## Notre Dame Journal of Formal Logic

- Notre Dame J. Formal Logic
- Volume 51, Number 1 (2010), 69-84.

### Inclosures, Vagueness, and Self-Reference

#### Abstract

In this paper, I start by showing that sorites paradoxes are inclosure paradoxes. That is, they fit the Inclosure Scheme which characterizes the paradoxes of self-reference. Given that sorites and self-referential paradoxes are of the same kind, they should have the same kind of solution. The rest of the paper investigates what a dialetheic solution to sorites paradoxes is like, connections with a dialetheic solution to the self-referential paradoxes, and related issues—especially so called "higher order" vagueness.

#### Article information

**Source**

Notre Dame J. Formal Logic, Volume 51, Number 1 (2010), 69-84.

**Dates**

First available in Project Euclid: 4 May 2010

**Permanent link to this document**

https://projecteuclid.org/euclid.ndjfl/1273002110

**Digital Object Identifier**

doi:10.1215/00294527-2010-005

**Mathematical Reviews number (MathSciNet)**

MR2666570

**Zentralblatt MATH identifier**

1198.03034

**Subjects**

Primary: 03B52: Fuzzy logic; logic of vagueness [See also 68T27, 68T37, 94D05] 03B53: Paraconsistent logics

Secondary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30}

**Keywords**

sorites paradoxes vagueness paradoxes of self-reference inclosure schema paraconsistency extended paradoxes higher order vagueness

#### Citation

Priest, Graham. Inclosures, Vagueness, and Self-Reference. Notre Dame J. Formal Logic 51 (2010), no. 1, 69--84. doi:10.1215/00294527-2010-005. https://projecteuclid.org/euclid.ndjfl/1273002110