Notre Dame Journal of Formal Logic

Logical Consequence and First-Order Soundness and Completeness: A Bottom Up Approach

Eli Dresner

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Abstract

What is the philosophical significance of the soundness and completeness theorems for first-order logic? In the first section of this paper I raise this question, which is closely tied to current debate over the nature of logical consequence. Following many contemporary authors' dissatisfaction with the view that these theorems ground deductive validity in model-theoretic validity, I turn to measurement theory as a source for an alternative view. For this purpose I present in the second section several of the key ideas of measurement theory, and in the third and central section of the paper I use these ideas in an account of the relation between model theory, formal deduction, and our logical intuitions.

Article information

Source
Notre Dame J. Formal Logic Volume 52, Number 1 (2011), 75-93.

Dates
First available: 13 December 2010

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1292249612

Digital Object Identifier
doi:10.1215/00294527-2010-038

Zentralblatt MATH identifier
05862017

Mathematical Reviews number (MathSciNet)
MR2747164

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

Keywords
first-order logic soundness completeness measurement theory

Citation

Dresner, Eli. Logical Consequence and First-Order Soundness and Completeness: A Bottom Up Approach. Notre Dame Journal of Formal Logic 52 (2011), no. 1, 75--93. doi:10.1215/00294527-2010-038. http://projecteuclid.org/euclid.ndjfl/1292249612.


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