Abstract

Non-existence provides big problems for ontology and modest for logic. Logical problems of non-existence consist in licensing inferences in which sentences with empty terms are involved. The standard predicate logic solves this question by presupposing that every individual constant has an object to which it refers. This means that empty domains are excluded from semantics for the first-order logic. However, there is a temptation to consider logic without existential presuppositions.The ontological problem of non-existence leads to the question of the meaning of 'nothing'. We encounter "various conceptions of nothing" in the history of philosophy from Parmenides to our times. However, nothing is always a negation of being. Since we have distributive and collective concepts of being, we also should distinguish nothing in the distributive and mereological meaning. This difference is important because only the former leads to the paradox of nothing of all nothings, analogical to the paradox of all sets. A closer analysis of the nothing in the distributive sense shows that any meaningful talk about non-existence requires a relativisation to a fixed domain of discourse. This seems; to entail that the empty set is the formal model of nothing what means that the concept of absolute nothing in the distributive sense is simply inconsistent. To some extent, being and nothing are mutually dual. This motivates that the concept of nothing is governed by so-called dual logic connected with processes of rejection. More specifically, statements on "nothing" are not asserted but rejected.