I may have misunderstood your argument Thomas. Are you saying that because it’s possible to construct a paradox ( in this case Yablo’s paradox ) using an infinitude, that the concept of infinity is itself paradoxical?
Couldn’t you make a similar argument about finite systems such as, say?:
A: B is false,
B: A is false
Here are only two sentences. Is the number two therefore paradoxical? I apologize if it sounds like I’m trying to parody your argument—I really would like to learn that I’ve misunderstood it, and in what way.
using an infinitude, that the concept of infinity is itself paradoxical?
I have to admit, that no. Perhaps it is something else wrong here. It might be. Not very likely, but still possible. We see, that finite lists don’t suffer because of Yablo’s paradox, infinite lists do. Still, it may be something else which really causes the A & NOT A situation..
Couldn’t you make a similar argument about finite systems such as, say?:
A: B is false, B: A is false
You can. And you have a contradictory little system here. Which is therefore useless. So you take another one, like the rules for the game of chess. Hoping, that there is no paradox there. (But there is. You can’t believe it, but there is a paradox inside the chess rules!)
In practice, you can continue to play chess and use infinities. But that is at your own risk.
I may have misunderstood your argument Thomas. Are you saying that because it’s possible to construct a paradox ( in this case Yablo’s paradox ) using an infinitude, that the concept of infinity is itself paradoxical?
Couldn’t you make a similar argument about finite systems such as, say?:
A: B is false, B: A is false
Here are only two sentences. Is the number two therefore paradoxical? I apologize if it sounds like I’m trying to parody your argument—I really would like to learn that I’ve misunderstood it, and in what way.
I have to admit, that no. Perhaps it is something else wrong here. It might be. Not very likely, but still possible. We see, that finite lists don’t suffer because of Yablo’s paradox, infinite lists do. Still, it may be something else which really causes the A & NOT A situation..
You can. And you have a contradictory little system here. Which is therefore useless. So you take another one, like the rules for the game of chess. Hoping, that there is no paradox there. (But there is. You can’t believe it, but there is a paradox inside the chess rules!)
In practice, you can continue to play chess and use infinities. But that is at your own risk.