This work contains the substance of Lectures delivered during J-a number of years in Cambridge; at first to members of my own College, and afterwards to students generally in the University. Although the main outlines were sketched long ago, and a large portion of the materials had been delivered for several years in nearly the form now presented, the chapters here offered to the reader have been throughout written out afresh for the present occasion.<br><br>As many readers will probably perceive, the main original guiding influence with me, - as with most of those of the middle generation, and especially with most of those who approached Logic with a previous mathematical or scientific training, - was that of Mill. But, as they may also perceive, this influence has subsequently generated the relation of criticism and divergence quite as much as that of acceptance; though I still continue to regard the general attitude towards phenomena, which Mill took up as a logician, to be the soundest and most useful for scientific study.<br><br>This attitude of the scientific logician, as I conceive arid interpret it, has been so fully explained in the introductory chapter, that I need only say that it is based upon that fundamental Duality in accordance with which it becomes the function of the logician to reduce to order, to interpret, and to forecast the complex of external objects which we call the phenomenal world.