I think it is unfair to give Shannon too much credit, Boltzmann and Gibbs came up with the exact definition Shannon gave S = -k \Sigma p_i ln(p_i), including

I think it is unfair to give Shannon too much credit, Boltzmann and Gibbs came up with the exact definition Shannon gave S = -k \Sigma p_i ln(p_i), including a suitable information theoretic interpretation. As physicists they only thought about ignorance of the exact particles position and momentum in systems of 10^24 particles, but the essential idea is the same. Moreover von Neumann had generalized that notion to quantum mechanics S = - tr(\rho ln(\rho)), which gives it a form that is even more abstract than the information theoretic formulation. It was only ignorance on Shannons part that he was not familiar with the work of physicists and mathematicians before him on the subject.