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Alan Rhoda
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| Posted 4/15/2004 7:01 AM (GMT -6) |   | Okay, folks. For the past year or so now, Tom, Doc, myself, and a few others have been discussing the logic of the open view and have developed a corresponding "indeterminacy logic". Currently, Doc, Tom, and I are putting the finishing touches on a paper that lays it all out. In it we respond to various philosophical objections. Most of these are not difficult to deal with, but there is one that I'm finding a tough nut to crack. In my view, this is THE main philosophical obstacle to earning a wide hearing for indeterminacy logic. If we can show how to give a plausible rebuttal to this argument, then I think many more Christian philosophers will begin to take open theism seriously. Without further ado, here's the argument:
quote:
The temporal invariance argument (TIA). The truth value of any tenseless statement, it will be urged, is temporally invariant, precisely because it is tenseless. Thus, if the statement is ever true, then it is always true. Now, for any possible future state of affairs S and future time t there are tenseless statements of the form “S obtains at t” and “S does not obtain at t.” Now, when t arrives it will surely be the case that either S will have obtained or it will be the case that S will not have obtained. If it turns out that S obtains at t, then “S obtains at t” is true at t. And if it turns out that S does not obtain at t, then “S does not obtain at t” is true at t. Whichever statement is true, by the temporal invariance thesis that statement must have been true at all times prior to t. So at all times prior to t it is true either that “S obtains at t” or that “S does not obtain at t.” If the first is true at all times prior to t, then the tensed statement “S will obtain at t” is also true at all times prior to t. And if the second is true at all times prior to t, then the tensed statement “S will not obtain at t” is true at all times prior to t. It follows that either “S will obtain at t” or “S will not obtain at t” is true at all times prior to t for all S and for all t, which is to say that the future is (and always has been) exhaustively settled.
Broken out into numbered statements the TIA looks like this:
The temporal invariance argument (TIA).
(1) The truth value of any tenseless statement is temporally invariant, precisely because it is tenseless. Thus, if the statement is ever true, then it is always true.
(2) For any possible future state of affairs S and future time T there are tenseless statements of the form “S obtains at T” and “S does not obtain at T.”
(3) Therefore, for any possible future S and future T, the tenseless statements "S obtains at T" and "S does not obtain at T" are either always true or always false. (1,2)
(4) When time T arrives it must be the case that either S will have obtained or it will be the case that S will not have obtained.
(5) If it turns out that S obtains at T, then “S obtains at T” is true at T.
(6) If it turns out that S does not obtain at T, then “S does not obtain at T” is true at T.
(7) Therefore, at T, it must be the case that either "S obtains at T" is true or "S does not obtain at T" is true. (4,5,6)
(8) Therefore, either "S obtains at T" or "S does not obtain at T" is true at all times prior to T. (3,7)
(9) If "S obtains at T" is true at all times prior to T, then the future-tense statement "S will obtain at T" is also true at all times prior to T.
(10) If "S does not obtain at T" is true at all times prior to T, then the future-tense statement "S will not obtain at T" is also true at all times prior to T.
(11) Therefore, either "S will obtain at T" or "S will not obtain at T" is true at all times prior to T. (8,9,10)
(12) Therefore, the future is and always has been exhaustively settled. (11)
(13) Therefore, the future is not even partly open. (12)
As far as I can see, this argument is deductively valid. Moreover, all of the premises seem quite plausible. The conclusion, however, is a direct denial of the central tenet of open theism. So either open theism is false, or there is a faulty assumption in the argument. If there is a faulty assumption it would have to lie in one of the independent premises, namely (1), (2), (4), (5), (6), (9), or (10). But it is far from obvious which premise, if any, can be plausibly denied.
A successful response will not only have to deny one of those premises, but it will also have to show that that denial is plausible. Any ideas on how this might be done? I have a couple, but I'll let y'all chew on this for a bit.
Thanks in advance for any input.
Alan | | Back to Top | | |
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GregBoyd
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| Posted 4/15/2004 10:18 AM (GMT -6) | | Seems to me the difficulty is generated by premise (1): The truth value of any tenseless statement is temporally invariant, precisely because it is tenseless. Thus, if the statement is ever true, then it is always true.
If one assumes an open view of reality rather than an exhaustively and eternally settled view of reality, the truth value of any tenseless statement is not temporarry invariant. If at T1 reality is open to "S obtaining" or "S not obtaining," then the tensless statement "S obtains at T2 is false, for what is true is "S may and may not obtain at T2." "S obtains at T2" BECOMES TRUE only when it becomes factual that "S obtains at T2" rather then "So may and may not obtain at T2."
In short, it seems to me that the Temporal Invariant Argument presupposes an exhaustively settled view of reality rather than argues for it.
What think ye?
Greg
ps. Just curious... how would the TIA handle "S may and may not obtain at T1"? Is THIS tenselessly true? Obviously it can't be, which simply exposes the question begging nature of the TIA. It must assume all statements are settled statements -- hence all reality is settled reality.
"The responsibility is with the chooser -- God is blameless." Plato, Republic, 10. | | Back to Top | | |
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JET
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| Posted 4/15/2004 11:05 AM (GMT -6) | | As a non-philospher, I have difficulty seeing how "S obtains at T" is a tenseless statement. It seems like saying:
S obtains at T
is exactly the same as saying:
At T, it is true that (S now obtains).
seems to be a (time-indexed) present-tense statement; i.e., a statement about the present tense reality at T.
Is a tenseless statement?
How is any different than ?
Thanks,
JET
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Alan Rhoda
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| Posted 4/15/2004 1:08 PM (GMT -6) | | Greg: Seems to me the difficulty is generated by premise (1): The truth value of any tenseless statement is temporally invariant, precisely because it is tenseless. Thus, if the statement is ever true, then it is always true.
Alan: I agree that premise (1) is the most likely candidate for rejection. The challenge is making that rejection seem plausible. Simply pointing out that it begs the question may not be enough if we can't give a positive analysis of the semantics of tenseless statements that makes premise (1) lose its intuitive allure.
Greg: If one assumes an open view of reality rather than an exhaustively and eternally settled view of reality, the truth value of any tenseless statement is not temporarry invariant. If at T1 reality is open to "S obtaining" or "S not obtaining," then the tensless statement "S obtains at T2 is false, for what is true is "S may and may not obtain at T2." "S obtains at T2" BECOMES TRUE only when it becomes factual that "S obtains at T2" rather than "S may and may not obtain at T2." In short, it seems to me that the Temporal Invariant Argument presupposes an exhaustively settled view of reality rather than argues for it.
Alan: I think this is a good start, and it is the approach I currently pursue in our paper. My only qualm is that I think we may need to say more to make our denial of (1) look plausible. For many opponents of open theism may grant that (1) technically begs the question against open theism but then go on to say "I reject open theism because (1) seems much more plausible to me than its denial." If we cannot undermine the intuitiveness of (1) then I doubt indeterminacy logic will get a wide and sympathetic hearing among philosophers.
Greg: How would the TIA handle "S may and may not obtain at T1"? Is THIS tenselessly true? Obviously it can't be, which simply exposes the question begging nature of the TIA. It must assume all statements are settled statements--hence all reality is settled reality.
Alan: I'm not sure this is a problem for the TIA. Premise (1) only claims that the truth value of tenseless statemetns is temporally invariant. It does not claim that this is true of tensed statements, or that all tensed statements can be translated into tenseless statements without loss of meaning.
Appreciate the quick response, Greg. I'm gonna keep thinking this over.
Alan | | Back to Top | | |
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Alan Rhoda
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| Posted 4/15/2004 2:19 PM (GMT -6) | | JET: I have difficulty seeing how "S obtains at T" is a tenseless statement. It seems like saying "S obtains at T" is exactly the same as saying "At T, it is true that (S now obtains)." seems to be a (time-indexed) present-tense statement; i.e., a statement about the present tense reality at T. Is a tenseless statement? How is any different than ?
Alan: Good point, JET. There is something very artificial sounding about so-called "tenseless statements". In ordinary conversation no one ever says things like "Jack and Jill travel to Tahiti on June 1, 1990". The only time we seem to use statements like that is if we are labelling things like events on a timeline or photos in a biography or scholarly work.
Whether or not, such statements are strictly tenseless, it does seem to be standard practice among philosophers to treat them as such. I think the reason for this is that, unlike clearly tensed statements using 'will' or 'was', 'obtains at T' seems to be abstracted from a temporal context. Thus, 'will' tells us that the hypothetical speaker is situated at some point in time and is looking forward to some later point in time. Likewise, 'was' tells us that the speaker is situated at some point in time and is looking backward to some earlier point in time. But 'obtains at T' gives us no information about the temporal situation of the speaker with respect to T. It could be uttered at a point prior to T, concurrent with T, or subsequent to T. So the "tenseless" manner of speaking seems to lift us out of the flow of time to a kind of 'God's eye' perspective on the matter. Perhaps such statements aren't so much "tenseless" as "indeterminately tensed".
This observation may give us a useful way of semantically analyzing statements like "S obtains at T". We can see them as a kind of incomplete statement, somewhat like "x + 2 > 4" is an incomplete statement because we cannot properly assess its truth value until we know the value of x or the range of permissible values for x. Thus if asked "Is it true that 'x + 2 > 4'?" We should respond, "That depends on how you specify x." Similarly, if someone asks "Is it true that 'S obtains at T'?" we should respond, "That depends on how you specify S, on how you specify T, and on where T is situated with respect to the present."
By George, I think that's the ticket!
Let's reflect a bit on what a statement like "S obtains at T" might mean. If a person were to assert this, despite the fact that it would sound quite odd, it seems that they would be affirming that it is NOW true that S obtains at T, which commits them to the claim that the future is already settled in that respect. So the claim would be true only if the future is in fact settled in that respect, which the open view insists is NOT something that can be simply taken for granted. What this means is that the truth of "S obtains at T" is crucially dependent upon the relation of T to the time of the utterance. If T is in the past, then the statement makes historical report. If T is in the present, then the statement claims that something is taking place right now. And if T is in the future, then the statement makes a prediction or forecast about the future. The only case in which the relation of T to the time of the utterance would NOT be relevant is if the open future view is false and the whole course of history is exhaustively settled. So we have confirment that (1) does indeed beg the question against the open future view. Moreover, we have a semantic analysis of "tenseless statements" that explains why the time of their utterance is relevant to their truth value.
Gee, thanks guys.
Any further input appreciated, but I think I now see the way forward.
God bless,
Alan | | Back to Top | | |
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Alan Rhoda
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| Posted 4/15/2004 4:02 PM (GMT -6) | | quote:
Originally posted by albert
Albert replies: Hello guys! I'm looking forward to seeing the paper when it's available ... you can probably guess I'll be interested to see how you end up dealing with "mights"!
Sorry to disappoint, Albert, but the paper doesn't at present discuss "mights" or counterfactuals, though the extension of the logical apparatus to conditionals is pretty straitforward. Perhaps in a follow-up piece we'll fill in that lacuna.
Regards,
Alan | | Back to Top | | |
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Tom
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| Posted 4/15/2004 6:16 PM (GMT -6) | | Alan: What this means is that the truth of "S obtains at T" is crucially dependent upon the relation of T to the time of the utterance.
Tom: This is THE fundamental claim we must prove plausible. It’s why I said some time ago that there's a difference between being ‘grammatically tenseless’ and ‘metaphysically tenseless.’ Mathematical truths are metaphysically tenseless and thus TIA applies. Philosophers incorrectly assume that one can take the numbers out of a tenseless equation and put events and choices in their place. But there IS no atemporal tense (grammatically speaking) for verbs, though there is in math. Saying “JFK is assassinated…” isn’t grammatically tenseless. First “is” is not tenseless (it’s present tense) and “assassinated” is past tense. There's tense all over the place. Philosophers may claim to recognize such language as mathematically tenseless, but that's just reading into language their own metaphysic. Grammar doesn't get you there. TIA is quite counterintuitive on its own (except for mathematical equations, in which case it's perfectly intuitive).
We might want to pursue the claim that there really is a difference between being “metaphysically tenseless” and “grammatically tenseless.” The truth value of mathematical truths is truly timeless because their truth values are metaphysically unrelated to ANY event in our temporal world. 2 + 2 = 4 doesn’t depend for its truth-value on the actualizing of ANY event whatsoever. It was only ‘discovered’ by us to be true at some point in time that two plus two equals four. But it can NEVER be said of propositions describing “events” in our world that their truth-value does not depend on ANY event in our temporal world. Quite the opposite. So, I would show that your premise (1) is not plausible by pointing out the difference between truly timeless truth-values (mathematical ones) and temporally-defined (viz., temporally UTTERED in addition to temporally INDEXED) truth-values and showing how propositions describing temporal events by definition have truth-values relevant to the relationship between the time they are spoken and the metaphysical state of affairs they posit. To be true, a proposition must correspond to an actual state of affairs. To be false, a proposition must fail to correspond to an actual state of affairs. “JFK is assassinated in 1963” spoken in 1964 is true not by virtue of so-called tenseless grammar but by virtue of correspondence between grammar and a particular metaphysical state of affairs (viz., that actual event of JFK’s assassination in 1963). But spoken in 1920 the same proposition is false by virtue of the failure of correspondence between its grammar and the metaphysical state of affairs necessary to making it true (viz., the actual event of JFK’s assassination in 1963). This gets us back to truth-makers and the grounding objection, which Craig will deny forever perhaps, but which many other philosophers admit and so will hopefully see the point here.
Alan: If T is in the present, then the statement claims that something is taking place right now. And if T is in the future, then the statement makes a prediction or forecast about the future.
Tom: This is why TIA is also used to assume true and false future tense statements from timeless ones. “JFK will be assassinated in 1963” is true at all times prior to 1963 BECAUSE the tenseless “JFK is assassinated in 1963” is true at all times period.
Tom | | Back to Top | | |
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Alan Rhoda
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| Posted 4/17/2004 10:09 AM (GMT -6) | | Tom: We might want to pursue the claim that there really is a difference between being “metaphysically tenseless” and “grammatically tenseless.” The truth value of mathematical truths is truly timeless because their truth values are metaphysically unrelated to ANY event in our temporal world. 2 + 2 = 4 doesn’t depend for its truth-value on the actualizing of ANY event whatsoever. It was only ‘discovered’ by us to be true at some point in time that two plus two equals four. But it can NEVER be said of propositions describing “events” in our world that their truth-value does not depend on ANY event in our temporal world. Quite the opposite. So, I would show that your premise (1) is not plausible by pointing out the difference between truly timeless truth-values (mathematical ones) and temporally-defined (viz., temporally UTTERED in addition to temporally INDEXED) truth-values and showing how propositions describing temporal events by definition have truth-values relevant to the relationship between the time they are spoken and the metaphysical state of affairs they posit.
Alan: This is a helpful distinction, Tom, which adds to what I have already said and gives a further reason for thinking that the truth of statements of the form "S obtains at T" or "Event E happens at T" is dependent on, among other things, the relation between T and the time the statement is uttered. I like the way you ground this distinction in the temporal contingency of truth conditions. I think we can go a step further by introducing the following distinctions:
A statement is temporally contingent iff it is possibly true at some times and not at others.
A statement is temporally necessary iff it is necessarily true at all times.
A statement is temporally invariant iff it has the same truth value at all times.
A statement is temporally variant iff it does not have the same truth value at all times.
Some statements (e.g., "2 + 2 = 4") are necessarily true at all times and are therefore temporally invariant.
Some statements (e.g., "Bill Clinton is the current president of the U.S.") are true at some times and not at others. They are temporally contingent and temporally variant.
Some statements are in fact true at all times but are not necessarily true at all times. Examples are harder to come by here, but suppose God has eternally settled that some particular S obtains at some particular T (or at all T), then "S obtains at T" is true at all times, but would not have been true if God had not settled it. Such statements are temporally contingent but are nevertheless temporally invariant.
The first class is especially relevant here, for there temporal invariance does not hold, and therefore, whether the statement is true or not depends on when the statement is uttered. If the Clinton example were uttered between 1992 and 2000 it would be true. Uttered at any other time it would be false.
The issue, then, is whether statements of the form "S obtains at T" or "E happens at T" fall into the class of temporally invariant statements or into the class of temporally variant statements. The TIA claims the latter, but is this plausible for all S, E, and T? One thing is clear, where T is in the future, such statements will be temporally invariant iff the future is exhaustively settled. Suppose this is not the case. If the future is open wrt S's obtaining at T then it is not true NOW that S obtains at T (even though that might turn out to be true at T), nor is true NOW that S does not obtain at T (even though that might turn out to be true at T). So the truth value of neither "S obtains at T" nor "S does not obtain at T" can be NOW be true because things might not turn out that way. So their truth values must NOW be false, which means that at T, or possibly before, one of those truth values will change. Since it could be either that changes, they are temporally variant, and so the time of the utterance is relevant to their truth.
God bless,
Alan | | Back to Top | | |
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GregBoyd
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| Posted 4/26/2004 9:21 AM (GMT -6) | | Alan: This observation may give us a useful way of semantically analyzing statements like "S obtains at T". We can see them as a kind of incomplete statement, somewhat like "x + 2 > 4" is an incomplete statement because we cannot properly assess its truth value until we know the value of x or the range of permissible values for x. Thus if asked "Is it true that 'x + 2 > 4'?" We should respond, "That depends on how you specify x." Similarly, if someone asks "Is it true that 'S obtains at T'?" we should respond, "That depends on how you specify S, on how you specify T, and on where T is situated with respect to the present."
By George, I think that's the ticket!
Greg: Isn't that what I said earlier? Anyway, the mathematical analogy clarifies the question-begging nature of the issue. The thing is, I don't see how one can assess "tenseless statements" in a way that doesn't beg the question. That is, whether the situation is x+2>4 or [say] 3+2>4 depends on the view of the future you presuppose. Does the future include undefined variables OR NOT. The issue has to be settled on other grounds. But a draw on THIS issue is fine. Our only task is to show that tenseless statements don't REFUTE the open view by showing that we have a way of making sense out of them.
As you say, "By George... that's IT".
Good work. Send me the essay ASAD (As soon as done).
Blessings
Greg
"The responsibility is with the chooser -- God is blameless." Plato, Republic, 10. | | Back to Top | | |
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Alan Rhoda
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| Posted 5/10/2004 3:03 PM (GMT -6) | | - Greg, Tom,
Now that the semester's finally almost over, I'm hard at work on the paper. Refining some of the arguments and addressing an objection against our indeterminacy logic raised by Craig, Belnap, and others. Should have it done by the middle of next week.
Additional musings on matters of logic:
As used in ordinary speech, the future-tense qualifier "will" is vague.
For example, we sometimes use it to mean "definitely will", as in "If you drop that rock, then it will fall." Here the understanding is that there is no real possibility that things might turn out otherwise.
We also sometimes use it to mean "probably will", as when a mother warns her child "Don't go outside in the cold without your jacket, or you will get sick." Here the understanding is not that getting sick is inevitable, but rather that it has a high likelihood of coming to pass.
We also sometimes use "will" in an even weaker sense, as when someone asks you to predict which number will turn up on the roulette wheel and you say, "I think it will land on 20". Everyone understands that you are not claiming that this outcome is inevitable or even probable. You're just picking, more or less at random, one of the available possibilities and positing it.
This flexibility of the word "will" has severely hampered the foreknowledge debate. For it should be clear that "definitely will" and "might not" are contradictories and that "probably will" and "might not" are compatible--in fact, the former entails the latter. Proponents of the settled future view who believe in genuine future contingency (like Craig) exploit this ambiguity to their advantage. When they want to emphasize the settled nature of the future, they interpret "will" as "definitely will". And when they want to create space for human freedom and real contingency, they interpret "will" as "probably will" or something weaker. This equivocation is systematic, largely unnoticed by the parties in the discussion, and the source of no small amount of confusion and misunderstanding.
One virtue of our indeterminacy logic is that it fixes the meaning of "will" to mean "definitely will". Appropriate qualifiers like "probably" are added whenever something weaker is intended. This allows us to avoid the multiple conflations that have so confused the foreknowledge debate.
Alan | | Back to Top | | |
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Tom
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| Posted 5/10/2004 5:43 PM (GMT -6) | | quote:
Originally posted by GregBoyd
Alan: This observation may give us a useful way of semantically analyzing statements like "S obtains at T". We can see them as a kind of incomplete statement, somewhat like "x + 2 > 4" is an incomplete statement because we cannot properly assess its truth value until we know the value of x or the range of permissible values for x. Thus if asked "Is it true that 'x + 2 > 4'?" We should respond, "That depends on how you specify x." Similarly, if someone asks "Is it true that 'S obtains at T'?" we should respond, "That depends on how you specify S, on how you specify T, and on where T is situated with respect to the present."
By George, I think that's the ticket!
Greg: Isn't that what I said earlier? Anyway, the mathematical analogy clarifies the question-begging nature of the issue. The thing is, I don't see how one can assess "tenseless statements" in a way that doesn't beg the question. That is, whether the situation is x+2>4 or [say] 3+2>4 depends on the view of the future you presuppose. Does the future include undefined variables OR NOT. The issue has to be settled on other grounds. But a draw on THIS issue is fine. Our only task is to show that tenseless statements don't REFUTE the open view by showing that we have a way of making sense out of them.
Yes, Doc and Alan, but in this case isn't it true you get the draw at the cost of giving up bivalence? Doesn't what you say above, Alan, suggest the denial of bivalence by conceding that future indedeterminate events are undefined variables without truth value? Or am I missing your point in positing undefined varialbes? I thought infinite intelligence meant there are no undefined variables.
Tom | | Back to Top | | |
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Alan Rhoda
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| Posted 5/10/2004 10:07 PM (GMT -6) | | quote:
Originally posted by TGB
Yes, Doc and Alan, but in this case isn't it true you get the draw at the cost of giving up bivalence? Doesn't what you say above, Alan, suggest the denial of bivalence by conceding that future indedeterminate events are undefined variables without truth value? Or am I missing your point in positing undefined varialbes? I thought infinite intelligence meant there are no undefined variables.
Bivalence says that all propositions are either true or false. It says nothing about propositional forms like x+2=4. An propositional form is not a type of proposition. It is not a proposition at all. So bivalence is maintained. Infinite intelligence means God knows what all the variables are and all the possible ways they may be combined. Thus God knows the truth value of x+2=4 for every substitution instance of x, but no amount of intelligence or knowledge can know the truth value of x+2=4 for some unspecified x, unless it is the case that every substitution instance yields the same result. x+2=4 is not a proposition, but a propositional form which has as many instances as there are substitution values for x.
Here's another example: If p, then q. Is that true? Is it false? It's impossible to say until both p and q are specified. Until then all we have is a propositional form, but no proposition, nothing that could carry a determinate truth value.
Anyway, I'm not claiming that "future indeterminate events are undefined variables without truth value". I'm claiming that so-called "tenseless" statements describing future contingencies fail to express a proposition as long as the time of the utterance is unspecified. Consequently, the time of the utterance is crucially relevant to the truth or falsity of the statement, which means that premise (1) of TIA is false.
God bless,
Alan | | Back to Top | | |
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Tom
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| Posted 5/11/2004 1:36 AM (GMT -6) | | | | |
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