David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 35 (1):129-145 (2004)
How natural is natural deduction?– Gentzen's system of natural deduction intends to fit logical rules to the effective mathematical reasoning in order to overcome the artificiality of deductions in axiomatic systems (¶ 2). In spite of this reform some of Gentzen's rules for natural deduction are criticised by psychologists and natural language philosophers for remaining unnatural. The criticism focuses on the principle of extensionality and on formalism of logic (¶ 3). After sketching the criticism relatively to the main rules, I argue that the criteria of economy, simplicity, pertinence etc., on which the objections are based, transcend the strict domain of logic and apply to arguments in general (¶ 4). (¶ 5) deals with Frege's critique of the concept of naturalness as regards logic. It is shown that this concept means a regression into psychologism and is exposed to the same difficulties as are: relativity, lack of precision, the error of arguing from `is' to `ought' (the naturalistic fallacy). Despite of these, the concept of naturalness plays the role of a diffuse ideal which favours the construction of alternative deductive systems in contrast to the platonic conception of logic (¶ 6).
|Keywords||argument constructivism extensionality formalism logical consequence natural deduction natural language platonism principle of conditionalisation psychologism truth-functions|
|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
No citations found.
Similar books and articles
Moritz Cordes & Friedrich Reinmuth, Ein Redehandlungskalkül. Ein pragmatisierter Kalkül des natürlichen Schließens nebst Metatheorie.
Allard Tamminga & Koji Tanaka (1999). A Natural Deduction System for First Degree Entailment. Notre Dame Journal of Formal Logic 40 (2):258-272.
John M. Martin (1997). Aristotle'S Natural Deduction Reconsidered. History and Philosophy of Logic 18 (1):1-15.
Andrzej Indrzejczak (2003). A Labelled Natural Deduction System for Linear Temporal Logic. Studia Logica 75 (3):345 - 376.
Maria Luisa Bonet & Samuel R. Buss (1993). The Deduction Rule and Linear and Near-Linear Proof Simulations. Journal of Symbolic Logic 58 (2):688-709.
Hartley Slater (2008). Harmonising Natural Deduction. Synthese 163 (2):187 - 198.
Torben BraÜner (2005). Natural Deduction for First-Order Hybrid Logic. Journal of Logic, Language and Information 14 (2):173-198.
Sun-Joo Shin (1999). Reconstituting Beta Graphs Into an Efficacious System. Journal of Logic, Language and Information 8 (3):273-295.
Torben Braüner (2004). Two Natural Deduction Systems for Hybrid Logic: A Comparison. [REVIEW] Journal of Logic, Language and Information 13 (1):1-23.
Yannis Delmas-Rigoutsos (1997). A Double Deduction System for Quantum Logic Based on Natural Deduction. Journal of Philosophical Logic 26 (1):57-67.
Added to index2009-01-28
Total downloads15 ( #171,927 of 1,725,600 )
Recent downloads (6 months)2 ( #268,736 of 1,725,600 )
How can I increase my downloads?