Is Russell's vicious circle principle false or meaningless?

P. Vardy asserts the thesis that the vicious circle principle has the same structure as Russell's paradox. But structure is not the thing itself. It is the thing objectivated from the wiewpoint of a mathematician. So this structure can be expressed in a mathematical formalism, e. g. the Λ-calculus. Russell's paradox is understood as a result of the error of taking purely logical concepts, like negation, as lkiewise formalisable without change of meaning. The illusion of meaning in the liar's proposition: Yl'am telling a lie can also be explained be the formalisable self-referential structure of this proposition. Yet it remains an illusion because the logical intention cannot follow the structure

Study of logical paradoxes

By a paradox we understand a seemingly true statement or set of statements which lead by valid deduction to contradictory statements. Logical paradoxes - paradoxes which involve logical concepts - are in fact as old as the history of logic. The Liar paradox, for instance, goes back to Epimenides (6th century B.C.?). In the late 19th century a new impetus v/as given to the investigation of logical paradoxes by the discovery of new logico-mathematical paradoxes such as those of Russell and Burali- Porti. This came about in the course of attempts to give mathematics a rigorous axiomatic foundation. Sometimes a distinction is maintained between a paradox and an antinomy. In a paradox, it is said, semantical notions are involved and a certain "oddity", "strangeness", or what may be called "paradoxical situation", resides in its construction. The resolution of a paradox is therefore not simply a matter of removing contradiction, but also requires clarifying and removing the "oddity". On the other hand, an antinomy is said to consist in the derivation of a contradiction in an axiomatic system and its resolution lies in revising the system so as to avoid the contradiction. In discussing paradoxes and antinomies, we shall not be strictly bound by this usage of these terms: we use "paradox" and "antinomy" interchangeably. Indeed, from our point of view, even antinomies in an axiomatic system ultimately need semantic clarification and thus removal of paradoxical situations