I should weary the reader if I attempted to illustrate the multitude of forms which disjunctive reasoning may take; and as in the next chapter we shall be constantly treating the subject, I must here restrict myself to a single instance. A very common process of reasoning consists in the determination of the name of a thing by the successive exclusion of alternatives, a process called by the old name abscissio infiniti. Take the case:
| Red-coloured metal is either copper or gold | (1) |
| Copper is dissolved by nitric acid | (2) |
| This specimen is red-coloured metal | (3) |
| This specimen is not dissolved by nitric acid | (4) |
| Therefore, this specimen consists of gold | (5) |
Let us assign the letter-symbols thus—
A = this specimen
B = red-coloured metal
C = copper
D = gold
E = dissolved by nitric acid.
Assuming that the alternatives copper or gold are intended to be exclusive, as just explained in the case of fresh and salt water, the premises may be stated in the forms
| B = BCd ꖌ BcD | (1) |
| C = CE | (2) |
| A = AB | (3) |
| A = Ae | (4) |
Substituting for C in (1) by means of (2) we get
B = BCdE ꖌ BcD
From (3) and (4) we may infer likewise
A = ABe