Construction of proposition: apoha and non-classical logics

This talk will aim to provide an account of the apoha theory of delineation by analogy with the construction of propositions in some non-classical logics. In such logics, not all sets of possible worlds are taken to be propositions. In quantum logic, for example, an arbitrary set of states may not exactly represent the semantical counterpart of a legitimate proposition. Moreover, the negation operator in intuitionistic logic is essentially a closure operator. A well-known result is that the double-negated propositions of intuitionistic logic behave as if they were propositions of classical logic. In logics where disjunction behaves differently from classical disjunction, a closure operator often delivers a certain kind of well-behaved proposition. In some cases, it constructs a proposition which is legitimate in a semantics where states as primitive. This talk will propose a reading of the notion of apoha in Yogacara as a closure operation. In Yogacara, a language consists of names, phrases, and sentences. All components are classified, on the basis of no-entity and no-mind, as dependent apon mental phenomena. Names are the epistemic basis of the world. The application of a name leads to nimitta, and the application of language leads to misplacing non-existent artha as real. Thus, the meaning of a word does not correspond to a positive and previously existing entity; its delimitation is circumscribed only negatively in relation to words. The same applies to concepts as to words. Apoha, as an epistemic closure, plays an essential role in construction of images out of emptiness. A consequence of this proposal is that understanding in Yogacara can be read as the counterpart of a completeness proof in formal logic.