The problem in logic with which the present work is concerned has its roots in the Principia Mathematica of Whitehead and Russell. The authors of that work define 'p implies q' as 'It is not the case that p is true and q is false’, whence arises the conclusion that a true proposition is implied by any proposition and a false proposition implies any proposition. These paradoxical results have met with protest, and C. L. Lewis of Harvard has attempted to supply a definition of 'p implies q' which is adequate to 'implies' as generally understood.