1870.] 



Performance of Logical Inference. 



1G7 



fingers, and of the abacus of the Greeks and Romans may be adduced as 

 examples. Mathematicians have constantly delighted in devising me- 

 chanical modes of calculations, as in the case of Napier's bones, mechani- 

 cal globes, slide rules, &c. Actual machines for performing difficult cal- 

 culations have been designed or constructed at various times since the 

 early part of the 17th century, by Pascal, Morland, Leibnitz, Gersten, 

 Babbage, and Scheutz. 



In logic, on the contrary, we meet with a total absence of any actual 

 mechanism, although logical works abound with expressions implying the 

 need of such aid. The name of Aristotle's logical treatises, the ' Organon,' 

 or Instrument, and many definitions of logic, clearly express this idea, 

 which is also distinctly stated by Bacon in the second aphorism of his 

 1 New Organon.' 



This inability of logicians to realize their notions of a mechanical logic 

 in a material form, analogous to the many kinds of calculating machines, 

 can only be explained by the extreme incompleteness of their doctrines. 

 It is the advance of logical science, chiefly due to the late Dr. Boole, 

 Prof. De Morgan, and George Bentham, which now enables us to pro- 

 duce a truly mechanical logic. 



Boole, in his celebrated work on the ' Laws of Thought,' first put forth 

 the problem of logical science in its complete generality : — Given certain 

 logical premises or conditions s to determine the description of any class of 

 objects under those conditions. The ancient forms of logical deductions 

 are but a few isolated cases of this general problem, which Boole solved 

 in a complete but exceedingly obscure manner. In my * Pure Logic ' 

 (London, 1864, Stanford) and my 'Substitution of Similars' (London, 

 1869, Macmillan), I have endeavoured to show that the mysterious mathe- 

 matical form of Boole's logical system is altogether superfluous, and that 

 in one point of great importance he was deeply mistaken. His logical 

 views, when simplified and corrected, give us a method of indirect de- 

 duction of extreme generality and power, founded directly upon this most 

 fundamental Law of Thought. A proof of the truthfulness and power of 

 this system is to be found in the fact that it can be embodied in a machine 

 just as the Calculus of Differences is embodied in Mr. Babbage's calcula- 

 ting machine. 



To explain the nature of the logical machine alluded to, it may be 

 pointed out that the third of the fundamental Laws of Thought allow us to 

 affirm of any object one or the other of two contradictory attributes, and 

 that we are thus enabled to develope a series of alternatives which must 

 contain the description of a given class or object. Thus, if we are consi- 

 dering the propositions — 



Iron is metal, 

 Metal is element, 



we can at once affirm of iron that it is included among the four alterna- 

 tives : — 



