S
Spock
Guest
The proposition “this sentence is a lie” does **not have a true or false value **associated with it. You can either say that the quoted sentence is a paradox, or you can say that it is self-contradictory. A paradox **is **a contradiction. Now, I did not say that omniscience - in and by itself - is self-contradictory. Only that a revealed omniscient prediction is impossible. If the prediction is not revealed, then there in no problem - except that an unrevealed prediction is useless.There are two key premises to your argument, Spock.
You must be committed to #2, in order to prove what you’re saying. And yet, #2 cannot possibly be established.
- If an omniscient being said that you would do x, and you have free will, you would be free not to do x.
- An omniscient being is such that he would tell you to do x, being aware of all the facts in the case (including the fact that you would choose to be a contrarian).
Consider:
The conditional statement is true (although incompletely true), but #2 in this situation is obviously false. Significantly, this does not prove that Bob is not always honest.
- If Bob is always honest, and Bob says “This sentence is a lie”, then Bob is lying.
- Bob is capable of saying such a sentence.
All you’ve discovered is a paradox of omniscience, not a contradiction contained within it.
But my proposed scenario still stands. OG can make his prediction assuming (or knowing?) that I will act contrarian. That still does not allow to make a valid prediction. The point is that as soon as the prediction is revealed to me, the who-can-outwit-whom ends, and the ball is in my court.
Suppose that OG tells me: “I know that you would do X, if I did not reveal it. Now, since I did reveal it, you will not do X. But taking that into consideration, since I tell you that you will not do X, therefore you will do X…” etc… but the process cannot go to infinity, since it would not be a prediction. At one point OG must stop and either predict that I will do X, or that I will not do X. And then it is my turn to act - and guess, what I will do?