This might be better placed somewhere else, but I just thought I’d comment on Pascal’s Wager here. To me both the convenient and inconvenient resolutions of Pascal’s Wager given above are quite unsatisfactory.
To me, the resolution of this wager comes from the concept of sets of measure zero. The set of possible realities in which belief in any given God is infinitely beneficial is an infinite set, but it is nonetheless like Cantor Dust in the space of possible explanations of reality. The existence of sets of measure zero explains why it is reasonable to assign the value zero to the probability of something which is not literally impossible. To me, the only true resolutions to this paradox are to either convert, dispute the use of infinity in the utility (which I would also do, although I’m not yet completely convinced either way), or accept that not just is zero an acceptable probability for something that’s not literally impossible but that it’s also the correct value to assign to the probability of an infinitely vindictive God. Everything else is just convenience, egotism or missing the point. Cancelling infinities against other (possibly negative) infinities is simply bad maths, refusing to change your beliefs on the basis of utility rather than evidence is simply not acting in your own best interest and dismissing it based on contradictions in any particular religion or on the existence of other religions is as this article says simply assumed convenience.
In this case, your least convenient world kind of misses the point then. As soon as Omega tells me there’s a non-zero probability of Catholicism being correct (whether Omega has actually told me that or not is not entirely clear mind you) then sure, I’m converting. But this is such a substantial change to reality that I would say it’s essentially removed the paradox. The principle is fine though, I guess my point is just that the least convenient world is not a fixed thing but relative to a particular argument.
It’s interesting to me that the mathematics to resolve the paradox didn’t even exist at the time it was raised. Most people knew there was a problem with it, but at the time (and even today for most people’s level of maths understanding) they had simply no way of expressing it correctly. To me this is actually some justification for a little bit of inertia of beliefs—just because you can’t refute an argument doesn’t mean it’s correct, and your intuition can often tell you something’s wrong before you know what it is. It just needs to be balanced against the many situations where intuition is demonstrably misleading. Innertia and an immovable object are not the same thing.
This might be better placed somewhere else, but I just thought I’d comment on Pascal’s Wager here. To me both the convenient and inconvenient resolutions of Pascal’s Wager given above are quite unsatisfactory.
To me, the resolution of this wager comes from the concept of sets of measure zero. The set of possible realities in which belief in any given God is infinitely beneficial is an infinite set, but it is nonetheless like Cantor Dust in the space of possible explanations of reality. The existence of sets of measure zero explains why it is reasonable to assign the value zero to the probability of something which is not literally impossible. To me, the only true resolutions to this paradox are to either convert, dispute the use of infinity in the utility (which I would also do, although I’m not yet completely convinced either way), or accept that not just is zero an acceptable probability for something that’s not literally impossible but that it’s also the correct value to assign to the probability of an infinitely vindictive God. Everything else is just convenience, egotism or missing the point. Cancelling infinities against other (possibly negative) infinities is simply bad maths, refusing to change your beliefs on the basis of utility rather than evidence is simply not acting in your own best interest and dismissing it based on contradictions in any particular religion or on the existence of other religions is as this article says simply assumed convenience.
In this case, your least convenient world kind of misses the point then. As soon as Omega tells me there’s a non-zero probability of Catholicism being correct (whether Omega has actually told me that or not is not entirely clear mind you) then sure, I’m converting. But this is such a substantial change to reality that I would say it’s essentially removed the paradox. The principle is fine though, I guess my point is just that the least convenient world is not a fixed thing but relative to a particular argument.
It’s interesting to me that the mathematics to resolve the paradox didn’t even exist at the time it was raised. Most people knew there was a problem with it, but at the time (and even today for most people’s level of maths understanding) they had simply no way of expressing it correctly. To me this is actually some justification for a little bit of inertia of beliefs—just because you can’t refute an argument doesn’t mean it’s correct, and your intuition can often tell you something’s wrong before you know what it is. It just needs to be balanced against the many situations where intuition is demonstrably misleading. Innertia and an immovable object are not the same thing.