> If theories could be "proven" in the mathematical sense then they wouldn't be falsifiable
Ack! This is not what "falsifiable" means.
Falsifiability is the property that states, there exists some hypothetical evidence which would be accepted as conclusive disproof of the theory. For instance, newton's third law ("equal and opposite") can be falsified by the discovery of a method of applying force which avoids any opposite application.
Extrapolating some, we can see that for all falsifiable theories, there is an extensive class of evidence which doesn't quite prove the theory wrong, but does weigh against the theory. Non-falsifiable theories don't have this property - for any method of assigning a probability of correctness to a non-falsifiable theory, there is a positive number below which that probability cannot go.
The reason the giant-collision theory should not be said to be "proven" incorrect is that it has not been. Its probability of correctness is still non-zero (and significant). However, it's not true that scientific theories cannot be "proven" incorrect - classical mechanics has been, for instance.
In what sense can a scientific theory be "proven" correct of incorrect in the same way that a purely mathematical statement can? Aren't they two completely different things - with the mathematical argument being binary (it's either true or false) and the scientific argument, as you say, involving degrees of confidence based upon supporting or contradictory evidence?
[Of course, a scientific theory could be disproven by being based on incorrect mathematical reasoning - but that's presumably not very interesting]
Ack! This is not what "falsifiable" means.
Falsifiability is the property that states, there exists some hypothetical evidence which would be accepted as conclusive disproof of the theory. For instance, newton's third law ("equal and opposite") can be falsified by the discovery of a method of applying force which avoids any opposite application.
Extrapolating some, we can see that for all falsifiable theories, there is an extensive class of evidence which doesn't quite prove the theory wrong, but does weigh against the theory. Non-falsifiable theories don't have this property - for any method of assigning a probability of correctness to a non-falsifiable theory, there is a positive number below which that probability cannot go.
The reason the giant-collision theory should not be said to be "proven" incorrect is that it has not been. Its probability of correctness is still non-zero (and significant). However, it's not true that scientific theories cannot be "proven" incorrect - classical mechanics has been, for instance.