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Tom
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| Posted 11/29/2003 5:07 AM (GMT -6) |   | I’m bring this portion of Alan’s comments here from the thread “Open Theism and it’s Critics” because it deals with logical arguments for the open view. I’d like to keep it here for easy reference later.
quote:
Alan: I agree with you, Tom. Though I have some new thoughts on this issue sparked by an email conversation I've been having with Dale Tuggy, a Christian philosopher and open theist who is delivering one of the papers at this conference. Dale construes open theism, like Sennett, as the view that propositions about future contingents are neither true nor false. Thus he denies bivalence, but doesn't think that's a problem. When I described in summary fashion our indeterminacy logic, though, his reaction was and probably still is quite skeptical. On his view, if one affirms bivalence, then either "Craig does go to the movies tomorrow" D(c,m,t) or he does not, since D(c,m,t) and not-D(c,m,t) are contradictories. Which means, he argues, that our indeterminacy logic is inconsistent. I pointed out in response that his argument assumes that D(c,not-m,t) is equivalent to not-D(c,m,t). But that is something an indeterminacy logician would deny since not-D(c,m,t) is consistent with both D(c,not-m,t) and "It is indeterminate whether Craig goes to the movies tomorrow."
So Dale hasn't refuted indeterminacy logic. But what his objection reveals is that many otherwise sympathetic philosophers are trying to express open theism from within the frame of reference established by what is perhaps the philosophically "orthodox" understanding of these notions, whereas we are trying to express open theism from within a frame of reference that deliberately and explicitly treats indeterminacy as a real ontological possibility. As is often true in physics, one frame of reference can be transformed to the other, provided we are willing to make suitable modifications in our usage of key terms like "truth", "actual world", etc. Shifting from frame of reference to the other, however, requires something like a Gestalt shift.
What I am suggesting is that there are (at least) two ways to cash out open theism. One way is to affirm what Richard Purtill has called the "temporal invariance" of truth values and deny bivalence. Dale and Sennett pursue this approach. Another way is to deny the temporal invariance of truth values and affirm bivalence. You, me, and Doc have been pursuing this approach. In the first case reality is supposed to be fully determinate one way or the other (i.e., for all states of affairs S, either Z(S) or Z~(S)), and we accommodate indeterminacy by positing three truth values (T, F, and I). In the second case reality is supposed to be partly indeterminate (i.e., for all states of affairs S, either Z(S), Z~(S), or Q(S)), and we have only two truth values (T and F). Both of these approaches are, it seems to me, different ways of trying to say the same thing. So the choice of one over the other is more one of convenience than substance. Do we want to talk as if indeterminacy resides in the truth of propositions, or in the nature or reality? I think we would both agree that the latter approach is the one we should adopt because it makes clear, as the former approach does not, that the issues in question are metaphysical and not merely semantic or epistemic.
Thanks so much for the response, Alan. Very interesting approach your friend Dale has. Now David Lewis’ book Counterfactuals makes better sense. The whole possible world semantics is difficult to grasp. Now I get it better.
But if Dale and Sennett’s fundamental argument is that “reality is…fully determinate one way or the other” then how is it possible to posit three truth values (T, F, and I)? I’m assuming that the truth value of propositions is grounded in the ontology described by the propositions. Propositions “get” their truth value from the states of affairs that make it now the case that the events they describe “will” or “will not” happen (assuming with Dale that reality is fully determinate). In other words:
a) If “I” is a truth-value other than T and F, and
b) If truth values are ontologically grounded (grounded in reality), and
c) If ontology/reality is fully determinate (either Z or Z~), and
d) If there are propositions possessing truth value “I”, then
e) What reality grounds the truth value of propositions possessing value “I”?
Maybe I don’t grasp three-valued logic or the notion of possible worlds sufficiently. I’m having difficulty understanding how someone who believes reality is exhaustively determinate (either Z(S) or Z~(S)) can at the same time accommodate indeterminacy. Do they deny that truth values are ontologically grounded?
It’s all very strange, really. I mean, Craig fights for bivalence but denies that anything grounds truth value. He wants to close the door to the possibility of there being propositions that are either true or false, thinking thereby to have successfully argued that the future is either a “will” or a “will not” matter (as if “true” and “false” somehow demand “will” and “will not”, like truth values and ontology have to be BOTH bivalent). But that’s not so. All that’s needed is to introduce a third ontological option (indeterminacy) into a bivalent logic. But Dale and Sennett want to deny bivalence and agree that the future is exhaustively determinate. I don’t see how their “indeterminacy” is not purely an epistemological dream. Without an ontology grounding indeterminacy, what gives propositions that are neither neither T nor F but "I” their truth-value?
Interesting! I have to admit that I think there is more to the difference between our view (bivalence and three-fold ontology) and Dale’s (three-valued logic and a bivalent—exhaustively either Z or Z~–ontology) than semantics. But I’m WIDE open-minded! 
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Magneton
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| Posted 11/29/2003 5:48 AM (GMT -6) | | OK, Tom, I'm feeling a little dense here. You described different senses of "might" earlier. For the 3 statements
(1) It is determinately the case that x occur
(2) It is determinately the case that x not occur
(3) It is indeterminately the case that x occur
ontological indeterminacy is expressed by (3). Epistemic indeterminacy is expressed by "(1) OR (2) is true". When I say might this way I mean that the fate of x is determined, but I don't know in which direction.
In either of these 2 cases, I say "x might or might not occur." You have suggested that some people (maybe non-OV) would suggest there are propositions where might is true but might not is false. Could you give an example of where someone would say "x might occur" but they couldn't say "x might not occur"?
Thanks,
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Tom
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| Posted 11/29/2003 11:38 AM (GMT -6) | | I’d like to throw something in here about how I understand Alan’s three metaphysically distinct states of affairs regarding the future. I’m wondering if there are some who mistakenly think when we talk about indeterminacy being “ontological” we mean to say that the “future states of affairs” (the events described in propositions like “Tom will come to St. Paul in 2004) possess an ontology. I don’t think they do. I hope this doesn’t shock anybody. If the future doesn’t exist in any dimension of time, if it’s not actual, the events described as “will’s” “will not’s” and “might’s” can’t have an actual ontology.
So what do we mean when we talk about indeterminacy being a metaphysical state of affairs or as being an ontological affair? When I say “Tom will come to St. Paul in 2004” is true and that this describes a “determinate state of affairs,” I of course mean to say that it is what is NOW true, NOW the case, that makes my coming to St. Paul next year determinately the case (as opposed to determinately not the case or indeterminately the case). Ontology is universally a PRESENT reality. So it must be what reality now is that is responsible for the truth value of future tense propositions. Such propositions get their truth value from the present moment, from the present state of reality. What makes it true that “Tom will come to St. Paul is 2004” (assuming for the moment that this is true) is not the future, not anything not yet actual. On the contrary, my coming to St. Paul DESCRIBES a future states of affairs, and yes it is (now) determinately the case that this state of affairs will actualize. But it’s the present (and all the past that stands behind it) that makes it now determinately the case that I will come to St. Paul next year. So distinguish between two states of affairs: that future state of affairs “described” in a future tense proposition (Tom’s coming to St. Paul, Bush’s running for President, Doc’s finishing the third in his trilogy, etc.), and that present state of affairs that makes it true or false that the events described “will,” “will not,” or “might and might not” occur.
Just wanted to clarify that point. The “ontology of the future” is perhaps not the best way to describe it come to think of it. It’s more accurately described as how the PRESENT opens and closes certain doors regarding what is to follow. An event p that “will not” occur is like a closed door. This world we live in, because of what it is NOW, cannot pass through that door. A single door that’s open is a “will.” This world we live in, because of what it is NOW, will certainly pass through this door. And two or more open doors constitute a “might and might not.” The world we now live in, because of what it now is, might and might not walk through either or these open doors.
Hope that helps.
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Tom
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| Posted 11/29/2003 1:13 PM (GMT -6) | | quote:
Magneton: OK, Tom, I'm feeling a little dense here. You described different senses of "might" earlier. For the 3 statements
(1) It is determinately the case that x occur
(2) It is determinately the case that x not occur
(3) It is indeterminately the case that x occur
ontological indeterminacy is expressed by (3). Epistemic indeterminacy is expressed by "(1) OR (2) is true". When I say might this way I mean that the fate of x is determined, but I don't know in which direction.
In either of these 2 cases, I say "x might or might not occur." You have suggested that some people (maybe non-OV) would suggest there are propositions where might is true but might not is false. Could you give an example of where someone would say "x might occur" but they couldn't say "x might not occur"?
I’m gonna cry (where’s that crying face graphic?) and then kick myself around the block if I can’t get you to see this.
Magneton: For the 3 statements…ontological indeterminacy is expressed by (3).
Tom: Right.
Magneton: Epistemic indeterminacy is expressed by "(1) OR (2) is true.” When I say might this way I mean that the fate of x is determined, but I don't know in which direction.
Tom: For a non-open theist who believes (1) and (2) exhaust the possibly true future tense propositions, yes. But an open theist can say not only this (provided (3) is known to be false), but if nothing is known about the truth value of a particular future tense proposition, then an open theist would have to enlarge it a bit and say, “(1) or (2) or (3) is true.” That is, “(1) might be true, (2) might be true, and (3) might be true.” This “might” expresses nothing about what the truth of the matter is. It just expresses our ignorance about what the truth of the matter is. Right.
Magneton: In either of these 2 cases, I say "x might or might not occur."
Tom: Right. You couldn’t say “x might AND might not occur” because that would be laying claim to the truth of (3), “indeterminacy.” But if you said, “x might or might not occur” (we’re talking the logic of the square now), what you’d be saying is, “x is not indeterminately the case, it’s either determinately the case that x will occur or determinately the case that x will not occur.”
Magneton: You have suggested that some people (maybe non-OV) would suggest there are propositions where might is true but might not is false. Could you give an example of where someone would say "x might occur" but they couldn't say "x might not occur"?
Tom: Sure. Taking the three metaphysically distinct states of affairs regarding x’s occurring, let’s say I know that (2) is false. How would I falsify it? I’d say “x might occur.” This claim is, logically speaking, the minimal amount of truth-value needed to falsify (2). But it’s not enough to tell me that “might not” is also true. In saying “x might happen,” that is, in falsifying (2), I can’t justifiably conclude that “x might not occur” is also true, for this would be laying claim to both “might” AND “might not” and therefore to (3). But merely falsifying (2) cannot give me the right to claim (3), for (1) could just as easily be the case instead of (3). And if (1) is the case, “might not” is false.
If this were to pop up in an every day conversation, it might go like this: Somebody claims “Doc will not take Tom out to lunch next October.” This person has just offered (2) regarding Doc’s taking me out to lunch. I can falsify this with EITHER (1) OR (3), right? I could say, offering (1), “No, I know for a fact (because God revealed it to me) that Doc will take Tom out to lunch next October when he comes.” Or I could say, offering (3), “No, it’s not true that Doc will certainly not take Tom to lunch. It’s actually indeterminately the case that Doc will take him to lunch. Doc might take him to lunch and Doc might not take him to lunch. And if it’s ‘indeterminately the case’ you can’t say it’s ‘determinately the case’.” But what if I don’t know whether (1) or (3) is the case but I still want to falsify the claim (2) that “Doc will not take Tom to lunch”? In logical lingo, all I’d have to say is, “No, Doc might take Tom to lunch next October.” (2) is falsified and nothing is said about (1) and (3). So, if you don’t know the truth value of (1) and (3) but you DO know that (2) is false, you would use “might” but not “might not.”
There a second situation in which we’d say “might” but not “might not.” Start with the three metaphysical states of affairs. OK, assume that (1) (“x will do y”) is TRUE. Ah. Now we know more. Now we know that (2) and (3) are both false. If it’s true that “x WILL do y” logic (‘subalternism’) says “x MIGHT do y” is also true, because “might” is the subaltern of “will.” Remember the square?
“will” ----- “will not”
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“might” --- “might not”
If “will” is true, its subaltern “might” is true and its contradictory “will not” is false. If it’s true the “Tom will come” then it’s true that “Tom might come.” If you and I are at a meeting, and I know Doc is in his car on his way to join us, and you say, “Is Doc coming tonight?” and I answer with only “Doc might come” I haven’t lied. Well, at least 2,300 years of logicians say I haven’t lied. Though we don’t usually (as Hasker explains it) make a ‘weaker’ claim when we know a ‘stronger’ claim to be true, it isn’t untruthful to make the weaker claim. The stronger claim entails the weaker. So if it’s true, for example, that “God WILL exist tomorrow” it’s also true that “God MIGHT exist tomorrow.” You certainly don’t want to say that “God might exist tomorrow” is false do you? If it is false, then its contradictory “God will not exist tomorrow” is true!
So there are two cases in which we can say “might” but cannot say “might not.” The first is when all we know is that “might” is true and therefore falsify “will not.” In this case we’re falsifying (2) and leaving open the question of (1) and (3). The second case is whenever (1) is known to be true. Here we’re logically allowed to make the weaker (subaltern) claim of “might” and logically forbidden to make the contradictory claim of “might not.”
It’s confusing because our every day speech isn’t designed to make the precise distinctions that logic demands we make. Though it’s logically possible for me to, say, only know that (2) is false and not know the truth of (1) or (3), I don’t know that we actually come by our knowledge in such tiny pieces and odd arrangements. We’re more likely either to know that an event will, will not, or might and might not take place, period. So we’ve set our expressions on default in this respect. Given this, we simply shorten “might and might not” (and “it is indeterminately the case that…”—who goes around speaking like THAT!) to “might” and let it express indeterminacy (understanding that “might” entails “might not”). But we do recognize other uses for “might” even if we haven’t set our language settings to assume them by default. Indeterminacy is the default understanding of “might” we work with in our every day lives. But it’s not too difficult to imagine, or to recall actual situations, where “might” doesn’t express indeterminacy and where we’re required to be more specific.
Clear as mud?
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Magneton
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| Posted 12/1/2003 8:46 AM (GMT -6) | | Tom: I’m gonna cry (where’s that crying face graphic?) and then kick myself around the block if I can’t get you to see this.
Magneton: No need to beat yourself up. The fog is finally clearing. Thanks for your patient and thorough explanations.
My difficulty was in 2 main areas:
(A) I was using "might" in an epistemic rather than ontological sense.
(B) I was defining "might" as exclusive of certainty, while you are using a definition that is inclusive of certainty.
For the 3 statements
(1) It is determinately the case that x occur
(2) It is determinately the case that x not occur
(3) It is indeterminately the case that x occur
(A) I was saying that as long as I'm not certain which statement is true, I could say, "x might happen." I was saying this in an epistemic sense, more like "For all I know, x could happen." In this same sense, I could say, "For all I know, x may not happen," i.e. x might not happen.
You are using "might" in an ontological sense. In falsifying an ontological statement (2) you say, "x might happen," by which you mean, "There is nothing standing in the way to prevent x from happening."
You similarly are using "might not" in an ontological sense. In falsifying an ontological statement (1) you say, "x might not happen," by which you mean, "There is nothing forcing x to happen."
I can see the value of building logic on ontological statements. A “Logic of Ignorance” would have more limited utility.
(B) I was surprised to find that “might” can be used when we know that (1) is true.quote:
Tom: If “will” is true, its subaltern “might” is true and its contradictory “will not” is false. If it’s true the “Tom will come” then it’s true that “Tom might come.” If you and I are at a meeting, and I know Doc is in his car on his way to join us, and you say, “Is Doc coming tonight?” and I answer with only “Doc might come” I haven’t lied. Well, at least 2,300 years of logicians say I haven’t lied. Though we don’t usually (as Hasker explains it) make a ‘weaker’ claim when we know a ‘stronger’ claim to be true, it isn’t untruthful to make the weaker claim. The stronger claim entails the weaker.
I was working under the assumption that we share all that we know in order to be honest (kind of a “truth, the whole truth, and nothing but the truth” thing). But I guess we’re talking about logical connections rather than facing questioning in a court of law. So in this context I’m OK with that. And it does make a clearer distinction between the meaning of “might” and “might not” if “will” is included in “might” and “will not” is included in “might not.”
Magneton
Truth is a gem that is found at a great depth; whilst on the surface of this world, all things are weighed by the false scale of custom. Byron
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Tom
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| Posted 12/1/2003 8:59 AM (GMT -6) | | Magneton: A “Logic of Ignorance” would have more limited utility.
Tom: I'm writing a book on that!
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Tom
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| Posted 12/1/2003 9:02 AM (GMT -6) | | Doc and Alan-
Here’s an argument against the possible truth of “might and might not” and thus against bivalence. By numbering this I don’t mean to offer a formal argument. I’m just trying to pin down the parts. This was recently offered to me:
1) If bivalence is true, then a proposition’s contradictory must bear the opposite truth value.
2) If it can be shown that a proposition is equivalent to its contradictory, then bivalence will have been disproved.
3) The contradictory of “x might or might not do y” is “It is not the case that x might or might not do y.”
4) “It is not the case that x might or might not do y” is by DeMorgan’s theorem equivalent to “x might not do y and x might do y,” which is equivalent to the original “x might or might not do y” which is supposedly it’s contradictory.
5) Bivalence doesn’t hold.
That’s how my friend put it to me.
Here are DeMorgan’s two famous theorems:
~(p ^ q) = (~p v ~q) [“It is not the case that ‘p and q’” is true if and only if “It is not the case that p” OR “It is not the case that q”]
and
~(p v q) = (~p ^ ~q) [“It is not the case that ‘p or q’” is true if and only if “It is not the case that p” AND “It is not the case that q”]
Note: the “=” sign should have three slashes for the biconditional “if and only if.”
These theorems seem sound to me. Doc or Alan, can you tell me why someone would think DeMorgan’s first theorem would challenge bivalence using “might and might not”?
Taking p as “might” and q as “might not,” it goes like this:
1) The contradictory of (p ^ q) [might and might not] is ~(p ^ q) [~(might and might not)].
2) ~(p ^ q) [~(might and might not)] is, by DeM's first theorem, true if and only if (~p v ~q) [(~might or ~might not)].
3) The final equivalent in #2 above, (~p v ~q) [(~might or ~might not)] is equivalent to the original proposition (p ^ q) [might and might not] to which it is also contradictory.
4) Bivalence doesn’t hold.
Alan, why does he think DeM’s final equivalent (~might or ~might not) is equivalent to its contradictory (might and might not)? What am I not seeing here?
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Alan Rhoda
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| Posted 12/1/2003 11:00 AM (GMT -6) | | Tom: If Dale and Sennett’s fundamental argument is that “reality is…fully determinate one way or the other” then how is it possible to posit three truth values (T, F, and I)? ... I’m having difficulty understanding how someone who believes reality is exhaustively determinate (either Z(S) or Z~(S)) can at the same time accommodate indeterminacy. Do they deny that truth values are ontologically grounded?
Alan: Great question, Tom. I think I have misrepresented Dale's position. It could be more accurately expressed as the view that all possible worlds are fully determinate, not that reality is fully determinate. Thus, given this assumption about possible world and the view that the 'actual world' is a possible world, it follows, as he argues, that the real world is not an actual world because the future is not fully determinate. That sounds bizarre, of course, but what's even more bizarre is that, on this account, the real world is not even a possible world. Instead, the real world is an actual/possible world in the making. I think Dale would say that truth values are to be assessed relative to possible worlds, which means that we can only assign 'true' or 'false' to propositions pertaining to the real world insofar as it is an actual world, that is, only insofar as the truth value of those propositions is now settled. For all other propositions, the appropriate truth value, it is claimed, is 'indeterminate'.
I hope that clarifies.
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Alan Rhoda
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| Posted 12/1/2003 11:56 AM (GMT -6) | | Tom: I understand Craig affirms the correspondence theory of truth but denies the grounding objection offered against affirming both EDF and libertarian free will. Doesn’t the correspondence theory of truth require that the truth-value of propositions “correspond” to something, some reality, that “makes” them true? How does Craig affirm the CTT but deny that anything “grounds” the correspondence? The correspondence that accounts for the truth-value of propositions runs between the state of affairs described in the propositions and...what?
Alan: Good question. I've wondered about this myself. How can one take truth as correspondence seriously without taking the grounding objection to Molinism seriously? My impression from what I've read of Craig's work is that he generally doesn't engage the issue head on, e.g., by spelling out a theory of correspondence that shows how CCR's are grounded. Rather, he typically tackles the issues indirectly, (1) arguing THAT some CCF's are true by (a) citing what he takes to be plausible examples (e.g., "I know that my wife would take a cookie if offered") and (b) by using the prediction argument that Freddoso gives in his intro to Molina's Disputations; and (2) challenging particular claims about what is required for grounding to show that they don't conclusively undermine the truth of CCF's. When Craig has brought up the issue of correspondence directly, as he does at one point in The Only Wise God (see his citation of Rescher), he does so in a way that is simply question-begging against open theism.
I must, confess, however, that I need to examine Craig's works more closely on this issue.
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Alan Rhoda
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| Posted 12/1/2003 12:09 PM (GMT -6) | | Tom: Here’s an argument against the possible truth of “might and might not” and thus against bivalence:
1) If bivalence is true, then a proposition’s contradictory must bear the opposite truth value.
2) If it can be shown that a proposition is equivalent to its contradictory, then bivalence will have been disproved.
3) The contradictory of “x might or might not do y” is “It is not the case that x might or might not do y.”
4) “It is not the case that x might or might not do y” is by DeMorgan’s theorem equivalent to “x might not do y and x might do y,” which is equivalent to the original “x might or might not do y” which is supposedly it’s contradictory.
5) Bivalence doesn’t hold.
Alan, why does he think DeM’s final equivalent (~might or ~might not) is equivalent to its contradictory (might and might not)? What am I not seeing here?
Alan: (1) is obviously correct, but I think (2) is false. How could a proposition possibly be equivalent to its contradictory? That wouldn't be a violation of bivalence, but rather a violation of the law of non-contradiction! Anyway, (4) is also false. "x might not do y and x might do y" is NOT equivalent to "x might or might not do y". DeMorgan's theorem doesn't license this move.
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Magneton
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| Posted 12/1/2003 4:00 PM (GMT -6) | | quote:
Magneton: A “Logic of Ignorance” would have more limited utility.
Tom: I'm writing a book on that!
Why don't we collaborate on a 2-volume set? You could write “The Logic of Ignorance” and I could write "The Ignorance of Logic." 
Magneton
The test of a first-fate intelligence is the ability to hold two opposed ideas in mind at the same time and still retain the ability to function. One should, for example, be able to see that things are hopeless and yet be determined to make them otherwise. - F. Scott Fitzgerald | | Back to Top | | |
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Tom
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| Posted 12/1/2003 11:14 PM (GMT -6) | | DeMorgan’s first theorem:
~(p ^ q) = (~p v ~q) not (p and q) = (not p or not q)
If it is not the case that I am tall and thin then I am either short or fat (or both). And if it is not the case that “x might do y and might not do y” then x either “will not do y” or “will do y.”
A step further and perhaps a little more complicated. Alan, back on page three I think, we agreed on theorem #11:
Q(p ^ q) = (Zp ^ Qq) v (Qp ^ Zq) v (Qp ^ Qq)
If we falsify the first, do we just falsify the equivalencies throughout? Like this:
~Q(p ^ q) = ~(Zp ^ Qq) v ~(Qp ^ Zq) v ~(Qp ^ Qq)
or do we carry DeM’s theorem through the equivalencies? Like this:
~Q(p ^ q) = (~Zp v ~Qq) ^ (~Qp v ~Zq) ^ (~Qp v Qq)
See what I mean? Is it “v” inside each (), like DeM’s, and then “^” between the ()? It’s also confusing because we’re introducing operators Q and Z. I’m not sure how they pan out in DeM’s law.
Come on! You only have a dissertation to defend. What’s keeping ya?
Seriously…take your time.
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Tom
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| Posted 12/4/2003 10:08 AM (GMT -6) | | Check out this A. N. Prior quote:
quote:
What I want to say…is that nothing can be said to be truly ‘going-to-happen’…until it is so ‘present in its causes’ as to be beyond stopping; until that happens, neither ‘It will be the case that p’ nor ‘It will be the case that not p’ is strictly speaking true. What Thomas [Aquinas] says is that neither of them is true determinate; and what this appears to mean is that though they somehow share truth and falsehood between them, neither is as yet definitely attached to either proposition rather than the other. I don’t myself now think – though I once did – that this complication is necessary; it is enough to distinguish (as Thomas did not) between the form ‘It will be the that it is not the case that p’ (which commits one to the futurition of not-p) and the form ‘It is not the case that it will be that p’ (which could also be true if it is simply as yet undertermined whether it is p or not-p that the future holds). Writing ‘F’ for the simple ‘It will be that’, ‘~’ for ‘Not’…I would say that we have at this stage
~(Fp v F~p)
(‘Neither it-will-be-that p nor it-will-be-that not-p’). And this state of affairs we can alter, changing it to
Fp v F~p
when it is in our power to decide one way or the other and we do so. But what is past cannot be thus altered, for it is always the case the either p has been the has or not-p has, i.e. we always have
Pp v P~p
and there can be no question of changing from this to its opposite or vice versa.
I keep reading this paragraph which begins Prior’s fuller argument of how to account for future contingents. It just gets worse and worse. And it all begins with his second step. He first acknowledges that “nothing can be said to be truly ‘going-to-happen’…until it is so ‘present in its causes’ as to be beyond stopping.” That’s cool. And what can be said about p’s occuring in such a case? Prior answers, “…until that happens, neither ‘It will be the case that p’ nor ‘It will be the case that not p’ is strictly speaking true.” And I say ‘Amen.’ And Prior even ascribes to this the same expression we use in indeterminacy logic, that is, ~(Fp v F~p) (“Neither ‘p will occur’ nor ‘p will not occur’). Prior here admits that there are some events that occur about which before they occur it would have been false to claim that they “will” occur, and also many events which do not occur about which before they did not occur it would have been false to claim that they “will not” occur.
So far we agree. But Prior (and it’s beyond me how he does it) slips a logical disk when he says we can alter ~(Fp v F~p) to Fp v F~p. That is we can alter:
“Neither ‘p will occur’ nor ‘p will not occur’
to
“Either p will occur or p will not occur.”
By what logic? He doesn’t here say. Prior said this back in ’64 I think, but it’s being repeated today by open theist philosophers who deny bivalence and it seems to be that for some reason they think DeMorgan’s theorems require it. But DeMorgans theorems perfectly support our indeterminacy logic:
DeM: ~(Fp v F~p) = (~Fp ^ ~F~p)
That is, what the left side of the equation, ~(Fp v F~p), can be altered to is not
Fp v F~p (or “Either p will occur or p will not occur”)
but rather (according to DeM),
(~Fp ^ ~F~p) or (“Neither ‘p will occur’ nor ‘p will not occur’”)
which is none other than “p might and might not occur.” DeMorgan agrees that ~(Zp v Z~p) = (~Zp ^ ~Z~p), which of course equals our Qp. I’m baffled by Prior’s misstep here; baffled.
But look at Prior’s exact words. ~(Fp v F~p) can be altered to Fp v F~p “…when it is in our power to decide one way or the other and we do so.” Interesting.
Here’s what I think Prior (and other open theists who deny bivalence) might be thinking. Take propositions that describe p’s occurring at T1. Those who deny bivalence will affirm that “p will occur” and “p will not occur” can both be FALSE prior to p’s occurring or not, but they won’t say what is TRUE if these are both false. Fact is, they claim nothing is true in this case, certainly not “might and might not p.” Why? Well, because p either will or will not occur! How so if “either p or not p” is false? I think their reasoning goes like this. Let’s suppose that at T we’re discussing propositions about p’s occurring or not at T1. What IS true at T is something like this: “It is now the case that at T2 p either will have or will not have occurred.” And this is certainly true at T! Ahh. What’s going on? It’s THIS proposition, spoken at T, describing what ‘will’ be the case at T2 about p’s having occurred or not at T1 that is, I believe, confusing Prior and other deniers of bivalence. They are falsely assuming that since at T2 there are only TWO bivalent propositions about p’s actuality at T1 (viz., either “p occurred at T1” or “p did not occur at T1”; there are no other options for p at T1, it either occurred or it did not), there must necessarily be only two bivalent propositions describing p prior to T1, and those two are “will” and “will not.” “Might and might not” is neither true nor false.
There’s more to say about Prior’s confusing at this point. He contradicts himself in this quote. Never mind mentioning it now.
Tom | | Back to Top | | |
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Alan Rhoda
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| Posted 12/4/2003 1:32 PM (GMT -6) | | quote:
Alan, back on page three I think, we agreed on theorem #11:
Q(p ^ q) = (Zp ^ Qq) v (Qp ^ Zq) v (Qp ^ Qq)
If we falsify the first, do we just falsify the equivalencies throughout? Like this:
~Q(p ^ q) = ~(Zp ^ Qq) v ~(Qp ^ Zq) v ~(Qp ^ Qq)
or do we carry DeM’s theorem through the equivalencies? Like this:
~Q(p ^ q) = (~Zp v ~Qq) ^ (~Qp v ~Zq) ^ (~Qp v Qq)
The second equation here is mistaken. If you negate the left hand side then you have to negate the whole right hand side. Thus,
~Q(p ^ q) = ~[(Zp ^ Qq) v (Qp ^ Zq) v (Qp ^ Qq)]
Now we can use De Morgan's law on the right hand side to get:
~Q(p ^ q) = ~(Zp ^ Qq) ^ ~(Qp ^ Zq) ^ ~(Qp ^ Qq)
Using De Morgan's again on each RHS conjunct gives us:
~Q(p ^ q) = (~Zp v ~Qq) ^ (~Qp v ~Zq) ^ (~Qp v ~Qq)
So your second proposal is correct (with the exception of the missing tilde in the last conjunct).
Cheers,
Alan | | Back to Top | | |
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Alan Rhoda
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| Posted 12/4/2003 2:00 PM (GMT -6) | | Tom: Where is that Arthur Prior quote from? Is it from his essay on "The Formalities of Omniscience"? I just got my copy of his Papers on Tense and Time yesterday, so I haven't yet had a chance to go through it. Wish this darn dissertation were over so I could put more of my time into reading and researching this stuff. Oh well, just over one week to go.
quote:
Writing ‘F’ for the simple ‘It will be that’, ‘~’ for ‘Not’…I would say that we have at this stage
~(Fp v F~p)
(‘Neither it-will-be-that p nor it-will-be-that not-p’). And this state of affairs we can alter, changing it to
Fp v F~p
when it is in our power to decide one way or the other and we do so. But what is past cannot be thus altered, for it is always the case the either p has been the has or not-p has, i.e. we always have
Pp v P~p
and there can be no question of changing from this to its opposite or vice versa.
I think I follow Prior's argument here. The difficulty here is in interpretating his claim that "we can alter" the first state into the second, "when it is in our power to decide one way or the other and we do so." On a charitable reading, I think he is correct. Note that he is not saying that the one logically follows from the other. Clearly it doesn't. What he seems to be saying is that by making a choice to engage in some future action we can bring it about that Fp v F~p is true. Note the conditions he specifies: (1) it is in our power to decide one way or the other, and (2) we do decide one way or the other. It seems to me that all he's saying is that in some cases we can take an unsettled state of affairs, viz. ~(Fp v F~p), and settle it by making a choice.
So, Tom, I think you are right that the second state of affairs does not logically follow from the first, but I don't think that's what Prior was trying to say.
Tom: Here’s what I think Prior (and other open theists who deny bivalence) might be thinking. Take propositions that describe p’s occurring at T1. Those who deny bivalence will affirm that “p will occur” and “p will not occur” can both be FALSE prior to p’s occurring or not, but they won’t say what is TRUE if these are both false.
Alan: Actually, those who deny bivalence will typically say that “p will occur” and “p will not occur” are neither true nor false.
PS: Have you read Thomas Flint's book on Molinism? I just got it. Looks quite good. When I get back from my dissertation defense I'd like to discuss some of his responses to the grounding objection. I think that our indeterminacy logic may offer a way of undermining his responses.
Take care,
Alan | | Back to Top | | |
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Tom
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| Posted 12/4/2003 9:37 PM (GMT -6) | | quote:
If you negate the left hand side then you have to negate the whole right hand side. Thus,
~Q(p ^ q) = ~[(Zp ^ Qq) v (Qp ^ Zq) v (Qp ^ Qq)]
Now we can use De Morgan's law on the right hand side to get:
~Q(p ^ q) = ~(Zp ^ Qq) ^ ~(Qp ^ Zq) ^ ~(Qp ^ Qq)
Using De Morgan's again on each RHS conjunct gives us:
~Q(p ^ q) = (~Zp v ~Qq) ^ (~Qp v ~Zq) ^ (~Qp v ~Qq)
So your second proposal is correct (with the exception of the missing tilde in the last conjunct).
Man I’m glad you are here!
quote:
Tom: Where is that Arthur Prior quote from? Is it from his essay on "The Formalities of Omniscience"? I just got my copy of his Papers on Tense and Time yesterday…
Yeah, it’s from that book from that essay. I sent you the essay, but now you have it in the book. There are some other good essays in there too. I often find myself agreeing with him, saying “Yes! That’s it!” up until he denies bivalence, then he gets contorted.
quote:
I think I follow Prior's argument here. The difficulty here is in interpretating his claim that "we can alter" the first state into the second, "when it is in our power to decide one way or the other and we do so." On a charitable reading, I think he is correct. Note that he is not saying that the one logically follows from the other. Clearly it doesn't. What he seems to be saying is that by making a choice to engage in some future action we can bring it about that Fp v F~p is true. Note the conditions he specifies: (1) it is in our power to decide one way or the other, and (2) we do decide one way or the other. It seems to me that all he's saying is that in some cases we can take an unsettled state of affairs, viz. ~(Fp v F~p), and settle it by making a choice.
Yeah, I’m sure the charitable reading is accurate. He really believes in libertarian free will and that our “choice” that resolves Fp v F~p is not determinately known in God’s mind. But he still expresses that choice as ‘either’ Fp ‘or’ F~p. And though its true that I will have either chosen p or not chosen p after the window of choice has closed, this fact is not necessarily limited to Fp v F~p before that window closes.
quote:
Tom: Here’s what I think Prior (and other open theists who deny bivalence) might be thinking. Take propositions that describe p’s occurring at T1. Those who deny bivalence will affirm that “p will occur” and “p will not occur” can both be FALSE prior to p’s occurring or not, but they won’t say what is TRUE if these are both false.
Alan: Actually, those who deny bivalence will typically say that “p will occur” and “p will not occur” are neither true nor false.
Right. I shouldn't have said they affirm that "will" and "will not" can both be false. I guess what I wanted to say was that I think they refuse to say these are both false and that "might and might not" is true because it is NOW true that "It will be the case at T2 that 'p either occured or did not occur at T1'." This I think is leading Prior to assume at T that either Fp at T1 or F~p at T1 "when it is in our power to decide." If he didn't qualitfy Fp v F~p with these words THEN he'd clearly be contradicting his earlier claim that Fp and F~p are neither true not false. If they're neither true nor false then why is he saying Fp v F~p? Well, he's not saying Fp v F~P 'unqualified.' He's qualifying it by saying WE DETERMINE whether p or not-p; since at T2 we will certainly HAVE EITHER DONE p or NOT DONE p at T1, he thinks it follows that either p or not-p at T (even though we determine which).
It seems that perhaps Prior (and others who deny bivalence) are ascribing determinacy and indeterminacy to different things than we are. Not sure. Prior feels he has to say Fp at T1 v F~p at T1 because he believes that if "It will be the case at T2 that p either occured or did not occur at T1" is true at T (and it is!), this limits him to Fp and F~p at the same T. But he wants to affirm libertarianism! So he has to deny that Fp and F~p are either really true or false! Poor guy! This whole contorted attempt to account of p at T1 is founded on the false assumption that if "It will be the case at T2 that p either occured or did not occur at T1" is true at T that libertarianism is destroyed if bivalence is affirmed (for bivalence would then means Fp v F~p would have to be TRUE!). My point is, "It will be the case at T2 that 'Either p or not-p occured at T1'" is perfectly explainable at T on the basis of ~Fp at T1 ^ ~F~p at T1 but Qp at T1.
quote:
I hope this is not taken as a hijack of the thread, but I was taking a test the other day and came to a question, the multiple choices to which were:
1. True
2. False
3. Not able to be determined.
Is this similar to what you guys are talking about in this thread?
Hi John! I think understanding your three responses depends on knowing the question. What’s the question? (3) might just mean “Either 1 or 2 is true but I’m not able to determine which is which,” or it might mean “Neither 1 or 2 is true; there IS NO true or false answer to the question. The answer has not yet been determined.”
Now, I (and Alan and Doc) would say, it’s perfectly OK for the answer to the question to not yet be determined, but we don’t have to deny bivalence to affirm this, since we claim that “indeterminacy” is as real as determinacy, is either the case or not, and is therefore either true or false. What we do is delimit the POSSIBLE answers, all the possible ways the question might resolve itself and express this in a proposition that is TRUE. Let’s assume the question is stated like this: “p will occur.” So, if you believe “p will occur” is true you answer (1). If you believe “p will not occur” you answer (2). But what if you believe p’s occurring is not yet determinate? Personally, I’d check (2) and (3). I’d check (2) because “p will occur” is false. But I wouldn’t ONLY check (2) because I don’t believe “p will not occur” is true and is why “p will occur’ is false. I’d check (3) to say “p is indeterminate.”
But I would understand (3) differently than would those who deny bivalence. For if p’s occurring is in fact indeterminate, then I would express this in a proposition like this: “It is indeterminately the case that p occur.” So “p will occur” must be FALSE (so I’d check (2). But in saying “p will occur” is false I don’t mean to affirm that “p will not occur” is true. “p will not occur” is ALSO false. What is TRUE is that ‘p might and might not occur’.”
But those who deny bivalence would say this (I think): The answer to “p will occur” is not yet determined, therefore it’s neither true nor false that p will occur. Though it’s true that p either will or will not have occurred after the window is closed, it’s not now determinate whether it will or will not. So (1) and (2) are neither true nor false. It’s (3). They’d say, “p either will or will not occur, but it’s not yet determinate WHETHER p will or occur or WHETHER p will not occur.”
Doc, Alan, and I are arguing bivalence, so if p’s occurring is indeterminate (and deniers of bivalence don't seem to deny that it's indeterminate) THEN IT’S TRUE THAT IT’S INDETERMINATE and it HAS to be FALSE THAT IT'S DETERMINATE. There’s no need to say "will" and "will not" are neither true nor false just because is will be the case that p either occured or did not occur.
Clear as mud?
Tom | | Back to Top | | |
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John Earp
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Total Posts : 1715
| Posted 12/4/2003 10:07 PM (GMT -6) | | Thanks for your answer, Tom!
The original question, if I recall correctly, was:
Jill is taller than Susie. Sarah is shorter than Jill. Susie is definitely taller than Sarah.
Based on the first two sentences, is the last sentence true, false, or not able to be determined?
(Names have been changed to protect the innocent). 
The correct answer was (C) Unable to be determined (in this case based on limited knowledge). Obviously, this has nothing to do with the future, but it did get me to thinking.
At the following website: http://en.wikipedia.org/wiki/Principle_of_bivalence
It states that the principle of bivalence is that every proposition (P or non-P) is either true or false. Is this your understanding of bivalence?
If so, I am left to wonder how an Open Theist can hold to bivalence, for OVT states that some propositions are possibilities, not certainties, and therefore presently these possibilities are neither true nor false (except with regard to their being real possibilities or not, of course).
Are you saying that future possibilities don't reflect a "maybe"? It seems to me that that is precisely what possibilities are.
I am sorry that I have not been able to wade through all the pages and pages of philosophy diagrams and terminology, but I would like to know what is so unique about Open Theism if not the fact that we believe the future includes genuine possibilities?
"The Discovery of new truth will modify old views and opinions, and there is perhaps no end to this process with finite minds in any world." Charles G. Finney, Systematic Theology.
revivaltheology.net
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Tom
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| Posted 12/4/2003 10:30 PM (GMT -6) | | John: It states that the principle of bivalence is that every proposition (P or non-P) is either true or false. Is this your understanding of bivalence?
Tom: Yes, exactly.
John: If so, I am left to wonder how an Open Theist can hold to bivalence, for OVT states that some propositions are possibilities...
Tom: The 'propositions' are not possibilities. Propositions describing future events are just propositoins. What they describe, that is the states of affairs they describe, are possibilities. Look at it this way, John; Do these propositions ever truthfully describe the events they describe 'as possibilities'? That is, when you say, "x is a possibility" are you not correct? Is this claim not ture? Is x not a genuine possibility? Of course it is. A future event is either a real possibility or not. ANd if it is, then a proposition describing it as a possibility is TRUE. This support the OV.
John: ...and therefore presently these possibilities are neither true nor false (except with regard to their being actual possibilities or not, of course).
Tom: The possibilities themselves, the actual states of affairs these propositions describe, are not yet actual at the present moment. True. But this doesn't mean we can't truely or falsely talk about these events. Take future events that ARE determined. They're not 'actual' either. They events describe in proposiions that posit determined events are not actual either, so why should we allow that the propositions describing these events to be bivalent? That the events descirbed are not yet 'actual' shouldn't influence whether or not bivalence holds for propositions describing them. If an event IS determinate, then it's TRUE to say "It is determinately the case that x occur." And if an event is indeterminate, then it's TRUE to say "It is indeterminately the case that x occur."
John: Are you saying that future possibilities don't reflect a "maybe"? It seems to me that that is precisely what possibilities are.
Tom: No, I'm saying future possibilities ARE "maybe's". They're also "maybe not's". All I'm saying is that a proposition saying a particular possibility is a "might and might not" is TRUE. Just as you said, it's a "maybe." Is your claim that "possibilities are maybe's" true or false?
John: I am sorry that I have not been able to wade through all the pages and pages of philosophy diagrams and terminology, but I would like to know what is so unique about Open Theism if not the fact that we believe the future includes genuine possibilities?
Tom: This IS our unique claim. But I think that claim is weakened somewhat if we deny that propositions describing those 'genuine possibilities' are 'genuinely true'. If you described one of those 'genuine possibilities' would your description be neither true nor false? That's what you'd have to admit if you deny bivalence.
It's the propositions that are bivalent, not the possibilities they describe.
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Tom
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| Posted 12/5/2003 1:07 AM (GMT -6) | | quote:
It seems we're talking about present-tense true statements, whether possibilities or certainties. This ties into OVT's view of omniscience in that we can affirm God is speaking the truth when he says, "maybe," "if" and "perhaps."
Bingo!
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Alan Rhoda
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Total Posts : 680
| Posted 12/5/2003 8:00 AM (GMT -6) | | quote:
Originally posted by John Earp
I was taking a test the other day and came to a question, the multiple choices to which were:
1. True
2. False
3. Not able to be determined.
Is this similar to what you guys are talking about in this thread?
Good question, John. Tom has already responded, but I'll add my two cents anyway. The type of indeterminacy in view in option (3) is epistemic, not ontic or metaphysical. That is, it has to do with whether or not we, in light of the information available to us, can definitely conclude that something is either true or false. Option (3) just says that, for all we know it may be true, and for all we know it may be false. In contrast, the kind of indeterminacy that is the focus of indeterminacy logic is real or metaphysical or absolute indeterminacy, not indeterminacy relative to our state of knowledge. In this sense, "it is indeterminate that Tom goes to the movies tomorrow" means that reality is not now settled one way or the other with respect to Tom's going to the movies tomorrow.
Hope that helps.
Alan | | Back to Top | | |
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Alan Rhoda
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| Posted 12/5/2003 10:04 AM (GMT -6) | | Some thoughts on indeterminacy for everyone's edification.
How are these two types of indeterminacy (epistemic and ontic) related? Most fundamentally, epistemic indeterminacy pertains to propositions, whereas ontic indeterminacy pertains to states of affairs. A proposition is the assertable content of a statement. Thus the statement "the cat is on the mat" expresses the proposition that the cat is on the mat and asserts that this proposition is true. A state of affairs, on the other hand, is a possible way for things to be; it is that which is asserted to be by a statement. Thus the statement "the cat is on the mat" asserts that the state of affairs of the cat's being on the mat obtains or is actual. As you can see from the definitions, propositions and states of affairs are correlative. To every proposition there corresponds a state of affairs, and a proposition is true if and only if its corresponding state of affairs is the case. In other words, the proposition the cat is on the mat is true if and only if the state of affairs of the cat's being on the mat is actually the case. More simply, "the cat is on the mat" is true iff the cat is, in fact, on the mat.
Now apply this to the 'grounding objection' to Molinism. Responses to this objection from Craig and Plantinga have charged that notions like 'ground' and 'truthmaker' implicit in the objection are deeply problematic. This seems an overstatement to me. I grant that there are some tough philosophical puzzles here, mostly having to do with things like the Liar's Paradox and statements about impossibilia (e.g., "If you put a square circle on an inclined plane, it would roll and not slide."), where it seems difficult to define clear truth conditions. But the notion that all true propositions require a ground for their truth, a truthmaker, if you will, follows directly from a correspondence theory of truth, which nearly all parties in this debate accept, and is thus no more problematic than the correspondence theory itself.
At any rate, Craig has argued that if the grounds of truth for a proposition is just the obtaining of the state of affairs posited by that proposition, then "would" counterfactuals of freedom like "If placed in circumstances C, Peter would freely deny Christ" are grounded in that the counterfactual is true just in case the state of affairs of Peter's freely denying Christ if C obtains. On the Molinist view, in every case either a "would if" or a "would not if" state of affairs obtains, and does so from eternity, prior to God's decision to create. Now I think open theists can grant the Molinist that "If placed in circumstances C, Peter would freely deny Christ" are grounded in the counterfactual is true just in case the state of affairs of Peter's freely denying Christ if C obtains. What open theists will deny, of course, is that such states of affairs obtain. Here's where indeterminacy logic becomes important. Molinists, and most other philosophers, it seems, assume that "would if" and "would not if" are contradictories, such that if one is false then the other is necessarily true. Given this, it follows that either "would if" or "would not if" is true. Indeterminacy logic undermines this assumption by showing that "would if" and "would not if" are contraries, not contradictories. Thus both can be false, and "might and might not if" can be true. What's more, we can argue that, where counterfactuals of libertarian freedom are concerned, both "would if" and "would not if" are necessarily false because their truth is inconsistent with libertarian freedom. It takes another argument to show that, however, so I'll stop here for now.
Adios for now,
Alan
PS: I'll be in New York for my dissertation defense from 12/8-12/16, with the defense taking place on 12/12. I probably won't be posting on this board during that time. | | Back to Top | | |
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