Few alterations of importance have been made in preparing this second edition. Nevertheless, advantage has been taken of the opportunity to revise very carefully both the language and the matter of the book. Correspondents and critics having pointed out inaccuracies of more or less importance in the first edition, suitable corrections and emendations have been made. I am under obligations to Mr. C. J. Monro, M.A., of Barnet, and to Mr. W. H. Brewer, M.A., one of Her Majesty’s Inspectors of Schools, for numerous corrections.
Among several additions which have been made to the text, I may mention the abstract (p. 143) of Professor Clifford’s remarkable investigation into the number of types of compound statement involving four classes of objects. This inquiry carries forward the inverse logical problem described in the preceding sections. Again, the need of some better logical method than the old Barbara Celarent, &c., is strikingly shown by Mr. Venn’s logical problem, described at p. 90. A great number of candidates in logic and philosophy were tested by Mr. Venn with this problem, which, though simple in reality, was solved by very few of those who were ignorant of Boole’s Logic. Other evidence could be adduced by Mr. Venn of the need for some better means of logical training. To enable the logical student to test his skill in the solution of inductive logical problems, I have given (p. 127) a series of ten problems graduated in difficulty.
To prevent misapprehension, it should be mentioned that, throughout this edition, I have substituted the name Logical Alphabet for Logical Abecedarium, the name applied in the first edition to the exhaustive series of logical combinations represented in terms of A, B, C, D (p. 94). It was objected by some readers that Abecedarium is a long and unfamiliar name.
To the chapter on Units and Standards of Measurement, I have added two sections, one (p. 325) containing a brief statement of the Theory of Dimensions, and the other (p. 319) discussing Professor Clerk Maxwell’s very original suggestion of a Natural System of Standards for the measurement of space and time, depending upon the length and rapidity of waves of light.
In my description of the Logical Machine in the Philosophical Transactions (vol. 160, p. 498), I said—“It is rarely indeed that any invention is made without some anticipation being sooner or later discovered; but up to the present time I am totally unaware of even a single previous attempt to devise or construct a machine which should perform the operations of logical inference; and it is only, I believe, in the satirical writings of Swift that an allusion to an actual reasoning machine is to be found.” Before the paper was printed, however, I was able to refer (p. 518) to the ingenious designs of the late Mr. Alfred Smee as attempts to represent thought mechanically. Mr. Smee’s machines indeed were never constructed, and, if constructed, would not have performed actual logical inference. It has now just come to light, however, that the celebrated Lord Stanhope actually did construct a mechanical device, capable of representing syllogistic inferences in a concrete form. It appears that logic was one of the favourite studies of this truly original and ingenious nobleman. There remain fragments of a logical work, printed by the Earl at his own press, which show that he had arrived, before the year 1800, at the principle of the quantified predicate. He puts forward this principle in the most explicit manner, and proposes to employ it throughout his syllogistic system. Moreover, he converts negative propositions into affirmative ones, and represents these by