first place, a complete series of all the combinations of terms involved in it. If there be two terms A and B, the utmost variety of combinations in which they can appear are
| AB | a B |
|---|---|
| A b | ab . |
The term A appears in the first and second; B in the first and third; a in the third and fourth; and b in the second and fourth. Now if we have any premise, say
we must ascertain which of these combinations will be rendered self-contradictory by substitution; the second and third will have to be struck out, and there will remain only
Hence we draw the following inferences
Exactly the same method must be followed when a question involves a greater number of terms. Thus by the Law of Duality the three terms A, B, C, give rise to eight conceivable combinations, namely
| ABC | (α) | a BC | (ε) |
|---|---|---|---|
| AB c | (β) | a B c | (ζ) |
| A b C | (γ) | ab C | (η) |
| A bc | (δ) | abc . | (θ) |
The development of the term A is formed by the first four of these; for B we must select (α), (β), (ε), (ζ); C consists of (α), (γ), (ε), (η); b of (γ), (δ), (η), (θ), and so on.
Now if we want to investigate completely the meaning of the premises
| A = AB | (1) |
|---|---|
| B = BC | (2) |
we examine each of the eight combinations as regards each premise; (γ) and (δ) are contradicted by (1), and (β)