David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
History and Philosophy of Logic 29 (2):103-113 (2008)
The idea of an ?inversion principle?, and the name itself, originated in the work of Paul Lorenzen in the 1950s, as a method to generate new admissible rules within a certain syntactic context. Some fifteen years later, the idea was taken up by Dag Prawitz to devise a strategy of normalization for natural deduction calculi (this being an analogue of Gentzen's cut-elimination theorem for sequent calculi). Later, Prawitz used the inversion principle again, attributing it with a semantic role. Still working in natural deduction calculi, he formulated a general type of schematic introduction rules to be matched ? thanks to the idea supporting the inversion principle ? by a corresponding general schematic Elimination rule. This was an attempt to provide a solution to the problem suggested by the often quoted note of Gentzen. According to Gentzen ?it should be possible to display the elimination rules as unique functions of the corresponding introduction rules on the basis of certain requirements?. Many people have since worked on this topic, which can be appropriately seen as the birthplace of what are now referred to as ?general elimination rules?, recently studied thoroughly by Sara Negri and Jan von Plato. In this study, we retrace the main threads of this chapter of proof-theoretical investigation, using Lorenzen's original framework as a general guide
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
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.
Citations of this work BETA
Stephen Read (2010). General-Elimination Harmony and the Meaning of the Logical Constants. Journal of Philosophical Logic 39 (5):557-76.
Enrico Moriconi (2012). Steps Towards a Proof-Theoretical Semantics. Topoi 31 (1):67-75.
Wagner de Campos Sanz & Thomas Piecha (2009). Inversion by Definitional Reflection and the Admissibility of Logical Rules. Review of Symbolic Logic 2 (3):550-569.
Similar books and articles
Lieven Decock & Igor Douven (2013). Qualia Compression. Philosophy and Phenomenological Research 87 (1):129-150.
Austen Clark (1985). Spectrum Inversion and the Color Solid. Southern Journal of Philosophy 23 (4):431-43.
David J. Cole (1990). Functionalism and Inverted Spectra. Synthese 82 (2):207-22.
Peter Schroeder-Heister (2007). Generalized Definitional Reflection and the Inversion Principle. Logica Universalis 1 (2):355-376.
Myron Glassman & R. Bruce Mcafee (2005). Pay Inversion at Universities: Is It Ethical? [REVIEW] Journal of Business Ethics 56 (4):325 - 333.
Neil Campbell (2004). Generalizing Qualia Inversion. Erkenntnis 60 (1):27-34.
Clayton Littlejohn (2009). On the Coherence of Inversion. Acta Analytica 24 (2):127-137.
Jeff Speaks (2011). Spectrum Inversion Without a Difference in Representation is Impossible. Philosophical Studies 156 (3):339-361.
Added to index2010-08-10
Total downloads39 ( #50,352 of 1,410,157 )
Recent downloads (6 months)1 ( #155,015 of 1,410,157 )
How can I increase my downloads?