To show this let
A = carbon,
B = metallic,
C = capable of powerful magnetic influence.
The premises readily take the forms
| b = bc, | (1) |
| A = Ab, | (2) |
and substitution for b in (2) by means of (1) gives the conclusion
| A = Abc. | (3) |
Our principle of inference then includes the rule of negative premises whenever it is true, and discriminates correctly between the cases where it does and does not hold true.
The paralogism, anciently called the Fallacy of Undistributed Middle, is also easily exhibited and infallibly avoided by our system. Let the premises be
| Hydrogen is an element, | (1) |
| All metals are elements. | (2) |