Peirce and Schröder on the auflösungsproblem

Davide Bondoni

DOI: http://dx.doi.org/10.12775/LLP.2009.002

Abstract


The aim of this article is Schröder’s treatment of the so called solution problem [Auflösungsproblem]. First, I will introduce Schröder’s ideas; then I will discuss them taking into account Peirce’s considerations in The Logic of Relatives ([13, pp. 161–217] now republished in [9, pp. 288–345]).


Keywords


solution problem; elimination problem; algebra of logic; calculus of relations

Full Text:

PDF

References


Kolmogorov, A. N., A. P. Yushkevich, Matematika XIX veka: Matematicheskaya logika, algebra, teoriya chisel, teoriya veroyatnostei, lzdatel’stvo Nauka, Moskva, 1978.

Kolmogorov, A. N., A. P. Yushkevich (eds.), Mathematics of the 19th Century, Mathematical Logic, Algebra, Number Theory, Probability Theory, Birkhäuser Verlag, Basel – Boston – Berlin, 2001. Second revised edition, translated from the Russian by A. Shenitzer, H. Grant and O.B. Sheinin.

Bondoni, Davide, La teoria delle relazioni nell’algebra della logica schröderiana, Led, Edizioni Universitarie di Lettere Economia Diritto, Milano, 2007.

Bondoni, Davide, Review of [7], Logic and Logical Philosophy 17, 4 (2008), 355–360.

Boole, George, An Investigation of the Laws of Thought, on which are founded the Mathematical Theories of Logic and Probabilities, Walton & Maberly, London, 1854. Reprinted Dover, New York, ca. 1958.

Boole, George, An Investigation of the Laws of Thought on which are founded the Mathematical Theories of Logic and Probabilities, Dover Publications, Inc., New York, 1958. First American printing.

Brady, Geraldine, From Peirce to Skolem. A Neglected Chapter in the History of Logic, Elsevier, 2000.

Fenstad, Jens Erik (ed.), Selected Works in Logic by Th. Skolem, Universitetsforlaget, Oslo – Bergen – Tromsö, 1970.

Hartshorne, Charles, and Paul Weiss (eds.), Collected Papers of Charles Sanders Peirce, vol. 3, Exact Logic, and vol. 4, The Simplest Mathematics, Belknap Press of Harvard University Press, 1960.

Löwenheim, Leopold, “Über Möglichkeiten im Relativkalkül”, Math. Ann. 76 (1915), 447–470.

Peckhaus, Volker, “Schröders Logic”, in Dov M. Gabbay and John Woods (eds.), Handbook of the History and Philosophy of Logic, vol. 3, Elsevier, 2004.

Peirce, Charles Sanders, “On the algebra of logic”, American Journal of Mathematics 3 (1880), 15–57.

Peirce, Charles Sanders, “The logic of relatives”, The Monist (1897), 161–217.

Schröder, Ernst, Der Operationskreis des Logikkalkuls, Teubner, 1877.

Schröder, Ernst, Vorlesungen über die Algebra der Logik, Exakte Logik, vol. 3, “Algebra und Logik der Relative”, B.G. Teubner, 1895.

Schröder, Ernst, Der Operationskreis des Logikkalkuls, Wissenschaftliche Buchgesellschaft, 1966.

Schröder, Ernst, Vorlesungen über die Algebra der Logik, Exakte Logik, vol. 3, “Algebra und Logik der Relative”, Chelsea Publishing Company, 1966.

Skolem, Thoralf, “Logisch-kombinatorische Untersuchungen über die Erfüllbarkeit oder Beweisbarkeit mathematischer Sätze nebst einem Theoreme über dichte Mengen”, Videnskaps. skrift., I. Matem.-natur. klasse 4 (1920).

van Heijenoort, Jean, From Frege to Gödel. A Source Book in Mathematical Logic, 1879–1931, Harvard University Press, 1967.








Print ISSN: 1425-3305
Online ISSN: 2300-9802

Partnerzy platformy czasopism