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A formal theory of substances, qualities, and universals
 In Achille Varzi and Laure Vieu, editors, Formal Ontology in Information Systems (FOIS'04
, 2004
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Russell's Paradox Of The Totality Of Propositions
, 2000
"... on this analysis, and although Oksanen quoted Russell's description of the paradox in detail, he did not show how it is explained in NFU after his resolution of the other related modal paradoxes; in fact, it is not at all clear how this might be done in NFU. 1PoM, p. 527. 2See, e.g., Grim ..."
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on this analysis, and although Oksanen quoted Russell's description of the paradox in detail, he did not show how it is explained in NFU after his resolution of the other related modal paradoxes; in fact, it is not at all clear how this might be done in NFU. 1PoM, p. 527. 2See, e.g., Grim 1991, pp. 92f. 3See, e.g., Grim 1991, p. 119 and Jubien 1988, p. 307. 4See Oksanen 1999. NFU is a modified version of Quine's system NF. It was first described in Jenson 1968 and recently has been extensively developed in Holmes 1999. Nordic Journal of Philosophical Logic, Vol. 5, No. 1, pp. 2537. 2000 Taylor & Francis. 26 nino b. cocchiarella One reason why Russell's argument is dicult to reconstruct in NFU is that it is based on the logic of propositions, and implicitly in that regard on a theory of predication rather than a theory of membership. A mo
Handbook of the History of Logic. Volume 6
"... ABSTRACT: Here is a crude list, possibly summarizing the role of paradoxes within the framework of mathematical logic: 1. directly motivating important theories (e.g. type theory, axiomatic set theory, combinatory logic); 2. suggesting methods of proving fundamental metamathematical results (fixed p ..."
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ABSTRACT: Here is a crude list, possibly summarizing the role of paradoxes within the framework of mathematical logic: 1. directly motivating important theories (e.g. type theory, axiomatic set theory, combinatory logic); 2. suggesting methods of proving fundamental metamathematical results (fixed point theorems, incompleteness, undecidability, undefinability); 3. applying inductive definability and generalized recursion; 4. introducing new semantical methods (e. g. revision theory, semiinductive definitions, which require nontrivial set theoretic results); 5. (partly) enhancing new axioms in set theory: the case of antifoundation AFA and the mathematics of circular phenomena; 6. suggesting the investigation of nonclassical logical systems, from contractionfree and manyvalued logics to systems with generalized quantifiers; 7. suggesting frameworks with flexible typing for the foundations of Mathematics and Computer Science; 8. applying forms of selfreferential truth and in Artificial Intelligence, Theoretical Linguistics, etc. Below we attempt to shed some light on the genesis of the issues 1–8 through the history of the paradoxes in the twentieth century, with a special emphasis on semantical aspects.