Abstract
In §179 of his 1928 Logical Structure of the World or Aufbau, Carnap notes that:
“We have repeatedly pointed out that the formation of the constructional system as a whole is the task of unified science, while construction theory is merely engaged in carrying out the appropriate logical investigations. By placing the objects of science in one unified constructional system, the different “sciences” are at the same time recognized as branches of the one science and are themselves brought into a system (§179).”1
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Notes
Unless otherwise noted references are to sections of Rudolf Carnap, Der logische Aufbau der Welt. Hamburg: Felix Meiner 1928, subsequently published as Rudolf Carnap, The Logical Structure of the World & Pseudoproblems in Philosophy. R.A. George (Trans.), Berkeley: University of California Press 1967.
I follow Bullwinkle’s excellent dissertation (David S. Bullwinkle, Epistemology and Unity of Science in Carnap’s Aufbau, PhD thesis, Northwestern University 2000) in thinking of Carnap’s position as a moderate one. This work has been of great help for this paper more generally in understanding Carnap’s subtle views on the unity of science.
Bullwinkle, op. cit., p. 246. See pp. 246–255 for the argument. Bullwinkle cites Creath and Richardson as having given “undeveloped versions of this claim.” See Richard Creath, “The unity of science: Carnap, Neurath, and beyond,” in: Peter Galison and David J. Stump (eds.), The Disunity of Science: Boundaries, Contexts, and Power. Stanford University Press 1996, pp. 158–169 and Alan Richardson, Carnap’s Construction of the World: The Aufbau and the Emergence of Logical Empiricism. Cambridge University Press 1998, esp. pp. 37–40 & 183 – 184.
Heinrich Rickert, The Limits of Concept Formation in Natural Science. G. Oakes (ed. & trans.), abridged edition, Cambridge University Press 1986, pp. 38–39. Cited at Richardson, op. cit., pp. 37–38.
See, e.g. Michael Friedman, Reconsidering Logical Positivism. Cambridge University Press 1999, pp. 90–94.
Hermann Weyl, Space Time Matter. H.L. Brose (Trans.), 4th edition, Dover, New York, 1952.
See §57 for the argument that “it is in principle possible to reduce all psychological objects to physical objects.”
Rudolf Carnap, “Über die Abhängigkeit der Eigenschaften des Raumes von denen der Zeit,” in: Kant-Studien 30, 1925, pp. 331–345.
Rudolf Carnap, Abriss der Logistik. Vienna: Springer, 1929.
Hans Reichenbach, Axiomatik der relativistischen Raum-Zeit-Lehre. Braunschweig: Vieweg & Sohn, 1924, subsequently published as Hans Reichenbach, Axiomatization of the Theory of Relativity. M. Reichenbach (ed. & trans.), University of California Press: Berkeley, 1969.
I would like to thank Tom Ryckman for drawing this letter to my attention and for many helpful discussions about its significance.
Carnap to Reichenbach, June 20, 1923. Archives for Scientific Philosophy, Pittsburgh University, 016–28–11. “Es handelt sich um eine Strukturlehre der Weltlinien, oder in Ihrer Sprache: Axiomatik der Topologie der Zeit [...] Er verhält sich zu Ihrer Arbeit etwa, wie Russells Logik zur Mathematik, z.B. zur Arithmetik. Während die Ar. von Zahlen u. zwischen ihnen bestehenden Axiomen ausgeht, fängt R. weiter vor an: von rein log. Grundbegriffen und Axiomen ausgehend kommt man zu komplizierten Begriffen u. Lehrsätzen, die die Grundbegr. u.-sätze der Ar. bilden. So gehe ich von Axiomen (in zieml. grosser Zahl) aus, die nur Begriffe der Logik (besonders der Beziehungslehre) enthalten, u. gelange schliesslich zu komplizierten, abgeleiteten Sätzen, die (teilweise) Ihren Axiomen entsprechen.”
Archives for Scientific Philosophy, Pittsburgh University, RC 081–02–07.
“Eigenzeitbeziehung” is used in Carnap, Aufbau, op. cit., §62 and Carnap, Abriss, op. cit., p. 80: “Mit der (topologischen, maßfreien) Eigenzeitbeziehung xZy ist gemeint: x, y sind “genidentische” Weltpunkte, d.h. Weltpunkte derselben Weltlinie (Punktereignisse an demselben physikalischen Element), und zwar ist x zeitlich vor y.” However, the more awkward “Genidentitätszeitbeziehung” is used in the manuscript.
In §6 of the manuscript Carnap suggests that there are two possible interpretations for his symbols “K” and “Z “: 1) they are associated with non-logical relations or 2) they occur as variables in the axioms and these axioms are then associated with the appropriate physical relations. This is a problematic passage because Carnap seems to accept in the second reading something like Reichenbach’s coordinative definitions. I do not believe that this is what Carnap has in mind, though I cannot argue for this here. For a different interpretation of the significance of this passage see Don Howard, “Relativity, Eindeutigkeit, and Monomorphism: Rudolf Carnap and the Development of the Categoricity Concept in Formal Semantics,” in: R. Giere and A. Richardson (Eds.), Origins of Logical Empiricism. University of Minnesota Press 1996, pp. 115–164, esp. pp. 151–161.
Archives for Scientific Philosophy, Pittsburgh University, RC 081–02–07, p. 39.
Ibid., p. 41
Carnap, “Über die Abhängigkeit der Eigenschaften des Raumes von denen der Zeit,” op. cit.
Rudolf Carnap, Physikalische Begriffsbildung. Karlsruhe: G. Braun 1926.
Carnap, “Über die Abhängigkeit der Eigenschaften des Raumes von denen der Zeit,” op. cit., p. 334. “aus den topologischen Eigenschaften der Zeitordnung und der Koinzidenz können die topologischen Eigenschaften der Raumordnung abgeleitet werden. (Die weitergehende These, daß aus denselben Bestimmungen alle Eigenschaften der Raumordnung, also auch die metrischen, abgeleitet werden können, sei hier ohne Begründung oder weitere Erörterung nur vermerkt.)”
See Carnap, “Über die Abhängigkeit der Eigenschaften des Raumes von denen der Zeit,” op. cit., esp. pp. 343–345 for Carnap’s only published references to the Topologie manuscript and also for a reference to Reichenbach’s Axiomatization.
Carnap, Physikalische Begriffsbildung, op. cit., p. 16. “Alle Messung irgend einer Größe wird in der Physik auf Messung räumlicher Länge zurückgeführt [...]”.
In §16 Carnap remarks in passing that the two relations of the physical construction system “are uniquely [eindeutig] determined through the character of the schema.” This suggests that Carnap does not take these two relations as primitives. However, what he appears to have in mind is the possibility of eliminating these relations in the same kind of way that he claims that the basic relation of the psychological system can be eliminated. See §§153–155.1 do not think that either of these eliminations goes through, but I also do not think that they are a central part of Carnap’s project.
See Christian Thiel, “Carnap und die wissenschaftliche Philosophie der Erlanger Tagung 1923,” in: R. Haller and F. Stadler (eds.), Wien-Berlin-Prag: Der Aufstieg der Wissenschaftlichen Philosophie, Vienna: Hölder-Pichler-Tempsky 1993, pp. 175–187 and Rudolf Carnap, “Intellectual Autobiography,” in: P.A. Schilpp (ed.), The Philosophy of Rudolf Carnap, Cambridge University Press 1963 for more on this conference.
Reichenbach, Axiomatization of the Theory of Relativity, op. cit., p. xiii.
A review of Reichenbach’s publications during this period suggests that the subject of the talk was the connection between causal relations and temporal order as reflected in Hans Reichenbach, “The Causal Structure of the World and the Difference between Past and Future,” in: M. Reichenbach and R.S. Cohen (eds.), Selected Writings: 1909–1953, Vol. 2, D. Reidel: Dordrecht, 1978. This paper is closely connected to the 1924 book.
Reichenbach, Axiomatization of the Theory of Relativity, op. cit., p. 6.
Ibid., p. 8. See Hans Reichenbach, The Philosophy of Space and Time. M. Reichenbach (trans.), Dover: New York, 1958, I §4, esp. p. 14 for more discussion of coordinative definitions. There Reichenbach claims that “This coordination cannot be replaced by an explanation of meanings, it simply states that this concept is coordinated to this particular thing.”
Reichenbach, Axiomatization of the Theory of Relativity, op. cit., p. 9, Hans Reichenbach, The Theory of Relativity and A Priori Knowledge. M. Reichenbach (ed. & trans.), University of California Press: Berkeley, 1965, ch. IV
While Reichenbach and Schlick came to agree on these basic points, they disagreed on others. See Klaus Hentschel, “Die vergessene Rezension der ‘Allgemeinen Erkenntnislehre’ Moritz Schlicks durch Hans Reichenbach — ein Stück Philosophiegeschichte,” in: Erkenntnis 35, 1991, pp. 11–28, Hans Reichenbach, The Theory of Relativity and A Priori Knowledge, op. cit., p. 85, fn27, pp. 115–116, and Moritz Schlick, General Theory of Knowledge. A.E. Blumberg (trans.), 2nd edition, Open Court: La Salle, 1985, p. 384, fn48 (added in the second edition) for some evidence of this.
I would like to thank Tom Ryckman, Hans Sluga, Paolo Mancosu and Don Howard for their helpful comments and constant encouragement. Longer versions of this paper were presented at the Vienna Circle and Logical Empiricism conference and at the Vienna International Summer University in July of 2001. I would like to thank both audiences for their comments. The support of a Humanities Research Grant from U.C. Berkeley is gratefully acknowledged. All unpublished material is quoted by permission of the University of Pittsburgh. All rights reserved.
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Pincock, C. (2003). Carnap and the Unity of Science: 1921–1928. In: Bonk, T. (eds) Language, Truth and Knowledge. Vienna Circle Institute Library [2003], vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0151-8_6
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