OBJETOS ABSTRACTOS: PROPUESTAS A FAVOR Y EN CONTRA. UNA SOLUCION NEO-CARNAPIANA

Abstract Objects: For and Against.A Neo-Carnapian Way Out

https://www.usc.es/gl/investigacion/proxectos/aofa/

In this new project, we intend to go beyond Carnap’s thought to pursue a new interpretation of his idea that ontological commitments are always internal to a linguistic framework. The novelty of the proposal would result from connecting Carnap’s idea to Thomasson’s conception of some abstract objects as artifacts. This possible interpretation would not be trivial since there are some difficulties with it; one of them is that Thomasson presumably wants to distinguish between artifacts and naturally occurring objects, whereas in Carnap’s view tables and chairs are as much the creatures of linguistic frameworks as are numbers or fictional characters. A neo-Carnapian, and probably heterodox, way to explore this could be to consider that all the objects provided by a linguistic framework are constituted objects—be they individuals, properties or relations-— and hence, abstract objects. Moreover, it could be considered that some of them (not necessarily all) stand for concrete objects. Concrete objects would be posited as targets, as whatever is out there that abstract objects mean to represent. Positing them as targets would be compatible with defending that some of the concrete objects advanced by the theories (or stories) really exist, but also with maintaining an agnostic position about which are the existing concrete objects. In both cases, it is assumed that there are concrete entities. This would be so because we do mean to take empirical sciences seriously and, in order to do so it has to be assumed that there are concrete objects, while there is no need to believe that we really know which they are.

In relation to the the existence of abstract objects, we will explore an original proposal advocating platonism but not heavy duty Platonism. The proposal connects, once more, ideas from Thomasson about the nature of artifacts, Zalta’s theory of abstract objects and Carnap’s idea that existence questions make sense only within a linguistic framework. An attractive feature of De Donato and Falguera’s account is that it is not limited to the case of abstract mathematical objects, but also accounts for other abstract objects that play important roles in our scientific theorizing, such as scientific models, scientific laws and references of theoretical terms.

This way of thinking about abstract objects has led us to consider that there might be an account of our knowledge of abstract objects that is compatible with agnostic, Carnapian and constitutivist positions concerning their ontology. Assessing the latter hypothesis involves clarifying why the epistemological account of the sort just mentioned is not compatible with a fictionalist or a heavy realist position regarding the existence of abstract objects.

Finally, It will be essential for our project to contrast this view with different sorts of Platonism—not only Lightweight but also Heavy Duty Platonisms—and to see how the contrast works in different philosophical arenas. That is so because it is crucial to the hypothesized view that abstract objects are ubiquitous (even if we acknowledge the special relevance of posited abstract mathematical entities). Hence, we need to see how it works, not only at the generic level of analysis, but also for particular fields and kinds of abstract entities.

KEY WORDS

Abstract object, Carnap, abstract artifact, Lightweight Platonism, Heavy Duty Platonism, constitutivism