DVA PRISTUPA PARADOKSIMA U LOGICI I MATEMATICI
TWO WAYS OF APPROACHING THE PARADOXES IN LOGIC AND MATHEMATICS

Summary/Abstract: It is usual to think of the paradoxes appearing inside a particular logical or mathematical theory as the serious obstacles hindering any further development of that theory. Paradoxes are supposed to show that a theory in question is built on an unstable, or even contradictory foundation, and thus point the need for its complete revision. However, a different view on the paradoxes is also possible. They could instead be understood as the arguments which show that some particular assumptions concerning the objects with respect to which they appear, or the ways of reasoning about them, are wrong. If treated in that way, paradoxes or their solutions could lead to some new insights into the nature of objects they concern. They could thus turn out to make a useful focus in developing the understanding of these objects. In this work, the effect that the first approach towards the paradoxes had on development of logic and mathematics, in particular set theory, will be described. Using some examples, we will try to show that the alternative view on the paradoxes or their formal equivalents actually leads to some important results in logic, and at the same time, opens the door to a new logical theory - the so-called theory of concepts.

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