Formal ontology and nominalistic semantics in B. Russel’s philosophy of mathematics
V.V. Tzelishchev
Institute of philosophy and law SB RAS, Novosibirsk
Keywords: Substitutional theory, ontology, formal system, set-theoretical paradoxes, Principia Mathematica, Russell, elimination, propositional function, nominalism, semantics
Abstract
The article is devoted to formal ontology in the systems proposed by В. Russell between his Principles of Mathematics (1903) and Principia Mathematica (with A. N. Whitehead-1911-1913). Based on manuscripts published in the 1970 's from the archive B. Russell, it is described the unknown system Substitutional theory proposed by Russell for resolution of the set-theoretic paradoxes, along with the well-known Zigzag theory and the Theory of limited size. It is shown that Substitutional theory is a version of elimination ontology of propositional functions, according to strategy of nominalistic elimination of ontology classes within No-Class theory. It is demonstrated a possibility of emulating with Substitutional theory of Simple theory of types. Explained the reason for abandoning Substitutional theory in favor of Ramified theory of Types in Principia Mathematica, due to the opening of the paradox of propositional functions. It is demonstrated the benefits of Substitutional theory and possibility of remedy its weaknesses as foundations of mathematics.
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