Notre Dame Journal of Formal Logic

Elementary Propositions and Independence

John L. Bell and William Demopoulos


This paper is concerned with Wittgenstein's early doctrine of the independence of elementary propositions. Using the notion of a free generator for a logical calculus–a concept we claim was anticipated by Wittgenstein–we show precisely why certain difficulties associated with his doctrine cannot be overcome. We then show that Russell's version of logical atomism–with independent particulars instead of elementary propositions–avoids the same difficulties.

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Notre Dame J. Formal Logic Volume 37, Number 1 (1996), 112-124.

First available in Project Euclid: 16 December 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30}
Secondary: 03B10: Classical first-order logic


Bell, John L.; Demopoulos, William. Elementary Propositions and Independence. Notre Dame J. Formal Logic 37 (1996), no. 1, 112--124. doi:10.1305/ndjfl/1040067320.

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