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Regular version of the site

Book chapter

Виртуальные объекты, интенциональные объекты и возможные миры

С. 186-213.

Troubles with possible objects force some modal theorists resort to the help of the quantification over such entities. Unfortunately, introducing the special quantifier for such objects (the usual remedy in such a case) we are faced with the situation where the definition of impossible objects splits: we obtain the definition of impossible objects and the definition of virtual ones respectively. Striving to bypass the question of the status of such entities K. Lambert and B. van Fraassen suggest to exploit the substitutional quantification elaborated by Beth, Marcus, Dunn and others. In this case we quantify not objects but terms and the $-quantifier  means “under the substitution of some term”. An exploitation of substitutional quantification suggests us to make good use of St. Leśniewski’s system of Ontology while analyzing the notion of virtual object since in his system the mechanism of quantification encompasses substituional aspects from the very beginning. Another advantage of such using is that the notions of “existence” and “object” are introduced by means of definitions. But in order to deal with the virtual objects in the framework of Leśniewski’ system we need to use its modal extension, e.g. S. Lebiediewa’s system, which would be obtained by enriching Leśniewski’s Ontology with the axioms of Łukasiewicz’s four-valued modal logics. Unfortunately there is no possible world semantics suitable for these aims. Another alternatives give us author’s version of so called non-fregean logics (introduced firstly by polish logician R. Suszko whose “situational” semantics is essentially based on ideas of L. Wittgenstein). Here we have the connectives of situational implication (situational involvement for propositions) and situational involvement of objects (one object situational involve another one) when objects are determined by the set of situations in which they participate. In semantics of such version of non-fregean logics the possible worlds are represented by the maximally large situations. But either in case of Lesniewski’s Ontology or in case of non-fregean logics we have an opportunity of direct work with objects and have an opportunity to produce both possible and virtual objects by means of intentional (object modal) operators. Here we also obtain a kind of worlds but they are not possible worlds but “intentional” worlds constituted by the intentional analogues of possible and virtual objects.