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Tom
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| Posted 8/11/2003 11:59 PM (GMT -6) |   | Sometime ago I submitted the following syllogism in favor of the open view:
Let it be given that omniscience means: God knows all truths and believes no falsehoods.
P1 God is omniscient
P2 The principal of bivalence is universally true.
P3 God knows the truth-value of all propositions (from 1 and 2)
P4 Propositions about the future are of three sorts:
“X will do Y”
“X would do Y”
“X might do Y”
P5 No two of these types of propositions may be simultaneously true (from 2)
P6 There are some true propositions of the type “X might do Y”
P7 God knows the future partly as what “might” be (from 3, 4, 5, and 6)
What we’ve been debating essentially for months now is P5, that is, whether or not “will” and “might” may ever both be true. The rule of subalternism says that if one begins with a true “will” the subaltern “might” is necessarily true. So both may be true.
Doc and I have been challenging this on the basis that the definition of “might” which permits both “will” and “might” to be simultaneously true is too weak a definition to secure “might not’s” contradicting “will.” On the basis of this stronger definition of “might” Doc and I have argued that any true “might” implies “might not,” that these two are essentially one undivided truth-claim, and that therefore what we need is a triangle and not a square to express propositions about future contingencies.
Not many have joined our camp, which is disconcerting to me but an encouragement to Doc! He’s been at this longer than I have.
There is a weaker argument that secures the logical possibility of the open view:
P1 God is omniscient
P2 The principal of bivalence is universally true.
P3 God knows the truth-value of all propositions (from 1 and 2)
P4 Propositions about the future are of three sorts:
“X will do Y”
“X would do Y”
“X might do Y”
P5 “Might” and “might not,” being subcontrary propositions, MAY both be true, in which case contraries “will” and “will not” as well as “would” and “would not” would be false.
P6 An omniscient being would know the truth value of any TRUE “might and might not” proposition (from P3 and P5).
P7 It is logically possible for God to know the future partly as what “might and might not” obtain.
This establishes the logical possibility of open theism.
One could argue that though logically possible, there are in fact no true conjoined “might and might not” propositions, that for every event that ever happens, it was true before it happened that it “will” (or “would”) happen. Thus, all true “mights” are in fact subsumed under true “wills.” Of course, those who believe THIS have offered no real argument for believing there are no true “might and might not” propositions. It is entirely assumed to be the case that no such propositions exist.
There is a slightly stronger argument that secures more than just the logical possibility of the open view, and that would be an argument that includes the claim that subcontraries “might” and “might not" are in reality sometimes both true.
P1 God is omniscient
P2 The principal of bivalence is universally true.
P3 God knows the truth-value of all propositions (from 1 and 2)
P4 Propositions about the future are of three sorts:
“X will do Y”
“X would do Y”
“X might do Y”
P5 “Might” and “might not,” being subcontrary propositions, may both be true, in which case contraries “will” and “will not” as well as “would” and “would not” would be false.
P6 God would know the truth value of any true “might and might not” proposition (from P3 and P5).
P7 There exist true “might and might not” propositions.
P8 God knows the future partly as what “might and might not” occur.
Here P7 is the key: there exist true “might and might not” propositions.
The advantage of this argument is that is a) establishes the truth of the open view and not just the mere logical possibility of the open view, and b) renders pointless the debate about whether or not “might” always implies “might not.” It doesn’t at all question subalternism. It relies only on the nature of contradiction, for if both “might” and “might not" are true, both “will” and “will not” (as well as “would” and “would not”) are false. If there exist true conjoined might-might not propositions, then it is false that for every event that ever happens it was true before it happened that it “will” or “would” happen. Bivalence being true, these “will” and “will not” propositions (as well as “would” and “would not” propositions) are all FALSE, even if the event in question ends up occurring. All that was true about them prior to their obtaining was that they “might and might not” obtain.
So, all we need, Doc, is an argument that proves that subcontraries “might” and “might not” are in reality sometimes BOTH TRUE. Arguing that “might and might not” is meaningful whereas “will and will not” is not meaningful is a good start. But more is needed. What MAKES “might and might not” meaningful? That’s what needs to be laid out. Whether “might” is ever true (on the square) without “might not” also being true is something only open theists themselves would want to argue about anyhow and we can do that later. Whether a triangle is more accurate than the square (it clearly IS in the case of conjoined might/might not) is a decoration we get to do AFTER we’ve proven our case, but it’s beside the point for now. All that’s now needed is to show that subcontraries “might” and “might not” are in reality sometimes both true.
THIS is all I want to talk about now.
Somebody prove to me that subcontraries “might” and “might not” are in reality sometimes BOTH TRUE.
What is already demonstrably true that supports the claim that “might” and “might not” are in reality sometimes both true?
P1 ?
P2 ?
P3 ?
P4 ?
P5 Therefore, subcontraries “might” and “might not” are sometimes in reality both true.
Fill in the blanks.
Clinch THIS, and you logically establish the truth of the open view. However, if it can be demonstrated that there are in reality no true propositions of the form "might and might not" then one will have disproven the open view in spite of its being a logically consistent view.
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Tom
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| Posted 8/12/2003 3:27 AM (GMT -6) | | What “might and might not” obtain is by definition historically contingent. So somebody define historically contingent state of affairs for us.
a) It is certainly a logically possible state of affairs (that is, it is not self-contradictory).
b) It is obtainable, that is actualizable, given the present state of reality. The world as it now is can "get to" that state of affairs from where it now is.
c) It is neither necessary nor inevitable that it obtain.
Anything else?
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Starkman
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| Posted 8/12/2003 6:02 AM (GMT -6) | | Tom,
Thanks SO much for the sum of all the conversation!
Now, I've offered an illustration of which may or may not be helpful. It starts with reality, and if it can be worked into a logical formality, wonderful.
God appears before me and tells me that in 60 seconds, I'm going to do X, Y, and Z. As I see it, only three assessments exist: 1) either God has determined that X, Y, and Z will happen; 2) I have the option to not do X, Y, Z; 3) X, Y, and Z are out of my control (i.e., my heart is giving and I will die).
Note that even when it is determinism, there is still free-will interaction. Jonah, for instance, rebelled; he was not an automaton when God told him he was goign to Nineveh. Now, when Jesus told Peter he was going to deny Jesus, it isn't clear that it was determinism--Peter becomes unable to stop his own mouth because it's been determined. (I argued for Peter being free to have changed the events, but Christ new Peter's heart all too well; Peter wasn't even going to give it the time of day to think that he could possibly deny His Lord. He was, however, already denying Jesus before he spoke a word when he was dodging those who might have recognized him. Here's the link to my illustration and argument: www.gregboyd.org/gbfront/forum/topic.asp?TOPIC_ID=2360) The point being that even if we were to concluded determinism, there is something of the free-will at work.
If it can be demostrated just one time that the future doesn't go according to the way God says it will--in the context of my illustration (and I believe Scripture is full of such examples where God speaks and acts as if it were supposed to have gone one way and didn't)--then could it not be said in that one instance, where God dictates X, Y, and Z, "It might or might not come to pass"? (Note that this even being when God has specifically said that something was going happen, not just in the general events of the principle of bivalence.) I maintain that my illustration (at least in reality) proves that the future HAS to be partly open. (God may say I'm going to do something, but I can do otherwise. Not always, but sometimes.) I haven't got the slightest clue, however, to turn the illustration into formal logic.
I cannot help but see that reality testifies to not only a partly open future, but that it can't be otherwise. I also feel that it's nonsense to say something "might or might not" happen and at the same time state that it "will or will not." Just because time moves on and reveals which way the "might or might not" went is no logical reason to conclude determimism. this isn't formal logic holding determinism together, but the a priori that the future is already settled. But, again, I can't argue "logically," as you are.
Hope this helps,
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Starkman
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| Posted 8/14/2003 4:04 AM (GMT -6) | | Tom, my good man, any thoughts on what I wrote?
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Tom
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| Posted 8/14/2003 4:38 AM (GMT -6) | | Starkman-
Back atcha in a bit! Sorry.
Albert-
I'm stupified.
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Tom
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| Posted 8/14/2003 10:07 PM (GMT -6) | | Albert: Firstly, I think that all you need to prove in logical terms is that the open view is possible. I don't think you need to prove that the open view is true from logic alone. As a matter of fact, I don't think the open view can be proven true from logic alone (i.e. I don't think it is necessarily true).
Tom: Not everything that is true and that can be proven to be true is "necessarily true."
Albert: If God wanted to determine everything, as Calvinists think he does, I think that he could do so. In that case there would be no true "might and might not" propositions.
Tom: Of course.
Albert: But I cannot think of a way of proving that there have to be true "might and might not" propositions, purely on logical grounds.
Tom: First, I'm not looking to prove that there "have" to be true "might and might not" propositions. I'm looking to prove that there "are" true "might and might not" propositions. Secondly, I admitted that whether or not there in reality ARE any true "might and might not" propositions cannot be shown to be the case (or not to be the case) on logic alone. This is obvious. I agree, if we are to show that there are true "might and might not" props (or conversely, if our opponents are to show that there are in reality no true "might and might not" props) we will have to bring in arguments from elsewhere (biblical-theological, exegetical, and existential).
Albert: I seriously doubt such a proof could be developed.
Tom: Do me this favor then. You obviously believe there are in reality true "might and might not" propositions. So, just tell me WHY you believe this. That's all I'm looking for right now. What evidence is there that there are in fact true "might and might not" propositions.
Albert: This I absolutely disagree with. In the previous thread, I have given rigorous definitions of "will" and "might" which permit "will" and "might" to be simultaneously true, but which also result in "might nots" contradicting "will". I assert that I have simply proved this, period (or full-stop as we would say).
Tom: Well, then perhaps you can just pray that Doc and I will see the logic of your arguments. But pray very hard, because I surely do not see, as you argue, that “x MIGHT do y in z” means “there is at least one possible world in which x WILL do y in z.” Consider yourself to have proved your case full-stop if you wish, but I am far from seeing it.
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Tom
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| Posted 8/15/2003 1:58 AM (GMT -6) | | Albert: I proved from my propositional definitions on the previous thread that A and O on my definition were contradictories, and that seems to have been conveniently ignored.
Tom: I have always affirmed that A and O are contradictories. Always.
Albert: I suppose I could pray for you to come to a correct understanding of "might" and "will", but frankly I have far more important things to pray for!
Tom: Well, toss up a desperate prayer or two when you think of us!
Thanks,
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Tom
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| Posted 8/15/2003 2:54 AM (GMT -6) | | Starkman-
Heads up!
Al-
Oh, did I mention that Doc and I want a revolution in the canons of logic?
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ReasonableDoubt
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| Posted 8/15/2003 4:55 AM (GMT -6) | | | Albert, how do your 7 arguments prove open theism? It seems like they're just arguments for libertarianism. you haven't shown in any of those points why open theism necessarily follows from libertarianism. | | Back to Top | | |
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Tom
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| Posted 8/15/2003 9:30 AM (GMT -6) | | Let me try this.
Al seems to think that my and Doc’s beef with the semantics of counterfactual logic has been with the nature of contradictoriness. As I’ve thought on it, it appears to me that my problem is rather with the nature of subalternism when the subalterns regard future contingencies. I’m far from nailing down my hunches, but let me toss this out. (By the way, Doc, in your year-long mastery of logic, check out Arthur N. Prior, the father of Tensed Logic. He may have something to say to us.)
So…
1) In “x will do y” x’s doing y is not a future contingent event. Anybody doubt this? I take historically contingent with regard to some future event to mean the event is neither necessary nor inevitable. If an event “will” happen, then its occurrence is not contingent.
2) But on the standard square, “x might do y” is the subaltern of the above “x will do y” and must by the rule of subalternism be true. Just as the truth of “All grass is green” entails the subaltern “Some grass is green,” in counterfactual logic the truth of “x will do y” entails the truth that “x might do y.” [Given that (A) “x will do y” is true, it follows that the subaltern (I) “x might do y” is true and the contradictory (O) “x might not do y” is false. My beef does not lie with contradictories (A) and (O), but rather with the nature of subalternism when the propositions in question regard future contingency. And it is the nature of contingency itself which drives my suspicions.]
3) If (1) and (2) above are correct, then it follows that “mights” which are true by virtue of being the subalterns of true “wills” cannot be contingent, that is, these particular “mights” cannot describe contingent events, for their truth-value is entailed via the law of subalternism by “x will do y,” that is, by a statement which describes an event about which there is no historical contingency—“x WILL do y.” According to the law of non-contradiction, x’s doing y cannot be BOTH historically contingent AND historically non-contingent. It follows then that “mights” which are true subalternately cannot posit the contingent nature of the events they describe. They “will” happen, THEREFORE they “might” happen. Nothing contingent about these “mights.”
4) Consider on the other hand “mights” which are NOT true by virtue of being subalterns of “wills.” These would be “mights” that are true along with their subcontrary “might nots.” In this case both contraries “will” and “will not” are false by virtue of being contradictories. Here we have “might” and “might not” together describing a future event the occurrence of which IS historically contingent, and it is the job of these “mights” to posit THIS contingency.
5) We clearly have TWO different sorts or classes of “mights” running around on the square. One group of “mights” is those which are true by virtue of being subalterns to true “wills” and thus are incompatible with historical contingency. These do NOT describe future events the occurrence of which is historically contingent. Quite the opposite. These “mights” describe non-contingent events, event that "will" happen. The second group of “mights” consists of those “mights” which are NOT true by virtue of subalternism but rather are conjointly true with their subcontrary “might not.” These “mights” DO posit the historical contingency of the events they describe.
Does ANYBODY out there under the sound of my voice see what I see here? See the inconsistency? See how true “mights” that are entailed by true “wills” cannot MEAN the same thing as “mights” that are conjointly true with their subcontrary “might nots”? The first is entailed by and compatible with the denial of historical contingency. The latter specifically asserts historical contingency. This is my problem with the traditional square. It has two different “mights” running around. It’s not consistent.
I’ve no doubt Al will come back with a full-stop proof to dismantle my argument. And I no doubt will continue to doubt him. 
Doc? Anybody? Heaven? Gabriel? Lucifer (we love you too)? Got any thoughts on this? I’m all ears.
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Tom
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| Posted 8/15/2003 6:01 PM (GMT -6) | | Starkman-
I think I follow ya. There are instances of God declaring “x will happen” and the event does not happen. So what was up? Doesn’t “x will” describe a non-contingent event? So why didn’t x happen? What the he…!
I don’t think most of us (excluding Bill Craig and Albert of course) walk around speaking formal logic. We’re much more free, thank God. So often drop qualifications like “conditionals” that would be necessary in formal logic. In logic “x will do y” means x WILL do y; y is gonna happen period. But in everyday speech we use “will” to express what we know is a contingent event but which we fully intend to follow through on, or which we fully believe will be followed through on. That it’s conditional or contingent is simply understood. Everyday speech is not so exact.
“I will pick you up a 7:00 AM.” Really? Not 6:58? Not 7:02?
“I’ll see ya tomorrow!” Really? No chance at all that I might not see ya tomorrow? Of course there is. I might die. You might die.
It’s my feeling that God speaks our everyday language (or that of everyday Jews 3,000 years ago) and NOT the formal language of logicians.
“Hezekiah, you’re going to die of this disease. Get ready! You will surely die.”
“Nineveh will be destroyed in 40 days!”
“Tyre will be destroyed and reduced to rubble.” It was not.
Though God said the events “will” surely happen, they didn’t. So they MUST have been contingent! Obviously. So why didn’t God say “might”? Because he must have “intended” that they happen. He was resolved on the matter. And formal logic doesn’t take this sort of thing into consideration when it posits “x will do y in z.” Normal talk between persons is more dynamic.
What we normally do not do in everyday speech is make a weaker claim when a stronger one is true. For example, we just mowed all our yard and then declare, “Some of the grass is mowed.” Is this false? No. I did mow some of the grass. I mowed it all, but it’s also true that I mowed any portion of the yard you might specify. So the weaker “I mowed some of the grass is true.” Or let’s say I know that you’re attending a seminar. You’re on your way in your car. You and I speak on your new cellular phone and you tell me you’re just pulling into the church parking lot. I’m already inside having coffee and Springs asks me, “Is Starkman coming to the seminar this morning?” and I answer (knowing that you’ve just pulled into the seminar and ARE attending), “Starkman might attend the seminary today.” In formal logic, I haven’t said anything that isn’t true, because for every true “will” (Starkan WILL attend the conference), there is a subaltern which is also true, and that subaltern is “Starkman might come to the conference. Though there is nothing historically ‘contingent’ about your attending the conference, it’s still true that you “might” attend.
It’s this subalternism that I’m uncomfortable with, because if you were sitting at home thinking about whether to attend or not, undecided, your attending would be “historically contingent” and both “might” and “might not” would be true, in which case both “will” and “will not” would be false. In THIS case if I said “Starkman might attend the conference” I clearly MEAN SOMETHING DIFFERENT than when I say “Starkman might attend the conference” where you are pulling into the church parking lot. The first “might” is the might of historical contingency: You might attend. You might not attend. The latter might is the “might” of—I don’t know what to call it—historical ‘possibility’? Logical possibility? Whatever. But there is nothing contingent about this latter “might,” for it is entailed by a true “will.” I hope you see my point. “Might” in these two cases doesn’t MEAN the same thing. Albert will argue that they DO mean the same thing. But I consider my point proved, full-stop, done deal, case closed.  Formal logic on the square doesn’t exactly know what to do with “mights” nor does it seem to have any specific language for future contingencies. It’s uncomfortable with the idea. Why is that?
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Tom
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| Posted 8/15/2003 6:30 PM (GMT -6) | | I'm getting worn out here.  Doc, if you don't get your butt over here I'm gonna agree with Albert.
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Tom
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| Posted 8/15/2003 6:40 PM (GMT -6) | | Albert-
Is this rewording fine by you?
(A) "X will" means X is entailed by what is the case.
(E) "X will not" means -X is entailed by what is the case.
(I) "X might" means X is does not contradict what is the case or what is entailed by what is the case.
(O) "X might not" means -X does not contradict what is the case or what is entailed by what is the case.
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Tom
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| Posted 8/15/2003 8:20 PM (GMT -6) | | Don't be so happy too quickly!  I was just clarifying. As it stands I think I agree. I mean, it's certainly true that future contingents do not contradict what is the case or what is entailed by what is the case. What bothers me is that there is NO way, no single truth-claim, that stardard logic recognizes as expressing "future contingency." Don't you find this odd? For something as fundamental a claim as future contingency, it is a weakness indeed that our formal expressions of logic possess no modal operator expressing this. [And the modal operator (the small pyramid) "possibly" does not mean "indeterminate" in the sense of "historically contingent."] So I agree with your square, but I am not convinced that it is complete.
The person who just might provide what I think is the missing link is Arthur N. Prior. Please read this: http://plato.stanford.edu/entries/prior/
Doc, check out this article.
I would like to see you, Albert, a little more critical, or rather suspicious, of established canons of logic. Reading you I get the feeling that the present state of knowledge regarding logic is perfectly complete and exhaustive, that there's nowhere to go from here. And yet we've managed to keep pushing the envelope until now. Hmmm. Aren't you glad they didn't settle for what they knew 100, 500, or 1,000 years ago? I guess my point is that the people who came up with, say, the modal logics you've been resting on did so not by accepting the conventions of logic prevalent in their day but by questioning those conventions (that is, whether or not they were complete).
Challenge it Albert. Think outside the box...not because there is no box, but because it might not contain everything there is or that can be said to be true.
I'd love to know your thoughts on the article re: Prior.
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Tom
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| Posted 8/15/2003 9:22 PM (GMT -6) | | Let's see if Al will move toward the center some too.
Al-
Agreeing with the square (as summarized at the end of the previous page) is certainly enough to go on for now. It clearly establishes the logical possibility of open theism. It cannot (and I have admitted this though you misunderstood me here too) prove that there are in fact any conjointly true subcontrary “might” and “might not” propositions. This has to be concluded on other grounds (theological, exegetical, existential, blah blah blah).
Not only is the question of whether or not there are in reality any conjointly true subcontrary “might” and “might not” propositions not answered by logic, but neither is it answer by defining omniscience, and I am assuming Bill Craig’s definition (which he claims is THE orthodox definition), which is: “God knows all truths and believes no falsehoods.” Craig seems to think that the open view has something to fear here. But this definition does not in itself tell us whether or not there are in reality any conjointly true subcontrary “might” and “might not” propositions. So neither logic itself nor an orthodox definition of omniscience can tell us whether or not there are any such true propositions. In fact, both demand that if there are any such propositions, an omniscient God must know them.
Where do we go to determine whether or not there are in fact any true “might and might not” propositions? We go where the debate really IS, where it has always been: our doctrine of Creation. What do we believe reality is? What’s it consist of? And here surely there can be nothing heretical in adopting a closed-system view of reality and the universe or an open-system view of reality.
I also want to suggest that we take a look at “indeterminacy” and “determinacy.” Notice, Al, that whereas determinacy is allocated a single place, a single truth-claim, in formal logic, indeterminacy is not. Determinacy is irreducible and singular. It’s present in “x will do y.” Boom. Determinate. There is is: x WILL do y. It’s present in “x will not do y.” Boom. Determinate. There it is: x WILL NOT do y.
But indeterminacy is as real, as irreducible, and as singular as determinacy. Why then is there no corner of the square, no single proposition, no indivisible truth-claim which formal logic recognizes as positing indeterminacy? Surely this is bazaar. Don’t you find that odd? Why must indeterminacy be at best deduced, composed from other propositions (conjointly true “mights” and “might nots”)?
This is my beef. Formal logic is well suited to recognize determinacy but ill-suited to equally account for indeterminacy. It is prejudiced toward a deterministic view of the world. We can squeeze indeterminacy out of the Square. OK. This is testament to the indestructible power of indeterminacy! But we only get there by deducing it from multiple truth claims (“might” and “might not”). Why is this? If indeterminacy is every bit as real, irreducible, and singular a truth-claim as determinacy, why is Western logic so uncomfortable with expressing indeterminacy? By that I mean, why should indeterminacy be a composite truth-claim we arrive at by combining separate truth-claims whereas determinacy is propositionally singular? Shouldn’t indeterminacy be propositionally singular? It certainly should be. But there’s no room for it on our present “maps” of reality. And I think Doc is still right, we need a new map. Not one that denies our present map, but rather one that redraws it with larger borders.
This includes modal logics. The operator for "necessary that" (viz., the square) and the operator for "possibly that" (viz., the pyramid) are not all there is to the story. An operator is needed for "indeterminate that" (you get my meaning I trust).
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Tom
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| Posted 8/16/2003 1:38 AM (GMT -6) | | Albert-
Another thing, indeterminacy is just as much a matter of "what is the case" as is determinacy. I sometimes get the feeling, Albert, that for you future “determinate” events are rooted in the cement of “what is the case” or “what is entailed in what is the case" while future “indeterminate” events are somehow floating around with no place to lay their head. But if a future event is indeterminate, it’s indeterminacy is, as equally as is the case with determinacy, defined by what is the case. Is this perhaps another point on which we can agree?
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GregBoyd
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| Posted 8/16/2003 7:24 AM (GMT -6) | | I LOVE TOM'S PERSISTANCE!!!!
and I LOVE this topic!!!
Tom: All that’s now needed is to show that subcontraries "might" and "might not" are in reality sometimes both true.
Doc: Nope. To prove the logical possibility of Open Theism – viz. to prove that Omniscience does not exclude knowledge of "mights" – you don’t need to prove that they are sometimes true (viz. actualized), only that they are NOT NECESSARILY FALSE. And if they are not necessarily false, then they ARE necessarily TRUE – if not in this world, then in OTHER possible worlds. Hence, we not only prove that Omniscience does not exclude knowledge of "mights," but that it NECESSARILY INCLUDES knowledge of "mights" – even if he decided to create a deterministic world in which they are all FALSE.
Starkman: If it can be demostrated just one time that the future doesn't go according to the way God says it will--in the context of my illustration (and I believe Scripture is full of such examples where God speaks and acts as if it were supposed to have gone one way and didn't)--then could it not be said in that one instance, where God dictates X, Y, and Z, "It might or might not come to pass"?
Doc: Good point. A friend of mine (Nathan) is working on a paper in which he’s framing all this in terms of the square of opposition. The classical view must maintain the (A) position – ALL future events are certain to God. To render this view false, you only need to defend its contradictory (0) – at least ONE future event was/is not certain to God. His basic thesis is that Open Theists have been mistaken in trying to argue for their position by trying to explain each and every problem text – as though the burden were on them. Rather, they should show that neither Scripture nor reason requires to (A) pole, and at least one scripture (but in fact there are tons) best fit with the (0) pole.
Albert: If God wanted to determine everything, as Calvinists think he does, I think that he could do so. In that case there would be no true "might and might not" propositions.
Doc: No no no. There would be no true conjoined mights relative to this world, but there would be true conjoined mights in every other non-deterministic possible world. And this is significant, for it shows that logic requires that we be open theists, if not about THIS world, then about other possible worlds.
In other words, the classical view has to argue that there are no possible worlds in which conjoined mights are true.
Which means they must show that conjoined mights are NECESSARILY FALSE, for only logical necessities cross all possible worlds.
Which means they must show there is something inherently contradictory about "might and might not," for only what is contradictory is necessarily false.
Which means that the burden is not on US to show that might and might not entail each other, but on them to show that "might" NECESSARILY EXCLUDES "might not." You are right in insisting against TGB and me that we can’t prove that mights always entail might-not. But can anyone prove that might necessarily EXCLUDES might not???? Good luck! 
Albert: you only confirm that A and O are contradictories if "might" means some strange thing which you and Greg have never, ever, specified. However, when I said that I had proved that A and O were contradictories, I meant A and O in my sense, which satisfies also the condition that "will" entails "might".
Doc: I think you’re misreading this a bit Albert. We’re not STARTING from a "mysterious sense" of might (which I thought we did define -- historically or feasible possibility). We’re starting from the fact that "might and might not" makes sense, which then raises problems for the view that (A) entails (I) and (E) entails (O) when talking about woulds and mights.
Tom: Is this rewording fine by you?
(A) "X will" means X is entailed by what is the case.
(E) "X will not" means -X is entailed by what is the case.
(I) "X might" means X is does not contradict what is the case or what is entailed by what is the case.
(O) "X might not" means -X does not contradict what is the case or what is entailed by what is the case.
Doc: So far as I can see, this is precisely what Albert was arguing for. Now, the interesting thing is what happens when you assert "(I) and (O)"… for now we have to say that X AND –X do not contradict what is the case or what is entailed by what is the case. But this contradicts BOTH (A) AND (E). Which, it seems to me, then shows that (I) and (0) cannot IN THIS CASE but subalterns of (A) and (E).
And THIS raises the question of what "might" means. But THAT is secondary.
Am I missing something here Albert?
I concede your earlier argument works. No problem. But I don’t see that it handles conjoined mights.
Doc
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Tom
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| Posted 8/16/2003 11:20 AM (GMT -6) | | Doc: Now, the interesting thing is what happens when you assert "(I) and (O)"… for now we have to say that X AND –X do not contradict what is the case or what is entailed by what is the case. But this contradicts BOTH (A) AND (E). Which, it seems to me, then shows that (I) and (0) cannot IN THIS CASE but subalterns of (A) and (E).
Tom: Well, they're subalterns by position, but subalternism is only a) one-way, b) running from top to bottom (not bottom to top), c) provided the top prop is TRUE. So if (A) is true, (I) must be true. If (E) is true, (O) must be true. That's all subalternism requires. But if (A) is false, no valid deduction can on this fact alone be made about (I). If (E) is false, no valid deduction can be made about (O). Likewise, where (I) or (O) is true, no valid deduction can be made on this fact alone regrading the truth value of (A) or (E) respectively.
[Note: My whole suspicion with the square is with subalternism where the propositions in question regard determinacy and indeterminacy, future settledness and future contingency, for it seems clear to me that determinacy and indeterminacy are not quantifiable, except to say that what is determinate is logically possible. But intedeterminacy claims more than mere logical possibility. And where truth-claims are not quantifiable, subalternism has no place. But this is just a hunch (if it even makes sense).]
Good stuff! Let's worship the God of the Possible tomorrow and meet back on Monday!
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Tom
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| Posted 8/16/2003 11:27 AM (GMT -6) | | Doc: A friend of mine (Nathan) is working on a paper in which he’s framing all this in terms of the square of opposition.
Tom: And will Nathan be sharing the treasures of his research with us underprivileged souls?
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Tom
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| Posted 8/20/2003 4:21 AM (GMT -6) | | Albert-
Thanks for the post! I’ve enjoyed these posts on “might-might not.” I’ve got them all ready to print out and bind for future reference (or burning!).
We’re obviously approaching the question with different epistemologies and assumptions. Not sure what they all are. We apparently agree that future determined event x and future indeterminate event y are determinate and indeterminate because of what the present state of reality is. Yet you ground determinacy in this present state but refuse to ground indeterminacy in anything. Indeterminacy, you agree, “floats” in the air with nowhere to lay its head.
In my view, both the determinacy of future event x and the indeterminacy of future event y are equally grounded in what is now the case and ought both to be propositionally singular (which you apparently do not think). I asked for a “spot” on the square that posits indeterminacy. You offered BOTH “might” and “might not” corners. Exactly my point. There is no one corner, not one truth-claim, no single proposition on the square, no single operator that logic recognizes as posting indeterminacy.
I need some more time to research and figure out my thoughts on this. That certainly is true. I’ve got some books on order and intend to race Doc over the next 10 months to see who can make a better fool of himself arguing for this wacko idea of ours.
You said that “the concept of determinacy brings with it the concept of indeterminacy, in the same way as the concept of truth brings with it the concept of falsity.” Now this seems fishy. In an exhaustively determined world (which we admit was a possible world God could have created) there would be no indeterminacy. It’s ‘exhaustively’ determined. In such a world determinacy would not entail indeterminacy. If you’re correct, then an exhaustively determined world would be as impossible as truth existing without falsity. And in what sense does truth and falsity exist for God if he does not possess propositional knowledge? Or did you not deny this? My brains are fried.
You state again that “indeterminate things don't exist,” which of course I’ve agreed they don’t. But neither do future events that are determined. They don’t exist either, yet you treat them differently than indeterminate events.
Well, I’m gonna tuck this all away and just read what I can for the next six, nine, forty, or five hundred months. Then I’ll bring it all back out and see what’s what.
You’re awesome Albert!
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Tom
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| Posted 8/20/2003 4:30 AM (GMT -6) | | Doc-
Why doesn't your friend Nathan jump in this discussion?
Peace,
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Iconoclast
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| Posted 8/20/2003 6:22 PM (GMT -6) | | Albert
POINT 3:
Tom wrote: I would like to see you, Albert, a little more critical, or rather suspicious, of established canons of logic.
Albert replies: As for formal logic, great strides have been made in the twentieth century in this field. I don't doubt that many future developments will occur. However, I doubt that this will involve overthrowing well establishing and proven theorems. If someone comes to me and tells me that they have found a logical flaw in calculus, I will obviously treat their claim with scepticism. I will listen to what they say, and be open to considering it. But it will take a lot to convince me that well established proofs in mathematics are wrong. So it is with Western logic.
Iconoclast
What we have seen again and again is NOT that some theorem is disproved but rather that it is simply a special case of some larger theory. An example is Newtonian physics being a special case of relativity theory (when speeds are a fraction of the speed of light).
Perhaps standard logic is completely accurate but only in the special case of everything being determined (chance does not exist). Perhaps there is a yet-to-be-discovered General Indeterminacy Logic Theory where standard logic is but a special case where the indeterminacy is zero (or rather where probabilities approach 1). This would be analogous to linear and dynamic equations. Linear equations are really but a very small subset of the overall equation space. One can really think of it as being a large space of dynamic equation where there is a very small and simplistic subset that are linear.
Also - didn't Charles Sanders Peirce do a lot of work in logic with the presupposition that Tychism (chance) was true.
Tom - it seems to me that all you have to do to show this is to come up with the "relativity theory" of logic. One of the key aspects that led to relativity theory was to do away with the presupposition that space is fixed - that everything operates on a fixed background. And isn't this exactly what the problem is with the square of opposition - it is based on the presumption of a fixed background - that everything is determined - chance does not exist. All you have to do is come up with how logic functions when chance does exist and then show that when probabilities approach the limit of 1 that the square of opposition can be derived from your "equations". Shouldn't take more than a couple of weeks 
And come to think of it - it shouldn't be any more complex than Quantum Mechanics. Didn't Quantum Mechanics simply introduce indeterminacy into the picture?
thanks,
Iconoclast
"The benefit overran the merit the first day, and has overrun the merit ever since. The merit itself, so-called, I reckon part of the receiving." - Ralph Waldo Emerson | | Back to Top | | |
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Iconoclast
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| Posted 8/20/2003 6:52 PM (GMT -6) | | Albert
Time for me ultimately is subjective (in the existentialist sense, e.g. Heidegger). The objective world just is. It doesn't progress or have some structural feature called "time".
Iconoclast
My understanding is that "time" is simply "rate of change". Would you agree that "rate of change" is an objective phenomenon in that us humans all agree (at sub-relativity speeds) about the "rate of change" of some event?
Albert
I hold to a view called occasionalism, so I don't regard the laws of physics or science as being anything more than descriptions of regularities in the way God acts.
Iconoclast
Then would you agree that God acts indeterminately at least at scales that Quantum events happen? That God's "regularity" of acting includes "indeterminate acting" at quantum scales?
Albert
Time exists subjectively for God, and also subjectively for us, and God and us both act on the world.
Iconoclast
But again, if time is simply rate of change, then isn't it really an objectively measurable phenomenon in that we can all agree on the rate of God's changes and the rate of our changes - that there is an objective (everyone agrees) unit of measure for rates of change?
Albert
But on my view, the world just "sits there inert", except when we or God act on it. We can measure change in the objective world (for example by the movement of the hands of a clock) - then we come up with the idea of "time" as it is expressed in science.
Iconoclast
Would you agree that it only "sits there inert" for very brief "periods" before God changes it again? I am thinking of electrons orbiting the nucleus of some atom. The very latest thinking on the subject (Loop Quantum Gravity) suggests that there is a smallest unit of change. It of course denies that "time" really exists as some fixed sort of background concept. "Time" is simply a concept that is useful for objectively measuring rates of change.
If it is true that God is constantly acting on this world to change it in a regular way that includes indeterminacy then wouldn't it be appropriate to say that possibilities truly exist now as God's dispositional intent to continue to regularly act on this world to change things in a way that includes indeterminacy?
thanks,
Iconoclast
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