- A B C D e F
- A B c D E f
- A b C D E F
- A b C D e F
- A b c D e F
- a B C D E f
- a B c D E f
- a b C D e F
- a b C f e F
- a b c D e f
- a b c d e f
Induction of Simple Identities .
Many important laws of nature are expressible in the form of simple identities, and I can at once adduce them as examples to illustrate what I have said of the difficulty of the inverse process of induction. Two phenomena are conjoined. Thus all gravitating matter is exactly coincident with all matter possessing inertia; where one property appears, the other likewise appears. All crystals of the cubical system, are all the crystals which do not doubly refract light. All exogenous plants are, with some exceptions, those which have two cotyledons or seed-leaves.
A little reflection will show that there is no direct and infallible process by which such complete coincidences may be discovered. Natural objects are aggregates of many qualities, and any one of those qualities may prove to be in close connection with some others. If each of a numerous group of objects is endowed with a hundred distinct physical or chemical qualities, there will be no less than 1/2(100 × 99) or 4950 pairs of qualities, which may be connected, and it will evidently be a matter of great intricacy and labour to ascertain exactly which qualities are connected by any simple law.
One principal source of difficulty is that the finite powers of the human mind are not sufficient to compare by a single act any large group of objects with another large group. We cannot hold in the conscious possession of the mind at any one moment more than five or six different ideas. Hence we must treat any more complex group by successive acts of attention. The reader will perceive by an almost individual act of comparison that the words Roma and Mora contain the same letters. He may perhaps see at a glance whether the same is true of Causal and Casual, and of Logica and Caligo. To assure himself that the letters in Astronomers make No more stars, that Serpens in akuleo is an anagram of Joannes Keplerus, or Great gun do us a sum an anagram of Augustus de Morgan, it will certainly be necessary to break up the act of comparison into several successive acts. The process will acquire a double character, and will consist in ascertaining that each letter of the first group is among the letters of the second group, and vice versâ, that each letter of the second is among those of the first group. In the same way we can only prove that two long lists of names are identical, by showing that each name in one list occurs in the other, and vice versâ.