Carnap's Geometrical Methodology
Explication as a transfer principle
DOI:
https://doi.org/10.15173/jhap.v11i4.5406Abstract
In this paper, I will offer a novel perspective on Carnapian explication, understanding it as a philosophical analogue of the transfer principle methodology that originated in nineteenth-century projective geometry. Building upon the historical influence that projective geometry exerted on Carnap’s philosophy, I will show how explication can be modeled as a kind of transfer principle that connects, relative to a given task and normatively constrained by the desiderata chosen by the explicators, the functional properties of concepts belonging to different conceptual frameworks. Moreover, I will demonstrate how, in light of this characterization, we can better appreciate the evolution of Carnap’s metaphilosophy.
References
Awodey, Steve and André Carus, 2003. “Carnap versus Gödel on Syntax and Tolerance.” In Logical Empiricism: Historical and Contemporary Perspectives, edited by P. Parrini, W. C. Salmon and M. H. Salmon, pp. 57–64. Pittsburgh: University of Pittsburgh Press.
———, 2007. “Carnap’s Dream: Gödel, Wittgenstein, and Logical Syntax.” Synthese 159(1): 23–45.
———, 2009. “Wittgenstein’s Prison to the Boundless Ocean: Carnap’s Dream of Logical Syntax.” In Wagner (2012), pp. 79–108.
Beaney, Michael, 2013. “Analytic Philosophy and History of Philosophy: The Development of the Idea of Rational Reconstruction.” In Reck (2013), pp. 231–60.
Biagioli, Francesca, 2020. “Structuralism and Mathematical Practice in Felix Klein’s Work on Non-Euclidean Geometry.” Philosophia Mathematica 28(3): 360–84.
Brun, Georg, 2016. “Explication as a Method of Conceptual Re-Engineering.” Erkenntnis 81(6): 1211–41.
———, 2020. “Conceptual Re-Engineering: From Explication to Reflective Equilibrium.” Synthese 197(3): 925–54.
Cappelen, Herman, David Plunkett and Alexis Burgess, eds., 2020. Conceptual Engineering and Conceptual Ethics. New York: Oxford University Press.
Carnap, Rudolf, 1922. Der Raum: Ein Beitrag zur Wissenschaftslehre. Berlin: Kant-Studien, Ergänzungshefte.
———, 1928a. Der logische Aufbau der Welt. Berlin: Weltkreis.
———, 1928b. Scheinprobleme in der Philosophie. Berlin: Weltkreis.
———, 1934. Logische Syntax der Sprache. Vienna: Springer.
———, 1947. Meaning and Necessity. Chicago: University of Chicago Press.
———, 1950a. “Empiricism, Semantics, and Ontology.” Revue Internationale de Philosophie 4(11): 20–40.
———, 1950b. Logical Foundations of Probability. Chicago: University of Chicago Press.
———, 1963a. “Carnap’s Intellectual Autobiography.” In Sch63, pp. 3–84.
———, 1963b. “The Philosopher Replies.” In Sch63, pp. 859–1013.
———, 1966. Philosophical Foundations of Science. New York: Basic Books. Reprinted as An Introduction to the Philosophy of Science, 1972.
Carsten, Klein and Steve Awodey, eds., 2004. Carnap Brought Home—The View from Jena. La Salle, IL: Open Court.
Carus, André, 2007. Carnap and Twentieth-Century Thought: Explication as Enlightenment. Cambridge: Cambridge University Press.
———, 2012a. “Engineers and Drifters; The Ideal of Explication and Its Critics.” In Wagner (2012), pp. 225–39.
———, 2012b. From Analysis to Explication. Unpublished Manuscript.
———, 2017. “Carnapian Rationality.” Synthese 194: 163–84.
Chang, Hasok, 2004. Inventing Temperature: Measurement and Scientific Progress. New York: Oxford University Press.
Coffa, Alberto, 1986. “From Geometry to Tolerance: sources of conventionalism in nineteenth-century geometry.” In From Quarks to Quasars: Philosophical Problems of Modern Physics, edited by R. G. Colodny, pp. 3–70. Pittsburgh: University of Pittsburgh Press.
———, 1991. The Semantic Tradition From Kant to Carnap: To the Vienna Station. Cambridge: Cambridge University Press.
Creath, Richard, 1992. “Carnap’s Conventionalism.” Synthese 93: 141–65.
———, 2012. “Before Explication.” In Wagner (2012), pp. 161–74.
De Benedetto, Matteo, 2021. “Explication as a Three-Step Procedure: the case of the Church-Turing Thesis.” European Journal for Philosophy of Science 11(21).
———, 2022. “Explicating ’Explication via Conceptual Spaces.” Erkenntnis 87: 853–89.
Dutilh Novaes, Catarina and Erich Reck, 2017. “Carnapian Explication, Formalisms as Cognitive Tools, and the Paradox of Adequate Formalization.” Synthese 194(1): 195–215.
Eder, Günther, 2019. “Frege and the Origins of Model Theory in Nineteenth Century Geometry.” Synthese 198(6): 5547–75.
———, 2021. “Projective Duality and the Rise of Modern Logic.” Bulletin of Symbolic Logic 27(4): 351–84.
Friedman, Michael, 1999. Reconsidering Logical Positivism. New York: Cambridge University Press.
———, 2000. A Parting of the Ways: Carnap, Cassirer, and Heidegger. New York: Open Court.
———, 2011. “Carnap on Theoretical Terms: Structuralism without metaphysics.” Synthese 180(2): 249–63.
———, 2012. “Rational Reconstruction, Explication, and the Rejection of Metaphysics.” In Wagner (2012), pp. 190–204.
Friedman, Michael and Richard Creath, 2008. The Cambridge Companion to Carnap. Cambridge: Cambridge University Press.
Gärdenfors, Peter, 2000. Conceptual Spaces: The Geometry of Thought. Cambridge, MA: MIT Press.
Gray, Jeremy, 2007. Worlds Out of Nothing: A Course in the History of Geometry in the 19th Century. New York: Springer.
———, 2008. Plato’s Ghost: The Modernist Transformation of Mathematics. Princeton, NJ: Princeton University Press.
Hanna, Joseph F., 1967. “An Explication of ’Explication’.” Philosophy of Science 35: 28–44.
Hawkins, Thomas, 1988. “Hesse’s Principle of Transfer and the Representation of Lie Algebras.” Archive for History of Exact Sciences 39: 41–73.
Hesse, Ludwig Otto, 1866a. “Vier Vorlesungen aus der analytischen Geometrie.” Zeitschrift für Mathematik und Physik 11: 369–425.
———, 1866b. “Ein Uebertragungsprincip.” Journal für die reine und angewandte Mathematik 66: 15–21.
Horsten, Leon, 2011. The Tarskian Turn. Deflationism and Axiomatic Truth. Cambridge, MA: MIT Press.
Jeffrey, Richard Carl, 1994. “Carnap’s Voluntarism.” In Logic, Methodology and Philosophy of Science IX, Studies in Logic and the Foundations of Mathematics 134, edited by D. Prawitz, B Skyrms and D. Westerstáhl, pp. 847–66. Amsterdam: Elsevier.
Justus, James, 2012. “Carnap on Concept Determination: Methodology for Philosophy of Science.” European Journal for Philosophy of Science 2: 161–79.
Klein, Felix, 1872. Vergleichende Betrachtungen über neuere geometrische Forschungen. Erlangen: Deichert.
Lavers, Gregory, 2016. “Carnap on Abstract and Theoretical Entities.” In Ontology After Carnap, edited by S. Blatti and S. Lapointe, pp. 200–19. Oxford: Oxford University Press.
Leitgeb, Hannes and André Carus, 2020. Rudolf Carnap. Stanford Encyclopedia of Philosophy (Summer 2020 Edition), https://plato.stanford.edu/archives/sum2020/entries/carnap/.
Menger, Karl, 1943. “What is Dimension?” The American Mathematical Monthly 50(1): 2–7.
———, 1979a. Selected Papers in Logic, and Foundations, Didactics, Economics, Vienna Circle Collection Vol. 10. Dordrecht: Springer.
———, 1979b. “On Definitions, Especially of Dimension.” In Menger (1979a), pp. 207–17. This includes reprinted sections of Menger (1943).
Mormann, Thomas, 2000. “Carnaps Philosophie als Möglichkeitwissenschaft.” Zeitschrift für philosophische Forschung 55(1): 79–100.
———, 2008. “Geometrical Leitmotifs in Carnap’s Early Philosophy.” In Friedman and Creath (2008), pp. 43–64.
Psillos, Stathis, 1999. Scientific Realism: How Science Tracks Truth. London.
———, 2000. “Rudolf Carnap’s ’Theoretical Concepts in Science’.” Studies in History and Philosophy of Science 31: 151–72.
Quinon, Paula, 2019. “Can Church’s Thesis Be Viewed as a Carnapian Explication?” Synthese 198(Suppl. 5): 1047–74.
Reck, Erich, 2012. “Carnapian Explication: a Case Study and Critique.” In Wagner (2012), pp. 96–116.
———, ed., 2013. The Historical Turn in Analytic Philosophy. London: Palgrave Macmillan.
Reck, Erich and Michael Price, 2000. “Structures and Structuralism in Contemporary Philosophy of Mathematics.” Synthese 125(3): 341–83.
Reck, Erich and Georg Schiemer, eds., 2020. The Pre-History of Mathematical Structuralism. Oxford: Oxford University Press.
Richardson, Alan, 1997. Carnap’s Construction of the World: The Aufbau and the Emergence of Logical Empiricism. Cambridge: Cambridge University Press.
———, 2003. “The Geometry of Knowledge: Lewis, Becker, Carnap and the formalization of philosophy.” Studies in the History and Philosophy of Science Part A 34(1): 165–82.
———, 2013. “Taking the Measure of Carnap’s Philosophical Engineering: Metalogic as Metrology.” In Reck (2013), pp. 60–77.
Schiemer, Georg, 2020a. “Transfer Principles, Klein’s Erlanger Program, and Methodological Structuralism.” In Reck and Schiemer (2020), pp. 106–41.
———, 2020b. “Carnap’s Structuralist Thesis.” In Reck and Schiemer (2020), pp. 383–420.
———, 2021. “Non-Standard Logicism.” In The Routledge Handbook of Logical Empiricism, edited by T. Uebel and C. Limbeck-Lilienau, pp. 211–19. New York: Routledge.
———, 2022. “Logicism in logical empiricism.” In Origins and Varieties of Logicism, edited by F. Boccuni and A. Sereni, pp. 243–66. New York: Routledge.
Schilpp, P. A., ed., 1963. The Philosophy of Rudolf Carnap. La Salle, IL: Open Court.
Sieg, Wilfried, 2002. “Calculations by man and machine: Conceptual analysis.” In Reflections on the Foundations of Mathematics. Essays in honor of Solomon Feferman, Lecture Notes in Logic 115, Assoc. for Symbolic Logic, edited by W. Sieg, R. Sommer and C. Talcott, pp. 390–409. Natick, MA: AK Peters.
Stein, Howard, 1992. “Was Carnap Entirely Wrong After All?” Synthese 93: 275–95.
Steinberger, Florian, 2016. “How Tolerant Can You Be? Carnap on Rationality.” Philosophy and Phenomenological Research 92(3): 645–68.
Strawson, Peter Frederick, 1963. “Carnap’s Views on Constructed Systems versus Natural Languages in Analytic Philosophy.” In Schilpp (1963), pp. 503–18.
Sznajder, Marta, 2018. “Inductive Logic as Explication: The Evolution of Carnap’s Notion of Logical Probability.” The Monist 101(4): 417–40.
Tappenden, James, 2005. “Metatheory and Mathematical Practice in Frege.” In Gottlob Frege: Critical Assessments of Leading Philosophers, Vol. II, edited by M. Beaney and E. Reck, pp. 190–228. New York: Routledge.
———, 2006. “The Riemannian Background to Frege’s Philosophy.” In The Architecture of Modern Mathematics: Essays in History and Philosophy, edited by J. Ferreirós and J. Gray, pp. 107–50. Oxford: Oxford University Press.
Tarski, Alfred, 1933. “The concept of truth in formalized languages.” In Logic, Semantics: Metamathematics, pp. 152–278. Oxford: Oxford University Press. English translation (1956).
Turing, Alan Mathison, 1936. “On Computable Numbers, with an Application to the Entscheidungsproblem.” Proc. London Math. Soc. 2(42): 230–65.
———, 1937. “A correction.” Proc. London Math. Soc. 2(43): 544–46.
Uebel, Thomas, 2011. “Carnap and Kuhn: On the Relation between the Logic of Science and the History of Science.” Journal for General Philosophy of Science 42: 129–40.
———, 2012. “The Bipartite Conception of Metatheory and the Dialectical Conception of Explication.” In Wagner (2012), pp. 117–30.
———, 2018. “Carnap’s Transformation of Epistemology and the Development of His Metaphilosophy.” The Monist 101(4): 367–87.
Wagner, Pierre, ed., 2012. Carnap’s Ideal of Explication and Naturalism. London: Palgrave Macmillan.
Wilson, Mark, 1992. “Frege: The Royal Road from Geometry.” Noûs 26(2): 149–80.
Wussing, Hans, 1984. The Genesis of the Abstract Group Concept: A Contribution to the History of the Origin of Abstract Group Theory. Cambridge, MA: MIT Press.
Downloads
Published
Issue
Section
License
The Public Knowledge Project recommends the use of the Creative Commons license. The Journal for the History of Analytical Philosophy requires authors to agree to a Creative Commons Attribution /Non-commercial license. Authors who publish with the Journal for the History of Analytical Philosophy agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons BY-NC license.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access)
This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.
