The significance of Quasizerlegung for Carnap’s Aufbau and scientific philosophy in general


  • Caterina Del Sordo University of the Basque Country
  • Thomas Mormann



Rudolf Carnap, W.V.O. Quine


In this introduction to the first English translation of Carnap's Quasizerlegung, we summarize the history of its reception and its role as groundwork for Carnap's Der logische Aufbau der Welt (The logical structure of the World). We aim to stress the philosophical significance of the Quasizerlegung as a prototype of mathematical philosophy by uncovering the many points of convergence between the philosophical and mathematical enterprises of neutral monism and representations.


Banks, Erik, 2003, Ernst Mach’s World Elements. A Study in Natural Philosophy, Springer, Dortrecht.

Banks, Erik, 2004, “The Philosophical Root of Ernst Mach’s Economy of Thought”, Synthese 138, 1: 23-53.

Banks, Erik, 2014, The realistic Empiricism of Mach, James and Russell. Neutral Monism Reconceived, Cambridge University Press, Cambridge.

Beiser, Frederick, 2014, The Genesis of Neo-Kantianism, 1796-1880, Oxford University Press, Oxford.

Brockhaus, Klaus, 1963, Untersuchungen zu Carnaps Logischem Aufbau der Welt, Unpublished Dissertation, Universität Münster, Germany.

Bergson, Henry, 1907, L’Évolution créatrice, Félix Alcan, Paris; Eng. tr. by Arthur Mitchell 1998, Creative Evolution, Dover, New York.

Cassirer, Ernst, 1907, “Kant und die moderne Mathematik”, Kant-Studien 12: 1‑49.

Cassirer, Ernst, 1910, Substanzbegriff und Funktionsbegriff, Wissenschaftliche Buchgesellschaft, Darmstadt.

Carnap, Rudolf, 1922a, Vom Chaos zur Wirklichkeit, unpublished manuscript RC-081-05-01, University of Pittsburgh.

Carnap, Rudolf, 1922b, “Der Raum. Ein Beitrag zur Wissenschaftslehre”, Kant-Studien, Ergänzungsheft 56, Verlag von Reuther und Reichard, Berlin.

Carnap, Rudolf, 1923, Die Quasizerlegung – Ein Verfahren zur Ordnung nichthomogener Mengen mit den Mitteln der Beziehungslehre, Unpublished Manuscript RC-081-04-01, University of Pittsburgh.

Carnap, Rudolf, 1928, Der logische Aufbau der Welt, Weltkreis, Berlin; Eng. tr. Rolf George 1967, The logical structure of the World, University of California Press, Berkeley/Los Angeles.

Carnap, Rudolf, 1929, Abriss der Logistik. Springer, Wien <>.

Carnap, Rudolf, 1957, Unpublished autobiography. UCLA Carnap Papers, Box 2, CM3: B29-B36.

Carus, André, 2007, Carnap and Twentieth-Century Thought. Explication as Enlightenment, University Press Cambridge, Cambridge.

Chalmers, David, 2012, Constructing the World, Oxford University Press, Oxford.

Damböck, Christian, Gereon Wolters, 2021, eds. Der junge Carnap in historischem Kontext: 1918 – 1935/Young Carnap in an Historical Context: 1918 – 1935, Veröffentlichungen des Instituts Wiener Kreis, Springer, Wien.

Damböck, Christian, 2021, “Die Entwicklung von Carnaps Aufbau 1920 – 1928”, in Damböck, Wolters eds. : 19 – 53

Davey, Brian, Hilary Priestley, 2002, Introduction to Lattices and Order, Cambridge University Press, Cambridge.

Del Sordo, Caterina, 2016, “Commentary. Die Quasizerlegung. Ein Verfahren zur Ordnung nichthomogener Mengen mit den Mitteln der Beziehungslehre by Rudolf Carnap”, in Lanfredini, Roberta, Nicola Liberati, Andrea Pace Giannotta, Elena Pagni eds. The Enactive Approach to Qualitative Ontology in Search of New Categories, Humana.mente Journal of Philosophical Studies, 31,9: 205-10.

Del Sordo, Caterina, 2021, Rappresentazione Strutturale delle Entità neutrali. Il Monismo Neutrale da un Punto di Vista Analitico e Storico-filosofico, Ph.D. Dissertation, University of Urbino (Italy) / University of the Basque Country UPV/EHU (Spain).

Dummett, Micheal, 1993, Origins of Analytical Philosophy, Duckworth, London.

Givant, Steven, 2017, Introduction to relation algebras, Relation Algebra, 1, Springer.

Goodman, Nelson, 1951, The structure of appearance, Harvard University Press, Harvard.

Grosholz, Emily, 2007, Representation and Productive Ambiguity in Mathematics and the Sciences, Oxford University Press, Oxford.

Hacking, Ian, 1983, Representing and Intervening, Introductory Topics in the Philosophy of Science, Cambridge University Press, Cambridge,

Husserl, Edmund, 1913, Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie, Max Niemeyer, Halle; Eng. tr. by Fred Kersten 1982, Ideas Pertaining to a Pure Phenomenology and to a Phenomenological Philosophy—First Book: General Introduction to a Pure Phenomenology, Nijhoff, The Hague

Koppelberg, Sabine, 1989, Handbook of Boolean Algebras, in Monk, Donald, Robert Bonnet eds. 1, North-Holland, Amsterdam and New York.

Lakoff, George, Rafael Núñez, 2000, Where Mathematics comes from. How the Embodied Mind brings Mathematics into Being, Basic Books, MIT press, New York.

Leitgeb, Hannes, 2007, “A New Analysis of Quasi-Analysis”, Journal of Philosophical Logic: 181-226.

Leitgeb, Hannes, 2013, “Scientific Philosophy, Mathematical Philosophy and All That”, Metaphilosophy, 44, 3, Blackwell Publishing: 267-275.

Mach, Ernst, 1896, Populär-wissenschaftliche Vorlesungen, Johann Ambrosius Barth, Leipzig; Eng. tr. by Thomas McCormack 1898, Popular Scientific Lectures, Open Court, Chicago

Mac Lane, Saunders, 1986, Mathematics. Form and Function, Springer, New York.

Mac Lane, Saunders, 1992, The Protean Character of Mathematics, in Echeverria, Javier, Andoni Ibarra, Thomas Mormann, eds. The Space of Mathematics. Philosophical, Epistemological, and Historical Explorations, de Gruyter, Berlin: 3 – 13.

Maddux, Roger, 1991, “The origin of relation algebras in the development and axiomatization of the calculus of relations”, Studia Logica, 50: 421-455.

Maddux, Roger, 2006, Relation Algebras, Studies in Logic and the Foundations of Mathematics, 150, Elsevier Science, Amsterdam.

Marciszewski, Witold, 1981, “Abstraction Operators”, in Marciszewski, Witold, ed. Dictionary of Logic as Applied in the Study of Language, Springer, Dortrecht.

Mormann, Thomas, 1994, “A Representational Reconstruction of Carnap’s Quasianalysis”, Philosophy of Science Association, 1, University of Chicago Presse, Seattle: 96‑104

Mormann, Thomas, 2003, “Synthetic Geometry and Aufbau”, in Bonk, Thomas, ed. Language Truth, Knowledge. Contributions to the Philosophy of Rudolf Carnap, Springer, Dordrecht: 45-65.

Mormann, Thomas, 2006, “Between Heidelberg and Marburg. The Aufbau‘s neo-Kantian origins and the AP/CP-Divide”, Sapere Aude! Revista de Filosofía. México, F.Z., 1: 22-50.

Mormann, Thomas, 2009, “New Work for Carnap’s Quasi-Analysis”, Journal of Philosophical Logic, 38, 3:249‑282

Mormann, Thomas, 2016, “Carnap’s Aufbau in the Weimar Context”, in Damböck, Christian ed., Influences on the Aufbau, Vienna Circle Institute Yearbook, 18: 115‑137

Mormann, Thomas, 2018, “Structure-preserving representations, constitution, and the relative a priori”, Synthese,

Mundy, Brent, 1986, “On the General Theory of Meaningful Representation”, Synthese, 67: 391‑437.

Proust, Joëlle, 1986, Questions de forme: Logique et proposition analytique de Kant à Carnap, Fayard, Paris ; Eng. tr. by Anastasios Brenner 1989, Questions of form, logic and the analytic proposition from Kant to Carnap. University of Minnesota Press, Minneapolis.

Quine, Willard Van Orman, 1969, Ontological Relativity and Other Essays, Open Court, LaSalle and Chicago.

Ramharter, Esther, Georg Rieckh, 2006, Die Principia Mathematica auf den Punkt gebracht, öbv und hpt, Wien.

Rheinberger, Hans-Jörg, 2010, On historicizing epistemology. An essay, Stanford University Press, Stanford.

Richardson, Alan, 1998, Carnap’s Construction of the World: The Aufbau and the Emergence of Logical Empiricism, Cambridge University Press, Cambridge.

Russell, Bertrand, 1914, Our Knowledge of External World as a Field for Scientific Method in Philosophy, Open Court, London.

Schilpp, Paul, 1963, ed. The Philosophy of Rudolf Carnap, The Library of Living Philosophers, 11, Open Court, La Salle, Illinois.

Schnädelbach H (1983) Philosophie in Deutschland 1831–1933, Suhrkamp Verlag, Frankfurt am Main; Eng. tr. by Eric Matthews 1984, Philosophy in Germany 1931-1933, Cambridge University Press, Cambridge.

Simmons, Harold, 2011, An introduction to Category Theory, Cambridge University Press, Cambridge.

Stubenberg, Leopold, 2016, “Neutral Monism”, in Edward Zalta ed. The Stanford Encyclopedia of Philosophy, Winter 2016,

Suppes, Patrick, 2002, Representation and invariance of scientific structures, CSLI Publications, Stanford.

Swoyer, Chris, 1991, “Structural Representation and Surrogative Reasoning”, Synthese 87: 449 – 508

Textor, Mark, 2021, “Mach’s Neutral Monism”, HOPOS (The Journal of the International Society for the History of Philosophy of Science), 11, 1: 143 – 165.

Tully, Robert, 2003, “Russell’s Neutral Monism”, in Griffin, Nicholas, ed. The Cambridge Companion to Russell, Cambridge University Press, New York: 332-371

van Fraassen, Bas, 2006, Scientific Representation: Paradoxes of Perspective, Clarendon press, Oxford.

Wille, Rudolf, Bernhard Ganter, 1999, Formal Concept Analysis. Mathematical Foundations, Springer- Verlag.

Wishon, Donovan, 2021, “Radical Empiricism, Neutral Monism, and the Elements of Mind”, in Strawson, Galen, ed. Monism, The Monist, 104, 1: 125-151,

Ziche, Paul, 2016, “Theories of order in Carnap’s Aufbau”, in Damböck, Christian ed. Influences on the Aufbau, Vienna Circle Institute Yearbook, 18: 77-98.

Ziehen, Theodor, 1913, Erkenntnistheorie auf psychophysiologischer und physikalischer Grundlage. Verlag von Gustav Fischer, Jena.

Ziehen, Theodor, 1920, Lehrbuch der Logik, A. Marcus & E. Webers Verlag, Bonn






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