of things not-man or b is seen from the two last combinations to be always a or not-Socrates, but either mortal or not-mortal as the case may be. 51. "Precisely the same obvious system of analysis is applicable to arguments however complicated. As an example, take the premises treated in Boole's Laws of Thought,' p. 125. " “‘(1.) Similar figures consist of all whose corresponding angles are equal, and whose corresponding sides are proportional. "(2.) Triangles whose corresponding angles are equal have their corresponding sides proportional, and vice versa.' "Let A = similar, B = triangle, C = having corresponding angles equal, having corresponding sides proportional. "The premises may then be expressed in Qualitative Logic, as follows: = A = CD, BC = BD. "Take the set of 16 slips out of the A's reject those which are not CD; out of the CD's reject those which are not A; out of the BC's reject those which are not BD; and out of the BD's reject those which are not BC. There will remain only six slips, as follows: "From these we may at once read off all the conclusions laboriously deduced by Boole in his obscure processes. We at once see, for instance, that the class a, or 'dissimilar figures, consist of all triangles (B) which have not their corresponding angles equal (c) and sides proportional (d), and of all figures not being triangles (b) which have either their angles equal (C) and sides not proportional (d), or their corresponding sides proportional (D) and angles not equal, or neither their corresponding angles equal nor corresponding sides proportional.' (Boole, p. 126.) 52. "The selections as made upon the abacus are of course subject to mistake, but only one easy step is required to a logical machine, in which the selections shall be made mechanically and faultlessly by the mere reading down of the premises upon a set of keys, or handles, representing the several positive and negative terms, the copula, conjunctions, and stops of a proposition." 53. In the last paragraph I alluded to a further mechanical contrivance, in which the combination slips of the abacus should not require to be moved by hand, but could be placed in proper order by the successive pressure of a series of keys or handles. I have since made a successful working model of this contrivance, which may be considered a machine capable of reasoning, or of replacing almost entirely the action of the mind in drawing inferences. When I have an opportunity of describing the details of its construction, I think it will be found to afford a physical proof, apparent to the eyes, of the extreme incompleteness of the Aristotelian logic. Not only are the syllogisms and other old forms of argument capable of being worked upon the machine, but an indefinite number of other forms of reasoning can be represented by the simple regular action of levers and spindles. 54. The most unfortunate feature of the long history of our present traditional logic has been the divorce existing between the logic of the schools and the logic of common life. There has been no apparent connexion whatever between the formal strictness of the syllogistic art and the more loose but useful suggestions of analogy from particulars to particulars. It is owing to this separation, as I apprehend, that a succession of English writers from Locke down to Mr. J. S. Mill have been led to underestimate the value of the syllogism. In Mr. Mill's system of logic the syllogism occupies a very anomalous position-that of an extraneous form of proof which may be employed when we wish to ensure correctness of inference, but which is useless for the discovery of truth. I believe that the new view of the syllogism which I am now proposing will remedy this lamentable disconnexion of the parts of what should be one most harmonious and consistent whole. There is no subject in which we might expect more perfect unity and system to exist, and more wide-ruling generalizations to be discoverable, than in the science of the laws of thought; and I conceive that a prime object of any logical reform should be to reconcile the strict doctrine with the looser forms of ordinary thought. This reconciliation will really be effected, I believe, by adopting as the fundamental principle the modified axiom of Aristotle which I have called the substitution of similars. I hope at some future time to explain fully the results which seem to follow from the principle and the harmony which it creates between the several branches of logical method, and I will only attempt in this tract a few slight illustrations. 55. The most frequent mode of inference in common life is that known as reasoning from analogy or resemblance, by which we argue from any thing or event we have known to a like thing or event encountered on another occasion. This seems to be Mr. Mill's view of the ordinary process of reasoning, for in discussing the functions and value of the syllogism he says: "From instances which we have observed, we feel warranted in concluding that what we found true in those instances holds in all similar ones, past, present, and future, however numerous they may be." And again he explains more fully: 2" I believe that, in point of fact, when drawing inferences from our personal experience, and not from maxims handed down to us by books or tradition, we much oftener conclude from particulars to particulars directly, than through the intermediate agency of any general proposition. We are constantly reasoning from ourselves to other people, or from one person to another, without giving ourselves the trouble to erect our observations into general maxims of human or external nature. When we conclude that some person will, on some given occasion, feel or act so and so, we sometimes judge from an enlarged consideration of the manner in which human beings in general, or persons of some particular character, are accustomed to feel and act; but much oftener from 66 1 'System of Logic," vol. i. p. 210, fifth edition. |