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Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia

Volume 12, Issue 1, Enero 1997

Francisco Rodriguez Consuegra
Pages 125-137

Nominal definitions and logical consequence in the Peano School

This paper is devoted to show the development of some of the model-theoretic ideas which are clearly present in the main members of the Peano school (Peano himself, Burali-Forti, Pieri and Padoa) as a result of their conception of nominal definitions. Also, their semantic definition of logical consequence (Pieri, Padoa) is viewed as one of the outcomes of that conception. Some examples of their use of the expression “nominal definition” are presented first. Second, the main advantages of this kind of definition, as they saw them, are briefly explained, mainly in a philosophical context. Finally, already in the kernel of the paper, some of the details of the model-theoretic view itself are shown, first in Peano, then in Pieri and Padoa, including in both cases some study of their semantic definitions of logical consequence.

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