This post is a thought experiment. As is evident from the number of comments on the first Bayes’s theorem post below, it has sparked quite a debate. I’d like to step into my opponent’s shoes for a moment and think about this debate from the point of view that I’m seeing presented.
<tongue in cheek>
Suppose I give a demonstration of a certain fact. Then suppose some person unknown to me comes along and asserts that the fact is false. What am I to make of this?
First, I consider my own judgment of the probability of the truth of my demonstration. I judge it to be at least as certain as, say, the argument by which Rutherford proved the existence of the proton, and additionally strongly confirmed by personal experience, which I don’t have regarding the existence of the proton.
Second, I think about this in relation to someone’s contradiction of the position. Clearly, a person’s contradiction of such a highly probable fact significantly raises the probability that the person for whatever reason is prone to making assertions opposite what is actually the case. Ultimately, I judge this to be the most likely hypothesis.
Third, I reason as follows: “A person who I have reason to believe has a probability greater than 0.5 of making assertions opposite what is actually the case has just asserted not-X. Clearly, this increases the probability of X.” Consequently, I judge that this assertion actually confirms my original belief, so I am now more sure than ever that it is true.
Further, this hypothesis allows me to make predictions about the person’s future behavior, namely making similar assertions about related issues. When what actually obtains turns out to be exactly what my hypothesis predicts, my hypothesis is confirmed even more strongly, along with my original position. Interestingly, there is nothing the person can do about this—all further arguments against my position simply serve to further confirm it.
</tongue in cheek>
Yes, that was tongue in cheek. However, it is precisely the sort of reasoning that the opposing position must ultimately lead to. In fact, it is worse, since it implies that any time anyone disagrees with me, I should view their position as increasing the probability of my own view rather than theirs. For even if I judge the person to be more probably correct than me on the general subject in question, I cannot judge them to be more probably correct with regard to the exact proposition being disputed; since if I thought this I could not disagree about it.
<tongue in cheek>
Now, I predict responses to this telling me why I’m wrong, that the opposing position does not imply these consequences. This will, of course, further confirm my hypothesis, causing me to become more certain of the truth of my position.
</tongue in cheek>
it implies that any time anyone disagrees with me, I should view their position as increasing the probability of my own view rather than theirs.
Is ‘tonge in cheek’ the HTML code for enclosing a straw-man?
The bottom line is that assertions aren’t arguments. Arguments are what convince. Assertions may convince, if backed by arguments. It depends.
My position is and has always been ‘it depends’.
The “tongue in cheek” emphasizes to other readers that I think the argument is silly and doesn’t work. It is true, however, that it is the logical consequence of the position you presented below. But as I suggested, I don’t believe it would be worthwhile to discuss it further, so I won’t.
I am going to do one more post on probability, a puzzle, before moving on to something else, but it doesn’t involve propositions or lying or knowledge vs. ignorance or other complicating factors. Feel free to take a shot at it.
The “tongue in cheek” emphasizes to other readers that I think the argument is silly and doesn’t work.
And meanwhile the “straw man” emphasizes to other readers that it wasn’t my argument in the first place.
Bye,