PERFORMANCE OF LOGICAL INFERENCE. 
513 
A a a a a 
B B b b b 
C C C c c 
D D D D d 
hence we learn that A, B, and C are all I) ; that B, C, and D may or may not be A ; 
that what is not D is not A, not B and not C ; and so on. The conditions of this pro- 
blem form what would be called a Sorites in the old logic, and we have not only obtained 
its conclusion A is D, but have performed a complete analysis of its conditions, and the 
inferences which may be drawn from those conditions. 
45. The problem being supposed complete, we press the Finis key, which differs from 
all the others in moving two levers, one of which (fig. 13) is of the ordinary character 
and returns any rods which may happen to be in the second position into the first, 
while the other (fig. 8) has a much longer radius, is moved by a cord or flexible wire 
p, passing over a pulley q and through a perforation r in the flat board which forms the 
lever itself, in this case a lever of the second order. This broad lever sweeps the rods 
from the fourth position as well as any which may be in the third into the first, and 
together with the other lever (fig. 13) it reduces the whole of the rods to the neutral 
position, and renders the machine, as it were, a tabula rasa , upon which an entirely new 
set of conditions may be impressed independently of previous ones. Its office thus is to 
obliterate the effects of former problems. 
46. When several of the letter keys on the subject side only or the predicate side only 
are pressed in succession, the effect is to select the combinations possessing all the letters 
marked on the keys. Thus if the keys A, B, C be pressed there will remain in the abece- 
darium only the combinations A B C D and ABC<I; and if the key D be now pressed, 
the latter combination will disappear, and A B C D will alone remain. The effect will 
be exactly the same whatever the order in which the keys are pressed, and if they be 
pressed simultaneously there will be no difference in the result. The machine thus per- 
fectly represents the commutative character of logical symbols which Mr. Boole has 
dwelt upon in pp. 29-30 of the ‘ Laws of Thought.’ What I have called the Law of 
Simplicity of logical symbols, expressed by the formula AA=A*, is also perfectly fulfilled 
in the machine ; for if the same key be pressed two or more times in succession, there 
will be no more effect than when it is pressed once. Thus the succession of keys 
A A C B B A C would have merely the effect of A B C. This applies also to the pre- 
dicate keys, but not of course to an alternation of subject and predicate keys. 
47. To impress upon the machine the condition 
A B is C D, 
or whatever combines the properties of A. and B combines the properties of C 1), we strike 
in succession the subject keys A and B, the Copula, the predicate keys C and D and 
the Full stop. The subject keys throw into the second position both the a combinations 
MDCCCLXX. 
* Pure Logic, p. 15. Boole’s ‘ Laws of Thought,’ p. 31. 
4 A 
