What is a good example of a paradox?

[BrianSoddingBoru4]

That wasn't the point of my question. The point is that "I always tell lies" is not a paradox, because the definition of a lie is not "a false statement", for starters.

Hmm, the Oxford dictionary offers:

lie2



NOUN

• 1An intentionally false statement.
  ‘they hint rather than tell outright lies’
  
  ‘the whole thing is a pack of lies’
  

Unless "intentional" is the only thing that is different, missing, then your statement seems to vie with the above.

Well, 'intentional' is the operative word.  An unintentionally false statement is normally called 'a mistake'.  For example, if I say, 'The population of Auckland is two million' when it is actually one and a half million, I haven't told a lie as long as I believe the population to be two million.

All lies are false statements, not all false statements are lies.

Boru