So, taking that a bit further, some seem to think that we can invoke the Copernican Principle as the catalyst to infer the existence of exo-life, as it leads to a view that Earth is not ‘special’ or ‘privileged’. Earth contains life, therefore life will exist elsewhere in the universe, right? Extending this further, ‘the numbers’ of ‘Earth-like exo-planets’, implies that life will therefore be ‘likely’ within this population, yes?
Sounds logical, right?
The above argument is an attempted example of
the Mediocrity Principle, which formally states that if an item is drawn at random from one of several sets (or categories), it's likelier to come from the most numerous category, rather than from any one of the less numerous categories. In other words: life is on Earth .. Earth is a random sample of a Copernican Principled Universe, thus via this principle, it is ‘likely’ there’ll be Earth-like life elsewhere.
Unfortunately, this attempt fails on several counts.
First of all, there is no knowledge about the characteristics of the population, (in this case the existence or non existence of life in the Universe). Secondly, the only sample comes from Earth which is
not a random sample. Arguing that life on Earth supports the existence of life in the Universe, becomes
a circular statement because the Mediocrity Principle has been reversed, and it is now claimed that the characteristic of the non-random sample, determines the dominating characteristic of the population, rather than the other way around.
The fallacy lies in the circular statement.
Even ignoring this fallacy, basing an argument on such reasoning, implies that the Mediocrity Principle, when applied correctly, is less likely than than the fallacious argument!