“I would have say I would never tell Bob that DefectRock will cooperate with him. But by Löb’s theorem, that means I would tell you this obvious lie!”
I’ve read this several times, and I can’t get any intuitive reason why that’s true. Which means that I would have to rely on the mathematical argument, but I don’t really get that either. Your argument seems to be saying “if (~A) then (A → anything)”. I understand why that’s a valid claim, but I don’t see how you’ve shown that Shady will say that, let alone that “Shady says (~A)” is equivalent to “Shady says ‘if (~A) then (A → anything)’ ”.
Suppose I make the following argument:
If Shady says “If you ask me whether 1 is odd, I would say ‘yes’ ”, that’s equivalent to Shady saying “If you ask me whether 1 being even would mean that 1 is odd, I would say ‘yes’ ”. So if Shady says that 1 is odd, then Shady would say that 1 is even. So clearly Shady would never say that 1 is odd.
How is this argument different from yours? What essential defect exists in my argument that doesn’t exist in yours?
The difference is that Shady isn’t talking at the object level about the truth of (~A), he is talking at the meta level of what he will say about (~A). That’s the difference that makes this argument work.
If you delude yourself into thinking that everything you think is true is actually true, then you can get ‘hacked’ in the following way: Consider the statement L = “If you think L is true, then A is true”—where the A can be chosen arbitrarily. If you trust yourself blindly, this statement can jump out of a hypothetical into what you actually believe. Say you were thinking about what would happen if you thought L were true. Well, based on what L says, you would see that in this hypothetical situation, you would think A was true also. But that argument is just what L says is true! So you would think that you thought L was true.
Here is the ‘hack’. If you trusted yourself—thinking that you thought L was true would mean that you think L is true. But thinking L is true implies you will actually believe A. So you are hacked into believing A, no matter what A is.
In Inception universe, your dream self is your real self—if you would do something in a dream, you would also do that thing in real life (yeah, yeah I know this isn’t canon, but bear with me).
Now you’re minding your own business when a charismatic man you have never seen before comes up and starts talking to you. In the conversation, he brings up the following idea into you—“If you dream that this idea is true, then you will sell your father’s company.” You don’t believe him, but the thought lingers in your subconscious...
You find yourself musing on the thought. If I did dream that the idea was true, that would be the same as if I had a dream where I dreamed it was true, and then my dream self sold my father’s company.
Later you realize that if you dreamed that this idea was true, then your dream self would also dream that the idea was true—and that would mean your dream self would sell your father’s company. Or in other words, if you dreamed the idea was true, then your dream self would sell your father’s company.
And since your dream self does the same things as your real self, you see that if you had a dream where that idea was true, then you would actually sell your father’s company. And then… you wake up! INCEPTION
So that—that means that you were dreaming that the idea was true! Which means...
Later that day, Robert Fischer makes the surprising announcement that he will sell the company he inherited from his late father.
“I would have say I would never tell Bob that DefectRock will cooperate with him. But by Löb’s theorem, that means I would tell you this obvious lie!”
I’ve read this several times, and I can’t get any intuitive reason why that’s true. Which means that I would have to rely on the mathematical argument, but I don’t really get that either. Your argument seems to be saying “if (~A) then (A → anything)”. I understand why that’s a valid claim, but I don’t see how you’ve shown that Shady will say that, let alone that “Shady says (~A)” is equivalent to “Shady says ‘if (~A) then (A → anything)’ ”.
Suppose I make the following argument:
How is this argument different from yours? What essential defect exists in my argument that doesn’t exist in yours?
The difference is that Shady isn’t talking at the object level about the truth of (~A), he is talking at the meta level of what he will say about (~A). That’s the difference that makes this argument work.
If you delude yourself into thinking that everything you think is true is actually true, then you can get ‘hacked’ in the following way: Consider the statement L = “If you think L is true, then A is true”—where the A can be chosen arbitrarily. If you trust yourself blindly, this statement can jump out of a hypothetical into what you actually believe. Say you were thinking about what would happen if you thought L were true. Well, based on what L says, you would see that in this hypothetical situation, you would think A was true also. But that argument is just what L says is true! So you would think that you thought L was true.
Here is the ‘hack’. If you trusted yourself—thinking that you thought L was true would mean that you think L is true. But thinking L is true implies you will actually believe A. So you are hacked into believing A, no matter what A is.
In Inception universe, your dream self is your real self—if you would do something in a dream, you would also do that thing in real life (yeah, yeah I know this isn’t canon, but bear with me).
Now you’re minding your own business when a charismatic man you have never seen before comes up and starts talking to you. In the conversation, he brings up the following idea into you—“If you dream that this idea is true, then you will sell your father’s company.” You don’t believe him, but the thought lingers in your subconscious...
You find yourself musing on the thought. If I did dream that the idea was true, that would be the same as if I had a dream where I dreamed it was true, and then my dream self sold my father’s company.
Later you realize that if you dreamed that this idea was true, then your dream self would also dream that the idea was true—and that would mean your dream self would sell your father’s company. Or in other words, if you dreamed the idea was true, then your dream self would sell your father’s company.
And since your dream self does the same things as your real self, you see that if you had a dream where that idea was true, then you would actually sell your father’s company. And then… you wake up! INCEPTION
So that—that means that you were dreaming that the idea was true! Which means...
Later that day, Robert Fischer makes the surprising announcement that he will sell the company he inherited from his late father.