Abstract
In this paper I introduce a broader context, and sketch an integrated account with the purpose of examining the significance of Neurath’s attention to logic in early works and subsequent positions. The specific attention to algebraic logic is important in integrating his own interest in mathematics and combining, since Leibniz, the ideals of a universal language and of a calculus of reasoning. The interest in universal languages constitutes a much broader, so-called tradition of pasigraphy that extended beyond philosophical projects. I argue (1) that Neurath’s works can be embedded in a richer intellectual landscape that includes developments in logic and their local reception in Vienna, and that his attention to logic developed a sustained symbolic standpoint – with semiotic and typographic expressions –; (2) that specific aspects of the work in algebraic logic became a standard and a resource in subsequent work often thought independent, while its value was steadily challenged by the separate goal of empirical theorizing and practical application in social domains – including in the areas of economics, history and visual communication –; that (3), in particular, the presentation of systems of algebraic logic by Neurath’s sources such as Stanley Jevons and Schröder was not isolated from discussions of political economy; and finally (4) that some of his positions in matters of language, unity and epistemology in the articulation of logical empiricism and its debates are better understood in terms of shared but diversified acquaintance with pasigraphy, formal standards and logical projects.
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Notes
- 1.
- 2.
An early valuable discussion by Eckehart Köhler (1991) is otherwise cursory, dismissive and, equally significantly, isolated from his discussion of other work by Neurath.
- 3.
Lewis , expounding on Couturat’s narrative – and his narrow focus on Huntington’s recent formulation –, provided the main source for other authors.
- 4.
- 5.
Lewis (1918, 79 n. 121). Lewis cited the title incorrectly as “Some illustrations of the Science of Logic;” the series consists of the essays “The Fixation of Belief” and “How to Make our Ideas Clear,” “The Doctrine of Chances,” “The Probability of Induction,” “The Order of Nature” and “Deduction, Induction and Hypotheses.”
- 6.
I am grateful to Volker Peckhaus for a helpful discussion of the significance of Schröder’s contributions.
- 7.
- 8.
In Principia Mathematica, Whitehead and Russell pointed to both dimensions of Schröder’s contribution: his notation as one, alongside those of Frege and Peano , which they will adopt and modify as convenient, and to his calculus, for instance, his explanation of the proposition that ‘p and not-q imply r’ is equivalent to ‘p implies q or r’ (Whitehead and Russell 1910, vol 1, viii and 123). In the wake of reviews by Venn , Husserl , Peano and Peirce’s students, for instance, Whitehead and Russell’s mention might have drawn an even wider international attention to the work of the isolated teacher at a provincial German technical college.
- 9.
- 10.
- 11.
- 12.
Yet again, this text was surprisingly appended as a supplement on recent algebra to the Baden-Baden gymnasium program.
- 13.
- 14.
Schröder (1873, 146) noted that the key notion was contained in the statement about the general character of the product of indeterminate quantities, in the Lehrbuch.
- 15.
Peckhaus (2004, 585–588) calls Schröder’s geometry-inspired approach quasi-axiomatics; unlike derived principles, especially inductive ones such as duality, axioms are formal to the extent that they are derived from self-evident intuitions.
- 16.
- 17.
- 18.
By this time, discussions of logic included examples of human relationships and even a calculus such as Alexander Macfarlane’s, extending Leibniz’s combinatorial discussions; see Peckhaus (2004, 596, n.54).
- 19.
See van Heijenoort’s introduction to the translation of the Begriffsschrift in van Heijenoort (1967b, 1 n. b).
- 20.
- 21.
Here he was following both Lambert and the philologist Max Müller .
- 22.
The essay deserves close comparison with the symbolic, or semiotic, approach in both Mach’s Contributions to the Analysis of Sensations, of 1886, and Peirce’s subsequent writings on semiotics.
- 23.
Also in this respect Schröder’s writings should be compared to Mach’s and his appeal to a principle of economy of thought, rejected by philosophers such as Husserl and Jerusalem as an expression of psychologism, especially in matters of logic, the paradigmatic case of a priori; see Kusch (1995).
- 24.
I am grateful to Margaret Schabas for drawing my attention to the role of logic in connection to mathematics and its application in economics.
- 25.
The project was much in line with the standard set by the optimistic industrial culture of machines and engines prompted by the Industrial Revolution and placed at the heart of the economy. Jevons mentioned attempts by Blaise Pascal , Arthur Colmar , Charles Babbage and Alfred Smee (Jevons 1874, 123–124).
- 26.
See, for instance, Schröder (1890a), Lesson 40, sect 26 and especially Appendix 6.
- 27.
The tension between the roles of mathematics and logic is discussed in Schabas (1990, Ch. 4.), and in Mosselmans (2007, Ch. 4.). The value of Boole’s system, according to Jevons , lied only in an analogy between mathematics and logic, so that logic is the algebra of two terms, 0 and 1 (Jevons 1874, vol. 2, 293).
- 28.
Before his Leibnizian commitment to pasigraphy, Schröder had embraced this symbolic and typographic standpoint in the Lehrbuch der Arithmetik und Algebra (1873).
- 29.
Partly in association with Mill ; see Schröder (1890a, 177).
- 30.
- 31.
- 32.
I am indebted to Professor Karl Sigmund for providing the information; see Öffentliche Vorlesungen an der k.k. Universität zu Wien, Archiv der Universität Wien.
- 33.
Migerka was the organizer of a special exhibition on women at work at the Vienna World Fair of 1873 and married Otto Neurath’s future maternal aunt.
- 34.
- 35.
See W. Neurath’s autobiographical sketch, in Neurath and Cohen (1973, 2). W. Neurath died in March 1901.
- 36.
I am indebted for this information to Karl Sigmund; see Otto Neurath’s Nationale for winter 1902–3 and summer 1903, Archiv der Universität Wien.
- 37.
Neurath (1903); see especially the translation of the first and last paragraphs in Uebel (2004, 16).
- 38.
See Wilhelm Neurath’s textbook, W. Neurath (1896).
- 39.
Uebel (forthcoming) elaborates on this apparent inconsistency in Neurath’s position and its conflict with the established accounts of logical positivism in Uebel.
- 40.
- 41.
Uebel develops this point in Uebel (2004, 12–15).
- 42.
For the supporting documents, see “Ansuchen um Zulassung zu den Rigorosen”, Rigorosenakt Olga Hahn, Archiv der Universität Wien, Sig. PH RA 3111 and “Beurteilung der Dissertation Olga Hahn (von Adolf Stöhr)”, Rigorosenakt Olga Hahn, Archiv der Universität Wien, Sig. PH RA 3111. I am grateful to Karl Sigmund, Johannes Friedl and Christoph Limbeck for assistance.
- 43.
In his brief and dismissively critical overview, Köhler (1991, 109–112) somewhat misleadingly refers to sets and set-theoretic operations, whereas Schröder’s extensional approach, following Boole , is based on part-whole relations rather than membership.
- 44.
Neurath (1909a/1981, 1–3) and Appendix in this volume, 489–492.
- 45.
Here Köhler (1991, 110) speculates that the absence of the sign motivated Neurath to declare that one can “equate symbolically” ‘ab’ and ‘ba.’
- 46.
Köhler (1991, 111) introduces the symbol ‘&’ for conjunction, which Schröder and Neurath, after him, didn’t use, and he himself has noted the notational role in Neurath’s argument.
- 47.
This typographic standpoint is of course a matter of both types and concrete visible token marks.
- 48.
- 49.
Neurath (1909a/1981, 3) and this volume, 492.
- 50.
According to Köhler (1991, 111), it undermines the expressive power, namely, for representing the properties of operations. As a criticism, he also points to alternative treatments of the question of equality he considers more enlightening and influential such as Frege’s (1892) “On Sense and Reference.” Later, Carnap (1947), committed to his teacher Frege and to logicism, would offer also an intensional account of asymmetric identities in Meaning and Necessity. A different source is Waissmann’s (1936/1977) Wittgensteinian defense of redundancy in language and the treatment of identity.
- 51.
On the relation between syntacticism and physicalism, see Derek Anderson’s chapter in the present volume.
- 52.
The first volume of the Vorlesungen includes a full section on the topic.
- 53.
Neurath (1909b, 18), and this volume, 506.
- 54.
Neurath (1909b, 18), and this volume, 506.
- 55.
Nevertheless, with Axiom VIx’, below, for instance, Schröder could also define the products asymmetrically in terms of the more fundamental relation of subordination.
- 56.
- 57.
Axiom VIx’ is (x € a)(x € b) € (x € ab) (Schröder 1909, 23).
- 58.
Neurath (1910a/1981, 19–21), and in this volume, 509–11.
- 59.
Neurath (1910a/1981, 19), and this volume, 509.
- 60.
- 61.
Neurath (1910a/1981, 20), and this volume, 510.
- 62.
Note that as theoretical approach, Neurath had already adopted empirical classifications in his work in the history of economics, namely, with the classification of systems of organization of production and distribution of goods.
- 63.
Neurath (1910a/1981, 21), and this volume, 511.
- 64.
Walter Dubislav (1931) devoted an entire monograph to definitions in 1931, in a book, Die Definition, published in the Erkenntnis series edited by Carnap and Reichenbach , a collaboration between the Berlin and Vienna groups. He distinguished, following Leibniz , the following kinds of definitions: nominal, real, causal and essential (1931, 24). He also listed Neurath’s article in the bibliography, but, as in other authors’ bibliographical mentions, didn’t discuss it (1931, 155).
- 65.
O. Hahn (1909), and this volume, 507–9.
- 66.
O. Hahn (1909, 345), and this volume, 507.
- 67.
- 68.
O. Hahn (1909, 347), and this volume, 509. However, Schröder’s introduction of the operations in terms of subsumption is in fact based on asymmetric expressions.
- 69.
- 70.
Köhler (1991, 112) objects that Hahn and Neurath fare no better by appealing to a list of theorems too, but that is just as well, since the principle is not an axiom or a theorem, but a metatheoretic statement operating as a proof procedure. For Köhler, again, implicit in their argument is yet another redeeming metatheoretic intuition.
- 71.
- 72.
- 73.
In a note Neurath (1910b/2004, 290, n. 27) points out that “the above account required no examination of the motives” and, more radically, that if we ignore moral pleasure or pain, the transition from one distribution of wealth to a more satisfying one represents an improvement since it doesn’t constrain the particular kind of transfer of goods involved and takes into account, or at least makes room for, different possibilities.
- 74.
He introduced the notion of complementary goods as a fundamental concept also in his textbook on economics of the same year (Neurath 1910b, 1).
- 75.
For Schröder (1909, 26), the exhaustive conjunction of two domains of objects (including propositions) may be represented as a + b = 1 (totality, universe), so that negation allows the definition of a complementary (or reciprocal) domain b = not-a.
- 76.
Notice that Schröder’s Vorlesungen bore the subtitle Exakte Logik.
- 77.
On the influence of Neurath and Carnap on Stevens see Hardcastle’s (2003) discussion of Carnap and Stevens at the head of the so-called Harvard Science of Science Discussion Group, in 1940–41.
- 78.
On reasoning with inequalities, see Jevons (1874, vol. 1, 186–188).
- 79.
Neurath’s notation for the indeterminate relation when the inequality sign doesn’t apply was the question mark “?”.
- 80.
See, for instance, Jevons (1874, vol. 1, 122).
- 81.
Note that in the case of symbolic equalities, Neurath also pointed to the typographic artifact of one-dimensionality in our symbolic representations.
- 82.
On the role of analogies and their relation to Mach’s work also on optics, see Stöltzner (1996/1983).
- 83.
See Duhem (1906). Duhem was also concerned with classification as the proper aim of science, without deeper explanations.
- 84.
- 85.
On the optical illustration, see Gábor Zemplén’s chapter in the present volume.
- 86.
In the plural scene of nineteenth-century British new empiricism, the view can be traced back especially to Herschel and Mill , also Whewell .
- 87.
He was following Ampère, and indirectly a long literature going back to the seventeenth century. Duhem would adopt a more regulative and metaphysical notion of natural classification (Duhem 1906).
- 88.
This is similar to the structural description Carnap would introduce in his Aufbau later in the same decade.
- 89.
See Burke et al. (2013), also Angélique Groß’s chapter in the present volume.
- 90.
Mosselmans (2007, 50) quotes Neurath merely to identify in Jevons a “logical positivist attitude.”
- 91.
- 92.
- 93.
For an overview of the intellectual and associationist Viennese landscape, see Stadler (2001).
- 94.
Rather than subscribing to overdrawn contrasts between pre-1930, pre-1935 and post-1935 Neurath, drawn for instance by Mormann (1999), and equally between Neurath and Carnap, usefully drawn by Uebel and, especially after 1935, by Mormann, I want to emphasize any differences only in relation to a shared background and interest in symbolic language and logic.
- 95.
- 96.
Itelson , Couturat and Lalande made the proposal at the 1904 at the International Congress of Philosophy in Geneva.
- 97.
- 98.
In all the techniques Carnap was relying, also rhetorically, on modern scientific developments, both empirical, e.g., Gestalt psychology, and formal and foundational, e.g., set theory, axiomatics and logicism.
- 99.
Carus (2007, 103) stresses the Fregean connection.
- 100.
Neurath (1937a/1983, 174) later wrote, in relation to the new discipline of the logic of science, a replacement of philosophy, and linguistic (anti-metaphysical and social) unification, that “progress of the unification of scientific language requires a logical analysis of the sciences” and that “Mach’s far-reaching conclusions did not depend upon new experimental data, but simply upon a rigorous logical analysis of the traditional formulations.”
- 101.
- 102.
Carnap had done the same in the Abriss, of the same year.
- 103.
An important question that deserves attention is the distinction between sign and symbol. These authors often lack a systematic distinction, or a consistent statement of their equivalence: they sometimes use the terms interchangeably, or else their use is inconsistent in taking ‘sign’ as the more general term, almost in Peirce’s sense, or else as a concrete token of a symbol, or as an index, in contrast with the more conventional character of a symbol, restricted further by the rules of a specific system of symbols, or language, including mathematics.
- 104.
Carnap would soon add to the list of sources the material mode of expression.
- 105.
Neurath drew attention to the scientific value of general names (variables).
- 106.
Note also that for Peirce (1884), algebraic logic was a contribution to the ‘philosophy of notation.’
- 107.
In the followings sections, the Neurath-Carnap letters are quoted from the Carnap Archive at Pittsburgh (Rudolf Carnap Papers, 1905–1970, ASP.1974.01, Special Collections Department, University of Pittsburgh). All rights reserved.
- 108.
- 109.
- 110.
As he had done in the Aufbau, in the bibliography Carnap listed Gätschenberger’s Symbola (1920).
- 111.
In the tradition of Leibniz , Lambert and turn-of-the-century symbolic logic, Gätschenberger (1920, 126, 133, and 454) declared that sematology contributed to algebraic logic, especially to the calculus of relations sought by Peirce and Schröder, and from that standpoint, it was the mother of mathematics. On Gätschenberger’s relevance to Carnap’s early works, see Haller (1959); on his place in German semiotics, see Eschbach (1987).
- 112.
Neurath to Carnap, 3 November, 1932; RC 029-12-13. In the same letter Neurath also analyzed cases of empirical falsehood as forms of logical contradiction or nonsense.
- 113.
Neurath to Carnap, 5 April 1934; RC 029-10-77.
- 114.
Mormann adopts Hintikka’s terminology, paraphrasing van Heijenort’s focus on logic, language as universal medium and language as calculus.
- 115.
In a number of places, Neurath adopted the characaterization of the encyclopedia as a model, in a Duhemian sense, part of the opposition to the characaterization of unity as a system (Neurath 1936/1983, 145); but he used the term “model” also for a broader category to contrast the encylopedia with the system as models of knowledge (ibid., 156). In relation to Duhem, it must be noted that he adopted the notion of logical unity in the sense of oneness, as a fundamental feature of natural classification.
- 116.
I’m grateful to Adam Tamas Tuboly for drawing my attention to the letter.
- 117.
These are names listed by Neurath on the cover letter from 10 May 1937 with the proposal sent out for circulation. Nachlass K13. The Congress Report included a mention of the committee that listed Alfred Tarski and Olaf Helmer (Erkenntnis 7, 63).
- 118.
See also Adam Tamas Tuboly’s chapter in the present volume.
- 119.
Neurath to Carnap, 25 September, 1943 (RC 102-55-03). See letter 22 in the present volume.
- 120.
Neurath to Carnap, 16 June, 1945 (RC 102-55-11). See letter 31 in the present volume.
- 121.
Neurath to Carnap, 15 January, 1943 (RC 102-55-02). See letter 17 in the present volume.
- 122.
See letter to Carnap, 22 September 1945, unsent (RC 115-07-66). See letter 34 in the present volume.
- 123.
See letter to Carnap, 22 September 1945, unsent (RC 115-07-66). See letter 34 in the present volume.
- 124.
Neurath to Carnap 4 April 1941 (RC 102-55-20), see letter 5 in the present volume.
- 125.
Carnap to Neurath, 5 June 1941 (RC 102-55-19), see letter 6 in the present volume.
- 126.
Neurath to Carnap, 17 July 1942 (RC 102-56-04), see letter 11 in the present volume.
- 127.
Neurath to Carnap, 20 July 1942 (RC 115-07-57). See letter 12 in the present volume.
References
Blackmore, John, Ryoichi Itagaki, and Sezsuko Tanaka, eds. 2001. Ernst Mach’s Vienna 1895–1930. Dordrecht: Kluwer.
Boole, George. 1854. An Investigation of the Laws of Thought. Cambridge: Macmillan.
Burke, Christopher, Eric Kindel, and Sue Walker, eds. 2013. Isotype: Design and Contexts 1925–1971. London: Hyphen Press.
Carnap, Rudolf. 1928/1967. The Logical Structure of the World. Trans. R. George. Berkeley: University of California Press.
———. 1929. Abriss der Logistik. Wien: Springer.
———. 1930. Die alte und die neue Logik. Erkenntnis 1: 12–26.
———. 1932/1995. The Unity of Science. London: Thoemmes.
———. 1934/1937. The Logical Syntax of Language. London: Kegan Paul, Trench.
———. 1947. Meaning and Necessity. Chicago: University of Chicago Press.
Carnap, Rudolf, Hans Hahn, and Otto Neurath. 1929/1973. The Scientific Conception of the World: The Vienna Circle. In Neurath and Cohen (1973): 299–318.
Cartwright, Nancy, Jordi Cat, Lola Fleck, and Thomas Uebel. 1996. Otto Neurath: Philosophy Between Science and Politics. Cambridge: Cambridge University Press.
Carus, André. 2007. Carnap and Twentieth-Century Thought. Explication as Enlightenment. Cambridge: Cambridge University Press.
Cat, Jordi. 1995. The Popper-Neurath Debate and Neurath’s Attack on Scientific Method. Studies in History and Philosophy of Science Part A 26 (2): 219–250.
Church, Alonzo. 1936. A Bibliography of Symbolic Logic. Journal of Symbolic Logic 1 (4): 121–216.
Couturat, Louis. 1905/1914. The Algebra of Logic. Chicago: Open Court.
Dipert, Randall. 1978. Development and Crisis in Late Boolean Logic: The Deductive Logics of Peirce, Jevons and Schröder. Bloomington, IN: Indiana University Ph.D.
———. 1991. The Life and Work of Ernst Schröder. Modern Logic 1: 119–139.
Dubislav, Walter. 1931. Die Definition. Leipzig: Meiner.
Duhem, Pierre. 1906. La Théorie Physique: Son Object, et Sa Structure. Paris: Chevalier & Rivière.
Eschbach, Achim. 1987. Sematology as basic science. In R. Gätschenberger, Foundations of semiotics, i-xxi. Philadelphia: John Benjamin.
Fechner, Gustav. 1888. Elemente der Psychophysik. Vol. 1. Leipzig: Breitkopf and Härtel.
Frege, Gottlob. 1879. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle: Louis Nebert.
———. 1884/1968. The Foundations of Arithmetic. Trans. J.L. Austin. Oxford: Basil Blackwell.
———. 1892/1980. On Sense and Reference. In Translations from the Philosophical Writings of Gottlob Frege. Trans. Max Black. ed. Peter Geach and Max Black, 56–78. Oxford: Blackwell.
Freudenthal, Gideon, and Tatiana Karachentsev. 2011. G. Itelson – A Socratic Philosopher. In Otto Neurath and the Unity of Science, ed. John Symons, Olga Pombo, and Juan Manuel Torres, 95–108. Dordrecht: Springer.
Gätschenberger, Richard. 1920. Symbola. Karlsruhe: G. Braun.
George, Henry. 1882. Progress and Poverty. London: Kegan Paul, Trench & Co.
Grassmann, Hermann. 1844. Die lineale Ausdehnungslehre. Leipzig: Wiegand.
Grassmann, Robert. 1872. Die Formenlehre oder Mathematik. Stettin: R. Grassmann.
Grattan-Guinness, Ivor. 1975. Wiener on the Logics of Russell and Schröder. An Account of his Doctoral Thesis, and of his Subsequent Discussion of it with Russell. Annals of Science 32: 103–132.
———. 2000. The Search for Mathematical Roots, 1870–1940. Logics, Set Theories and the Foundations of Mathematics from Cantor Through Russell to Gödel. Princeton: Princeton University Press.
———. 2004. The Mathematical Turns in Logic. In Handbook of the History of Logic, ed. Dov M. Gabbay and John Woods, vol. 3, 545–556. Amsterdam: Elsevier.
Hahn, Olga. 1909. Zur Axiomatik des logischen Gebietkalkuls. Archiv für Philosophie, 2. Abteilung: Archiv für systematische Philosophie, Neue Folge, Bd. 15: 345–347. See also Appendix 1 in the volume.
———. 1910. Über die Koeffizienten einer logischen Gleichung und ihre Beziehung zur Lehre von den Schlüssen. Archiv für Philosophie, 2. Abteilung: Archiv für systematische Philosophie, Neue Folge, Bd. 16: 149–176.
Hahn, Olga, and Otto Neurath. 1909. Zum Dualismus in der Logik. Archiv für Philosophie, 2. Abteilung: Archiv für systematische Philosophie, Neue Folge, Bd. 15: 149–162. Reprinted in Haller and Rutte (1981): 5–16. See also Appendix 1 in the volume.
Hahn, Hans. 1929/1980. Empiricism, Mathematics, and Logic. In Hans Hahn: Empiricism, Logic, and Mathematics, ed. Brian McGuinness, 39–42. Dordrecht: D. Reidel.
Hailperin, Theodore. 2004. Algebraical Logic. In Handbook of the History of Logic, ed. Dov M. Gabbay and John Woods, vol. 3, 323–388. Amsterdam: Elsevier.
Haller, Rudolf. 1959. Das ‘Zeichen’ und die ‘Zeichenlehre’ in der Philosophie der Neuzeit. Archiv für Begriffsgeschichte 4: 113–157.
Haller, Rudolf, and Heiner Rutte, eds. 1981. Gesammelte philosophische und methodologische Schriften. Vienna: Hölder-Pichler-Tempsky.
Hardcastle, Gary. 2003. Debabelizing Science: The Harvard Science of Science Discussion Group, 1940–41. In Logical Empiricism in North America, ed. Gary Hardcastle and Alan W. Richardson, 170–196. Minneapolis: University of Minnesota Press.
Harman, Peter. 1998. The Natural Philosophy of James Clerk Maxwell. Cambridge: Cambridge University Press.
Hempel, Carl G., and Paul Oppenheim. 1936. Der Typusbegriff im Lichte der neun Logik: Wissenschaftstheorische Untersuchungen zu Konstitutionsforschung und Psychologie. Leiden: Sijthoff.
Howard, Don. 1996. Relativity, Eindeutigkeit, and Monomorphism: Rudolf Carnap and the Development of the Categoricity Concept in Formal Semantics. In Origins of Logical Empiricism, ed. Ronald N. Giere and Alan W. Richardson, 115–164. Minneapolis: University of Minnesota Press.
Janik, Allan, and Stephen Toulmin. 1973. Wittgenstein’s Vienna. New York: Simon and Schuster.
Jevons, William S. 1864. Pure Logic, or The Logic of Quality Apart from Quantity. Stanford: London.
———. 1869. The Substitution of Similars, the True Principle of Reasoning. London: Macmillan.
———. 1871. The Theory of Political Economy. London: Macmillan.
———. 1874. The Principles of Science. A Treatise on Logic and Scientific Method. 1st ed. 2 vols. London: Macmillan.
———. 1877. The Principles of Science. A Treatise on Logic and Scientific Method. 2nd ed. 2 vols. London: Macmillan.
Johnston, William M. 1972. The Austrian Mind. An Intellectual and Social History 1848–1938. Berkeley: University of California Press.
Jourdain, Philip E. B. 1914. Preface. In Couturat (1905/1914): iii-iix.
Köhler, Eckehart. 1991. On Neurath’s Writings on Logic, Ethics and Physics. In Rediscovering the Forgotten Vienna Circle, ed. Thomas Uebel, 109–116. Dordrecht: Kluwer.
Kusch, Martin. 1995. Psychologism. A Study in the Sociology of Philosophical Knowledge. London: Routledge.
Ladd, Christine. 1880. On De Morgan’s Extension of the Algebraic Logic. American Journal of Mathematics 3: 210–225.
Lambert, Johann H. 1764. Neues Organon. Leipzig: Wendler.
Lewis, Clarence I. 1918. A Survey of Symbolic Logic. Berkeley: University of California Press.
Menger, Karl. 1994. Reminiscences of the Vienna Circle and the Mathematical Colloquium. Dordrecht: Kluwer.
Mormann, Thomas. 1999. Neurath’s Opposition to Tarskian Semantics. In Alfred Tarski and the Vienna Circle: Austro-Polish Connections in Logical Empiricism, ed. Jan Woleński and Eckehart Köhler, 165–178. Dordrecht: Kluwer.
Mosselmans, Bert. 2007. William Stanley Jevons and the Cutting Edge of Economics. New York: Routledge.
Nemeth, Elisabeth, and Friedrich Stadler, eds. 1996. Encyclopedia and Utopia: The Life and Work of Otto Neurath (1882–1945). Dordrecht: Kluwer.
Neurath, Wilhelm. 1896. Elemente der Volkswirtschaftslehre. 3rd ed. Leipzig: Klinkhardt.
Neurath, Otto. 1904/2004. Interest on Money in Antiquity. In Otto Neurath. Economic Writings. Selections 1904–1945, ed. Thomas Uebel and Robert S. Cohen, 111–119. Dordrecht: Kluwer.
———. 1906–1907. Zur Anschauung der Antike über Handel, Gewerbe und Landwirtschaft (Cicero, De Officii, I 42). Jahrbücher für Nationalökonomie und Statistik 3, Folger 32 and 34.
———. 1909a. Ernst Schröders Beweis des 12. Theorems: Für die identischen Operationen gilt das ‘Kommutationsgesetz,’ Archiv für Philosophie, 2. Abteilung: Archiv für systematische Philosophie, Neue Folge, Bd. 15: 104–106. Reprinted in Haller and Rutte (1981): 1–3. See also Appendix 1 in the volume.
———. 1909b. Eindeutigkeit und Kommutativität des logischen Produktes ab. Archiv für Philosophie, 2. Abteilung: Archiv für systematische Philosophie, Neue Folge, Bd. 15: 342–344. Reprinted in Haller and Rutte (1981): 17–18. See also Appendix 1 in the volume.
———. 1909c. Antike Wirtschaftsgeschichte. Leipzig: Teubner.
———. 1910a. On the Theory of Social Science. In Otto Neurath. Economic Writings. Selections 1904–1945, ed. Thomas Uebel and Robert S. Cohen, 265–291. Dordrecht: Kluwer.
———. 1910b. Definitionsgleichheit und symbolische Gleichheit. Archiv für Philosophie, 2. Abteilung: Archiv für systematische Philosophie, Neue Folge, Band 16: 142–144. Reprinted in Haller and Rutte (1981): 19–21. See also Appendix 1 in the volume.
———. 1910c/2004. War economy. In Otto Neurath. Economic writings. Selections 1904–1945, ed. Thomas Uebel and Robert S. Cohen, 153–199. Dordrecht: Kluwer.
———. 1910d. Lehrbuch der Volkswirtschaftslehre. Wien: Alfred Hölder.
———. 1912/1973. The Problem of the Pleasure Maximum. In Neurath and Cohen (1973): 113–122.
———. 1913/1983. The Lost Wanderers of Descartes and the Auxiliary Motive (On the Psychology of Decision). In Otto Neurath: Philosophical Papers 1913–1946, ed. Robert S. Cohen and Marie Neurath, 1–12. Dordrecht: D. Reidel.
———. 1915/1973. On the Foundation of the History of Optics. In Neurath and Cohen (1973): 101–112.
———. 1916/1983. On the Classification of Systems of Hypotheses (With Special Reference to Optics). In Otto Neurath: Philosophical Papers 1913–1946, ed. Robert S. Cohen and Marie Neurath, 13–31. Dordrecht: D. Reidel.
———. 1917a/2004. The economic order of the future and the economic sciences. In Otto Neurath. Economic writings. Selections 1904–1945, ed. Thomas Uebel and Robert S. Cohen, 241–261. Dordrecht: Kluwer.
———. 1917b/2004. On the theory of social science. In Otto Neurath. Economic writings. Selections 1904–1945, ed. Thomas Uebel and Robert S. Cohen, 265–291. Dordrecht: Kluwer.
———. 1921/1973. Anti-Spengler. In Neurath and Cohen (1973): 158–213.
———. 1925/1973. The Social and Economic Museum in Vienna. In Neurath and Cohen (1973): 214.
———. 1928/1973. Personal Life and Class Struggle. In Neurath and Cohen (1973): 249–298.
———. 1930/1983. Ways of the Scientific World-Conception. In Otto Neurath: Philosophical Papers 1913–1946, ed. Robert S. Cohen and Marie Neurath, 32–47. Dordrecht: D. Reidel.
———. 1931a/1983. Physicalism: The Philosophy of the Vienna Circle. In Otto Neurath: Philosophical Papers 1913–1946, ed. Robert S. Cohen and Marie Neurath, 48–51. Dordrecht: D. Reidel.
———. 1931b/1983. Sociology in the Framework of Physicalism. In Otto Neurath: Philosophical Papers 1913–1946, ed. Robert S. Cohen and Marie Neurath, 58–90. Dordrecht: D. Reidel.
———. 1932/33/1983. On Protocol Statements. In Otto Neurath: Philosophical Papers 1913–1946, ed. Robert S. Cohen and Marie Neurath, 91–99. Dordrecht: D. Reidel.
———. 1933/1973. Museums of the Future. In Neurath and Cohen (1973): 218–223.
———. 1934/1983. Radical Physicalism and the ‘Real World.’ In Otto Neurath: Philosophical Papers 1913–1946, ed. Robert S. Cohen and Marie Neurath, 100–114. Dordrecht: D. Reidel.
———. 1935a/1983. The Unity of Science as a Task. In Otto Neurath: Philosophical Papers 1913–1946, ed. Robert S. Cohen and Marie Neurath, 115–120. Dordrecht: D. Reidel.
———. 1935b/1983. Pseudorationalism of Falsification. In Otto Neurath: Philosophical Papers 1913–1946, ed. Robert S. Cohen and Marie Neurath, 121–131. Dordrecht: D. Reidel.
———. 1936/1981. Die Entwicklung des Wiener Kreises und die Zukunft des Logischen Empirismus. In Haller and Rutte (1981): 673–702.
———. 1936a/1983. Individual Sciences, Unified Science, Pseudorationalis. In Otto Neurath: Philosophical Papers 1913–1946, ed. Robert S. Cohen and Marie Neurath, 132–138. Dordrecht: D. Reidel.
———. 1936b/1983. Encyclopedia as ‘Model.’ In Otto Neurath: Philosophical Papers 1913–1946, ed. Robert S. Cohen and Marie Neurath, 145–158. Dordrecht: D. Reidel.
———. 1936c/1983. Physicalism and the Investigation of Knowledge. In Otto Neurath: Philosophical Papers 1913–1946, ed. Robert S. Cohen and Marie Neurath, 159–171. Dordrecht: D. Reidel.
———. 1937/1987. Towards an Encyclopedia of Unified Science. In Unified Science, ed. Brian McGuinness, 130–165. Dordrecht: D. Reidel.
———. 1937a/1983. Unified Science and its Encyclopedia. In Otto Neurath: Philosophical Papers 1913–1946, ed. Robert S. Cohen and Marie Neurath, 172–182. Dordrecht: D. Reidel.
———. 1937b/1983. The New Encyclopedia of Scientific Empiricism. In Otto Neurath: Philosophical Papers 1913–1946, ed. Robert S. Cohen and Marie Neurath, 189–199. Dordrecht: D. Reidel.
———. 1937c/1983. The Concept of ‘Type’ in the Light of modern Logic. In Otto Neurath: Philosophical Papers 1913–1946, ed. Robert S. Cohen and Marie Neurath, 183–188. Dordrecht: D. Reidel.
———. 1941/1983. Universal Jargon and Terminology. In Otto Neurath: Philosophical Papers 1913–1946, ed. Robert S. Cohen and Marie Neurath, 213–229. Dordrecht: D. Reidel.
———. 1945/1973. Visual Education: Humanisation versus Popularisation. [Excerpts]. In Neurath and Cohen (1973): 227–248.
———. 1946/1983. The Orchestration of the Sciences by the Encyclopedism of Logical Empiricism. In Otto Neurath: Philosophical Papers 1913–1946, ed. Robert S. Cohen and Marie Neurath, 230–242. Dordrecht: D. Reidel.
———. 1996.Visual Education: Humanisation versus Popularisation. In Nemeth and Stadler (1996): 245–335.
Neurath, Marie, and Robert S. Cohen, eds. 1973. Empiricism and Sociology. Dordrecht: D. Reidel.
Neurath, Otto, and Anne Schapire-Neurath, eds. 1910. Lesebuch der Volkswirtschaftslehre. Leipzig: Klinkhart Second edition: 1913, Leipzig: Glöckner.
O’Connor, J.J., and E.F. Robertson. 2009. Ernst Schröder. MacTutor History of Mathematics Archive, University of St. Andrews. http://www-history.mcs.st-andrews.ac.uk/Biographies/Schroder.html
Pareto, Vilfredo. 1906. Manuale di Economia Politica. Milan: Società Editrice Libraria.
Peckhaus, Volker. 1999. 19th Century Logic Between Philosophy and Mathematics. Bulletin of Symbolic Logic 5 (4): 433–450.
———. 2004. Schröder’s Logic. In Handbook of the History of Logic, ed. Dov M. Gabbay and John Woods, vol. 3, 557–609. Amsterdam: Elsevier.
———. 2014. Ernst Schröder on Pasigraphy. Revue d’Historie des Sciences 67 (2): 207–230.
Peirce, Charles S. 1867. On an Improvement in Boole’s Calculus of Logic. Proceedings of the American Academy of Arts and Sciences 7: 250–261.
———. 1880. On the Algebra of Logic. American Journal of Mathematics 3: 15–57.
———. 1885. On the Algebra of Logic: A Contribution to the Philosophy of Notation. American Journal of Mathematics 7: 180–202.
Petzoldt, Joseph. 1895. Das Gesetz der Eindeutigkeit. Vierteljahrsschrift für wissentschaftliche Philosophie und Sociologie 19: 146–203.
———. 1900. Einführung in die Philosophie der reinen Erfahrung. Vol. 1. Leipzig: Teubner.
Popper, Karl R. 1973. Memories of Otto Neurath. In Neurath and Cohen (1973): 51–56.
Reck, Erich H. 2004. From Frege and Russell to Carnap: Logic and Logicism in the 1920s. In Carnap Brought Home. The View from Jena, ed. Steve Awodey and Carsten Klein, 151–180. Chicago: Open Court.
Reck, Erich H., and Steve Awodey. 2004. Frege’s Lectures on Logic and Their Influence. In Frege’s Lectures on Logic. Carnap’s Student Notes, 1910–1914, ed. Erich H. Reck and Steve Awodey, 17–42. Chicago: Open Court.
Reininger, Robert, ed. 1938. 50 Jahre Philosophische Gesellschaft an der Universität Wien 1888–1938. Vienna: Verlag Philosophische Gesellschaft an der Universität Wien, E. Kainz and J.B. Wallishausser.
Reisch, George. 2005. How the Cold War Transformed Philosophy of Science: To the Icy Slopes of Logic. New York: Cambridge University Press.
Russell, Bertrand. 1900. A Critical Exposition of the Philosophy of Leibniz. Cambridge: Cambridge University Press.
———. 1940. An Inquiry into Meaning and Truth. London: Allen & Enwin.
Sandner, Günther. 2014. Otto Neurath. Eine politische Biographie. Wien: Zsolnay.
Schabas, Margaret. 1990. A World Ruled by Numbers. W. Stanley Jevons and the Rise of Mathematical Economics. Princeton: Princeton University Press.
Schorske, Carl E. 1979. Fin-de-Siècle Vienna. Politics and Culture. New York: Alfred Knopf.
Schröder, Ernst. 1873. Lehrbuch der Arithmetik und Algebra für Lehrer und Studirende (pt. 1 and only). Leipzig: Teubner.
———. 1874a. Abriss der Arithmetik und Algebra für Schüler an Gymnasien und Realschulen (pt. 1 and only), Leipzig: Teubner.
———. 1874b. Über die Formalen Elemente der absoluten Algebra, appended to Beilage zum Programm des Pro- und Real-Gymnasiums in Baden-Baden für 1873–74. Stuttgart: Schweizbart.
———. 1877. Operationskreis des Logikkalkuls. Leipzig: Teubner.
———. 1880. Review of Frege’s Begriffsschrift. Zeitschrift für Mathematik und Physik, Hist.-literarische 25: 81–94.
———. 1884a. On the Most Commodious and Comprehensive Calculus. In Report of the Fifty-Third Meeting of the British Association for the Advancement of Science, 411–412. London: John Murray.
———. 1884b. Exposition of a Logical Principle, as Disclosed by the Algebra of Logic but Overlooked by the Ancient Logicians. In Report of the Fifty-Third Meeting of the British Association for the Advancement of Science, 411. London: John Murray.
———. 1890a. Vorlesungen über die Algebra der Logik (exakte Logik). Vol. 1. Leipzig: Teubner.
———. 1890b. Über das Zeichen. Leipzig: Fock.
———. 1891. Vorlesungen über die Algebra der Logik (exakte Logik), vol. 2, pt. 1, Leipzig: Teubner.
———. 1892. Signs and Symbols. The Open Court 6: 3431–3434, 3441–3444 and 3463–3466.
———. 1895. Vorlesungen über die Algebra der Logik (exakte Logik), vol. 3, pt. 1: Algebra und Logik der Relative. Leipzig: Teubner
———. 1898a. Über Pasigraphie, ihren gegenwärtigen Stand und die pasigraphische Bewegung in Italien. In Verhandlugen des Ersten Internationalen Mathematiker-Kongresses in Zürich vom 9. Bis 11. August 1897, ed. F. Rudio, 147–162. Leipzig: Teubner.
———. 1898b. On Pasigraphy. The Monist 9: 44–62 (corrigenda p. 320).
———. 1909. Abriss der Algebra der Logik. ed. K.E. Müller, pt. 1: Elementarlehre, Leipzig: Teubner.
Stadler, Friedrich. 2001. The Vienna Circle: Studies in the Origins, Development, and Influence of Logical Empiricism. Vienna/New York: Springer.
Stebbing, Susan. 1930/1942. A Modern Introduction to Logic. 3rd ed. London: Methuen.
Stöhr, Adolph. 1910. Lehrbuch der Logik in Psychologisiender Darstellung. Wien: Franz Deuticke.
Stöltzner, Michael. 1996. The auxiliary motive in the Forest and in optics. In Nemeth and Stadler (1996): 113–126.
Trendelenburg, Adolf. 1867. Über Leibnizens Entwurf einer allgemeinen Charakteristik. In Historische Beiträge zur Philosophie, vol. 3, 1–47. Berlin: Bethge.
Uebel, Thomas. 1992. Overcoming Logical Positivism from Within. Amsterdam: Rodopi.
———. 1995. Otto Neurath’s Idealist Inheritance: The Social and Economic Thought of Wilhelm Neurath. Synthese 103: 87–121.
———. 2004. Neurath’s economics in critical context. In Otto Neurath. Economic writings. Selections 1904–1945, ed. Thomas Uebel and Robert S. Cohen, 1–108. Dordrecht: Kluwer.
———. 2007. Empiricism at the Crossroads. La Salle: Open Court.
———. 2008. Writing a Revolution: On the Production and Early Reception of the Vienna Circle’s Manifesto. Perspectives on Science 16 (1): 70–102.
———. Forthcoming. Neurath on Verstehen. Forthcoming manuscript.
van Heijenoort, Jean, ed. 1967a. Logic as Calculus and Logic as Language. Synthese 17: 324–330.
———, ed. 1967b. From Frege to Gödel. A Source Book in Mathematical Logic. Cambridge, MA: Harvard University Press.
Vossoughian, Nader. 2008. Otto Neurath: The Language of the Global Polis. Rotterdam: NAi.
Waismann, Friedrich. 1936/1977. The Concept of Identity. In Friedrich Waismann: Philosophical Papers, ed. Brian McGuinness, 22–29. Dordrecht: D. Reidel.
Whitehead, Alfred N. 1898. A Treatise on Universal Algebra. Cambridge: Cambridge University Press.
Whitehead, Alfred N., and Bertrand Russell. 1910–1913. Principia Mathematica. 3 vols. Cambridge: Cambridge University Press.
Wundt, Wilhelm. 1880. Logik: Einte Untersuchung der Prinzipen der Erkenntnis und der Methoden wissenschaftlicher Forschung. 1st ed, vol. 1, Erkenntnislehre. Stuttgart: Enke.
———. 1893. Grundzüge der physiologischen Psychologie. Vol. 1. 2nd ed. Leipzig: Wilhelm Engelmann.
———. 1906. Logik: Einte Untersuchung der Prinzipen der Erkenntnis und der Methoden wissenschaftlicher Forschung. Vol. 1. 3rd ed. Erkenntnislehre. Stuttgart: Enke.
———. 1907. Logik. Vol. 2, 3rd ed. Logik der Exakten Wissenschaften. Stuttgart: Enke.
———. 1908. Logik. Vol. 3. 3rd ed. Logik der Geisteswissenschaften. Stuttgart: Enke.
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Cat, J. (2019). Neurath and the Legacy of Algebraic Logic. In: Cat, J., Tuboly, A. (eds) Neurath Reconsidered. Boston Studies in the Philosophy and History of Science, vol 336. Springer, Cham. https://doi.org/10.1007/978-3-030-02128-3_11
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