О жуликах и ворах, или о том, содержит ли «парадокс Ябло» самореференцию

Abstract

Исследуется парадокс Стивена Ябло, а также рассматривается ряд вопросов, связанных с природой парадоксальности для финитных и инфинитных последовательностей предложений типа Лжеца. В частности, поднимаются и анализируются две тесно связанные друг с другом проблемы: возможность построения финитной версии этого парадокса и вопрос о наличии или отсутствии признаков самореференции в предложенной Стивеном Ябло оригинальной инфинитной версии парадокса.

The article studies Yablo's paradox, and discusses a number of issues related to paradoxical nature of finite and infinite sequence of Liar-like sentences. In particular, here was raised and analyzed two closely related to each other problems: the possibility of constructing a finite version of this paradox and issue about the presence or absence of self-reference signs in original infinite version of the paradox which was proposed by Stephen Yablo. Finite version of Yablo's paradox is constructed with using so-called double-referential cycles for a groups of three sentences Sn, Sn+1, Sn+2. Such a group of sentences is an elementary part of any version of Yablo-like paradox (including finite and infinite versions). Formed by these groups of sentences the minimal segment of reference has no signs of selfreference, but created on the basis of these groups of sentences a finite cluster of reference, which presents the finite version of Yablo's paradox, contains a circular structure and some self-reference links. Thus, the paradoxical nature of any Yablo-like sequences of sentences (both finite and infinite) is closely related to a kind of referential excess, which occurs due to the presence double-referential cycles into such sequences of sentences. Analysis of the finite version of Yablo's paradox allows to make analogous conclusion about the presence of self-referential signs in original infinite version of the paradox which was proposed by Stephen Yablo. This conclusion forces us to recognize accuracy of widespread and fairly stable logical-linguistic belief, according to which the origin of any problems with the paradoxical for different sets of sentences is the use of semantically closed language, or to recognize the need to expand our understanding of the self-referential phenomenon and to consider any language, which doesn't inform us about anything beyond his borders, as a self-referential language.