516 
PROFESSOR JEVONS ON THE MECHANICAL 
1st. A, B, Copula, C, d , Conjunction, c, D, Full stop. 
2nd. B, C, Copula, A, D, Conjunction, a, d , Full stop. 
3rd. a , b, Copula, c, d, Full stop. 
c, d , Copula, «, b , Full stop. 
There will then be found to remain in the abecedarium the following combinations : 
ABcD «BCd 
AJ CD aBcD 
A b C d abed 
A b c D 
On pressing the subject key A, the A combinations printed above in the left-hand 
column will alone remain, and on examining them they yield the same conclusion as 
Boole's equation (p. 120), namely, “Wherever the property A is present, there either 
C is present and B absent, or C is absent.” 
Pressing the full-stop key to restore the a combinations, and then the keys b , C, we 
have the two combinations 
A5CD, 
A b C d, 
from which we read Boole’s conclusion, p. 120, “ Wherever the property C is present, 
and the property B absent, there the property A is present.” In a similar manner the 
other conclusions given by Boole in p. 129 can be drawn from the abecedarium. 
52. It is to be allowed that a certain mental process of interpreting and reducing to 
simple terms the indications of the combinations is required, for which no mechanical 
provision is made in the machine as at present constructed, but an exactly similar mental 
process is required in the Indirect Process of Inference, as stated in my ‘ Pure Logic,’ 
pp. 44, 45 ; and equivalent processes are necessary in Boole’s mathematical system. The 
machine does not therefore supersede the use of mental agency altogether, but it never- 
theless supersedes it in most important steps of the process. 
53. This mechanical process of inference proceeds by the continual selection and 
classification of the conceivable combinations into three or four groups. It should be 
noticed that in Boole’s system the same groups are indicated by certain quasi-mathe- 
matical symbols as follows : — 
the coefficient £ indicates an excluded combination 
„ x included „ 
„ x „ inconsistent „ 
„ -jj „ inconsistent „ 
It is exceedingly questionable whether there is any analogy at all between the signi- 
fications of these symbols in mathematics and those which Boole imposed upon them 
in logic. In reality the symbol 1 denotes in Boole’s logic inclusion of a combination 
under a term, and 0 exclusion. Accordingly -jj indicates that the combination is included 
in the subject and not in the predicate, and is therefore inconsistent with the proposition, 
