will either be an uninteresting triviality when we are in a context that determines the “is true” to the present, or else it will be equivalent to the false claim that “p was, is or will be true” = “p is now true”. Suppose we try to explain in such a language what “x is red (simpliciter)” means. The B-theorist can give as paradigm cases instances of yesterday’s sunset, tomorrow’s sunrise, etc. But the only paradigm case the presentist can give is that of present things. And, by giving such cases, the presentist cannot distinguish the concept of “is red (simpliciter)” from the concept of “is red (now)”.
I think the presentist’s best bet will be this: Explain to the speakers of the language that they are mistaken in thinking “is red” is an unambiguous claim. Rather, “is red” is ambiguous between three different claims: “is red (pastly)”, “is red (presently)” and “is red (futurely)”. A difficulty with this is it still doesn’t give a non-trivial account of “is red (simpliciter)”.

September 14, 2009 — 19:34
• Joshua Rasmussen

Those are all good points, Alex.
I guess it’s not really clear to me what ‘tenseless is’ is supposed mean, but for now I suspect it’s equivalent to ‘tensed is’. You pose a counter-example: “Napolean is (tenseless) defeated at Waterloo.” This you suggest is true, but not presently true (Napolean isn’t presently defeated at Waterloo). In reply, I suspect that historical narrative expressed in the present tense is like fiction read as if true. There is an implicit “at that time” or “in that world” clause before the whole thing. In the case of Napolean, we’d be saying “This story (proposition) was the case: Napolean is defeated at Waterloo.”
I don’t know how tenseless statements work in a tenseless language. If someone says “x IS red” in their tenseless language, are they trying to say that x is red at some time? Or are they merely trying to say that x is red (simpliciter) without reference to time? If it is the later, then I would explain that the difference between ‘x IS red’ and ‘x is presently red’ is that only the later is a claim about x’s being red at a particular time, namely at that time that IS true. Do you see a problem with this account?

September 16, 2009 — 8:16
• Joshua Rasmussen

OK, I suppose the problem with my account (above) would be if when someone in a tenseless language says ‘X IS red’ (without any time reference), it is compatible with what he says that X’s being red is something that will happen in the future (or did happen in the past). I don’t know enough about tensless languages to answer this, but if you say this is so, I will trust you.

September 16, 2009 — 8:25
• Joshua Rasmussen

I meant “it is compatible with what he says that X’s being red is something that will happen in the future and isn’t now happening.”

September 16, 2009 — 9:32
• So, I think what the presentist would have to say about tenseless languages is this. In those languages, there is a systematic ambiguity. When they say “x is red”, they are saying something that is ambiguous between “x is presently red” and a member of the family of claims “x was red (t units of time ago)” and a member of the family of claims “x will be red (t units of time in the future)” and a disjunctive claim (when the speaker doesn’t know her temporal relation to the event being reported). In most, but not all (the Psalms are a glaring example–the tenses are sometimes up for grabs, and the translator just has to guess whether God is delivering or God will deliver), cases there will be an explicit or contextual marker that solves the ambiguity, much as with the English “bank”.
Moreover, the presentist should add this: But it is not quite how it is with “bank”. For what we have here is not a case of pure equivocity, but of Aristotelian focal meaning, with “x is presently red” being the primary form, and the other meanings being derivative. The surface grammar of the language does not adequately reflect this.
I still think there is a challenge to the presentist here. It might be hard for the presentist to explain why it is that the “x is presently red” is the focal meaning, rather than the focal meaning being the temporally neutral (according to the presentist, disjunctive) claim. Note that in that language it does not seem that the presentist can explain presentism by saying “Only present things exist simpliciter.” For context either determines “exist simpliciter” to a particular tense, in which case the statement is trivial or false, or else context leaves “exists” ambiguous, in which case the explanation is unhelpfully ambiguous, or else context makes “exists” disjunctive (“existed, exists or will exist simpliciter”) in which case the statement is false, since it is false that only present things exist, existed or will exist.
I think that to some extent this is a worry in English, too. English has at least three versions of “exists”: present tense, disjunctive tense (was or is or will-be or eternally-is), ambiguous tense. To say “Only present things exist simpliciter”, the presentist cannot use one of these three versions (else the claim is trivial, false or ambiguous). So the presentist needs a fourth version of “exists”: an “exists simpliciter”. But I don’t know how to introduce that fourth version to someone who only knows the three.

September 16, 2009 — 11:09
• Joshua Rasmussen

Well, we’ve certainly strayed from the law of excluded middle. ๐ Thanks for following me along this path.
You’ve raised many things for me to think about. Rather than offer a further comment (which is tempting), for now I’ll close with a verse that might fit better with your perspective:
“Jesus answered, “before Abraham was born, I am!” (John 8:58).

September 16, 2009 — 14:50
• Joshua:
Yeah. There is, by the way, an interesting literature on whether the A/B distinction is merely verbal (there is a nice piece by Zimmerman that first works really hard to make it seem like it is, and then argues in the negative), and whether the presentist/eternalist distinction is merely verbal (there is a 1999 piece by Sider, and a 2006 piece by Sider, but the latter is to me somewhat marred by the fact that there in fact is a pretty easy way to translate quantified eternalist claims into presentist language, as long as there are no cross-time relations or names of present non-existents).

September 17, 2009 — 8:39