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Alan Rhoda
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| Posted 2/24/2004 9:15 AM (GMT -6) |   | Doc, Tom, et al.,
I recently came across the book "Facing the Future" by Nuel Belnap et al. The book is a very dense and rigorous development of an indeterminacy logic by a very prominent logician.
His approach differs in important respects from the version of indeterminacy logic that we've developed on this board. Specifically, he would say that "will" and "will not" statements about indeterminate aspects of the future are neither true nor false, but--here's the interesting point--he argues that this doesn't deny bivalence. The reason: ALL tensed statements have to be indexed to a possible world history. When it is indeterminate which history will become the actual world history, then generic, non-indexed "will" and "will not" statements have no truth value because they aren't complete statements. To use an example, Belnap wants to say that non-indexed "will" and "will not" statements are like "x + 2 > 5" -- such a statement has no truth value until the value of the variable 'x' is specified. Similarly, "S will obtain in h" is an incomplete statement until the value of 'h' is specified. Thus it has no truth value.
Now I am not convinced that this is the right way to handle things, but it does put another dialectical option on the table for the open theist. Belnap doesn't explore any connections with divine omniscience, but he does critique what he calls the "Thin Red Line" view of the future, according to which there is already an actual future out there waiting to happen.
Anyway, this seems like an important book on the indeterminacy logic issue.
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Alan Rhoda
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| Posted 2/25/2004 10:42 AM (GMT -6) | | Thanks for the reply, Laplace.
Laplace: Sounds like this person is saying that we can only view future events in terms of probabilities.
Alan: I don't think that what Belnap is saying. The book steers largely clear of probability theory, from what I've seen so far. Of course, I don't have the book in front of me at the moment so I can't verify that right now.
What I think he's saying is that "X will happen" and "X will not happen", where X is currently indeterminate - like, say, the decay of a particular uranium in the next 10 minutes - have no truth value unless relativized to a particular history (i.e., a possible complete timeline going all the way back and all the way forward). Let H1 be a history in which our uranium atom decays in the next 10 minutes. Belnap would say that "X will happen in H1" or "If H1, then X will happen" are true, but "X will happen" has no truth value.
Regards,
Alan
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Alan Rhoda
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| Posted 2/26/2004 7:27 AM (GMT -6) | | Laplace: But then that doesn't make too much practical sense. If one has the mindset that "I accept nothing as true (or false) unless it has actually happened" then one cannot make any decisions about anything until the event(s) has happened, which by then would be absurd.
Alan: The claim isn't being made that NOTHING is true or false until it actually happens. Insteat, the claim is restricted to matters that are REALLY (not merely epistemically) indeterminate. That being said, I do think you have a point here. For if non-history-indexed "will" and "will not" statements about real indeterminacies are neither true nor false, then it seems that "probably will" and "probably will not" must also be neither true nor false (unless we can find a way of quantifying over possible histories, which doesn't seem promising). But then it seems that we can say little of positive significance about the indeterminate future until it happens, which would render decision-making more precarious, to say the least.
Perhaps Belnap has a way around this problem. Perhaps, but I suspect there's a fundamental problem here. I'll have to look at the text with this issue in mind.
Regards,
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Tom
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| Posted 2/26/2004 11:45 AM (GMT -6) | | Sorry I didn't notice this thread earlier Alan. Sounds like an interesting book. Aruges like one denying bivalence but doesn't wanna deny bivalence.
I wanna comment when I can on the "temporal indexing" of the truth value fo propositions. Doc and I had a great time discussing this over breakfast with a few profs. It was really helpful.
Doc said you were gonna email me about something?
Gotta run,
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Alan Rhoda
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| Posted 3/24/2004 9:07 AM (GMT -6) | | Tom - still waiting to hear what you have to say about 'temporal indexing'. And did you get the "Indeterminacy Logic" paper I sent you? What do you think?
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Alan Rhoda
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| Posted 3/24/2004 10:44 AM (GMT -6) | | OK, here's an issue that Belnap raises against the kind of indeterminacy logic that we've developed here on this board. The same issue is also raised by Craig in his works.
The claim is that it seems semantically appropriate to say "Event X will happen, even though it might not". Our indeterminacy logic, however, claims that "will" and "might not" are contradictories. Thus, so the argument goes, our indeterminacy logic requires us to defend the semantically counterintuitive position that "Event X will happen, but it might not" is not meaningful, when it obviously is. So there must be something wrong with our indeterminacy logic.
The foregoing line of reasoning prompts Belnap to develop his more complicated indeterminacy logic requiring that statements about the future be relativized to a particular 'history' (i.e., a complete time-line from creation to kingdom come).
How ought we to respond? Should we give up our indeterminacy logic and follow Belnap's lead, or is there a flaw in the argument? I think the latter is the case. Here's why.
First, we need to recognize that "will" and "might" can be used in either an epistemic or an ontic sense. In the ontic sense, to say that X "will" happen is to say that the future IS settled in that respect; and to say that X "might" happen is to say that the future is NOT settled in that respect, but open. In the epistemic sense, to say that X "will" happen is to say "I am certain that X happens in the future"; whereas to say that X "might" happen is to say "I am uncertain whether X happens in the future."
Now, given the ontic and epistemic senses of these terms, we have four possible ways to interpret "X will happen but might not":
1. "will" (ontic), "might" (ontic)
2. "will" (ontic), "might" (epistemic)
3. "will" (epistemic), "might" (ontic)
4. "will" (epistemic), "might" (epistemic)
Thus, "X will happen but might not" could mean:
1. The future is settled wrt X and the future is not settled wrt X.
2. The future is settled wrt X, but I am uncertain whether that is so.
3. I am certain that the future is settled wrt X, but in fact it isn't.
4. I am certain that the future is settled wrt X and uncertain whether the future is settled wrt X.
(1) and (4) are explicitly contradictory. And (2) and (3), while not explicitly contradictory, are "semantically odd", to say the least. If one was not certain whether the future was settled or not, why would one claim that it is? In short, then, it is not our indeterminacy logic that leads to semantic weirdness, but its denial.
Why, then, does it seem to many, like it does to Craig, that "X will happen but might not" makes good sense? For example, Craig will affirm that "Peter will in fact deny Christ, but still he might not because he is a free agent. And if he were not to, then it would not have been true, as it is, that Peter will deny Christ." One possible reason Craig finds this intelligible is because he never fixes the meaning of the terms. Are "will" and "might" being used in an ontic or in an epistemic sense? Until the meaning is fixed the contradictoriness and/or semantic oddity of "X will happen but might not" never becomes apparent. Another, and I think more charitable, possibility is that Craig has failed to notice that we often use words imprecisely. Thus, we often say that X "will" happen, even though, when pressed, we mean only that X will probably happen. It makes perfectly good sense to say "X will probably happen, but might not" because the probability qualifier allows for exceptions. I propose that this is how we ought to interpret statements like "X will happen but might not". Notice, however, that it now poses no problem for our indeterminacy logic.
In sum, here's the dilemma. Either "X will happen but might not" is nonsense, in which case the fact that our indeterminacy logic prevents us from saying it is not a liability, or it means "X will probably happen but might not", in which case our indeterminacy logic can easily affirm it. Indeterminacy logic stands.
God bless,
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Tom
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| Posted 3/24/2004 5:58 PM (GMT -6) | | quote:
Originally posted by Alan Rhoda
Tom - still waiting to hear what you have to say about 'temporal indexing'. And did you get the "Indeterminacy Logic" paper I sent you? What do you think?
Alan
Hi Alan-
I'm back up till the end of the month. I got the paper. Looks good. Just a few comments. I'm gonna fire it back to Greg pretty soon.
Oh yeah, temporal indexing. When we were having breakfast last month with some of Greg's friends discussing the paper, Greg and both learned that "temporal indexing" is what we DON'T want to do. Greg and I thought temporal indexing was a way to ANCHOR a proposition in history (by adding a temporal indicator, as in "JFK is assassinated on Nov. 22, 1963") so that it would NOT be atermporally true. But this actually does the opposite. Temporally indexing in this manner cuts the ties that anchor the propositon in history. We want to argue against temporal indexing as is commonly understood, meaning not that one can't construct propositions like "JFK is assassinated on Nov. 22, 1963" but that temporally indexing propositions in this manner does not make them atemporally true. Their truth values are still relevant to the time indicator in the proposition.
I think that was it.
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Tom
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| Posted 3/24/2004 6:05 PM (GMT -6) | | Alan: Thus, so the argument goes, our indeterminacy logic requires us to defend the semantically counterintuitive position that "Event X will happen, but it might not" is not meaningful, when it obviously is.
Tom: Hmm. “X will happen but it might not” means “X will happen AND might not happen.” I’m not sure why the adversative “but.” But anyhow, we’re arguing that this IS meaningful? “Will” and “might not” are contradictories. How is it meaningful to arguing both are true? Am I missing something?
Alan: In sum, here's the dilemma. Either "X will happen but might not" is nonsense, in which case the fact that our indeterminacy logic prevents us from saying it is not a liability.
Tom: I'm saying "X will and might not happen" is nonesense. "Will" and "might not" are contradictories. But I'm confused as to how this PREVENTS us from saying it is NOT a liability. On the contrary, showing that "will" and "might not" are contradictories is exactly how we claim "X will and might not happen" is not a liability for us. How are self-contradictory propositions liabilities (except for the one laying claim to such a proposition, which we're not doing)?
Tom
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Tom
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| Posted 3/24/2004 6:10 PM (GMT -6) | | Alan: 1. The future is settled wrt X and the future is not settled wrt X.
2. The future is settled wrt X, but I am uncertain whether that is so.
3. I am certain that the future is settled wrt X, but in fact it isn't.
4. I am certain that the future is settled wrt X and uncertain whether the future is settled wrt X.
(1) and (4) are explicitly contradictory. And (2) and (3), while not explicitly contradictory, are "semantically odd", to say the least. If one was not certain whether the future was settled or not, why would one claim that it is?
Tom: Precisely. Who would ever express themselves with (2) or (3)? What would it really MEAN to claim (2) or (3)? I could say "Tom knows that x is determinate but Fred isn't sure." But the same person couldn't lay claim to both for herself.
Alan: In short, then, it is not our indeterminacy logic that leads to semantic weirdness, but its denial.
Tom: Yay!
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Tom
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| Posted 3/24/2004 6:13 PM (GMT -6) | | I'm less fond of using "settled" and "unsettled" to get at what we're wanting to express. They both require more defining and maintenance than the more precise and to the point "determinately the case that" and "indeterminately the case that" (or "determinately that" and "indeterminately that") which I much more prefer (when talking logic).
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JET
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| Posted 3/25/2004 1:42 AM (GMT -6) | | quote:
Why, then, does it seem to many, like it does to Craig, that "X will happen but might not" makes good sense?
Because, as a practical matter, Craig operates with a different notion of libertarian freedom than OV’ers do.
The standard definition of LFW is: Agents can be said to possess libertarian freedom if it lies within their power to do otherwise given the exact same set of antecedent conditions.
For Craig and Freddeso, “power to do otherwise” means:
(LFW1) There is nothing (physical or metaphysical) that is preventing me from doing otherwise (although it is certain that I won’t do otherwise).
Thus, to Craig it makes sense to say that X will do A, but might not do A. For Craig, this means X will do A, although there is nothing (physical or metaphysical) preventing X from doing ~A.
On the other hand, for OV’ers, “power to do otherwise” means:
(LFW2) I have the power to determine whether or not I do otherwise.
With this understanding of LFW, it makes no sense to say X will do A, but might not do A. If it has already been determined that X “will” do A, then X does not have the power to determine whether or not X will do A.
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Alan Rhoda
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| Posted 3/25/2004 10:16 AM (GMT -6) | | quote:
Originally posted by TGB
Alan: In sum, here's the dilemma. Either "X will happen but might not" is nonsense, in which case the fact that our indeterminacy logic prevents us from saying it is not a liability.
Tom: I'm saying "X will and might not happen" is nonesense. "Will" and "might not" are contradictories. But I'm confused as to how this PREVENTS us from saying it is NOT a liability.
Tom, you misinterpreted my statement. Let me rewrite it so the grammar is clear:
In sum, here's the dilemma. Either "X will happen but might not" is nonsense, in which case (the fact that our indeterminacy logic prevents us from saying it) is not a liability.
The whole phrase in parentheses is the thing I am saying is not a liability.
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Alan Rhoda
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| Posted 3/25/2004 10:49 AM (GMT -6) | | quote:
Originally posted by TGB
"Temporal indexing" is what we DON'T want to do. Greg and I thought temporal indexing was a way to ANCHOR a proposition in history (by adding a temporal indicator, as in "JFK is assassinated on Nov. 22, 1963") so that it would NOT be atemporally true. But this actually does the opposite. Temporally indexing in this manner cuts the ties that anchor the propositon in history. We want to argue against temporal indexing as it is commonly understood, meaning not that one can't construct propositions like "JFK is assassinated on Nov. 22, 1963" but that temporally indexing propositions in this manner does not make them atemporally true. Their truth values are still relevant to the time indicator in the proposition.
I agree. We need to say that the truth value of any statement (tensed or tenseless) is relative to the temporal context in which the claim is made. Thus, "It will rain in Las Vegas tomorrow" claims that it is NOW a settled fact that rain happens here tomorrow. A claim is true iff what it claims to be the case is the case, which means that "It will rain in Las Vegas tomorrow" is true iff it is NOW settled that it rains in Las Vegas tomorrow. Similarly, to assert NOW the tenseless statement "It rains in Las Vegas on April 1, 2010" is to claim that it is true NOW that it rains in Las Vegas on April 1, 2010. That, in turn, implies that that is NOW a settled fact about the future. It is therefore true iff it is NOW a settled fact, and false otherwise.
Many philosophers, it seems, have missed this simple point. They have wanted to assess the truth values of claims by looking at things, as it were, from a temporally invariant, quasi-"God's eye" perspective. To adopt such a perspective, however, is to assume that the course of history from creation to kingdom come is and always has been completely settled.
Blessings,
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Alan Rhoda
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| Posted 3/25/2004 10:57 AM (GMT -6) | | Tom: I'm less fond of using "settled" and "unsettled" to get at what we're wanting to express. They both require more defining and maintenance than the more precise and to the point "determinately the case that" and "indeterminately the case that" (or "determinately that" and "indeterminately that") which I much more prefer (when talking logic).
Alan: I don't see any distinct advantage to using "determinately the case that" and "indeterminately the case that" rather than "settled that" and " not settled that" (this is better than "unsettled"). The longer phrases seem to me to be more cumbersome without any counterbalancing advantage in clarity or precision. I'm open to discussing the matter, though. I will note that Belnap, who is a professional logician, uses the terms "settled" and "open" (i.e., "not settled"), and he doesn't seem to think there's any problem of imprecision with that.
Regards,
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Alan Rhoda
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| Posted 3/25/2004 11:08 AM (GMT -6) | | JET: As a practical matter, Craig operates with a different notion of libertarian freedom than OV’ers do.
Alan: Great observation, JET. I think you're right. Of course, the big question for Craig and Freddoso's
(LFW1) There is nothing (physical or metaphysical) that is preventing me from doing otherwise (although it is certain that I won’t do otherwise).
is "what makes it certain that I won't do otherwise?" By (LFW1) it can't be anything physical or metaphysical, but what's left? Nothing? As far as I can see, the only remotely plausible answer here is to invoke a kind of backward causation and say that by my choice I make it to have always been the case that I will choose what I did, but that seems deeply problematic to me. How can I make something to have been the case before I existed?
Thanks.
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JET
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| Posted 3/25/2004 12:00 PM (GMT -6) | | Alan: . . . Of course, the big question for Craig and Freddoso's
(LFW1) There is nothing (physical or metaphysical) that is preventing me from doing otherwise (although it is certain that I won’t do otherwise).
is "what makes it certain that I won't do otherwise?" By (LFW1) it can't be anything physical or metaphysical, but what's left? Nothing? As far as I can see, the only remotely plausible answer here is to invoke a kind of backward causation and say that by my choice I make it to have always been the case that I will choose what I did, but that seems deeply problematic to me. How can I make something to have been the case before I existed?
JET: For Craig, nothing “makes” CCF’s true. They just are. It is the nature of free creatures that, for any possible circumstances in any possible world, free creatures are entirely predictable (to an omniscient being). Molinists like Craig reject the possibility that God could make a free creature with the capability of exercising free will in manner that is less than 100% predictable. If they allowed that possibility, then God wouldn’t have middle knowledge. Although Craig sometimes sounds like he’s talking about backwards causation (i.e., “having the power to bring it about that God has always believed x”), when it comes down to it, Craig believes that free agents will always act in accordance with their corresponding CCF’s. Therefore, this “power” to bring about God’s “past beliefs” is merely theoretical. It is a “power” that has never been and never will be exercised by anyone. By saying that we theoretically have this power (and that God’s past beliefs are “soft facts”, etc.), Craig thinks he is affirming LFW. However, Craig would be the first to say that noone has ever brought it about that God believed anything concerning what a free agent “would” do other than what God has always believed. Even though it sounds at first as though Craig affirms LFW, clearly Craig’s idea of LFW is much, much different from that of the open view.
Thanks,
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Alan Rhoda
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| Posted 3/25/2004 2:49 PM (GMT -6) | | JET: For Craig, nothing “makes” CCF’s true. They just are. It is the nature of free creatures that, for any possible circumstances in any possible world, free creatures are entirely predictable (to an omniscient being). Molinists like Craig reject the possibility that God could make a free creature with the capability of exercising free will in manner that is less than 100% predictable. If they allowed that possibility, then God wouldn’t have middle knowledge.
Alan: You are right that, for Craig (and Flint, and other defenders of Molinism) CCF's just are true, without there needing to be anything that makes them so. And I think you are right that, taken to its logical conclusion, Craig's position requires abandoning libertarian freedom or redefining it in some idiosyncratic way. But I think Craig takes himself to be advocating libertarian free will in the classical sense. He argues on a priori grounds (bivalence, etc.) that the truth value of propositions about future contingents must in all cases be settled in advance, irrespective of whatever it is (if anything) that settles those facts. That's why he ignores the grounding problem. He thinks that if he can just show that CCF's have an antecedently settled truth value, then, by definition of omniscience, God innately knows them. To my mind, the major obstacle here is not that Craig is presupposing an idiosyncratic definition of LFW, but rather that he has a defective semantics and a defective temporal logic. It is these obstacles, I think, that prevent him from seeing that Molinism logically requires abandoning LFW.
God bless,
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JET
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| Posted 3/26/2004 12:31 AM (GMT -6) | | Alan, I think you, Tom and Doc have shown time and again that Craig's logic and semantics merely beg the question of the ontological status of the future--his entire system assumes that the future is settled. Molinism/Ockhamism offers nothing to the debate about the future. Its sole purpose is to attempt (by using logical and semantical constructs) to make a settled future seem compatible with LFW. But the way they do this is by affirming a very weak (and ultimately, I think, a merely theoretical) form of LFW. The fact that nothing is "preventing me from doing otherwise" says absolutely nothing about why I choose the way I do. The ultimate difference between the OV and other views (including Molinism) is that the OV affirms that we have the power to create our choices and that LFW in this sense is what is needed to affirm moral responsibility and to make loving relationships possible. No other system can affirm LFW in this sense. That is what I was trying to say in a thread about a year ago when I tried to argue that Molinists and OV'ers talk past each other because they are not talking about the same thing.
Thanks for the feedback and thanks for your participation on this board. It is always very helpful and much appreciated.
Thanks,
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Alan Rhoda
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| Posted 3/26/2004 9:12 AM (GMT -6) | | quote:
Originally posted by JET
Craig's logic and semantics merely beg the question of the ontological status of the future--his entire system assumes that the future is settled. ... [He affirms] a very weak (and ultimately, I think, a merely theoretical) form of LFW. The fact that nothing is "preventing me from doing otherwise" says absolutely nothing about why I choose the way I do. The ultimate difference between the OV and other views (including Molinism) is that the OV affirms that we have the power to create our choices and that LFW in this sense is what is needed to affirm moral responsibility and to make loving relationships possible.
Right on, JET. To say "nothing is preventing me from doing otherwise, so I'm free" could easily be an expression of compatibilism. It's definitely not sufficient for LFW.
It occurred to me last night that the settled future view is exactly what we would expect if determinism is true. For if something is determined then it is the only thing that could have happened given the antecedent conditions. So determinism gives rise to a linear succession of events comprising a single (non-branching) causal chain. On the other hand, if something is not determined then it is one of several causally possible outcomes given the antecedents. The causal chain branches. LFW, in rejecting determinism, holds that there are several causally possible outcomes to a particular choice given the antecedents. Thus, LFW leads us to expect that the future branches and that the future, therefore, is not exhaustively settled. It other words, the future is partly open, for there are multiple ways things could turn out. Now, Craig wants to affirm the settled future view and LFW. But these two commitments point to opposite and incompatible construals of the future. So the picture Craig paints is ultimately incoherent. Something has to give, and it's either got to be the settled future view or LFW.
Appreciate the interaction.
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Alan Rhoda
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| Posted 3/26/2004 10:46 AM (GMT -6) | | 'Nuther thought.
Craig et al. want to derive ontological claims about the future (namely, that the future is settled) by analyzing the semantics of how we talk about the future. I see two big problems with this methodology.
1) The way people talk about things is very often imprecise and/or ambiguous, so deriving metaphysical conclusions from semantic observations is fraught with risk. For example, Craig thinks it clear that "If my wife were offered cookies, she would take them" is true. And indeed, in natural language it is. But natural language doesn't distinguish between conditionals where the antecedent really is a sufficient condition for the consequent and ones where the antecedent is only nearly sufficient. Thus we often attribute truth to conditionals that are not, strictly speaking, true but are still true "for all practical purposes". If we were speaking strictly, we would say "If Craig's wife were offered cookies she would probably take them". For God to make infallible predictions based on CCF's, as Molinism maintains, requires that CCF's be strictly true, and not just true for all practical purposes. Thus, Craig's semantic observation that we would ordinarily accept as true that "If my wife were offered cookies, she would take them" proves absolutely nothing about the existence of the kinds of strictly true CCF's that Molinism requires.
2) In principle, one cannot establish ontological conclusions by purely semantic methods. The reason is simple: semantics tells us about the meaning of words, but it can't establish that those words refer. Thus, Craig says that "the future" is to be defined as that which "will be". Given that definition, it follows that the future is exhaustively settled. But all this shows is that IF certain assumptions are true, THEN they logically imply certain conclusions. Before we can infer that those conclusions are in fact true, we need to know that the assumptions are in fact true, and that cannot be established by semantics without simply begging the question. But this is exactly what Craig does. I submit that we call this the "semantic fallacy".
God bless,
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