AC = ABC
by an exactly similar act of substitution; and in every other case the rule will be found capable of verification by the principle of inference. The process when performed as here described will be quite free from the liability to error which I have shown[55] to exist in “Immediate Inference by added Determinants,” as described by Dr. Thomson.[56]
Inference with Two Simple Identities.
One of the most common forms of inference, and one to which I shall especially direct attention, is practised with two simple identities. From the two statements that “London is the capital of England” and “London is the most populous city in the world,” we instantaneously draw the conclusion that “The capital of England is the most populous city in the world.” Similarly, from the identities
Hydrogen = Substance of least density,
Hydrogen = Substance of least atomic weight,
we infer
Substance of least density = Substance of least atomic weight.
The general form of the argument is exhibited in the symbols
| B = A | (1) | |
| B = C | (2) | |
| hence | A = C. | (3) |