In certain concluding remarks I have expressed the conviction which the study of Logic has by degrees forced upon my mind, that serious misconceptions are entertained by some scientific men as to the logical value of our knowledge of nature. We have heard much of what has been aptly called the Reign of Law, and the necessity and uniformity of natural forces has been not uncommonly interpreted as involving the non-existence of an intelligent and benevolent Power, capable of interfering with the course of natural events. Fears have been expressed that the progress of Scientific Method must therefore result in dissipating the fondest beliefs of the human heart. Even the ‘Utility of Religion’ is seriously proposed as a subject of discussion. It seemed to be not out of place in a work on Scientific Method to allude to the ultimate results and limits of that method. I fear that I have very imperfectly succeeded in expressing my strong conviction that before a rigorous logical scrutiny the Reign of Law will prove to be an unverified hypothesis, the Uniformity of Nature an ambiguous expression, the certainty of our scientific inferences to a great extent a delusion. The value of science is of course very high, while the conclusions are kept well within the limits of the data on which they are founded, but it is pointed out that our experience is of the most limited character compared with what there is to learn, while our mental powers seem to fall infinitely short of the task of comprehending and explaining fully the nature of any one object. I draw the conclusion that we must interpret the results of Scientific Method in an affirmative sense only. Ours must be a truly positive philosophy, not that false negative philosophy which, building on a few material facts, presumes to assert that it has compassed the bounds of existence, while it nevertheless ignores the most unquestionable phenomena of the human mind and feelings.
It is approximately certain that in freely employing illustrations drawn from many different sciences, I have frequently fallen into errors of detail. In this respect I must throw myself upon the indulgence of the reader, who will bear in mind, as I hope, that the scientific facts are generally mentioned purely for the purpose of illustration, so that inaccuracies of detail will not in the majority of cases affect the truth of the general principles illustrated.
December 15, 1873.
PREFACE
TO THE SECOND EDITION.
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 means of the copula “is identic with.” Thus he anticipated, probably by the force of his own unaided insight, the main points of the logical method originated in the works of George Bentham and George Boole, and developed in this work. Stanhope, indeed, has no claim to priority of discovery, because he seems never to have published his logical writings, although they were put into print. There is no trace of them in the British Museum Library, nor in any other library or logical work, so far as I am aware. Both the papers and the logical contrivance have been placed by the present Earl Stanhope in the hands of the Rev. Robert Harley, F.R.S., who will, I hope, soon publish a description of them.[1]
By the kindness of Mr. Harley, I have been able to examine Stanhope’s logical contrivance, called by him the Demonstrator. It consists of a square piece of bay-wood with a square depression in the centre, across which two slides can be pushed, one being a piece of red glass, and the other consisting of wood coloured gray. The extent to which each of these slides is pushed in is indicated by scales and figures along the edges of the aperture, and the simple rule of inference adopted by Stanhope is: “To the gray add the red and subtract the holon,” meaning by holon (ὅλον) the whole width of the aperture. This rule of inference is a curious anticipation of De Morgan’s numerically definite syllogism (see below, p. [168]), and of inferences founded on what Hamilton called “Ultra-total distribution.” Another curious point about Stanhope’s device is, that one slide can be drawn out and pushed in again at right angles to the other, and the overlapping part of the slides then represents the probability of a conclusion, derived from two premises of which the probabilities are respectively represented by the projecting parts of the slides. Thus it appears that Stanhope had studied the logic of probability as well as that of certainty, here again anticipating, however obscurely, the recent progress of logical science. It will be seen, however, that between Stanhope’s Demonstrator and my Logical Machine there is no resemblance beyond the fact that they both perform logical inference.