Tuesday, June 12, 2018

Yet another counterexample to Nicod's Principle

Nicod’s Principle says that the claim that all Fs are Gs is confirmed by each instance.

Here’s yet another counterexample. Consider the claim:

  1. All unicorns are male.

We take this claim to be true, albeit vacuously so, since there are no unicorns.

But suppose an instance of (1), namely a male unicorn, were found. We would immediately conclude that (1) is probably false. For if there is a male unicorn, likely there is a female one as well.

The problem here is that when we learn of Sam that it is a male unicorn, we also learn that there are unicorns. And as soon as we learned that there are unicorns, that undercut the reason we had for believing (1), namely that we thought (1) was vacuously true.


anonymous said...

Why "yet another"? Looks as if this is a common counterexample. I don't know who was the first to come up with this type of counterexample (= instance of a generalisation thought to be vacuously true before encountering the instance). The earliest I'm aware of is Maher in his contribution to Contemporary Debates in Philosophy of Science (2004):

"Since Nicod’s condition has seemed very intuitive to many, this result might seem to reflect badly on our explicata. However, the failure of Nicod’s condition in this example is intuitively intelligible, as the following example shows. According to standard logic, “All unicorns are white” is true if there are no unicorns. Given what we know, it is almost certain that there are no unicorns and hence “All unicorns are white” is almost certainly true. But now imagine that we discover a white unicorn; this astounding discovery would make it no longer so incredible that a nonwhite unicorn exists and hence would disconfirm “All unicorns are white.”"

I'm sorry. Unless you think the trick has to with "male" (instead of "white"), the counterexample is a well-known one.

Alexander R Pruss said...

Yeah, I now know. Jon Kvanvig pointed out to me that I. J. Good had a counterexample like this in 1968.

Alexander R Pruss said...

It was new to me. :-(