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Tom
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| Posted 5/21/2003 6:57 PM (GMT -6) |   | Alan: Craig would have to show that the set of "mights" not covered by a "would" is empty. I imagine that he will argue that there is no good reason to suppose that there are any "mights" that do not follow from "woulds" that God knows and that to suppose otherwise compromises God's omniscience and/or sovereignty.
Tom: I agree. This is his only option. But from Doc's openning post on the bivalence thread:quote:
There are three distinct classes of statements about the future that are logically possible. There are "x will occur" statements, "x would occur" statement, and "x might or might not occur" statements. These are NOT logically reducible to each other (Craig conceded this, tentatively).
Craig probably no longer concedes this. Can't wait to read his argument!
By the way, Allan, you began the "Refutation of Molinism" thread because you were preparing to publish a counter-argument to Craig. What happened to that? And remember too that Craig talked about the the possibility that the "individual essence" of a thing being what rendered true counterfactual propositions about that thing?
Tom
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Alan Rhoda
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| Posted 5/22/2003 10:57 AM (GMT -6) | | quote:
Alan, you began the "Refutation of Molinism" thread because you were preparing to publish a counter-argument to Craig. What happened to that? And remember too that Craig talked about the the possibility that the "individual essence" of a thing being what rendered true counterfactual propositions about that thing?
I do plan to publish something on the topic relatively soon. But there are a couple bigger priorities right now. One is that I have to finish my dissertation by this Fall. Another is that I'm getting married in July. A third factor is that before I publish anything on Molinism I'll have to spend a couple months reading up on the literature so that I can find good references and make sure I'm up to date on the discussion.
Regarding individual essences, I think that would be a rather desperate move on Craig's part. The essence of a thing consists in those properties that are necessary for the being to be what it is. My individual essence, for example, consists in the set of conditions necessary for me to be the individual that I am. Now if Craig wants to say that the truth of counterfactuals of freedom follows from individual essences, then he commits himself to the claim that the free choices of an individual are necessary given the essence of the individual. In other words, being the individual that I am, I could not but have chosen as I did. This smacks of what Hasker calls "character determinism". It is also incompatible with libertarian freedom because no individual can ever chose otherwise.
Alan | | Back to Top | | |
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Laplace
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| Posted 5/22/2003 1:42 PM (GMT -6) | | From what LITTLE I know about logic and from my EVEN LESS understanding of the argument at hand (something to do with OVT, cookies and milk, green grass, The Matrix, and a slew of other things), I'd just to add something which may/may not/might/might not/would/would not (but I'll post it anyway) help.
Again, I fundamentally think the errors are not in the logical flow, but the assumptions (axioms) made. As I pointed out in another thread (http://www.gregboyd.org/gbfront/forum/topic.asp?TOPIC_ID=2040), this is quite futile since there is now way to know not only whether these axioms are (absolutely) true, but even consistent.
However, I think the discussion still to be of some merit. Now, I don't know much about counterfactual squares (understand the chart though), but if this is regarding the whole free will/determinism thing, the thread reminded me of something that Bertrand Russell stated. Given:
A = { X | X is not a member of X }
Now ask yourself, "Is A an element of A?" Both the assumption that A is a member of A and A is not a member of A lead to a contradiction. The set construction itself appears to give a paradox.
Russell's own response to the paradox came with the introduction of his theory of types. His basic idea was that reference to troublesome sets (such as the set of all sets which are not members of themselves) could be avoided by arranging all sentences into a hierarchy (beginning with sentences about individuals at the lowest level, sentences about sets of individuals at the next lowest level, sentences about sets of sets of individuals at the next lowest level, etc.). Using the vicious circle principle also adopted by Henri Poincaré, together with his so-called "no class" theory of classes, Russell was then able to explain why the unrestricted comprehension axiom fails: propositional functions, such as the function "x is a set", should not be applied to themselves since self-application would involve a vicious circle. On this view, it follows that it is possible to refer to a collection of objects for which a given condition (or predicate) holds only if they are all at the same level or of the same "type".
And while we're on the issue of choice (Matrix Reloaded coincidential) it also reminded me of the "Axiom of Choice" brought up by Zomelo:
The Axiom of Choice states that given any collection A of mutually exclusive non-empty sets, one can create a new set by choosing an element out of each set in A. It is equivalent to several other important statements about infinite sets (the Well-Ordering Principle, Zorn's Lemma, ...) and has been shown to be independent of the other set-theory axioms.
More on it here: http://www.math.vanderbilt.edu/~schectex/ccc/choice.html
Interesting questions which the answer would help us:
- Is Free Will and Determinism mutally exclusive?
- Even if they are, given what was stated in the Axiom of Choice, what would this new set be?
- What is the difference between EXISTENCE and CHOICE? Obviously, choice is dependent upon existence, thus stronger. But if something exists, is it possible not to be chosen? If it cannot -> Free Will. If not -> Determinism.
Back to Russell's paradox, if we were to define A as an Action (God's, ours, etc.) and X as a Situation. We translate into:
Action = { Situation | Situation is not a member of Situation }
Asking is the Action and element of that Action? What does this mean? Honestly, I don't know; but it looks interesting. But it may have something to do with EXISTENCE, CHOICE, and the all-important-but-you-can-never-be-sure ASSUMPTIONS.
Honestly, such pure theoretical mathematics is not my specialty (actually it's statistics), but perhaps these might help us. Maybe I can give a more cohesive argument once I brood over this some more. *Brood*
"Balance in all things" - Dak'kon, Planescape Torment | | Back to Top | | |
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Tom
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| Posted 5/22/2003 1:56 PM (GMT -6) | | [running two fingers back and forth over lips making the dummy sound "bhb-bhb-bhb-bhb-bhb"] Eh, yeah sure, ah, Starkman, like a, when would you like that simple explanation? Oh, eh, I just gotta write it up, it's, a right here in my noggin.
Tom
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Alan Rhoda
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Total Posts : 680
| Posted 5/22/2003 2:43 PM (GMT -6) | | Thanks for the input, Laplace, though it's a bit hard to follow. Maybe you can polish up your thoughts for us non-mathematicians.
Anyway, I don't see the relevance of the axiom of choice to the logic of neo-Molinism. We can construct a new set by choosing members from other mutually exclusive sets. OK, got it. What follows from that with respect to the relations between "would" and "might" counterfactuals or to the relation between determinism and free will? If determinism and free will are mutually exclusive (as I think they are), and we form a set {determinism, free will}, I don't see that it tells us anything. That one can form a set of two contradictory things does not imply that the set is metaphysically possible or describes a possibly true state-of-affairs.
quote:
Back to Russell's paradox, if we were to define A as an Action (God's, ours, etc.) and X as a Situation. We translate into:
Action = { Situation | Situation is not a member of Situation }
I don't get it. You seem to be defining an "action" as "the set of all situations that are not members of the set of situations"? Paradoxical, to be sure. But isn't that a SLIGHTLY bizarre way of defining an "action"? For the paradox to be a problem we first have to show that it follows from an initially plausible construal of the relevant terms ("action", in this case). I don't think you've given a plausible construal of "action" here, so I don't think there's a problem here.
I look forward to any clarification you can provide.
Yours in Christ,
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GregBoyd
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| Posted 5/23/2003 7:54 PM (GMT -6) | | Alan: Thus God knows the "mights" but not the corresponding "woulds". Craig would have to show that the set of "mights" not covered by a "would" is empty. I imagine that he will argue that there is no good reason to suppose that there are any "mights" that do not follow from "woulds" that God knows and that to suppose otherwise compromises God's omniscience and/or sovereignty.
Doc: When you say the set is "empty", do you mean "unactualized"? Unless one can show that might-counterfactuals not entailed by would-counterfactuals is logically impossible, the set is not empty. It consists of all possible might counterfactuals not covered by would counterfactuals. And it would be REQUIRED of omniscience – not a NEGATION of omniscience – to know this set. This is my whole point.
Of course, the entire set COULD be unactualized. But if it is so, it is so CONTINGENTLY. And as such, it is irrelevant to the point of Neo-Molinism.
I appreciate your feedback.
Greg
"The responsibility is with the chooser -- God is blameless." Plato, Republic, 10. | | Back to Top | | |
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GregBoyd
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| Posted 5/23/2003 8:06 PM (GMT -6) | | Alan: Regarding individual essences, I think that would be a rather desperate move on Craig's part.
Doc: Last I spoke with him, he thought the appeal to individual essences was unnecessary. He argued that God doesn’t need to GROUND his middle knowledge in anything: he simply knows. Yet, he did through out the "essence" doctrine as a way of answering the grounding objection in case one yet feels God’s knowledge needs to be grounded.
For my part, I think the grounding objection works if a) one holds to the principle of sufficient reason and b) one doesn’t want to make the facticity of the would-counterfactual possible worlds as well as the actual world an eternal attribute of God, or c) one doesn’t want to accept dualism (an eternal reality exists alongside God). I believe Craig denies sufficient reason (nothing causes God to have this knowledge) and unwittingly affirms either 2 or 3, since the uncaused facticity exists eternally either as part of God or alongside God.
Doc
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¡Que Payaso!
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Date Joined Jul 2001
Total Posts : 108
| Posted 5/23/2003 9:21 PM (GMT -6) | | Laplace,
Read this:
http://www.gregboyd.org/gbfront/index.asp?PageID=700
Payaso 
"I don't know half of you half as well as I should like; and I like less than half of you half as well as you deserve." - Bilbo Baggins | | Back to Top | | |
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