  The 20th century has revealed two important limitations of scientific
knowledge. On the one hand, the combination of Poincar\'e's nonlinear dynamics
and Heisenberg's uncertainty principle leads to a world picture where physical
reality is, in many respects, intrinsically undetermined. On the other hand,
G\"odel's incompleteness theorems reveal us the existence of mathematical
truths that cannot be demonstrated. More recently, Chaitin has proved that,
from the incompleteness theorems, it follows that the random character of a
given mathematical sequence cannot be proved in general (it is 'undecidable').
I reflect here on the consequences derived from the indeterminacy of the future
and the undecidability of randomness, concluding that the question of the
presence or absence of finality in nature is fundamentally outside the scope of
the scientific method.
