Funny, I was just reading the arguing by definition article, then clicked the red envelope and saw your reply. I looked it up because the post I just made here reminded me of it as well. However, I feel justified in this instance because anosognosia is characterized by absolute denial. As far as I can tell, this is an unusual form of brain damage because it is so black and white; 100% of anosognosics will absolutely deny their left arm is paralyzed. If they do not, it by definition (oops) is not anosognosia, just as someone with a paralyzed left arm by definition cannot move it. Consequently, I don't see the fallacy. I genuinely appreciate the criticism, though.
In any case, I avoided arguing the question, which itself is predicated on anosognosics assigning zero probability to their left arm being paralyzed. If they don't, then there is nothing to base our probability estimate on, and the question is meaningless, like asking "There are a hundred trees, one in ten trees has an apple on it, how many apples are there? (Some apples are oranges)".
Incidentally, I assign a probability of 1 to 2+2=4 and don't understand why you would not. Can you explain?
Incidentally, I assign a probability of 1 to 2+2=4 and don't understand why you would not. Can you explain?
You may find this post helpful.
Followup to: The Strangest Thing An AI Could Tell You
Brain damage patients with anosognosia are incapable of considering, noticing, admitting, or realizing even after being argued with, that their left arm, left leg, or left side of the body, is paralyzed. Again I'll quote Yvain's summary:
A brief search didn't turn up a base-rate frequency in the population for left-arm paralysis with anosognosia, but let's say the base rate is 1 in 10,000,000 individuals (so around 670 individuals worldwide).
Supposing this to be the prior, what is your estimated probability that your left arm is currently paralyzed?
Added: This interests me because it seems to be a special case of the same general issue discussed in The Modesty Argument and Robin's reply Sleepy Fools - when pathological minds roughly similar to yours update based on fabricated evidence to conclude they are not pathological, under what circumstances can you update on different-seeming evidence to conclude that you are not pathological?