LanCog Logic Seminar Series
Friday, March 10, 10:00—12:00 (UTC)
The University of Lisbon
Faculty of Letters, room B112.G (Library wing)
University San Raffaele, Milan
The Logical Ontology of Abstractionism
Neologicism aims at founding arithmetic on full second-order logic and Hume’s Principle, which states that the number of the Fs is identical with the number of the Gs if, and only if, there are as many Fs as Gs, and vice versa. Nevertheless, Neologicism faces the problem of the logical ontology (), according to which the underlying second-order logic is ontologically committal. In this paper, such a problem will be tackled by substituting second-order logic by Boolos’ plural logic ([2, 3]), augmented by the Plural Frege Quantifier Fmodelled on . The resulting theory (PHP) interprets second-order Peano arithmetic PA2. Its ontological innocence will be evaluated. In this respect, PHP provides an alternative that solves the problem of the logical ontology pervading Neologicism.
 Antonelli, A. (2010), ‘Numerical Abstraction via the Frege Quantifier’, Notre Dame Journal of Formal Logic 51(2): 161–179.
 Boolos, G. (1998a), ‘To be is to be the Value of a Variable (or the Values of Some Variables)’, in : 54–72.
 Boolos, G. (1998b), ‘Nominalist Platonism’, in : 73–87.
 Boolos, G. (1998c), Logic, Logic, and Logic, J. Burgess & R. Jeffrey (eds.), Cambridge, MA: Harvard University Press.
 Hale, B. & Wright, C. (2001), The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics, Oxford University Press.