Note: This is a translation of a model-theoretical logical approach of the "Are we alone?' dispute into basic English. Any translation has a loss of information and many times leads to misunderstandings. My apologies.
The universe is sterile (except for the earth and some men made sattellites floating in the very nearby space).
A All universes one can think of are sterile (except for an extremely small minority of all thinkable universes).
B Those universes which are not sterile are either full of life or sterile (except for one unique exception).
C Our universe is not full of life.
D From B, C it follows: We are alone in our universe and no life originated but on earth.
End of proof.
Ad. A: Mathematicians designed many imaginable structures that could be interpreted as universes. None of these structures can house life.
Ad. B: 'Counting' universes is hard. Much knowledge of logic and mathematics is needed here. Hence the problem of translation. Translation for non-logicians: Most universes which are not sterile should have been sterile, but due to an extreme coincidence, at one location, life originated. Life originating at yet an other location is impossible (except for an extremely extremely small subgroup).
Ad. C: This is obvious, not only since we never found alien life but also because there is only one type of life that originated on earth.
Ad. D: This is a pure logical deduction.
Note that the statements above do not imply that we are unique and that humanity is unique. It states only that within our visible universe there is no other life except ours. However, no one knows what is there 'outside', besides our visible universe.
There may be a huge number of earth-like planets in our space. Till now (2012) we know of only one: The earth itself. Doing statistics based on only one instance is impossible. The proof above is not based on statistics, solely on logic.
Any scientist who states that the fact that there is an abundance of life on Earth makes it highly probable that there is life on other (earth-like) planets is doing bad statistics. He or she should rehearse basic probability calculus.