Subject: What is the rigorous scientific definition of 'In Principle' ?

I know the dictionary common usage meaning of " 
In Principle" but I would appreciate a more 
comprehensive explanation of the limits & 
boundaries of the term.I hear that, for 
example,a broken teacup could "in Principle" 
have all its pieces fly back together_IF_the 
initial conditions were correct for each 
piece .I have no idea how likely this 
possibility describes "Reality".??
What is the limit of "In Principle"? One chance 
in the age of the Universe? Lack of specific 
exclusion by some prevailing theory ? So many 
explanations include that qualifying phrase, I 
don't know what credence to accord them
Thank you for your time

Re: What is the rigorous scientific definition of 'In Principle' ?