third figure gives of itself, and at which the whole course of thought has aimed. Let us take another example:
All alkalis float in water;
All alkalis are metals:
Therefore some metals float in water.
When this is transposed into the first figure the minor must be converted, and thus runs: "Some metals are alkalis." It therefore merely asserts that some metals lie
in the sphere "alkalis," thus I Aikaii B .( ) Metais. ), while our
actual knowledge is that all alkalis lie in the sphere
/ Metala. >.
"metals," thus : ( / . ] It follows that if the first
figure is to be regarded as the only normal one, in order to think naturally we would have to think less than we know, and to think indefinitely while we know definitely. This assumption has too much against it. Thus in general it must be denied that when we draw inferences in the second and third figures we tacitly convert a proposition. On the contrary, the third, and also the second, figure exhibits just as rational a process of thought as the first. Let us now consider another example of the other class of the third figure, in which the separableness of two predicates is the result; on account of which one premiss must here be negative:
No Buddhist believes in a God;
Some Buddhists are rational:
Therefore some rational beings do not believe in a God.
As in the examples given above the compatibility of two properties is the problem of reflection, now their separableness is its problem, which here also must be decided by comparing them with one subject and showing
