Collapse, Plurals and Sets


  • Eduardo Alejandro Barrio Conicet - Universidad de Buenos Aires



This paper raises the question under what circumstances a plurality forms a set. My main point is that not always all things form sets. A provocative way of presenting my position is that, as a result of my approach, there are more pluralities than sets. Another way of presenting the same thesis claims that there are ways of talking about objects that do not always collapse into sets. My argument is related to expressive powers of formal languages. Assuming classical logic, I show that if all plurality form a set and the quantifiers are absolutely general, then one gets a trivial theory. So, by reductio, one has to abandon one of the premiss. Then, I argue against the collapse of the pluralities into sets. What I am advocating is that the thesis of collapse limits important applications of the plural logic in model theory, when it is assumed that the quantifiers are absolutely general.

Author Biography

Eduardo Alejandro Barrio, Conicet - Universidad de Buenos Aires

Investigador Independiente del Conicet y Profesor Regular de Lógica y Lógica Superior del Departamento de Filosofía de la UBA. Ha sido profesor visitante de las universidades de Oxford, MIT y Munich. Ha dirigido varios proyectos de cooperación internacional de la British Academy (University of Oxford) y de la DAAD (MCMP - Munchen). Recientemente, ha publicado La Lógica de la Verdad (en EUDEBA, BA, 2014) y los siguientes artículos: (junto con Lucas Rosenblatt y Diego Tajer)
"The Logic of Strict-Tolerant Logic" Journal of Philosophical Logic; Año: 2014. "Expresabilidad, Validez y Recursos Lógicos"Crítica; Lugar: México DF; Año: 2014. (junto con Lavinia Picollo) "Notes on w-inconsistent Theories of Truth in Second-Order Languages" REVIEW OF SYMBOLIC LOGIC; Lugar: Cambridge; Año: 2013 vol. VI p. 733 - 741, "Absoluta Generalidad y Validez lógica" NPSF (Notae Philosophicae Scientiae Formalis); Año: 2013 vol. 2 p. 106 - 127.