On The Possibility of Constructing Truth - Conditions For Self - Referential Propositions

Despite the remarkable problems encountered by classificatory treatments self-referential propositions, virtually all 'solutions' proposed to the paradoxes generated by these prepositions consist, as Andre Glucksmann has put it, "either in ruling out such propositions as nonsenses, absurdities, or in accepting them while making a hierarchical distinction." 1 Clearly, the ideal solution to paradoxes of selfreference would involve a) prevention of regeneration of the paradoxes at a level above that of the original occurrence, b) delimitation of clear criteria for the solution based upon arguments drawn from principles beyond those directly related to the paradoxes themselves (e.g., in the case of hierarchical solutions, a statement of and argument for conditions for hierarchical distinctions, beyond a mere ad hoc elimination of the paradoxical cases). Karl Popper has argued, quite cogently, that making a paradoxical self-reference meaningless merely regenerates the paradox at another level, 1 and Hans Regne11 has pointed out that generally "the theory of the object-language and the metalanguage does not state the ' necessary and sufficient conditions for the appearance of the antinomies. Nor does it make evident why these antinomies sometimes, but not always, appear when the distinction between object-language and meta-language is ignored."' On the other hand, many solutions which seem to work require sacrifices (such as that of substitutiv!ty of identicals) which most of us v/ould be unwilling to make, as Fitch has noted.* These problems, I believe, stem from asking the wrong sorts of questions about self-referential propositions--specifically, 'Might such propositions be classified as true or false?' rather than 'Under what conditions might such propositions really be true or false?' It seems to me just as odd to turn to formal logic to decide if 'This sentence is true' is true, as it would to decide if "The cat is on the mat" is true (or if "'The cat is on the mat' is true" is true). Formal logic, Karl Popper has emphasized, deals with "the transmission of truth and the retransmission of falsity"' from proposition to proposition; it does not