illustration of the mode of using this result the argument following:
| Vowels are letters which can be sounded alone, | (1) |
|---|---|
| The letter w cannot be sounded alone; | (2) |
| Therefore the letter w is not a vowel. | (3) |
Here we have a definition (1), and a comparison of a thing with that definition (2), leading to exclusion of the thing from the class defined.
Taking the terms
the premises are plainly of the forms
| A = B, | (1) |
|---|---|
| C = b C. | (2) |
Now by the Indirect method we obtain from (1) the Contrapositive
and inserting in (2) the equivalent for b we have
C = a C, (3)
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