we substitute this description in (γ) and (δ) we shall have self-contradictory combinations. Our second premise likewise informs us that metal is element, and applying this description to (β) we again have self-contradiction, so that there remains only (α) as a description of iron—our inference is
To represent this process of reasoning in general symbols, let
The premises of the problem take the forms
| A = AB | (1) |
|---|---|
| B = BC. | (2) |
By the Law of Duality we have
| A = AB ꖌ A b | (3) |
|---|---|
| A = AC ꖌ A c . | (4) |
Now, if we insert for A in the second side of (3) its description in (4), we obtain what I shall call the development of A with respect to B and C, namely
A = ABC ꖌ AB c ꖌ A b C ꖌ A bc . (5)
Wherever the letters A or B appear in the second side of (5) substitute their equivalents given in (1) and (2), and the results stated at full length are
The last three alternatives break the Law of Contradiction, so that
This conclusion is, indeed, no more than we could obtain by the direct process of substitution, that is by substituting for B in (1), its description in (2) as in p. 55; it is the characteristic of the Indirect process that it gives all possible logical conclusions, both those which we