ABSTRACT
We have seen that the validity of inference depends upon the relations of implication and not at all upon the truth or falsity of the premisses. It is sometimes possible to know that an implication holds between propositions without paying any attention to the internal structure, or form, of the proposi tions themselves. For example, I f p and q, then r implies Either (p or q) or r implies I f f , then either p or q, no matter what kind of propositions />, <7, r are. Frequently, however, this is not the case. When we used />, <7, r as illustrative symbols for the premisses and conclusion of a valid syllogism, we were able to represent the syllogism as an implicational form - I f p and q, then r. But nothing in this form enables us to know that No pets are ugly> All cats are pets, No cats are ugly are so related that the first two of these propositions jointly imply the third. We know this only because we can analyse the propositions into No M 's are P 's, All S's are M 's, No S's are P's; these forms show us that the first two do jointly imply the third.
