# thomblake comments on How confident is your atheism? - Less Wrong

10 14 June 2012 08:18PM

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Comment author: 19 June 2012 08:37:56PM 1 point [-]

I know you were speaking loosely, but you can't just multiply probabilities when they're not made independent.

Comment author: 19 June 2012 09:30:36PM -1 points [-]

That's false.

Let's say that we have 3 sets of propositions, A, B, and C. A is 40% likely. B is 90% likely if A is the case and 1% likely if A is not the case. C is 10% likely if B is not the case, 50% likely if A and B are both true, and 5% likely if B is true but A isn't.

B and C are clearly dependent variables. Nevertheless, simple math tells us that C is 8.17% likely, all other things being equal. Since Christianity is only true if all of the relevent propositions are true (as opposed to the scenario above) you can just multiply the probabilities together. (Unlike our A, B, C scenario, which also required some amount of addition.) You just multiply the probability within the conditional: that if God has a son that his one and only son is Jesus, rather than simply the probability that Jesus existed or that Jesus was the son of God. If Christianity could be true without Jesus being the one son of God, then addition would be required along with the multiplication, but this is not the case as the belief "Christianity" implies a zero-probability for these scenarios.

Comment author: 20 June 2012 01:38:37PM 1 point [-]

I somehow didn't notice the "given all of the above" shorthand.