@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 28 Mar 2024}, author = {Leibniz, G.W.}, subject = {Decidability}, note = {Berka I 329 Decision problem/Logic/Berka: appeared historically for the first time in Leibniz with the idea of a purely arithmetical "ars iudicandi". Behmann: (1922)(1): "The main problem of modern logic". Ackermann: (1954)(2): I. It is to be decided with exactly stated means, whether a relevant formula of a (logical) calculus is valid. II. If it is not universal, it is to be decided whether it is valid in none of the areas or whether it is valid in an area. If it is valid in any area, one must determine which cardinal number this area has. III. It is to be decided whether a relevant formula is valid in all areas with a finite number of elements or not." Berka: this is a basically semantic formulation of the E problem. E Problem/syntactical: it is to be decided with the help of exactly defined processes that have to fulfill certain conditions whether a relevant formula of a calculus is provable or refutable. Statement Calculus/E-Problem: by Lukasiewicz (1921)(3), Post (1921)(4), Wittgenstein (1921)(5) positively solved. 1. H. Behmann, Beiträge zur Algebra der Logik, insbesondere zum Entscheidungsproblem, Math. Ann. 86 (1922), 163-229 2. R. Ackermann, Solvable Classes of the Decision Problem, Amsterdam (3. ed.) 1968 3. J. Lukasiewicz, Logica dwuwartosciowa, PF 23 (1921), 189-205 4. E. L. Post, Introduction to a general theory of elemantary propositions, American Journal of Mathematics 43 (1921) , 163-185 5. L. Wittgenstein, Logisch-Philosophische Abhandlung, Ann. Naturphil. 14 (1921), 185-262}, note = { Lei II G. W. Leibniz Philosophical Texts (Oxford Philosophical Texts) Oxford 1998 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 }, file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=434158} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=434158} }