or, in words—In whatever relation a thing stands to a second thing, in the same relation it stands to the like or equivalent of that second thing. The identity between A and B allows us indifferently to place A where B was, or B where A was; and there is no limit to the variety of special meanings which we can bestow upon the signs used in this formula consistently with its truth. Thus if we first specify only the meaning of the sign ᔕ, we may say that if C is the weight of B, then C is also the weight of A. Similarly
If C is the father of B, C is the father of A;
If C is a fragment of B, C is a fragment of A;
If C is a quality of B, C is a quality of A;
If C is a species of B, C is a species of A;
If C is the equal of B, C is the equal of A;
and so on ad infinitum.
We may also endow with special meanings the letter-terms A, B, and C, and the process of inference will never be false. Thus let the sign ᔕ mean “is height of,” and let
A = Snowdon,
B = Highest mountain in England or Wales,