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Alan Rhoda
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Date Joined May 2002
Total Posts : 680
| Posted 10/1/2003 12:31 PM (GMT -6) |   | I've been away from this board for a couple months and I know that I've missed a lot of discussion, so forgive me if I inadvertently rehash old ground.
I want to address the counterfactual project that Doc, TGB, and others have been so involved with because I think I see a way to clarify some issues that have led to persistent disagreement.
On the one hand myself (and I think Albert) have argued that on a standard logical square of opposition 'would' and 'might' counterfactuals are related as follows:
www.pcigrp.com/Alan/square.pdf
On the other hand, Tom and Doc have been bothered by the idea that 'woulds' imply 'mights' (the subalternation relation on the square of opposition).
The difficulty I now see lies in applying the 4-way logical distinction of the square of opposition to what is in reality a 3-way ontological distinction.
The 3-way ontological distinction is that agent X either
(1) determinately will do Y in Z
(2) determinately will not do Y in Z, or
(3) indeterminately may or may not do Y in Z.
(3) describes the situation that Doc has captured by the phrase "conjoined might-counterfactuals". This is the sense of "might" that is important to open theism. The sense of "might" employed by the logical square of oppositions is weaker, being equivalent to "it is possible that X does Y in Z". In this sense, "might" unequivocally follows from "would". On that point Albert and myself are correct. But when "might" is used to refer to the kind of real indeterminacy described in (3) then it means something more: "it is BOTH possible that AND ontologically indeterminate whether X does Y in Z". On that point Doc and TGB are correct.
Much of the discussion back and forth has failed to maintain a consistent and clear distinction between the "might" of mere possibility (call this an "MP-might") and the "might" of ontological indeterminacy (call this an "OI-might"). As far as the discussion of open theism is concerned, it is the latter that we are interested in. "OI-might" entails both "MP-might" and "MP-might not" (Doc's conjoined counterfactuals).
Glad to be back.
Alan | | Back to Top | | |
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Tom
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Total Posts : 10353
| Posted 10/1/2003 5:43 PM (GMT -6) | | Alan-
Right on. There is an "ontological possibility" that we're arguing for which is only captured on the square by conjoined might/might not and nowhere else. "Would" entails MP-might (of logical possibility). But there's no propositionally singular position on the traditional square that expresses OP-might (of ontological indeterminacy). But if such indeterminacy is truly a feature of reality, why shouldn't logic have an operator for it? That's my and Doc's point. In the end the open view is still logically possible because there isn't anything contradictory about both subcontraries being true. This is allowable. But it does seem that Western logic is biased. It doesn't alot OP-mights a place at the table of propositions that express truth claims about what is and is not the case.
So, what do you think of our Triangle of Opposition?
I think it's probably less accurate to speak of OP-mights as "counterfactuals" at all. They are rather simple assertions of fact. So we really ought not call it the Triangle of Counterfactuals.
Tom  | | Back to Top | | |
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Alan Rhoda
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Date Joined May 2002
Total Posts : 680
| Posted 10/2/2003 2:41 PM (GMT -6) | | Tom: So, what do you think of our Triangle of Opposition?
Alan: Looks good, however saying "might AND might not" implies that you are referring to a "might of possibility" (MOP), not a "might of indeterminacy" (MOI). If you specify that you are referring to MOI's then you can change the bottom to "might (not)" or "might / might not". In other words:
Tom: There's no propositionally singular position on the traditional square that expresses OP-might (of ontological indeterminacy). But if such indeterminacy is truly a feature of reality, why shouldn't logic have an operator for it?
Alan: Good question. I think part of the answer it that logic develops, or rather, new logical systems are developed, in response to a perceived need that existing logical systems do not satisfy. As they say, necessity is the mother of invention. Thus, when it was discovered that Aristotelian logic was not good at handling complex predicates and relations, first-order predicate logic was developed. And when that proved inadequate for dealing with modal operators, modal logic was developed. Now, the fact that what we might call "indeterminacy logic" has been largely if not completely overlooked till now suggests that there has not been a perceived need for it--perhaps a reflection of what Doc calls a "bias toward the determinate".
Tom: I think it's probably less accurate to speak of OP-mights as "counterfactuals" at all. They are rather simple assertions of fact.
Alan: They can be counterfactual if lodged in the consequent of a conditional with a counterfactual antecedent. For example, "If I had had the opportunity to go to Harvard I might have done so." See my diagram above.
What's more it is important that MOI's can figure in counterfactuals because it is on the truth status of counterfactuals that the debate between Molinists and open theists hinges. By using the triangle of oppositions we can show that it is possible for both "would" and "would not" counterfactuals to be false and a "might" counterfactual to be true, thus undermining Molinism.
Love the interaction.
Alan
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Alan Rhoda
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Date Joined May 2002
Total Posts : 680
| Posted 10/2/2003 3:00 PM (GMT -6) | | I've been thinking a bit more about the different types of "mights" and I'd like to propose the following taxonomy:
A. Might of Possibility
A.1. might of logical possibility - e.g., "If x <= 5, then it might be the case that x < 0"
A.2. might of ontological possibility - e.g., "God might have created us with wings"
A.3. might of physical possibility - e.g., "It might rain tonight"
These are arranged in order from weakest (A.1) to strongest (A.3). Thus, A.3 implies A.2 implies A.1.
B. Might of Indeterminacy
B.1. might of ontic indeterminacy - e.g., "If we repent, God might show us mercy."
B.2. might of epistemic indeterminacy - e.g., "I suppose Goldbach's Conjecture might be true."
B.3. might of volitive indeterminacy - e.g., "Come to think of it, I just might ask her to marry me."
There are probably distinctions that I have missed, but I hope my examples are clear enough. My question is this: what are the relations between the "mights" in the first set (A) and those in the second (B).
God bless.
Alan | | Back to Top | | |
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GregBoyd
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Date Joined Jul 2001
Total Posts : 1818
| Posted 10/3/2003 5:55 AM (GMT -6) | | Some thoughts in response to Alan's taxonomy.
* The fact that both groups have THREE categories is one sign that you're on the right track. ... BUT
* It's not clear to me how A.2. differs from B.1. is it that B.1 refers to a future possibility where as A.2. refers to a past possibility? If I change A.2. to say, "God might give us wings in heaven," am I now in the B.2. category?
* Also, its not entirely clear how A.3 differs from B.2 -- unless you are assuming that weather patterns are truly indeterminate. But in ordinary language, I think we normally mean a B.2 class statement in asserting A.3.
* Relatedly, I'm not clear as to why "might of epistemic indeterminacy" is filed under "might of indeterminacy" rather than "might of possibility." There's no indeterminacy about the truth or falsity of Goldbach's Conjecture is there? If Goldbach's Conjecture was "it might rain tonight," it would be A.3. Clearly, something's amiss in the A.3/ B.2 distinction.
* Most fundamentally, I think the distinction between "possibility" and "indeterminacy" needs flushing out. All my quesitons, I think, relate to this. Clearly, there is a difference between "might of logical possibility" and "might of volitional indeterminacy." More broadly, there's a clear difference between "might of logical possibility" and "might of FUTURE indeterminacy." The triangle of opposition flushes THIS distinction out. But, as the questions I've raised may indicate, there seems to be fuzziness in your taxonomy as to A.2, A.3 and B.2 regarding how they fit these categories.
Maybe the categories should be something like this:
1) Mights of Logical Possibility
2) Mights of Ontological Possibility
3) Mights of Future Indeterminacy
I think this "might" cover all cases. This statement would fall under #2. Its more than logically possible, but NOT up to me to decide. So with all statements of "epistemic indeterminacy."
So too with all statements of unactualized possibilities. God might have created us with wings. It once was #3 for God (let us assume), but once he created us without wings, it transitions to #2. We MIGHT have been created with wings... it was more than merely logically possible. But IN FACT its no longer indeterminate.
*** The odd thing is, Are not all #1's also #2's for God prior to God acting? The category is more clear with regard to OUR transitioning #3's to #2.
What do you think?
LOVE this stuff. This is VERY important stuff. And its largely uncharted territory. Exciting.
Greg
"The responsibility is with the chooser -- God is blameless." Plato, Republic, 10. | | Back to Top | | |
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JET
Registered Member
Date Joined Jun 2002
Total Posts : 397
| Posted 10/3/2003 4:46 PM (GMT -6) | | quote:
Alan:
The 3-way ontological distinction is that agent X either
(1) determinately will do Y in Z
(2) determinately will not do Y in Z, or
(3) indeterminately may or may not do Y in Z.
If I understand correctly, you can say a future-tensed proposition is either:
(1) True;
(2) False; or
(3) Indeterminate
Or you can say a future-tensed proposition is either:
(1) True (if it is now determinately true); or
(2) False (if it is now determinately false or if it is not now indeterminately true)
From what little I've been able to read on the internet about Arthur N. Prior, I gather that he toyed with the idea of a three-valued logic, but ultimately settled on bivalence ala Doc's methodology (where the proposition "Hillary will be elected President" is now false if it is now indeterminate whether Hillary will become President).
Is there any practical difference between bivalence understood this way versus a three-valued logic? | | Back to Top | | |
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Tom
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Date Joined Jul 2001
Total Posts : 10353
| Posted 10/3/2003 10:12 PM (GMT -6) | | Speaking of possibilities…
I ran across an interesting argument for the existence of God in Keith Ward (God—A Guide for the Perplexed) yesterday. I like it very much. Let’s see what you think:
“The argument goes like this: everything that happens is obviously possible. If we think of everything that could possibly happen, then we have a complete array of possible worlds. But you cannot have possible worlds just existing, because they are merely possible, and not actual. So, if there really are possible worlds, they must exist in something actual, something that really exists. Now we have an actual real thing in which all possible worlds exist. The nearest we can some to imagining this is to think of an actual mind or awareness in which all possible world exist as ideas. That mind is God, and the possible worlds are ideas in the mind of God.”
What d’ya think?
Secondly, I wanna ask a question about the realism vs nominalism debate. As I understand it, nominalism does not deny that the chair I’m sitting on actually exists, but rather it denies that apart from the existence of actual chairs there exists the notion of “chairness” (same with trees, color, birds, whatever). Here’s my question: Does not God’s having conceived of our world before its actual existence imply the realist is correct? That is, God conceived of the notion of color, of trees, of grasses, etc., and this conception (the conception of these categories) preceded the creation of the individual items themselves.
Tom  | | Back to Top | | |
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GregBoyd
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Date Joined Jul 2001
Total Posts : 1818
| Posted 10/3/2003 10:27 PM (GMT -6) | | [JET: Is there any practical difference between bivalence understood this way versus a three-valued logic?
Doc: Not really, so far as I can see. The only PRACTICAL difference is that the vast majority of philosophers affirm bivalence. So if we can articulate future indeterminacy within this framework, it will be more compelling to more people.
TGB: What d’ya think? (About Ward’s argument)
Doc: I think its good. I think it’s a version of the cosmological argument. But instead of arguing from temporal contingency to eternal necessity, it argues from ontological possibilities to ontological actuality.
TGB: Does not God’s having conceived of our world before its actual existence imply the realist is correct? That is, God conceived of the notion of color, of trees, of grasses, etc., and this conception (the conception of these categories) preceded the creation of the individual items themselves.
Doc: This is sort of how Whitehead construed Plato’s IDEAS. A nominalist response could be something like this: You’re violating Occam’s razor. Why not just suppose that God conceive of each individual blade of grass, each tree… We’re the once who break things down in terms of how they’re the same and/or different (viz. green, round, sweet, etc…).
But dude, what does this have to do with mights?
Doc
"The responsibility is with the chooser -- God is blameless." Plato, Republic, 10. | | Back to Top | | |
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Tom
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Date Joined Jul 2001
Total Posts : 10353
| Posted 10/3/2003 11:40 PM (GMT -6) | | Doc: But dude, what does this have to do with mights?
Tom: Nothing I guess! I was just thinking out loud.
Breakfast Friday morning Oct. 24 duuuude! Be there!
Tom | | Back to Top | | |
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Alan Rhoda
Registered Member
Date Joined May 2002
Total Posts : 680
| Posted 10/7/2003 12:36 PM (GMT -6) | | JET: Is there any practical difference between bivalence understood this way versus a three-valued logic?
Alan: Hmmm. Good question. When I distinguished the three ontological possibilities: (1) determinately will, (2) determinately won't, and (3) indeterminately may / may not, I wasn't thinking in terms of a mult-valued logic--though I can see from your question how one might apply it. On my view propositions describing type (3) states of affairs can be determinately true or false, even though the state of affairs described is not determinately settled in some respects. In other words, sometimes it is determinately and completely TRUE that I MIGHT / MIGHT NOT do something and determinately false BOTH that I would do it and that I would not do it.
Rejecting bivalence in favor of a three-valued logic would imply that ontological indeterminacies weren't really TRUE, which to my mind would undermine a core thesis of open theism, namely, the genuine (though limited) openness of reality. Thus, I think we are better to hold onto bivalence.
Cheers,
Alan | | Back to Top | | |
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Alan Rhoda
Registered Member
Date Joined May 2002
Total Posts : 680
| Posted 10/7/2003 2:38 PM (GMT -6) | | quote:
Everything that happens is obviously possible. If we think of everything that could possibly happen, then we have a complete array of possible worlds. But you cannot have possible worlds just existing, because they are merely possible, and not actual. So, if there really are possible worlds, they must exist in something actual, something that really exists. Now we have an actual real thing in which all possible worlds exist. The nearest we can some to imagining this is to think of an actual mind or awareness in which all possible world exist as ideas. That mind is God, and the possible worlds are ideas in the mind of God.
Unlike Doc I don't think this argument works. It is a version of the ontological argument and, like other versions of the argument, conflates logical possibilities with ontological possibilities. The difference is that ontological possibilities are possible or not given reality as it actually is, whereas logical possibilities are not so constrained. Ontological possibility implies logical possibility, but the converse is not necessarily true. These two types of possibility coincide only IF an omnipotent God exists. Thus the argument begs the question by tacitly assuming what it purports to prove. Here's my detailed commentary:
Everything that happens is obviously possible.
True. Actuality implies possibility.
If we think of everything that could possibly happen, then we have a complete array of possible worlds.
Does "everything that could possibly happen" refer to everything that is logically possible, or to everything that is ontologically possible? This is not clear.
But you cannot have possible worlds just existing, because they are merely possible, and not actual. So, if there really are possible worlds, they must exist in something actual, something that really exists. Now we have an actual real thing in which all possible worlds exist.
Here it is clear that we are talking about ontologically possible worlds. In order for this argument to work, "all possible worlds" can't mean all logically possible worlds, but has to mean all worlds that are ontologically possible given the state of reality. In other words, it doesn't follow that we have an actual thing that contains the potency to realize all logical possibilities.
The nearest we can some to imagining this is to think of an actual mind or awareness in which all possible world exist as ideas.
Again, I don't see how this follows. If reality were different, the ontological possibilities would be different. Suppose there is no God and that the universe is just a random quantum fluctuation or something like that. In that case the ground of possibility would lie in the quantum field, not in a mind, not in God. All we need is an actual ground for the ontological possibilities that actually exist, which may be a very small subset of all logical possibilities.
That mind is God, and the possible worlds are ideas in the mind of God.
One can reach this conclusion only by assuming that all logical possibilities are ontologically possible, which is only the case if an omnipotent God exists.
Anyway, that's my take.
Alan | | Back to Top | | |
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Alan Rhoda
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Date Joined May 2002
Total Posts : 680
| Posted 10/7/2003 2:58 PM (GMT -6) | | Tom: As I understand it, nominalism does not deny that the chair I’m sitting on actually exists, but rather it denies that apart from the existence of actual chairs there exists the notion of “chairness” (same with trees, color, birds, whatever).
Alan: Not quite. Nominalism doesn't deny that the "notion" of chairness exists, but rather denies that chairness exists. In other words, it denies that chairs have a nature. There are chairs, but there is nothing that it is to be a chair.
Tom: Does not God’s having conceived of our world before its actual existence imply the realist is correct? That is, God conceived of the notion of color, of trees, of grasses, etc., and this conception (the conception of these categories) preceded the creation of the individual items themselves.
Alan: I think you are correct. A committment to realism is just a committment to the intrinsic intelligibility of reality, and insofar as the world was conceived in the mind of God it is intrinsically intelligible. The medieval realists would say that universals were "ante rem" (before things) in the mind of God, but also "in res" (in things). That is, things have natures. We don't just have a bunch of accidentally similar or dissimilar individuals (as the nominalist would hold), but we have, at least in some cases, individuals that are essentially the same (at least in some respects), however different they may be in accidental characteristics. In other words, the realist holds that there are "natural kinds". The realist need not hold that all nouns in our language denote a natural kind, but only that some do. The most obvious examples are the different species of living things and the fundamental constituents of matter (e.g., the atomic elements, protons, electrons, quarks, etc.). Denial of realism leads straight into epistemological relativism (postmodernism).
God bless,
Alan | | Back to Top | | |
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