If logic is done correctly, can it be used to answer all questions humans ask?

Logic fails at self-referencing statements.

Lets take this statement: “i am a liar, right?”.

It cannot be analysed logically because it refers to itself and becomes infinitely recursive (you would never come to a conclusion regarding its truth).

E.g.

   If i am telling the truth

      then my statement ("i am a liar, right") is true

         thus i must be lying.

But If i am lying

   then my statement ("i am a liar, right") must also be false

      so i am not a liar

         hence i must be telling the truth.

But if I am telling the truth...

   (And so the recursive cycle goes on).