Deductive practice and methodological theory
- Concha Martínez Vidal (dir. congr.)
- José L. Falguera López (dir. congr.)
- José M. Sagüillo (dir. congr.)
- Víctor M. Verdejo Aparicio (dir. congr.)
- Martín Pereira Fariña (dir. congr.)
Editorial: Servicio de Publicaciones e Intercambio Científico ; Universidad de Santiago de Compostela
ISBN: 978-84-9887-939-1
Ano de publicación: 2012
Páxinas: 682-688
Congreso: Sociedad de Lógica, Metodología y Filosofía de la Ciencia en España. Congreso (7. 2012. Santiago de Compostela)
Tipo: Achega congreso
Resumo
The issue of this paper is whether mathematical logic is descriptive of the underlying logic exhibited in mathematical practice or whether it is rather normative in indicating how such practice should be conducted. Once the meaning of ‘normativity’ in the present context is clarified as pertaining to pragmatics, the question arises where to locate normativity, whether in mathematical practice, in logical theory, or in both. The discussion is framed under the view of Logic as model (Corcoran 1973), the view that mathematical logic is about the underlying logic found in the prior practice of proof in real mathematics, and what I call Shapiro’s dilemma (2001), the difficulty in articulating how the view of logic as model could illuminate in what sense—if any—a given logical theory (a mathematical model of logic) can be said to be normative or can in fact be used to discriminate good from bad deductive practice.