Note 237 — Chapter VIII

On the assumption, however, that the universe of discourse can never be entirely emptied of content, Something is P may be inferred from Everything is P, and Something is not P may be inferred from Nothing is P. Again, as is shewn by Dr Venn (Symbolic Logic, pp. 142–9), the three universals All S is P, No not-S is P, All not-S is P, together establish the particular Some S is P. Any universe of discourse contains à priori four classes—(1) SP, (2) S not-P, (3) not-S P, (4) not-S not-P. All S is P negatives (2); No not-S is P negatives (3); All not-S is P negatives (4). Given these three propositions, therefore, we are able to infer that there is some SP, for this is all that we have left in the universe of discourse. As already pointed out, the assumption that the universe of discourse can never be entirely emptied of content is a necessary assumption, since it is an essential condition of a significant judgment that it relate to reality. If the universe of discourse is entirely emptied of content we must either fail to satisfy this condition, or else unconsciously transcend the assumed universe of discourse and refer to some other and wider one in which the former is affirmed not to exist.