Conceptual pluralism is the view that ordinary concepts can be adequately formalized in multiple different ways. Which formalization ought to be chosen depends on the intended usage of this formalized concept in a non-ordinary, often scientific application. In this talk I will argue in favour of conceptual pluralism and against its converse, conceptual monism. As a historical and methodological background I will draw on the works of Rudolf Carnap, particularly his method of explication and his principle of tolerance.

In the first part of the talk I will present the Sorites paradox (or the "Paradox of the Heap") as a case study to illustrate the difficulties that arise when formalizing vague predicates. I will consider Timothy Williamson's Classical Logic and Nicholas J. J. Smith's Fuzzy Logic as two competing monistic solutions to the paradox. Using this case study I will show that, depending on the intended application, each formal account of vague predicates can be useful and thus admissible.

Afterwards, in the second part I will elaborate on the position of conceptual pluralism by arguing that Williamson and Smith can be said the be talking past each other. That is, they are attempting to formalize different aspects of the ordinary concept of vagueness and thus naturally arrive at different formal concepts. I will attempt to diagnose whether their dispute is merely verbal or whether it could count as a substantive metalinguistic negotiation, arguing that the dispute could only be substantive insofar as they are making a normative claim as to which concept of vagueness one ought to formalize. Such a claim would amount to the claim that a particular monistic account of vagueness is correct due to the normative constraints that the ordinary concept puts on the formalized concept.

Finally, in the third part I will argue that such a normative claim cannot be defended, since which concept one "should" formalize depends on the intended application of the ordinary concept in a formal context. This application is not sufficiently determined by the ordinary concept, which is why a dispute about the correct application of an ordinary concept would again be merely verbal. It is not a substantive dispute, for instance, whether Williamson's or Smith's intended applications are the "right" ones.

Conceptual pluralism can hence be motivated due to the existence of multiple possible applications one could intend when formalizing an ordinary concept.

Literature
R. Carnap, The Logical Syntax of Language. London: Routledge, 1937.
R. Carnap, "P. F. Strawson on Linguistic Naturalism," in Schilpp (ed.), The Philosophy of Rudolf Carnap, La Salle: Open Court, pp. 933–940, 1963.
N. J. J. Smith, Vagueness and Degrees of Truth. Oxford: Oxford University Press, 2008.
P. F. Strawson, "Carnap's Views on Constructed Systems versus Natural Languages in Analytic Philosophy," in Schilpp (ed.), The Philosophy of Rudolf Carnap, La Salle: Open Court, pp. 503–519, 1963.
T. Williamson, Vagueness. London: Routledge, 1994.
T. Williamson, "Imagination, Stipulation and Vagueness," Philosophical Issues, vol. 8, pp. 215–228, 1997.
T. Williamson, "Précis of Vagueness," Philosophy and Phenomenological Research, vol. 57, no. 1, pp. 219–221, 1997.