denotes that B and C are the names of two objects or groups which are not identical with each other. Thus we may say
Acrogens ~ Flowering plants.
Snowdon ~ The highest mountain in Great Britain.
I shall also occasionally use the sign ᔕ to signify in the most general manner the existence of any relation between the two terms connected by it. Thus ᔕ might mean not only the relations of equality or inequality, sameness or difference, but any special relation of time, place, size, causation, &c. in which one thing may stand to another. By A ᔕ B I mean, then, any two objects of thought related to each other in any conceivable manner.
General Formula of Logical Inference.
The one supreme rule of inference consists, as I have said, in the direction to affirm of anything whatever is known of its like, equal or equivalent. The Substitution of Similars is a phrase which seems aptly to express the capacity of mutual replacement existing in any two objects which are like or equivalent to a sufficient degree. It is matter for further investigation to ascertain when and for what purposes a degree of similarity less than complete identity is sufficient to warrant substitution. For the present we think only of the exact sameness expressed in the form
A = B.
Now if we take the letter C to denote any third conceivable object, and use the sign ᔕ in its stated meaning of indefinite relation, then the general formula of all inference may be thus exhibited:—
From A = B ᔕ C
we may infer A ᔕ C