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Russell’s Theory of Types as Solution to the Semantical and Theory of Sets Paradoxes
The paper represents Russell’s Type theory as a way to solve semantic and set theoretic paradoxes. A remarkable feature of this theory is that it is proposed as a resolution of both of these groups of paradoxes – the other popular proposals are directed only to one of these groups: either to the semanticparadoxes or to the paradoxes of set theoretic. It is contended that for this to be possible a price has to be paid which is both ontological (the acceptance of the existence of the abstract entities of propositional functions and propositions) and methodological (setting this ontology as a basis of logic).
Keywords: Russell, Type theory, semantic paradoxes, paradoxes in set theory
After presenting a possible classification of paradoxes in general, a particular paradox is considered in the paper. It is maintained that there are no logical fallacies in the argumentation of the paradox but rather that there is a mistake of not taking into account all possible consequences of the premises. Nonetheless the conclusion is that the problem presented by the paradox is not resolved by showing that mistake, and it is suggested that because of this the paradox should be considered very seriously and its importance is comparable with the liar paradox.
Key words: paradox, liar paradox, logical fallacy, argumentation