If you base an argument on some statements which are highly likely to be true, it is still quite likely that the argument itself is true. Example: You have 4 statements and each statement has a probability of p=0.95 to be true. Then the probability that all 4 statements are true is p=0.815 (0.95^4). So the probability is still quite high, it only decreased by just 14.2%.

But if you have 4 statements which are moderately speculative, say p=0.5, the probability that all 4 statements are true is now only p=0.0625 (0.5^4). In this case, the probability changed extremely, it dropped by 87.5%! Here one starts with just moderately speculative hypotheses and ends up with an highly unlikely conclusion.

I guess that “new rationalists” unconsciously assume that reasoning with speculative hypotheses behaves similar to “ordinary” reasoning with highly likely hypotheses (“facts”), namely that the likelihood of the conclusion is a little lower, but still similar to the likelihood of the hypotheses. But thats not the case: The likelihood of the conclusion is MUCH lower than the hypotheses if the hypotheses are speculative.

]]>