C = 3,590 feet;
then it obviously follows since “3,590 feet is the height of Snowdon,” and “Snowdon = the highest mountain in England or Wales,” that, “3,590 feet is the height of the highest mountain in England or Wales.”
One result of this general process of inference is that we may in any aggregate or complex whole replace any part by its equivalent without altering the whole. To alter is to make a difference; but if in replacing a part I make no difference, there is no alteration of the whole. Many inferences which have been very imperfectly included in logical formulas at once follow. I remember the late Prof. De Morgan remarking that all Aristotle’s logic could not prove that “Because a horse is an animal, the head of a horse is the head of an animal.” I conceive that this amounts merely to replacing in the complete notion head of a horse, the term “horse,” by its equivalent some animal or an animal. Similarly, since
The Lord Chancellor = The Speaker of the House of Lords,
it follows that
The death of the Lord Chancellor = The death of the Speaker of the House of Lords;
and any event, circumstance or thing, which stands in a certain relation to the one will stand in like relation to the other. Milton reasons in this way when he says, in his Areopagitica, “Who kills a man, kills a reasonable creature, God’s image.” If we may suppose him to mean
God’s image = man = some reasonable creature,
it follows that “The killer of a man is the killer of some reasonable creature,” and also “The killer of God’s image.”
This replacement of equivalents may be repeated over and over again to any extent. Thus if person is identical in meaning with individual, it follows that