Friday, November 1, 2013

The irrationality of undue scepticism

One might think that sceptical tendencies are intellectually safe. It's clearly irrational for one's level of belief to exceed one's level of evidence. But it does not seem harmful to be more cautious, and hence to make one's level of belief be less than one's level of evidence.

However, if one's levels of belief are classical consistent probabilities, then when one's degree of belief in p is lower than what the evidence yields, one's degree of belief in not-p will be higher than what the evidence yields. And that is surely bad.

One might think it's not so bad as long as one's degree of belief in not-p stays well below 1/2. After all, in that case, one isn't believing not-p, and hence none of one's beliefs is irrational. Yes, but such errors are apt to add up. Suppose there are twelve independent propositions p1,...,p12 that one believes at the 0.75 level, instead of the 0.95 that the evidence supports. Then one's degree of belief in their conjunction will be (0.75)12=0.03, instead of the (0.95)12=0.54 that the evidence yields. And hence the sceptic will believe the negation of the conjunction of the 12 propositions to degree 0.97, instead of having a level of belief in the conjunction of only 0.46, as per the evidence. Excess of caution leads to excessive credulity.

That's true on classical sharp numerical probabilities. The sceptic may better off on interval-valued probabilities. But even so, depending on how one interprets the intervals, there may be a similar kind of criticism available.

The above underlines something I heard Bob Brandom say: one needs to have a reason to be a sceptic about something.

5 comments:

John Moore said...

The reason for being sceptical about something is because it's very different from your ordinary day-to-day experiences.

If you tell me a car drove down the street, I have no reason to be sceptical, but if you tell me a car flew over my house, I'll need to check on that before believing.

If you tell me time slows down when you travel close to the speed of light, I'll need to study that and check it carefully before I believe it.

If you tell me a man rose from the dead, again I'll need to study it carefully and understand why you're making such a claim.

Alexander R Pruss said...

Certainly there are times when scepticism is appropriate. My point is simply that excessive scepticism is no more innocent than excessive credulity--indeed, it is basically the same.

Douglas said...

Alex,

I picture the philosophical skeptic as someone who thinks of himself as having an accurate, if pessimistic, assessment the evidence. He finds the evidence to be worse than it is. As a result, he cautions us not believe to a degree greater than our evidence warrants (which may lead us to believe to a lower degree than our evidence warrants). However, he doesn't advise us to believe to a lower degree than the evidence warrants. He advises us to believe to a lower degree than the evidence is commonly thought to warrant.

I thought I might extend your argument to my skeptic like this: he believes to a lower degree than his evidence warrants, because he is mistaken about what his evidence warrants. But I am unsure this undercuts him dialectically.

Revisit p1...p12. He will believe the negation of their conjunction to degree .97, since he believes each conjunct to degree .75. But this skeptic also holds the evidence to warrant each to degree .75. There he is wrong: the evidence warrants each to .95. Thus, he objectively should not believe the negation to degree .97. Nonetheless, he seems to be rational in his belief, since he sincerely under appraises the evidence.

I'd like a way to convince him that he under appraises the evidence. I have no such way. Which causes me to doubt my evidence!

Thanks for the post. I found it thought provoking.

Alexander R Pruss said...

Douglas:

That raises the tough question whether it is rational to believe as the evidence warrants or as one thinks the evidence warrants.

Heath White said...

"whether it is rational to believe as the evidence warrants or as one thinks the evidence warrants."

Surely these are both virtues, and we should distinguish them. (E.g. as rational-1 and rational-2.) For the same reason we distinguish validity and soundness in logic.