Friday, 24 April 2009
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Matins for the Virgin of Guadeloupe
By Ignacio Jerusalem y Stella, Joseph Jennings, Chanticleer
see relatedA Rave Concerning Good, Evil, and Freedom: Part the Thirteenth
A Coin Toss
Imagine the toss of a fair coin. Now imagine one hundred such tosses and again a thousand. In one hundred fair tosses, one would expect about fifty to come up heads and fifty tails, with one thousand one would expect about five-hundred each. In fact, the more one tossed the coin the closer one would see a 50/50 break. As such, if one always called a side consistently (say always calling heads), one would be right about half the time. Now, of course these are probabilities. If one knew the initial conditions for each toss, one could predict the outcomes every time. Now imagine that the initial conditions were the same for each toss and those conditions did not determine the outcome. Let us exclude the possibility that the coin will come up edgewise. The coin must land heads or tail, but there is nothing that determines which side side the coin will land, only that it must land on one side or the other. The best one can now do is predict the outcome half the time (assuming one always chooses the same side for each toss). Now ask how it is that God's position is vis a vis possible worlds and free agents. For Peter van Igwagen there isn't. The above analogy is his and it is for this line of reasoning that he rejects Middle Knowledge. In embracing an incompatiblist view of freedom over possible worlds, van Inwagen holds that God (at least prior to creation) can only know what we would do with a certain amount of probability.
To shift the analogy to possible world talk, let us grant that there is some state of affairs T consistent with some person P and worlds W and W*. Now in W worlds , P performs some actions A and in W* P refrains. In saying this, P's action regarding A is indifferent to T. Now let us assume that there are as many worlds W as W*. God actualizes T and P performs A and actualizes W. God isn't happy with W. Lets say God chucks W and actualizes T again and again and again. Sooner or later W* should turn up. (If you don't like the idea of God destroying worlds and starting over again, imagine that God actualizes T over and over again—universes don't have to interact with each other). If God actualizes T an infinite number of times and W* never turns up, one should be justified in saying P really does not have it in her power to refrain from A. Van Inwagen holds that P can refrain from A, so Middle Knowledge is impossible.
What makes van Inwagen's argument that modern Molinism is flawed goes beyond a good analogy. The principle difficulty with Middle Knowledge is that it is a derivative notion. It is either a special case of natural knowledge or of free knowledge. In a modal scheme, God's knowledge breaks between what God knows of necessity and what God knows contingently, that is contingently on what God in fact does. Following the “movement” Molina describes, all possible worlds are part of God's natural (necessary) knowledge and suppose that God knows that if he actualizes some state of affairs T, the result will be W. That is,
If T is actualized, so is W.
However, what is true in one world is true in all, so (1) is a necessary truth. On the other hand, (1) is clearly part of God's Middle Knowledge, so Middle Knowledge is just a species of God's Natural Knowledge. Now, turn it around, lets say that (1) isn't true in all possible worlds until after God decides to actualize T. Now it is part of God's free knowledge. However, as Robert M. Adams points out, by this time it is too late. God couldn't have used (1) to determine whether to create W, because could not have known that W* and not W would not have resulted from his actualizing T. In retrospect, would seem that Adams and Hasker were critiquing Middle Knowledge under the assumption that it is a special case of Free Knowledge.
As the saying goes, one philosopher's modus pones is another's modus tollens. Let us assume that before God decided to create the world he did know what we would have done. What alternatives does that leave us and do these alternative mean that God could have created a significantly good world that did not include evil? Perhaps next time.
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Comments (5)
I think there is a problem with that coin analogy. It may be the case that the law of large numbers (asymptotic theory) says the fair coin show approach it's mean probability, it does not imply that if we merely chose one outcome that we would have any success at predicting the true outcome UNLESS we chose, also, a large number of times. Our choices would have to also converge on the probability, but if we were to, say, invest in a policy of "pick heads" and run with it, we might end up in a sequence of 20 tails. People often under represent the size of sequences in random generations, often employing that at most we'll have TTT or HHH, maybe a HHHH or TTTTT, but even more unlikely. We will pretty much always leave out sequences of HHHHHHHHHHHHHH which will occur.
Furthermore, the claim that "there is nothing that determines which side the coin will land on" is false. There is something that determines it, and that is physics. If we had a "God's eye view", as they say, then we would know all the details of the matter so that we could predict with absolute certainty every outcome of a flip. The randomness that is represented by our system of probability is a local phenomena having to do with what information is provided. Since we do not have absolute knowledge and are operating from a point of ignorance, the best we can do is take into consideration the facts of the matter surrounding the event and estimate the probability of outcomes. The randomness or stochastic analysis provides a way of obtaining a reliable method of determining future events that would otherwise be meaningless conjecture, and acts as a pivotal way of entering inductive reasoning into our decision practices.
To use such a coin analogy to God and modal logic seems to make God rather ignorant of what is going on. Maybe God chooses to be ignorant so that there is something meaningful behind the possibility of whatever outcomes occur. We wouldn't have any way of knowing. As such, we would be on equal ground perceiving the possible world we happen to be in as random!
Could you elaborate more on these kinds of knowledge you made use of, e.g., "middle" and "free"
@bryangoodrich - Granted that a coin toss is an epistemological issue. I did ask to imagine (counter to fact) that the coin toss was not determined by physics (I regret that I wasn't clear about that bit of fiction). This unreal coin toss would be a closer analogy than a real one for those who support an indeterminist view of human freedom. Van Inwagen's contention is that if A or ~A really is possible on P and P is not determined by T, then God really can't know whether A or ~A would obtain on T, only that one of them would.
The theory of Middle Knowledge was propounded by Luis de Molina. Molina propounded three "movements" in God's knowledge (mind you "movement" is an analogical term for Molina, since he accepted the view that God is simple).
Natural Knowledge: What God knows of necessity.
Free Knowledge: What God knows based on some free action on his part (say creating the world). For instance: Wetherbee typing on 4/24/09 would not be part of God's Natural Knowledge because God could have created a world that did not include Wetherbee.
Middle Knowledge: What God knows based on what would have happend had God freely done something other than what he in fact did do. Modern Molinists use possible world semantics and distinquish between what God strongly actualizes and weakly actualizes (the later being through secondary causes such as free creatures). God knows what free creatures could do and what the would do. God, then cannot weakly actualize worlds were free creatures could act better than they do but would not.
Its down right ancient now, but Alvin Plantinga's God Freedom and Evil and The Nature of Necessity still form the basis of this sort of discussion.
Let us assume that before God decided to create the world he did know
what we would have done. What alternatives does that leave us and do
these alternative mean that God could have created a significantly good
world that did not include evil?
We really don't know for sure, but this is the world that God chose to create, so I believe it's the best possible world in which love can exist and in which he can have fellowship with people that choose to love him and desire to have fellowship with him.
@musterion99 - Leaving aside the question of whether there can be such a thing as a best possible world, the last sentence was a rhetorical question introducing the next proposed post and prompted (in part) by some of your criticism of my rave on Subjective Counterfactuals.
@jimm_wetherbee - Ok, I'll wait to read the next one.