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
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.
In the first edition I inserted a section (vol. i. p. 25), on “Anticipations of the Principle of Substitution,” and I have reprinted that section unchanged in this edition (p. 21). I remark therein that, “In such a subject as logic it is hardly possible to put forth any opinions which have not been in some degree previously entertained. The germ at least of every doctrine will be found in earlier writings, and novelty must arise chiefly in the mode of harmonising and developing ideas.” I point out, as Professor T. M. Lindsay had previously done, that Beneke had employed the name and principle of substitution, and that doctrines closely approximating to substitution were stated by the Port Royal Logicians more than 200 years ago.
I have not been at all surprised to learn, however, that other logicians have more or less distinctly stated this principle of substitution during the last two centuries. As my friend and successor at Owens College, Professor Adamson, has discovered, this principle can be traced back to no less a philosopher than Leibnitz.
The remarkable tract of Leibnitz,2 entitled “Non inelegans Specimen Demonstrandi in Abstractis,” commences at once with a definition corresponding to the principle:—
“Eadem sunt quorum unum potest substitui alteri salva veritate. Si sint A et B, et A ingrediatur aliquam propositionem veram, et ibi in aliquo loco ipsius A pro ipso substituendo B fiat nova propositio æque itidem vera, idque semper succedat in quacunque tali propositione, A et B dicuntur esse eadem; et contra, si eadem sint A et B, procedet substitutio quam dixi.”
Leibnitz, then, explicitly adopts the principle of substitution, but he puts it in the form of a definition, saying that those things are the same which can be substituted one for the other, without affecting the truth of the proposition. It is only after having thus tested the sameness of things that we can turn round and say