- 50 Downloads
In this paper, the authors briefly summarize how object theory uses definite descriptions to identify the denotations of the individual terms of theoretical mathematics and then further develop their object-theoretic philosophy of mathematics by showing how it has the resources to address some objections recently raised against the theory. Certain ‘canonical’ descriptions of object theory, which are guaranteed to denote, correctly identify mathematical objects for each mathematical theory T, independently of how well someone understands the descriptive condition. And to have a false belief about some particular mathematical object is not to have a true belief about some different mathematical object.
KeywordsPhilosophy of mathematics Abstract objects Definite descriptions Denotation of individual terms
- Benacerraf, P. (1981). Frege: The last logicist. In P. French et al. (Ed.), Midwest studies in philosophy: VI (pp. 17–35). Minneapolis: University of Minnesota Press [reference is to the reprint in Demopoulos, W. (1995). Frege’s philosophy of mathematics (pp. 44–67). Cambridge, MA: Harvard University Press.Google Scholar
- Buijsman, S. (2017). Referring to mathematical objects via definite descriptions. Philosophia Mathematica, 3(25), 128–138.Google Scholar
- Zalta, E. (1988). Intensional logic and the metaphysics of intentionality. Cambridge, MA: MIT Press.Google Scholar
- Zalta, E. (2001). Fregean senses, modes of presentation, and concepts. Philosophical Perspectives (Noûs Supplement), 15, 335–359.Google Scholar