The explanatory function of abstract objects: their nature and cognoscibility
We will consider the argument that claims that mathematical entities are indispensable on behalf of their explanatory function, an argument that was formulated by Baker (2001, 2003, 2005), and Colyvan (2001, 2007), to propose that it also applies (via extrapolation) to other kinds of abstract objects that are clear examples of cultural products. We understand that hand in hand with the explanatory indispensability proposal, it is possible to formulate the concrete/abstract distinction in a new way. Such a new way would go in combination with some version of the abstraction principles (schema), and would add to the already established ways identified by Lewis (1986) (also Lowe 1999; 2002 chapter 20). As a result of this project, we would have the following ways of establishing the concrete/abstract contrast: a) the way of negation (what an abstract object is not); b) the way of paradigmatic cases; c) the way of coincidence with some other distinction (i.e., universal/particular); d) the way of abstraction; e) the way of the explanatory function.
In this Project we will vindicate that this last way, the way of the explanatory function, countenances a generalized argument to postulate abstract entities of diverse ilk. We believe this has to be so because, in general, explanations of many different phenomena demand positing abstract objects; this is so, regardless of the fact that the abstract objects posited can vary together with the phenomena-or with the aspects of the phenomena-to be explained. With this generalized argument as a guiding principle, we will approach the topic of abstract objects by taking into account two levels of analysis: i) analysis of how some of the various abstract objects contribute to the explanation of different problems; ii) study of abstract objects in themselves starting from some study cases in abstract objects, explanatory function, explanatory indispensability, abstraction principles, propositions, concepts, numbers, scientific models, theoretical entities,theories.
IPS José Luis Falguera López y Concepción Martínez Vidal
Equipo de investigación: José Miguel Sagüillo Fernández-Vega, UXía Rivas Monroy, Antonio Blanco Salgueiro, Javier Vilanova Árias
Equipo de trabajo: Xavier de Donato, Víctor Verdejo Aparicio, Matteo Plebani, Mary Leng, Sofia Miguens, Charles Travis, Danielle Giaretta, Pablo Lorenzano, palolo Mancosu