On Evans's Vague Object from Set Theoretic Viewpoint

Fuzzy Systems and Knowledge Discovery, 2005

Gareth Evans proved that if two objects are indeterminately equal then they are different in reality [Ev78]. He defined vague objects as having vague identity statement: a is a vague object if there exists an object b such that a= b is of indeterminate truth value. Let us assume there can be vague objects in the world; we call this Evans's Vagueness Assumption (EVA). Let a, b be vague objects, then

The Australasian Journal of Logic, 2010

This paper presents F, substructural logic designed to treat vagueness. Weaker than Lukasiewicz’s infinitely valued logic, it is presented first in a natural deduction system, then given a Kripke semantics in the manner of Routley and Meyer's ternary relational semantics for R and related systems, but in this case, the points are motivated as degrees to which the truth could be stretched. Soundness and completeness are proved, not only for the propositional system, but also for its extension with first-order quantifiers. The first-order models allow not only objects with vague properties, but also objects whose very existence is a matter of degree.

Erkenntnis, 2011

The supporter of vague objects has been long challenged by the following ‘Argument from Identity’: 1) if there are vague objects, then there is ontically indeterminate identity; 2) there is no ontically indeterminate identity; therefore, 3) there are no vague objects. Some supporters of vague objects have argued that 1) is false. Noonan (Analysis 68: 174–176, 2008) grants that 1) does not hold in general, but claims that ontically indeterminate identity is indeed implied by the assumption that there are vague objects of a certain special kind (i.e. vague objects*). One can therefore formulate a ‘New Argument from Identity’: 1′) if there are vague objects*, then there is ontically indeterminate identity; 2) there is no ontically indeterminate identity; therefore, 3′) there are no vague objects*. Noonan’s strategy is to argue that premiss 1′) is inescapable, and, as a consequence, that Evans’s alleged defence of 2) is a real challenge for any supporter of vague objects. I object that a supporter of vague objects who grants the validity of Evans’s argument allegedly in favour of 2) should reject premiss 1′). The threat of the New Argument from Identity is thus avoided.

2017

Vagueness is a phenomenon whose manifestation occurs most clearly in linguistic contexts. And some scholars believe that the underlying cause of vagueness is to be traced to features of language. Such scholars typically look to formal techniques that are themselves embedded within language, such as supervaluation theory and semantic features of contexts of evaluation. However, when a theorist thinks that the ultimate cause of the linguistic vagueness is due to something other than language-for instance, due to a lack of knowledge or due to the world's being itself vague-then the formal techniques can no longer be restricted to those that look only at within-language phenomena. If, for example a theorist wonders whether the world itself might be vague, it is most natural to think of employing many-valued logics as the appropriate formal representation theory. I investigate whether the ontological presuppositions of metaphysical vagueness can accurately be represented by (finitely) many-valued logics, reaching a mixed bag of results.

I develop a new theory of vagueness, which repudiates the notion of local indeterminacy (or borderline case) and replaces it with the notion of global indeterminacy.

Kriterion – Journal of Philosophy, 2020

This paper focuses on Jessica Wilson’s determinable-based account of metaphysical indeterminacy and its relationship to the concept of vague identity. The determinable-based account comprises a distinction between meta-level and object-level accounts of metaphysical indeterminacy. I first argue that the distinction cannot be clearly applied to some theories. In particular, I argue that even though Wilson categorizes the constitution account of metaphysical indeterminacy as a meta-level account, from one perspective it can be defensibly regarded as an object-level account, because it is bound to posit genuinely indeterminate states of affairs and provides an explanation of boundary indeterminacy that is structurally analogous to the explanation provided by Wilson’s object-level account. This interim conclusion is important, because it has been argued that the constitution account, when applied to some more complex types of boundary indeterminacy, cannot avoid commitment to vague identity, in spite of the declarations of some of its proponents. The ultimate goal of this paper is to argue that, contrary to Wilson’s claims, the determinable-based account must embrace vague identity too.

Philosophical Perspectives, 2008

Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011), 2011

In this paper we discuss the multifaceted nature of vagueness, the limits of (standard) set theory in dealing with the foundational aspects that a really innovating theory of vagueness should manifest, and the difficulties in outlining the possible features that such a type of new formalism should exhibit in order to be able to deal with such innovative aspects. We shall highlight some aspects of the role that Fuzzy Set Theory (FST) can play in this process.