Compare the above with pp. 156 to 162 of the present work.
M. Littré has quite recently pointed out12 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.
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
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.
It seems desirable that I should endeavour to answer some of the critics who have pointed out what they consider defects in the doctrines of this book, especially in the first part, which treats of deduction. Some of the notices of the work were indeed rather statements of its contents than critiques. Thus, I am much indebted to M. Louis Liard, Professor of Philosophy at Bordeaux, for the very careful exposition15 of the substitutional view of logic which he gave in the excellent Revue Philosophique, edited by M. Ribot. (Mars, 1877, tom. iii. p. 277.) An equally careful account of the system was given by M. Riehl, Professor of Philosophy at Graz, in his article on “Die Englische Logik der Gegenwart,” published in the Vierteljahrsschrift für wissenschaftliche Philosophie. (1 Heft, Leipzig, 1876.) I should like to acknowledge also the careful and able manner in which my book was reviewed by the New York Daily Tribune and the New York Times.
The most serious objections which have been brought against my treatment of logic have regard to my failure to enter into an analysis of the ultimate nature and origin of the Laws of Thought. The Spectator,16 for instance,