Logic in computer science (By Michael Huth,Mark Ryan, second edition, page 132) says
Every φ can, in principle, be discovered to be valid or not, if you are prepared to work arbitrarily hard at it; but there is no uniform mechanical procedure for determining whether φ is valid which will work for all φ.
For me, it sounds contradictory because I take your ability to decide any formula as a uniform mechanical procedure. If you can do it, then you have a uniform mechanical procedure. What do I fail to understand?
Just to be clear what validity means here, the discussion happens in the context of validity definition:
Given a logical formula φ in predicate logic, does ⊨ φ hold, yes or no?