## Notre Dame Journal of Formal Logic

### Restriction by Noncontraction

Elia Zardini

#### Abstract

This paper investigates how naive theories of truth fare with respect to a set of extremely plausible principles of restricted quantification. It is first shown that both nonsubstructural theories as well as certain substructural theories cannot validate all those principles. Then, pursuing further an approach to the semantic paradoxes that the author has defended elsewhere, the theory of restricted quantification available in a specific naive theory that rejects the structural property of contraction is explored. It is shown that the theory validates all the principles in question, and it is argued that other prima facie plausible principles that the theory fails to validate are objectionable on independent grounds.

#### Article information

Source
Notre Dame J. Formal Logic Volume 57, Number 2 (2016), 287-327.

Dates
Accepted: 14 October 2013
First available in Project Euclid: 28 January 2016

https://projecteuclid.org/euclid.ndjfl/1453993977

Digital Object Identifier
doi:10.1215/00294527-3429057

Mathematical Reviews number (MathSciNet)
MR3482748

Zentralblatt MATH identifier
06585189

Subjects
Primary: 03
Secondary: A05 B20 B47 B53 B65

#### Citation

Zardini, Elia. Restriction by Noncontraction. Notre Dame J. Formal Logic 57 (2016), no. 2, 287--327. doi:10.1215/00294527-3429057. https://projecteuclid.org/euclid.ndjfl/1453993977

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