Back to logic! (Cross-posted from Jack's comments.)
Jack and I talk about stuff. Here's a copy of my most recent (substantial) comment, somewhat edited for consumption by the general populace:After talking with Chris, I'm convinced that I've been talking past you. That's the nice way of saying it. The accurate way of saying it is that I'm full of shit on most of my talking points. At any rate, I think I more clearly understand where you're coming from. Let me get this straight, though: you're asking for a principled alternative to being agnostic toward an unfalsifiable proposition? I mean, we're certainly never going to falsify it, but by its own stipulations, we can't prove it either - I was just trying to say that it was reasonable to doubt MR since it can't be established. It seems we're stuck with Dawkins' Permanent Agnosticism in Principle on this. Chris says that if Lewis' logically possible worlds are truly independent of each other in all ways, then it quite simply doesn't make a difference whether they're there or not, since it literally doesn't make a difference to this reality either way; and therefore it doesn't matter what we believe about it, either.
Also, I wanted to clarify something: I wasn't trying to prove MR false, I was trying to show something which, if true (which I can't establish), would prove MR false. In other words, I was trying to establish a valid counterfactual, not trying to construct a sound argument. Here it is in a more standard format. First, some shorthand definitions:Proposistion X = "A logically possible world W may be predicated on the non-existence of a logically possible world V." (Or, "W exists IFF V does not exist.")
Proposition Y = "X entails a contradiction."
Proposition Z = "Y entails a contradiction."
Proposition Fuck You = Vote Yes! (Sorry, couldn't resist.)
For those who aren't savvy, "modus ponens" (abbreviated as "MP") is a rule of inference which states that, "if A implies B, and if A is the case, then B is the case." So if you can establish that A is the case, and modus ponens applies, you've effectively established that B is the case. Also, "punt" is the rule of non-contradiction: if it can be shown that "not X" entails a contradiction, then X must be the case because contradictions can't exist and therefore it's impossible for X to be false. (Jack, I know Deutsch used this term in his logic class, but I don't know if it's called "punt" anywhere else.) Now, the argument:1. If it is the case that Z is true, then Y is necessarily false. (By Z and Punt.)
2. If it is the case that Y is false, then X cannot entail any contradictions. (By 1 and Punt.)
3. Therefore, if Z is true, then X is possible. (By 1, 2, and MP.)
4. If it is the case that X is possible, then W and V can be considered logically possible worlds. (X is the case, in other words.)
5. W and V cannot both exist. (By X and MP.)
6. If MR is true, then all logically possible worlds (including W and V) must exist. (By MR & MP.)
7. The conjunction of MR and X is a contradiction. (By 5 & 6.)
C. Therefore, if Z is true, then MR is false. (By 3, 4, 5, 6, 7, MP, and Punt.)
I can't establish Z, I'm just saying that if it were established, then MR could not be the case. Conversely, if it could be shown that Y is true, then X must be false necessarily, and this would lend strong argumentative support to MR on my view. Is this clearer?
Isn't logic fun?
Also, I wanted to clarify something: I wasn't trying to prove MR false, I was trying to show something which, if true (which I can't establish), would prove MR false. In other words, I was trying to establish a valid counterfactual, not trying to construct a sound argument. Here it is in a more standard format. First, some shorthand definitions:Proposistion X = "A logically possible world W may be predicated on the non-existence of a logically possible world V." (Or, "W exists IFF V does not exist.")
Proposition Y = "X entails a contradiction."
Proposition Z = "Y entails a contradiction."
Proposition Fuck You = Vote Yes! (Sorry, couldn't resist.)
For those who aren't savvy, "modus ponens" (abbreviated as "MP") is a rule of inference which states that, "if A implies B, and if A is the case, then B is the case." So if you can establish that A is the case, and modus ponens applies, you've effectively established that B is the case. Also, "punt" is the rule of non-contradiction: if it can be shown that "not X" entails a contradiction, then X must be the case because contradictions can't exist and therefore it's impossible for X to be false. (Jack, I know Deutsch used this term in his logic class, but I don't know if it's called "punt" anywhere else.) Now, the argument:1. If it is the case that Z is true, then Y is necessarily false. (By Z and Punt.)
2. If it is the case that Y is false, then X cannot entail any contradictions. (By 1 and Punt.)
3. Therefore, if Z is true, then X is possible. (By 1, 2, and MP.)
4. If it is the case that X is possible, then W and V can be considered logically possible worlds. (X is the case, in other words.)
5. W and V cannot both exist. (By X and MP.)
6. If MR is true, then all logically possible worlds (including W and V) must exist. (By MR & MP.)
7. The conjunction of MR and X is a contradiction. (By 5 & 6.)
C. Therefore, if Z is true, then MR is false. (By 3, 4, 5, 6, 7, MP, and Punt.)
I can't establish Z, I'm just saying that if it were established, then MR could not be the case. Conversely, if it could be shown that Y is true, then X must be false necessarily, and this would lend strong argumentative support to MR on my view. Is this clearer?
Isn't logic fun?