[mannykannot]

This explains why it may not be a sound argument, not a demonstration of its invalidity. The distinction matters, because while invalid hypotheses can be summarily rejected, valid ones might turn out to be right.

Of course, if some people don't understand that this one is not an established fact, and that annoys you, I can't say you are wrong.

[pfdietz]

Yes. Of course, I was not arguing that life must be rare, I was arguing that the evidence we have does not compel one to believe life must exist elsewhere in the universe. The opposite of belief is not belief in the opposite.

[raxxorrax]

There are rare instances where people say that life exists elsewhere, other just state that there is a possibility > 0.

I agree that it is arbitrary that the dimension of the exponent of n has to be larger than the negative one of p. That probably stems from the assumption that the universe is endless.