Maybe I am the one who is confused. How does the definition of a libertarian include anyone from the left?

 Definition:  Noun,

  A person who advocates liberty, especially with regard to thought or conduct.

  A person who maintains the doctrine of free will.

                 Adjective,

 Advocating liberty or conforming to principles of liberty.

 Maintaining the doctrine of free will.

How can anyone on the left, who favors government ensuring/enforcing what they see as liberty, ever be called a libertarian when the libertarian purity of system has no central government or laws to tell anyone what to do or not to do? Libertarian nirvana is a society that does whatever it wants, without restriction. 

Please explain to me how that kind of system could in any way be called a left wing ideology?