Wittgenstein's Elimination of Identity for Quantifier-Free Logic

Authors
Markus Säbel
Universität Erlangen-Nürnberg
Timm Lampert
Humboldt-University, Berlin
Abstract
One of the central logical ideas in Wittgenstein's Tractatus logico-philosophicus is the elimination of the identity sign in favor of the so-called "exclusive interpretation" of names and quantifiers requiring different names to refer to different objects and different variables to take different values. In this paper, we examine a recent development of these ideas in papers by Kai Wehmeier. We diagnose two main problems of Wehmeier's account, the first concerning the treatment of individual constants, the second concerning so-called "pseudo-propositions" of classical logic such as a=a or a=b v b=c -> a=c. We argue that overcoming these problems requires two fairly drastic departures from Wehmeier's account: Not every formula of classical first-order logic will be translatable into a single formula of Wittgenstein's exclusive notation. Instead, there will often be a multiplicity of possible translations, revealing the original "inclusive" formulas to be ambiguous. Certain formulas of first-order logic such as a=a will not be translatable into Wittgenstein's notation at all, being thereby revealed as nonsensical pseudo-propositions which should be excluded from a "correct" conceptual notation. We provide translation procedures from inclusive quantifier-free logic into the exclusive notation that take these modifications into account and define a notion of logical equivalence suitable for assessing these translations.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 38,086
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

On Ramsey's 'Silly Delusion' Regarding Tractatus 5.53.Kai Wehmeier - 2009 - In Giuseppe Primiero & Shahid Rahman (eds.), Acts of Knowledge: History, Philosophy and Logic. College Publications.
Wittgenstein's Ab-Notation: An Iconic Proof Procedure.Timm Lampert - 2017 - History and Philosophy of Logic 38 (3):239-262.
Wittgensteinian Predicate Logic.Kai Wehmeier - 2004 - Notre Dame Journal of Formal Logic 45 (1):1-11.
Pure Second-Order Logic with Second-Order Identity.Alexander Paseau - 2010 - Notre Dame Journal of Formal Logic 51 (3):351-360.
The Power and the Limits of Wittgenstein's N Operator.James W. McGray - 2006 - History and Philosophy of Logic 27 (2):143-169.
Quantifier Elimination for Neocompact Sets.H. Jerome Keisler - 1998 - Journal of Symbolic Logic 63 (4):1442-1472.
Quantifier Elimination for Modules with Scalar Variables.Lou van den Dries & Jan Holly - 1992 - Annals of Pure and Applied Logic 57 (2):161-179.
The Role of Quantifier Alternations in Cut Elimination.Philipp Gerhardy - 2005 - Notre Dame Journal of Formal Logic 46 (2):165-171.
Non-Effective Quantifier Elimination.Mihai Prunescu - 2001 - Mathematical Logic Quarterly 47 (4):557-562.
Quantifier Elimination for Neocompact Sets.H. Keisler - 1998 - Journal of Symbolic Logic 63 (4):1442-1472.

Analytics

Added to PP index
2018-07-18

Total views
6 ( #728,655 of 2,313,336 )

Recent downloads (6 months)
3 ( #269,139 of 2,313,336 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature