PERFORMANCE OF LOGICAL INFERENCE. 
499 
8. The only reason which I can assign for this complete inability of logicians to devise 
a real logical instrument, is the great imperfection of the doctrines which they enter- 
tained. Until the present century logic has remained substantially as it was moulded 
by Aristotle 2200 years ago. Had the science of quantity thus remained stationary 
since the days of Pythagoras or Euclid, it is certain that we should not have heard of 
the arithmetical machine of Pascal, or the difference-engine of Babbage. And I 
venture to look upon the logical machine which I am about to describe as equally a 
result and indication of a profound reform and extension of logical science accomplished 
within the present century by a series of English writers, of whom I may specially name 
Jeremy Bentham, George Bentham, Professor De Morgan, Archbishop Thomson, Sir 
W. Hamilton, and the late distinguished Fellow of the Royal Society, Dr. Boole. The 
result of their exertions has been to effect a breach in the supremacy of the Aristotelian 
logic, and to furnish us, as I shall hope to show by visible proof, with a system of logical 
deduction almost infinitely more general and powerful than anything to be found in the 
old writers. The ancient syllogism was incapable of mechanical performance because 
of its extreme incompleteness and crudeness, and it is only when we found our system 
upon the fundamental laws of thought themselves that we arrive at a system of deduc- 
tion which can be embodied in a machine acting by simple and uniform movements. 
9. To George Boole, even more than to any of the logicians I have named, this great 
advance in logical doctrine is due. In his ‘Mathematical Analysis of Logic’ (1847), 
and in his most remarkable w T ork ‘Of the Laws of Thought’ (London, 1854), he first 
put forth the problem of logical science in its complete generality : — Given certain 
logical premises or conditions, to determine the description of any class of objects under 
those conditions. Such was the general problem of which the ancient logic had solved 
but a few isolated cases — the nineteen moods of the syllogism, the sorites, the dilemma, 
the disjunctive syllogism, and a few other forms. Boole showed incontestably that it 
was possible, by the aid of a system of mathematical signs, to deduce the conclusions of 
all these ancient modes of reasoning, and an indefinite number of other conclusions;. 
Any conclusion, in short, that it was possible to deduce from any set of premises or - 
conditions, however numerous and complicated, could be calculated by his method. 
10. Yet Boole’s achievement was rather to point out the extent of the problem 
and the possibility of solving it, than himself to give a clear and final solution. As 
readers of his logical works must be well aware, he shrouded the simplest logical pro- 
cesses in the mysterious operations of a mathematical calculus. The intricate trains of 
symbolic transformations, by which many of the examples in the ‘ Laws of Thought’ are 
solved, can be followed only by highly accomplished mathematical minds ; and even 
a mathematician would fail to find any demonstrative force in a calculus which fearlessly 
employs unmeaning and incomprehensible symbols, and attributes a signification to 
of meaning of terms ; but it was merely of an illustrative character, and does not seem to have been capable of 
performing any mechanical operations. 
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