M. Littré has quite recently pointed out[12] what he thinks is an analogy between the system of formal logic, stated in the following pages, and the logical devices of the celebrated Raymond Lully. Lully’s method of invention was described in a great number of mediæval books, but is best stated in his *Ars Compendiosa Inveniendi Veritatem, seu Ars Magna et Major*. This method consisted in placing various names of things in the sectors of concentric circles, so that when the circles were turned, every possible combination of the things was easily produced by mechanical means. It might, perhaps, be possible to discover in this method a vague and rude anticipation of combinational logic; but it is well known that the results of Lully’s method were usually of a fanciful, if not absurd character. [12] *La Philosophie Positive*, Mai-Juin, 1877, tom. xviii. p. 456. A much closer analogue of the Logical Alphabet is probably to be found in the Logical Square, invented by John Christian Lange, and described in a rare and unnoticed work by him which I have recently found in the British Museum.[13] This square involved the principle of bifurcate classification, and was an improved form of the Ramean and Porphyrian tree (see below, p. 702). Lange seems, indeed, to have worked out his Logical Square into a mechanical form, and he suggests that it might be employed somewhat in the manner of Napier’s Bones (p. 65). There is much analogy between his Square and my Abacus, but Lange had not arrived at a logical system enabling him to use his invention for logical inference in the manner of the Logical Abacus. Another work of Lange is said to contain the first publication of the well known Eulerian diagrams of proposition and syllogism.[14] [13] *Inventum Novum Quadrati Logici*, &c., Gissæ Hassorum, 1714, 8vo. [14] See *Ueberweg’s System of Logic*, &c., translated by Lindsay, p. 302. Since the first edition was published, an important work by Mr. George Lewes has appeared, namely, his *Problems of Life and Mind*, which to a great extent treats of scientific method, and formulates the rules of philosophising. I should have liked to discuss the bearing of Mr. Lewes’s views upon those here propounded, but I have felt it to be impossible in a book already filling nearly 800 pages, to enter upon the discussion of a yet more extensive book. For the same reason I have not been able to compare my own treatment of the subject of probability with the views expressed by Mr. Venn in his *Logic of Chance*. With Mr. J. J. Murphy’s profound and remarkable works on *Habit and Intelligence*, and on *The Scientific Basis of Faith*, I was unfortunately unacquainted when I wrote the following pages. They cannot safely be overlooked by any one who wishes to comprehend the tendency of philosophy and scientific method in the present day.