Abstract
It is well known that Russell’s 1903 Principles of Mathematics conceived of logic as the science of structure (of propositions). The thesis of Logicism, advanced in the work, held that the intuitions of all of non-applied mathematics could be shown to be logical intuitions—intuitions based on the science of propositions. Logicism, of course, died at Russell’s own hands. Valiant as it was, the ramified type-theory of the 1910 Principia Mathematica did not salvage Logicism from Russell’s paradoxes (of classes and predication). The system offers no genuine “solution” of the paradoxes. It requires an infinity axiom and an axiom (schema) of reducibility—neither of which can be counted as truths of logic.
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Landini, G. (1998). Russell’s Intensional Logic of Propositions: A Resurrection of Logicism?. In: Orilia, F., Rapaport, W.J. (eds) Thought, Language, and Ontology. Philosophical Studies Series, vol 76. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5052-1_4
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DOI: https://doi.org/10.1007/978-94-011-5052-1_4
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