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johnmd
Registered Member
Date Joined May 2002
Total Posts : 154
| Posted 1/6/2004 5:46 PM (GMT -6) |   | Open Theism (at least one variation) implies that God knows all possibilities, all possible future scenarios, etc. and is capable of reacting to any possible circumstance as if it were a certainty.
Mathematically, knowledge of all possibilities implies “certainty” (e.g., “integrating from 0 to infinity” to derive the “area under the curve”—the triangles become infinitely small) Hence, God’s knowledge of all possibilities and all factors impacting any given decision at any given time would seem to imply that God could, indeed, “know” the future (i.e., God’s knowledge and infinite wisdom accounts for every possible permutation and derives “the future” just as integral calculus accounts for every possible point “under the curve” to derive the area under the curve).
If, in fact, God knows all possibilities (i.e., every possible factor that impacts any human being at the point of a decision from the molecular level of the brain, to genetic and hereditary factors, to environmental and relational issues, to motives, etc., etc.), then it seems to follow that God in His infinite wisdom could “integrate” every point of knowledge and “know” what decision any individual or group will make at any point in time.
Just as the “procedure” of integral calculus does not “determine” the area under the curve but rather only derives or explains the area under the curve, it follows that God’s infinite wisdom in conjunction with His knowledge of all possibilities (? redundant) would enable Him to “know” the future without determining it—Hence, a functional (nonparadoxical) Arminianism? For example, God could express genuine regret despite His “certain” knowledge of the future because His knowledge did not “cause” the regrettable act.
Maybe Leibniz was right after all…“ ‘The Calculus’ ultimately will explain all physical and metaphysical reality.” ???
Can any of you mathematical whizzes out there help me work through this? If I am going in circles or too far out in left field rein me in.
Thanks,
John
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Iconoclast
Registered Member
Date Joined Oct 2001
Total Posts : 1227
| Posted 1/6/2004 8:05 PM (GMT -6) | | johnmd
then it seems to follow that God in His infinite wisdom could “integrate” every point of knowledge and “know” what decision any individual or group will make at any point in time.
Iconoclast
This is only true if every decision an individual makes is fully determined by antecedent causes. My understanding of the meaning of free will is that an individual can make a decision that is not bound by antecedent causes.
If all effects are fully determined by antecedent causes then we are not free-will beings - we are "mechanical" devices - really complicated mechanical devices but mechanical none the less.
If we are free will beings then even though God knows all the possible choices we can make it is impossible for Him to predict exactly what choice we will make. This suggests then that there are many possible cause-effect time lines very few of which become actual time lines. Calculus can give us probability curves in this situation, however, unlike standard probability functions with free will it is NOT true that in the long run the probability function will be accurate.
We know that the probability of a dice coming up 6 is 1/6. In a sufficient number of throws the number of times it comes up will tend towards 1/6. This is a limit function. Calculus is based on limit functions actually resulting in the calculated limit at infinity. With a free will dice even though our initial calculation is that the probability "ought" to be 1/6 for a six coming up the actual answer may vary from this dramatically - even over an infinite number of throws - the free-will dice might just decide to always come up 3, or it might decide to go back and forth between 1 and 2, or it might just change what it comes up based on what it thinks you want it to come up. Thus, true free will breaks the assumption of the limit function have a calculable value, which breaks the ability of the differential calculus from being useful in this case.
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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johnmd
Registered Member
Date Joined May 2002
Total Posts : 154
| Posted 1/7/2004 4:13 AM (GMT -6) | | Great
Please keep the responses coming.
I am not a mathematician and am dealing with a friend relative to this mathematical analogy. So, I need all the help I can get
Thanks
John | | Back to Top | | |
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Alan Rhoda
Registered Member
Date Joined May 2002
Total Posts : 680
| Posted 1/7/2004 6:39 AM (GMT -6) | | Both Icon and Laika have made the point that the application of the analogy with integration in calculus is seriously problematic when it comes to free will choices. I think they are correct.
There's another, and to my mind more fundamental, objection, which is that no knowledge of mere possibilities, however exhaustive, can in principle yield knowledge of actualities, much less "certainties". Integrating over a curve of possibilities won't tell you which of those possibilities will be actual and which will not. The most it could give would be knowledge of the range or scope or "area" of those possibilities, which isn't the same thing. To make the point, here's another dice analogy. If you have a fair die that will be repeatedly tossed and you knew in advance all possible values of the die, then you would know the following types of possibilities:
1,2,4,3,5,1,...
2,6,1,3,5,2,...
6,3,2,4,3,3,...
and so on
What you wouldn't know is which one of these potentially infinite number of sequences will be the actual sequence (assuming that there is NOW a truth of the matter about which sequence WILL be actual--itself a dubious proposition if, with Icon, we posit dice with free will).
Best wishes,
Alan
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