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Originally posted by Royce
From what I have read so far none of you have a very good understanding of probability or are not using it for the sake of this discussion.
If F has free will, there is a 50:50 chance that he will choose Choc. and a 50:50 chance that he will choose van. anyone time. As observers that is all that we can know with certainty because those are his only choices. At any given one time or one sample he has a 50:50 chance despite any history of him having a 70% preference for Choc.
If as observers we observe his choice 10 times and he chooses choc. 7 time and van. 3 time then we can say that there is an 86% probability that in any 10 samples F will choose choc. 7 times. If we observe F for 100 times then we can say the for any given 100 samples there is 96% probability that F will choose Choc. 70 times. If we observe the same behavior 1000 times we can say the there is a 99.6% probability that out of any 1000 samples F will choose Choc. 700 times. That is all that we can say as observers and it doesn't matter what may or may not influences F's choice so long as the ratios hold up and he has free will (Those figures are not statistically correct but you get the idea I'm sure.)
Never the less no matter how many times we sample or observe F for anyone time we can only say that he has a 50:50 chance of choosing choc. This is only if F has free will also D's behavior has no effect on F's choices.
Royce, I mean this with all due respect but it appears as if you are the one without a good understanding of probability.
If we can only say that F has a 50/50 chance of choosing one or the other, this is equivalent to saying F has no preference for one or the other-- it's also equivalent to saying that F chooses absolutely randomly. If F indeed has a preference, and acts on this preference, then this preference must have some expression in the choice that F ultimately makes. Since F can only choose one or the other-- chocolate or vanilla-- at one time, this preference will not immediately make itself known after one choice. This DOES NOT imply that the preference has not been factored into that choice-- hence, it does not imply that the choice was a 50/50 proposition.
Let's say we observe F n times, for n arbitrarily large. As you acknowledge, the more observations we perform on F, the more the proportion of times F chooses chocolate in our sample of n observations converges to the proportion of times F chooses chocolate overall, in all his infinite parallel universe incarnations. So let's get extravagant and say we perform 10 billion billion observations on 10 billion billion identical parallel universe incarnations of F at their respective t0's. From this massive sample, we get that F chooses chocolate 90% of the time. Now we perform one more observation on one more identical F-- what would you put your money on, F choosing chocolate or vanilla? From your perspective, you probably wouldn't bet at all since you think that there is a 50/50 chance F will choose chocolate. But this is absurd-- since we have seen that over 10 billion billion identical trials F chooses chocolate 90% of the time, it only stands to reason to say that for our next observation there will be a 90% chance that he will choose chocolate.
Think of the same concept, but for flipping a coin. If it is a fair coin, then over many flips we will converge on the result that there is a 50/50 split between heads and tails. If it is biased, we will converge on a different result over many flips-- say, 70/30. If we flip the coin 10 million times and see it lands on heads 70% of the time do you really think there is only a 50/50 chance it will land on heads on the next flip?
In the hypothetical situation I have posed, F has a natural preference for chocolate, so it is only natural to expect this to be reflected in his choice. Well, you might ask, why should F have any preference at all? If he is truly free, would that not imply that he is free from all external influences? If you want to define free will as such, fine-- but such a radical free will clearly cannot apply to us humans in any way, since we humans ARE affected by external influences, whether we have some degree of freedom in our ensuing choices or not. To deny this is to be blind to human nature.
Personally I think that we do have free will. Our choices may be influenced by our past and present mood but we are free to choose not compelled to choose one way or the other. If it were a deterministic world then we might just as well say tha astrology is an exact science as the position of the planets are as good an indiction of that which compells us as any other.
Free to choose, compelled to choose-- either way, there is an impact from our environment. I was taking this environmental impact into account when I posited that F chooses chocolate 70% of the time. If you say that for every free choice there is a uniform distribution of probabilities across all possible choices, this is no different than saying that the possessor of free will must always choose uniformly at random with no influence from his environment, and therefore ultimately must choose with no justification for his choice that can have external expression.
edit: Another way to think about it... based on the logic you have posed, you may as well ignore weather reports that say there is a 70% chance of rain today-- after all, there is only a 50/50 chance of this happening; either it rains or it does not rain. The (pseudo) deterministic (and more accurate) take on weather forecasting, on the other hand, is that there is a greater or lesser chance that it rains today based on prevailing weather patterns. I don't see how determinism, for you, makes indications of causally influenced human behavior absolutely arbitrary. If anything it is the opposite.
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