There are, apparently, certain Eastern philosophies that permit and even celebrate logical contradiction. To what extent this is metaphorical I couldn’t say, but I recently spoke to an adherent who quite firmly believed that a given statement could be both true and false. After some initial bewilderment, I verified that she wasn’t talking about statements that contained both true and false claims, or were informal and thus true or false under different interpretations, but actually meant what she’d originally seemed to mean.
I didn’t at first know how to argue such a basic axiom—it seemed like trying to talk a rock into consciousness—but on reflection, I became increasingly uncertain what her assertion would even mean. Does she, when she thinks “Hmm, this is both true and false” actually take any action different than I would? Does belief in NNC wrongly constrain some sensory anticipation? As Paul notes, need the law of non-contradiction hold when not making any actual assertions?
All this is to say that the matter which at first seemed very simple became confusing along a number of axes, and though Paul might call any one of these complaints “splitting hairs” (as would I), he would probably claim this with far less certainty than his original 100% confidence in NNC’s falsehood: That is, he might be more open-minded about a community of mathematicians explaining why actually some particular complaint isn’t splitting hairs at all and is highly important for some non-obvious reasons and due to some fundamental assumptions being confused it would be misleading to call NNC ‘false’.
But more simply, I think Paul may have failed to imagine how he would actually feel in the actual situation of a community of mathematicians telling him that he was wrong. Even more simply, I think we can extrapolate a broader mistake of people who are presented with the argument against infinite certainty replying with a particular thing they’re certain about, and claiming that they’re even more certain about their thing than the last person to try a similar argument. Maybe the correct general response to this is to just restate Eliezer’s reasoning about any 100% probability simply being in the reference class of other 100% probabilities, less than 100% of which are correct.
That second paragraph was hard for me. Seeing “a)” and “b)” repeated made me parse it as a jigsaw puzzle where the second “a)” was a subpoint of the first “b)”, but then “c)” got back to the main sequence only to jump back to the “b)”, the second subpoint of the first “b)”. That didn’t make any sense, so I tried to read each clause separately, and came up with “1. You are never safe. 2. You must understand. 3. On an emotional basis...” before becoming utterly lost. Only after coming back to it later did I get that repeated letters were references to previous letters.