Weak Assertion

Abstract

The paper contains references to a logical construction with two types of negation: an external (-) and internal (5) one, where the substitution of the dichotomous law of excluded middle (with the αω-α schema) by the trichotomy (αω¬αω±α) is proposed. With reference to an object belonging to a given universe and a given set of predicates some of them apply to it, whereas others do not. There can also exist such predicates which cannot be sensibly said to apply to it – they are indeterminate to it. What is proposed here is transferring these distinctions to a sentence calculus and devising a construction with a functor of weak assertion (+) as its primitive functor. This functor together with the functor of external negation allow an additional interpretation of the sentences falling into the third category described above (indirectness) whenever there is a need to express sentences referring to indirect states between the positive state and its negative counterpart.