In a recent series of papers F. Sommers has presented a logical theory which, if generally understood by philosophers, could revolutionize our views on logic and ontology. 1 Nevertheless, Sommers' presentation is not completely flawless. I want to show here that he has an unacceptable view of existence and that a correct view can be gleaned from his own previous work.
What Sommers' logic is clearly meant to replace is the modern predicate calculus, which, by allowing existence to be a syntactic logical operator rather than an extra-logical predicate, 'amounts to a system of formal ontology'. One of the most important ontological consequences of the predicate calculus is the thesis: Everything exists. 2 Unexpectedly, Sommers, too, seems to be committed to this thesis by statements he makes in the latest paper in the series mentioned above. He says (p. 161), "... since 'fails-to-exist' is not true of anything, 'exists' differs from most predicates in not having an applicable contrary." And later (p. 172): "... 'is inexistent' is never true of a thing.., the contrary of 'exists' is never applicable". Were this indeed the case, then 'exists' would be a predicate, but a special one in that, unlike normal predicates, its contrary is inapplicable. 'Red' is a normal predicate. We can sensibly say both 'somethings are red' and 'somethings are nonred (fail-to-be-red)'. But, supposedly, we cannot sensibly say 'something does not exist (is inexistent, fails-to-exist)'. Nothing fails-to-exist. Everything exists.
This thesis is neither warranted nor needed by Sommers' theory. His mistake here is due to his failure to take a note of a distinction which he himself introduced and argued so cogently for in an earlier series of papers. ~ In that series Sommers distinguished between a term, P, and the corresponding 'absolute term',/P/. An absolute term is equivalent to the disjunction of the term and its (logical) contrary (i.e./P/= P or nonP). All terms, including 'exists', have a corresponding contrary, and thus a