Abstract
This paper presents an outline of a new theory of relevant deduction which arose from the purpose of solving paradoxes in various fields of analytic philosophy. In distinction to relevance logics, this approach does not replace classical logic by a new one, but distinguishes between relevance and validity. It is argued that irrelevant arguments are, although formally valid, nonsensical and even harmful in practical applications. The basic idea is this: a valid deduction is relevant iff no subformula of the conclusion is replaceable on some of its occurrences by any other formula salva validitate of the deduction. The paper first motivates the approach by showing that four paradoxes seemingly very distant from each other have a common source. Then the exact definition of relevant deduction is given and its logical properties are investigated. An extension to relevance of premises is discussed. Finally the paper presents an overview of its applications in philosophy of science, ethics, cognitive psychology and artificial intelligence.
This paper is based on the first part of my habilitation Schurz (1989). For various helps and comments I am indebted to Paul Weingartner, Andrzej Wónski, Georg Kreisel, David Miller, Kit Fine, Terence Parsons and Peter Woodruff.
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References
Ackermann, W.: 1956, ‘Begründung einer strengen Implikation’, Journal of Symbolic Logic 21, 113–128.
Anderson, A. R. and Belnap, N. D.: 1975, Entailment. The Logic of Relevance and Necessity, Princeton University Press, Princeton.
Åqvist, L.: 1984, ‘Deontic Logic’, in D. Gabbay and F. Guenthner (eds.), pp. 605–714.
Barwise, J.: 1988, The Situation in Logic, Center for the Study of Language and Information, Stanford.
Bratko, I.: 1986, Prolog Programming for Artificial Intelligence, Addison-Wesley Publ. Comp., Wokingham.
Carnap, R.: 1936–37, ‘Testability and Meaning’, Philosophy of Science 3, 419–471
Carnap, R.: 1937, ‘Testability and Meaning’, Philosophy of Science 4, 1–40.
Carnap, R.: 1956, ‘The Methodological Character of Theoretical Concepts’, in: H. Feigl, and M. Scriven (eds.), Minnesota Studies in the Philosophy of Science, vol. I, University of Minnesota Press, Minneapolis, pp. 38–76.
Cleave, J. P.: 1973–74, ‘An Account of Entailment Based on Classical Semantics’, Analysis 34, 118–122.
Fitting, M.: 1983, Proof Methods for Modal and Intuitionistic Logics, Reidel, Dordrecht.
Friedman, M.: 1974, ‘Explanation and Scientific Understanding’, Journal of Philosophy 71, 5–19.
Glymour, C: 1980, ‘Hypothetico-Deductivism is Hopeless’, Philosophy of Science 47, 322–325.
Halldén, S. 1951: ‘On the Semantic Non-Completeness of Certain Lewis Calculi’. Journal of Symbolic Logic 16(2), 127–129.
Harrison, J.: 1972, ‘Ethical Naturalism’, in: P. Edwards (ed.). The Encyclopedia of Philosophy, Vol. 3–4, The Macmillan Company & The Free Press, New York, Reprint Edition, pp. 69–71.
Hempel, C. G.: 1965, Aspects in Scientific Explanation and Other Essays, Free Press, New York, London.
Hesse, M.: 1970, ‘Theories and Transitivity of Confirmation’, Philosophy of Science 37, 50–63.
Hume, D.: 1739–40: A Treatise of Human Nature, (L. A. Selby-Bigge, ed., Oxford 1888, Reprint 1951), Orig. 1739/40.
Kitcher, P.: 1976, ‘Comments and Criticism: Explanation, Conjunction and Unification’, Journal of Philosophy 73, 207–212.
Kitcher, P.: 1981, ‘Explanatory Unification’, Philosophy of Science 48, 507–531.
Kleene, S. C: 1971, Introduction to Metamathematics, Wolters—Noordhoff Publishing, Groningen.
Körner, S.: 1947, ‘On Entailment’, Proceedings of the Aristotelean Society 21, 143–162.
Körner, S. 1959, Conceptual Thinking, Dover Publ., New York.
Körner, S.: 1979, ‘On Logical Validity and Informal Appropriateness’, Philosophy 54, 377–379.
Kuipers, T. A. (ed.): 1987, What Is Closer-To-The-Truth ?, Poznan Studies in the Philosophy of Science and the Humanities, Vol. 10, Rodopi, Amsterdam.
Kutschera, F. v.: 1982, Grundlagen der Ethik, W. de Gruyter, Berlin—New York.
Lloyd, J.: 1984, Foundations of Logic Programming, Springer, Berlin.
Miller, D.: 1982, ‘Truth, Truthlikeness, Approximative Truth’, Fundamenta Scientiae, 3(1), 93–101.
Morscher, E.: 1984, ‘Sein-Sollen-Schlüsse und wie Schlüsse sein sollen’, in W. u.a. Krawietz, (eds.), Theorie der Normen (Festgabe für Ota Weinberger), Duncker and Humblot, Berlin.
Parry, W.: 1933, ‘Ein Axiomensystem für eine neue Art von Implikation (Analytische Implikation)’, Ergebnisse eines mathematischen Kolloquiums, 4, 5–6.
Popper, K.: 1948, ‘What Can Logic Do For Philosophy?’ Artistotelian Society Proceedings, Suppl. 22, 141–154.
Popper, K.: 1963, Conjectures and Refutations, Routledge and Kegan Paul, London.
Popper, K.: 1976, Logik der Forschung (6. Auflage), J. C. B. Mohr, Tübingen.
Prior, A. N.: 1954, ‘The Paradoxes of Derived Obligation’, Mind 63, 64–65.
Prior, A. N.: 1960, ‘The Autonomy of Ethics’, Australasian Journal of Philosophy 38, 199–206.
Ross, A.: 1941, ‘Imperatives and Logic’, Theoria 7, 53–71; reprint in Philosophy of Science 11, 1944, pp. 30–46.
Radnitzky, G.: 1980, ‘From Justifying a Theory to Comparing Theories and Selecting Questions’, Revue Internationale de Philosophie 131–132, 179–228.
Rautenberg, W.: 1979, Klassische und Nichtklassische Aussagenlogik, Friedr. Vieweg & Sohn, Braunschweig, Wiesbaden.
Schurz, G.: 1983, Wissenschaftliche Erklärung, Ansätze zu einer logisch-pragmatischen Wissenschaftstheorie, (dissertation), dbv-Verlag für die TU Graz.
Schurz, G.: 1983b, ‘Das deduktive Relevanzkriterium von Stephan Körner und seine wissenschaftstheoretischen Anwendungen’, Grazer Philosophische Studien 20, 149–177.
Schurz, G.: 1987, ‘A New Définition of Verisimilitude and its Applications’, in P. Weingartner and G. Schurz (eds.), Logic, Philosophy of Science and Epistemology, Proceedings of the 11th International Wittgenstein-Symposium, Hölder—Pichler—Tempsky, Vienna, pp. 177–184.
Schurz, G.: 1988, ‘Was ist wissenschaftliches Verstehen? Eine Theorie verstehensbewirkender Erklärungsepisoden’, in G. Schurz (ed.), pp. 235–298.
Schurz, G. (ed.): 1988, Erklären und Verstehen in der Wissenschaft. (With contributions by B. v. Fraassen, P. Gärdenfors, R. Tuomela, M. Friedman, P. Kitcher, G. Schurz and K. Lambert), R. Oldenbourg, München.
Schurz, G.: 1989, Relevant Deduction in Science and Ethics. With a Case Study of the Is-Ought Problem, (habilitation), Salzburg 1989.
Schurz, G.: 1990, ‘Paradoxical Consequences of Balzer’s and Gähde’s Criteria of Theoreticity. Results of an Application to Ten Scientific Theories’, Erkenntnis 32, 161–214.
Schurz, G.: 1991, ‘How Far Can Hume’s Is-Ought Thesis be Generalized? An Investigation in Alethic-Deontic Modal Predicate Logic’, Journal of Philosophical Logic 20, 37–95.
Schurz, G. and Weingartner, P.: 1987, ‘Verisimilitude Defined by Relevant Consequence-Elements. A New Reconstruction of Popper’s Idea’, in T. A. Kuipers (ed.), pp. 47–78.
Schurz, G. and Lambert, K.: 1991, ‘Outline of a Theory of Scientific Understanding’, submitted for publication.
Stegmüller, W.: 1970, Probleme und Resultate der Wissenschaftstheorie und Analytischen Philosophie, Band II, 1. Halbband, Springer, Berlin.
Stranzinger, R.: 1977, ‘Die Paradoxa der deontischen Logik’, in I. Tammelo and H. Schreiner (eds.), Grundzüge und Grundverfahren der Rechtslogik, Band 2, Verlag Dokumentation (UTB 685), München 1977.
Weingartner, P. 1985, ‘A Simple Relevance Criterion for Natural Language and Its Semantics’, in G. Dorn and P. Weingartner (eds.), Foundations of Logic and Linguistic, Plenum Press, Salzburg.
Weingartner, P. and G. Schurz: 1986, ‘Paradoxes Solved by Simple Relevance Criteria’, Logique et Analyse 113, 3–40.
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Schurz, G. (1991). Relevant Deduction. In: Spohn, W. (eds) Erkenntnis Orientated: A Centennial Volume for Rudolf Carnap and Hans Reichenbach. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3490-3_20
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DOI: https://doi.org/10.1007/978-94-011-3490-3_20
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