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A proof of nominalism: An exercise in successful reduction in logic

In Alexander Hieke & Hannes Leitgeb (eds.), Reduction, Abstraction, Analysis. Frankfurt: Ontos (2009)

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  1. If Logic, Definitions and the Vicious Circle Principle.Jaakko Hintikka - 2012 - Journal of Philosophical Logic 41 (2):505-517.
    In a definition (∀ x )(( x є r )↔D[ x ]) of the set r, the definiens D[ x ] must not depend on the definiendum r . This implies that all quantifiers in D[ x ] are independent of r and of (∀ x ). This cannot be implemented in the traditional first-order logic, but can be expressed in IF logic. Violations of such independence requirements are what created the typical paradoxes of set theory. Poincaré’s Vicious Circle Principle (...)
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  • An Empiricist Criterion of Meaning.Yann Benétreau-Dupin - 2011 - South African Journal of Philosophy 30 (2):95-108.
    The meaning of scientific propositions is not always expressible in terms of observable phenomena. Such propositions involve generalizations, and also terms that are theoretical constructs. I study here how to assess the meaning of scientific propositions, that is, the specific import of theoretical terms. Empiricists have expressed a concern that scientific propositions, and theoretical terms, should always be, to some degree, related to observable consequences. We can see that the former empiricist criterion of meaning only implies for theoretical terms not (...)
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