This Monograph Offers A New Foundation For Information Theory That Is Based On The Notion Of Information-as-distinctions, Being Directly Measured By Logical Entropy, And On The Re-quantification As Shannon Entropy, Which Is The Fundamental Concept For The Theory Of Coding And Communications.information Is Based On Distinctions, Differences, Distinguishability, And Diversity. Information Sets Are Defined That Express The Distinctions Made By A Partition, E.g., The Inverse-image Of Arandom Variable So They Represent The Pre-probability Notion Of Information. Then Logical Entropy Is A Probability Measure On The Information Sets, The Probability That On Two Independent Trials, A Distinction Or Dit Of The Partition Will Be Obtained.the Formula For Logical Entropy Is A New Derivation Of An Old Formula That Goes Back To The Early Twentieth Century And Has Been Re-derived Many Times In Different Contexts.