We now proceed to consider the variety of forms of propositions in which the truths of science must be expressed. I shall endeavour to show that, however diverse these forms may be, they all admit the application of the one same principle of inference that what is true of a thing is true of the like or same. This principle holds true whatever be the kind or manner of the likeness, provided proper regard be had to its nature. Propositions may assert an identity of time, space, manner, quantity, degree, or any other circumstance in which things may agree or differ. We find an instance of a proposition concerning time in the following:--“The year in which Newton was born, was the year in which Galileo died.” This proposition expresses an approximate identity of time between two events; hence whatever is true of the year in which Galileo died is true of that in which Newton was born, and *vice versâ*. “Tower Hill is the place where Raleigh was executed” expresses an identity of place; and whatever is true of the one spot is true of the spot otherwise defined, but in reality the same. In ordinary language we have many propositions obscurely expressing identities of number, quantity, or degree. “So many men, so many minds,” is a proposition concerning number, that is to say, an equation; whatever is true of the number of men is true of the number of minds, and *vice versâ*. “The density of Mars is (nearly) the same as that of the Earth,” “The force of gravity is directly as the product of the masses, and inversely as the square of the distance,” are propositions concerning magnitude or degree. Logicians have not paid adequate attention to the great variety of propositions which can be stated by the use of the little conjunction *as*, together with *so*. “As the home so the people,” is a proposition expressing identity of manner; and a great number of similar propositions all indicating some kind of resemblance might be quoted. Whatever be the special kind of identity, all such expressions are subject to the great principle of inference; but as we shall in later parts of this work treat more particularly of inference in cases of number and magnitude, we will here confine our attention to logical propositions which involve only notions of quality. *Simple Identities.* The most important class of propositions consists of those which fall under the formula A = B,