or “the letter w is not a vowel.”
Miscellaneous Examples of the Method.
We can apply the Indirect Method of Inference however many may be the terms involved or the premises containing those terms. As the working of the method is best learnt from examples, I will take a case of two premises forming the syllogism Barbara: thus
| Iron is metal | (1) |
| Metal is element. | (2) |
If we want to ascertain what inference is possible concerning the term Iron, we develop the term by the Law of Duality. Iron must be either metal or not-metal; iron which is metal must be either element or not-element; and similarly iron which is not-metal must be either element or not-element. There are then altogether four alternatives among which the description of iron must be contained; thus
| Iron, metal, element, | (α) |
| Iron, metal, not-element, | (β) |
| Iron, not-metal, element, | (γ) |
| Iron, not-metal, not-element. | (δ) |
Our first premise informs us that iron is a metal, and if 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
Iron = iron, metal, element.
To represent this process of reasoning in general symbols, let
A = iron
B = metal
C = element,