P
polytropos
Guest
All of this talk of induction is pretty irrelevant. As you note, we can know what would happen for a theoretical board of infinite size, but the point is that we could never play a game of tic tac toe on a board of infinite size, since an actual infinite number of moves would be required to finish. And if God were to list out the discrete possibilities, you would not live long enough to hear them all. God would not finish articulating his prediction, so you would never be able to act in defiance of his prediction.The tools of mathematics are much more complicated than they can be explained within a few short paragraphs. The concept of induction is more than inheritance from “n” to “n+1”. As long as the same behavior is established, one does not need to examine every single particular setup.
There is a generalized tic-tac-toe game, played on a “sufficiently large” (infinite) paper, where the two players have to place “n” X-s or O-s in a row, column or diagonal. The question is “can we decide if the first or the second player has the advantage, if both play the perfect strategy”. If “n” is 1, 2, 3 or 4, the starting player always wins. If the number is 9 or higher, the game is always a theoretical “draw”. For 5, 6, 7 and 8 the answer is unknown. The point is that we can know the result for infinitely many “n”-s without going through a formal induction. Don’t think that just hearing about the concept of induction you already “know” everything that can be known about it. Math is a heavy duty discipline.And no, your original argument does not hold.
Moreover, the behavior of groups containing free individuals can be analyzed with a different part of mathematics, namely statistics. However, all that is irrelevant as I explained before.
There is only one simple setup, which is repeated every time a prediction is made…
There is no need to go back to 1), we already know that the process will be repeated - without introducing any formal “n” to “n+1” step.
- prediction →
- freedom to choose →
- a choice different from the prediction.
If the “tentative” future is revealed, one can make a different choice and thus invalidate the prediction. I took pains to explain the two similar problems of “changing the past” and “knowing the future”. I suggest you ponder that. Though it is getting pretty sad that I invest time and energy into presenting some exhaustive explanation, and then it is being neglected, as if nothing was said.
But it doesn’t really matter whether Back2Church’s interpretation is right (one problem with it, if I am understanding it correctly, seems to be that the number of possibilities may not be infinite, but even that would not show that your thought experiment is sound). All that you can show is that it is logically impossible for God to reveal what a free agent is determined to contravene, which is decidedly unremarkable. It does not follow that God lacks any knowledge. Please respond to #76 and #77 if you disagree with this.