Carnap on unified science

CARNAP ON UNIFIED SCIENCE ANSTEN KLEV Abstract. Unified science is a recurring theme in Carnap’s work from the time of the Aufbau until the end of the 1930’s. The theme is not constant, but knows several variations. I shall extract three quite precise formulations of the thesis of unified science from Carnap’s work during this period: from the Aufbau, from Carnap’s so-called syntactic period, and from Testability and Meaning and related papers. My main objective is to explain these formulations and to discuss their relation, both to each other and to other aspects of Carnap’s work. Als Ziel schwebt die E i n h e i t s w i s s e n s c h a f t vor. Wissenschaftliche Weltauffassung In the opening sentence of a famous paper Oppenheim and Putnam (1958) complained that “the expression ‘Unity of Science’ is often encountered, but its precise content is difficult to specify in a satisfactory manner”. Oppenheim and Putnam will have encountered the expression, or some close relative of it, in many of Rudolf Carnap’s works; it is, however, not true of Carnap that he did not fill the expression with precise content. In fact, Carnap’s works from the time of Der logische Aufbau der Welt (1928a, hereafter cited as Aufbau) and about a decade onwards contain, more or less explicitly, three quite precise formulations of the thesis of the unity of science, or unified science, as I shall prefer to call it. It is the aim of this paper to state these various precise formulations, explain the technical terms they involve, and place the views of unified science they express in the context of Carnap’s work more generally during this period. Unified science is a recurring theme in Carnap’s works from the time of the Aufbau through the 1930’s, with connections to many other Carnapian themes, such as constitution theory, intersubjectivity, physicalism, protocol sentences and their place in scientific theories, and the logical empiricist theory of meaning in its various manifestations. It is therefore a topic worthwhile studying, not only because of its intrinsic interest, but also because of the light doing so may shed on the development of Carnap’s thought during this period. Although studies of the topic can be found in the secondary literature,1 it seems to me that few have clearly distinguished the various stages in Carnap’s thinking about unified science; nor, as far as I know, has anyone extracted precise formulations of the thesis of unified science from Carnap’s writings. Hence there is room for an addition to the Carnap literature attempting to do these things. 1 E.g. Creath (1996), Pincock (2003), Frost-Arnold (2005), Ouelbani (2005). 1 2 ANSTEN KLEV As already noted, one finds in Carnap’s work from the Aufbau until the latter part of the 1930’s three quite precise formulations of the thesis of unified science. Each formulation belongs to a separate period and can be associated with a subset of Carnap’s works during the period in question. In the Aufbau and writings relying on the constitution system developed in that work, the thesis of unified science is closely related to constitution theory and its aims. (1) All concepts of science can be explicitly defined from a handful of primitive relations within a simple type hierarchy whose base type consists of “elementary experiences”. During the “syntactic period”—covering Die physikalische Sprache als Universalsprache der Wissenschaft (Carnap, 1932b, hereafter cited as Universalsprache), Psychologie in physikalischer Sprache (1932c, hereafter cited as Psychologie), and Logische Syntax der Sprache (1934b, hereafter cited as Syntax )—Carnap turns from considering concepts and their constitution to considering languages and their relation to each other. (2) Every sentence of science can be translated into the language of physics, a certain higher-order language containing variables ranging over real numbers. From the rather abstract considerations that this formulation of the thesis of unified science gives rise to, Carnap turns to the life-world, as it were, in Testability and meaning (1936a; 1937b, hereafter cited as Testability I and II respectively) and a couple of related publications (Carnap, 1936b, 1938). Science is now to be built up from the so-called thing language, a language that speaks about the ordinary things surrounding us. The building is to be erected not only by means of explicit definition, as in constitution theory, but also by means of what Carnap calls reduction sentences. (3) All predicates of science can be either explicitly defined from or “reduced to” observable predicates. The terms highlighted in these various formulations by means of boldface type, italicization, and underlining may be considered as parameters, defining the objects, the means, and the target of the unification of science according to the formulation in question. Terms in different formulations highlighted in the same way can be said to play the same role in their respective formulations. Below each formulation will be dealt with in turn in sections 2–4. Section 1 is devoted to preliminary remarks. The final section 5 briefly discusses the place of the thesis of unified science in Carnap’s later works. Translations from German are as a rule my own. Translated passages quoted in the main text are accompanied by a footnote providing the original German. Passages quoted only in a footnote are given in English only. 1. Preliminary Remarks I take ‘unified science’ to be the proper translation of the German ‘Einheitswissenschaft’, whereas ‘unity of science’ rather translates ‘Einheit der Wissenschaft’. The term ‘Einheitswissenschaft’ occurs prominently in the Vienna Circle manifesto (Der Wiener Kreis, 1929), for instance in the sentence that serves as the epigraph of CARNAP ON UNIFIED SCIENCE 3 this paper. In Carnap’s own publications the term begins to appear in 1930.2 Before that, in particular in the Aufbau,3 Carnap had used the term ‘Gesamtwissenschaft’ in speaking about unified science. ‘Gesamtwissenschaft’ is sometimes translated as ‘the whole of science’,4 but in the context of Carnap’s work in general and the Aufbau in particular such a translation is inadequate for at least three reasons. Firstly, it makes nonsense of phrases like ‘die éine Gesamtwissenschaft’ occurring for instance in Aufbau §§ 2, 179.5 Secondly, it is clear from Aufbau §§ 2, 4, 179 that this one Gesamtwissenschaft is the unified science that the unification of the domain of objects effected by constitution theory makes possible (more on that later). Thirdly, Carnap continues to use ‘Gesamtwissenschaft’ also after adopting the term ‘Einheitswissenschaft’ and then only as a stylistic variant of the latter.6 Hence it is clear that in the context of Carnap’s work ‘Gesamtwissenschaft’ and ‘Einheitswissenschaft’ should be translated as the same word, and to my mind ‘unified science’ is the best choice in English. According to Carnap (cf. 1934b, p. 249) it was Neurath who introduced the term ‘Einheitswissenschaft’ (as well as the term ‘Physikalismus’) into the vocabulary of the Vienna Circle. Where Neurath had the term from I do not know, but Neurath (1932a, p. 395) cites Lewin (1925, p. 7) as noting that it is used by Oppenheimer (1919, pp. 3 ff.) in the relevant sense. Anyhow, it was through Neurath’s organizational activities that this term, in German as well as in the English translations ‘unified science’ and ‘unity of science’, became something of a trademark of logical empiricism. An important conference series with six instalments between 1935 and 1941 was called, in English, International Congress for the Unity of Science.7 A publication series initiated by Neurath was called Einheitswissenschaft.8 Another, very ambitious, publication project was the International Encyclopedia of Unified Science.9 Finally, one may mention Neurathian coinages such as ‘The Unity of Science Institute’ and ‘Unity of Science Movement’.10 Neurath’s own thinking regarding unified science was closely tied to these organizational activities and especially to the project of an encyclopedia. It would, however, take us too far afield to go into these topics here.11 2See Carnap (1930b, p. 24) and Carnap (1930e). 3But also in (Carnap, 1927). 4For instance by Damböck (2012, p. 83), who maintains that Gesamtwissenschaft is something “totally different” from Einheitswissenschaft. 5In the Aufbau Carnap writes ‘éin’ for the numeral, thus distinguishing it by means of an acute accent over the ‘e’ from the indefinite article ‘ein’. 6See Carnap (1932b, p. 448) and Syntax § 74. 7See Stadler (1997, pp. 402–436) for more details. 8The titles of this series have now been published in a single volume, Schulte and McGuinness (1992). 9On aspects of the history of this Encyclopedia, see Dahms (2005) and Morris (1960). 10What was the business of the Institute I do not know. The term ‘unity of science movement’ occurs in (Neurath, 1938, p. 1); Carnap (1942, p. 286) describes it as “a wider movemet [sc. than the Vienna Circle], comprising besides Logical Empiricism other groups and individuals with related views in various countries”. 11Besides Neurath (1932a,b), discussed below, see also Neurath (1933, 1935, 1936, 1938). Reisch (1994) provides a helpful discussion. Some comparisons of Carnap and Neurath on unified science can be found in Creath (1996), Frost-Arnold (2005), and Ouelbani (2005). 4 ANSTEN KLEV By science Carnap understands the total system of knowledge,12 or in a more syntactic formulation “the totality of accepted sentences.”13 That science is unified means that there is, in principle, only one science. It is a further question precisely what it means for there to be only one science. Although we shall find different formulations of the thesis of unified science defended by Carnap at different stages from the time of the Aufbau until the late 1930’s, there is an underlying idea that appears to guide much of his thinking regarding unified science during this period: science is unified if there is only one domain of objects for science to investigate. Thus, in Aufbau § 4 Carnap says: There is only one domain of objects, and therefore only one science.14 A couple of pages earlier, in Aufbau § 2, Carnap had claimed that only by establishing that there is only one domain of objects is it possible to argue that science is unified.15 It is clear from these passages that for Carnap the connection is tight indeed between the thesis of unified science and the thesis of a unified domain of objects. Sometimes, in fact, Carnap simply equates these two theses: so for instance in the introductory section of Universalsprache (pp. 433–435) and in the following passage from Syntax § 82:16 From this [sc. from the fact that the physical language is a universal language] it follows that science is a unified system, within which there are no fundamentally different domains of objects, say, a division into natural sciences and Geisteswissenschaften; that is the thesis of unified science. There are no fundamentally different domains of objects: that, so Carnap here, is the thesis of unified science. When Carnap saw such a tight connection between the thesis of unified science and the thesis of a unified domain of objects he may have been relying on the traditional idea that one science deals with one kind of objects. Aristotle defended such an idea in the Posterior Analytics. In chapter I.28 of that book one reads that “a science is one if it is concerned with one kind (genos)” and in chapter I.7 the related doctrine that forbids kind-crossing (metabasis eis allo genos) in scientific demonstrations is set out. Scholz (1930, pp. 29–30), basing himself on these passages, indeed defined a science in the sense of Aristotle as “a series of propositions (Sätze) 12Aufbau § 180: “Science, the system of conceptual knowledge,. . . ” Carnap (1934c, p. 6): “Philosophy is the theory of science (wherein here and in the following ‘science’ is always meant in the comprehensive sense of the collective system of the knowledge of any kind of entity: physical and psychic, natural and social entities.)” 13Carnap (1934a, p. 90): “By ‘science’ is here understood the totality of accepted sentences; here belongs not only the assertions of the scientist, but also those of everyday life: between these two domains there is no strict border.” 14Aufbau § 4: “E s g i b t n u r é i n G e b i e t v o n G e g e n s t ä n d e n u n d d a h e r n u r é i n e W i s s e n s c h a f t.” 15Aufbau § 2: “Only when one has succeeded in building such a unified system of concepts is it possible to overcome the falling apart of unified science [Gesamtwissenschaft] into individual, mutually unrelated partial sciences [Teilwissenschaften]. 16Syntax § 82: “Hieraus folgt, daß die Wissenschaft ein einheitliches System ist, innerhalb dessen es keine grundsätzlich verschiedenen Objektbereiche gibt, also keine Spaltung etwa in Natur- und Geisteswissenschaften; das ist die These der E i n h e i t s w i s s e n s c h a f t.” CARNAP ON UNIFIED SCIENCE 5 about elements of one and the same domain” meeting certain further conditions.17 The idea that one science deals with objects of one domain or of one kind seems also to have been common in the early 20th century. Husserl takes it for granted in his Ideen,18 a work Carnap had studied thoroughly.19 The Systematisches Wörterbuch der Philososphie of Clauberg and Dubislav (1923), another work Carnap appears to have read,20 divides the sciences according to their object, so that, for instance, sciences of one kind deal with ideal objects and sciences of another kind with real objects.21 In Carnap’s works traces of this traditional idea is found not only in the places where the argument for the unity of science from the unity of the domain of objects is given, but also in the following passage (Carnap, 1938, p. 45): How, then, are we to draw the boundary line between physics and biology? It is obvious that the distinction between these two branches has to be based on the distinction between two kinds of things which we find in nature: organisms and nonorganisms. Here Carnap seems to take it as obvious that the only way of distinguishing the sciences of physics and biology from each other would be by reference to the kinds of objects they study. Carnap’s intuitive conception of unified science as having to do with the notion of a domain of objects has important consequences for what needs to be said about logic and mathematics in an argument for the thesis of unified science. Wittgenstein’s so-called Grundgedanke in the Tractatus is that logical constants do not have a representative function (TLP 4.032). The Tractarian thesis that there are no logical objects (TLP 4.441, 5.4) would seem to be just a reformulation, or else a simple corollary, of this basic thought. The Tractatus was being discussed in the Schlick-circle when Carnap arrived in Vienna in 1926,22 and it seems to me that Wittgenstein’s basic thought made its way into the Aufbau, which Carnap was working on at the time. In Aufbau § 107 Carnap says the following:23 It is important to note that logical and mathematical objects are not proper objects in the sense of empirical objects (objects of the empirical sciences). [. . . ] The signs of logic (and mathematics) do not signify objects, but serve only as symbolic manifestations of conventions. 17So also according to what Betti and de Jong (2010) call “the classical model of science”. 18Husserl (1913, § 1): “To each science there corresponds a domain of objects [Gegenstandsgebiet], as the province [Domäne] of its researches.” 19There are detailed references to the Ideen in the Aufbau and, even more so, in Carnap (1922). 20In Aufbau § 3 Carnap cites this dictionary as an already existing example of a constitution system. 21Clauberg and Dubislav (1923, p. 538): “We group the sciences according to their objects.” 22Cf. e.g. (Stadler, 1997, chs. 6.1–6.2) or (Carnap, 1963a, pp. 24–29). From the latter source it appears that Carnap had read the Tractatus closely already before he first met Wittgenstein in the summer of 1927. There are explicit references to the Tractatus in Aufbau §§ 43, 183. 23Aufbau § 107: “Es ist wichtig, zu beachten, daß d i e l o g i s c h e n u n d m a t h e m a t i s c h e n G e g e n s t ä n d e n i c h t e i g e n t l i c h e G e g e n s t ä n d e im Sinne der Realgegenstände (der Objekte der Realwissenschaften) sind. D i e L o g i k (e n s c h l. d e r M a t h e m a t i k) b e s t e h t n u r a u s k o n v e n t i o n e l l e n F e s t s e t z u n g e n über den Gebrauch von Zeichen u n d a u s T a u t o l o g i e n auf Grund dieser Festsetzungen. Die Zeichen der Logik (und Mathematik) bezeichnen daher nicht Gegenstände, sondern dienen nur zur symbolischen Festlegung jener Festsetzungen.” 6 ANSTEN KLEV The only proper objects, thus Carnap, are empirical objects (Realgegenstände). Mathematical and logical objects are not empirical, hence they are not proper objects, and therefore, in a sense, not objects at all.24 The relevance of this idea to reconciling empiricism with the facts of logic and mathematics was emphasized in the writings of Hahn (1929, 1933);25 for current purposes its relevance to the thesis of unified science is more important. Carnap ends his contribution to a conference in Prague in 1934 (Carnap, 1935b) with the words:26 Hence our emphasis on the strict borders between formal science and empirical science leaves the unity of science untouched. Science is unified provided there is just one domain of objects for it to study. Formal science studies no objects at all. Hence, one can uphold the thesis of unified science while insisting that there are strict borders between formal and empirical science. Carnap is thus free to set aside mathematics and logic when discussing the thesis of unified science; which is also what he tends to do in his writings on the topic. In his intellectual autobiography Carnap associates the thesis of unified science with the question of how the Gesisteswissenschaften—roughly the humanities and the social sciences27—relate to the natural sciences (Carnap, 1963a, p. 52; cf. ibid. p. 23): This thesis must be understood primarily as a rejection of the prevailing view in German contemporary philosophy that there is a fundamental difference between the natural sciences and the Geisteswissenschaften This is not the place for a thorough discussion of this difference and how it was conceived by Dilthey, Windelband, Rickert, and others;28 but a few remarks may be made about how Carnap seemed to have conceived it. On the basis of what was said above, and in particular the passage quoted from Syntax § 82, it is natural to suggest that for Carnap what primarily distinguishes the Geisteswissenschaften from the natural sciences is the kind of objects that they study. That suggestion gains further support from Carnap’s discussion of Geisteswissenschaften in the Aufbau, where he repeatedly emphasizes that there is an independent domain of geistige Gegenstände, separate both from the objects of natural science and from the objects of psychology (cf. Aufbau §§ 23, 56, 151). That the Geisteswissenschaften and the natural sciences, if they are to be deemed fundamentally different from each 24A similar idea is expressed in Carnap (1927, pp. 358–359); see also Carnap (1926, p. 2). 25For more discussion, see Goldfarb (1996, esp. pp. 218–224). 26Carnap (1935b, p. 36): “Daher läßt unsere Hervorhebung der scharfen Grenze zwischen For- malwissenschaft und Realwissenschaft die Einheit der Wissenschaft unberührt.” 27That the term ‘Geisteswissenschaften’ is not easily translatable into English, or into the Ro- mance languages, is well known; see Diemer (1974) for a discussion of some alternatives. 28For instance by Carnap’s teachers at Jena, Bruno Bauch—a student of Rickert—and Herman Nohl—a student of Dilthey and advocate of the so-called geisteswissenschaftliche Pädagogik ; or by Husserl, who discussed the relation between nature and Geist in many of his seminars during the 1920’s. It is clear from Carnap’s diaries for the winter 1923/24 (Carnap, 1923a, 1924) together with (Schumann, 1977, p. 273) that Carnap took part in Husserl’s seminar Phänomenologische Übungen für Fortgeschrittene that semester. On Dilthey and Nohl’s influence on Carnap, see Gabriel (2004) and Damböck (2012); Friedman (1999, ch. 6) discusses the Aufbau in light of the works of Rickert among other Neo-Kantians (Carnap scholarship has tended, not without good reasons, to concentrate on the so-called Marburg school of Neo-Kantianism rather than the so-called Southwest school, to which Windelband and Rickert belonged). CARNAP ON UNIFIED SCIENCE 7 other, would have to be so deemed on the basis of such a material criterion may seem obvious. This was, however, not the view of everyone anxious to emphasize their difference. Windelband, for instance, in his Rektoratsrede at the University of Strasbourg (Windelband, 1894), argued that psychology, because of its methodology, ought to be classified with the natural sciences, whence that a division on the basis of the kind of object studied is insufficient, as it would place psychology with the Geisteswissenschaften. He therefore suggested a division based on a formal criterion: Geisteswissenschaften concentrate on the singular, the natural sciences on the general. Such a division, Windelband argued further, shows the need for a new logic, since traditional, Aristotelian logic is geared towards the general and not towards the singular.29 So much for the preliminary remarks; I now get to the main business of this paper, namely the discussion of the three formulations (1)–(3) of the thesis of unified science. Each formulation is dealt with in turn. In section 2 I discuss the conception of unified science found in the Aufbau, in section 3 the conception of unified science Carnap assumes during the syntactic period, and in section 4 the conception of unified science found in Testability and related works. 2. Unifed science in the Aufbau The aim of the Aufbau is the development of what Carnap calls a constitution system. A constitution system is a system of concepts, in which a small number of primitive concepts give rise to the rest, in the sense that the latter are defined in terms of the former. A constitution system as Carnap conceives it is, moreover, meant to comprehend all concepts of science, it is to be a “family tree” of concepts (Stammbaum der Begriffe) within which each concept of science finds its place (§ 1).30 In showing how such a system can be constructed Carnap employs the language of modern, Fregean logic; more specifically, he employs a form of simple type theory. Carnap holds that both a type hierarchy whose ground type consists of elements of a physical nature (§ 62) and a hierarchy whose ground type consists of elements of a psychological nature (§ 63) can serve as the framework of a constitution system. However, as he wishes the order of definitions in the constitution system to mirror the order of epistemic priority among concepts (§ 54), he settles on the latter kind of ground type (§ 64), in particular on a ground type consisting of what he calls elementary experiences (Elementarerlebnisse). Besides this ground type Carnap makes use of only one other non-logical primitive notion, namely a binary relation between elementary experiences which he calls recollection of similarity (Ähnlichkeitserinnerung). Let us consider some of the details. One of the basic ideas of Frege’s logic is to treat concepts as functions in the sense of mathematics (cf. e.g. Frege, 1891). Considering the fact that there are functions, such as the differential function, whose arguments are other functions, 29Carnap enthusiastically welcomes this suggestion in the note to Aufbau § 12; he probably has such a logic in mind when he speaks about the logic of the Geisteswissenschaften in Aufbau § 150. 30Carnap employs the term ‘Stammbaum der Begriffe’ in explaining the notion of a constitution system also in Carnap (1928b, § 6) and in Carnap (1930b, p. 29). The tree metaphor has of course had many uses in epistemology, but worth mentioning in this context is Kant’s Stammbaum des reinen Verstandes from the Critique of Pure Reason A82/B108, which was to be a system of all pure concepts. 8 ANSTEN KLEV one is led to distinguish first-level concepts from second-level concepts: a firstlevel concept is a function from individuals—what Frege called objects—to truthvalues, while a second-level concept is a function from first-level concepts to truthvalues. The simple type hierarchy arises by generalizing this distinction between first- and second-level concepts in two ways. Upwards, one continues to thirdlevel, fourth-level, etc., concepts. Sideways, as it were, one introduces concepts with several arguments, what Frege called relations. The resulting hierarchy of types, although implicit in Frege’s writings, was not spelled out by him. It seems to have been Carnap in his Abriss der Logistik (Carnap, 1929, pp. 30–32) who first gave an inductive definition of this hierarchy, the hierarchy of what Carnap (1931, p. 96), perhaps as the first, calls a simplified theory of types, in contrast to the “ramified” (verzweigte) type theory of Russell and Whitehead’s Principia Mathematica (Russell and Whitehead, 1910).31 Carnap’s inductive definition may be stated as follows. There is a type ι of individuals; if α1 , . . . , αn are types, then (α1 , . . . , αn ) is a type, namely the type of relations in extension whose k-th argument place is of type αk . That R is a relation in extension is just to say that the following identity criterion holds: R = R′ if and only if R and R′ agree on all arguments, namely if and only if for all a1 , . . . , an of the appropriate types, Ra1 . . . an is true if and only if R′ a1 . . . an is true. In this paper I take ‘relation’ to mean relation in extension. A class—Carnap’s term for a concept in extension—may be identified with a unary relation in extension. In the constitution system Carnap develops in the Aufbau the ground type ι consists of elementary experiences, experiences taken “in their totality and complete unity” (§ 67). Let us call the resulting type hierarchy E (‘E’ for experience). That E is to serve as a framework for constitution theory means that within it one is to define what Carnap calls “rational reconstructions” of all concepts of science. These definitions need to start somewhere, hence one or more relations of the type hierarchy must be given at the outset as primitive. For the outlines of the system given in the Aufbau it is, according to Carnap, enough to assume one such primitive relation, namely a binary relation over the ground type, a relation Carnap calls recollection of similarity. Recollection of similarity holds between elementary experiences x and y if a part of the recollection or retention of x is similar to a part of (the present elementary experience) y (§ 78). From this primitive relation new relations are formed by means of logical notions. The formation of new relations soon gets very complicated and we shall not look at any concrete examples here.32 The primitive logical notions Carnap assumes, and by means of which new relations are formed, are the Sheffer stroke,33 universal quantification over any type, 31An inductive definition of the ramified type hierarchy can be found in Church (1976). The importance of Carnap for the dissemination of simple type theory has been emphasized by Reck (2004, pp. 163–166). 32For more discussion of Carnap’s actual definitions, see Goodman (1951, ch. 5) and Richardson (1998, ch. 3). 33By the Sheffer stroke I mean the binary truth-function p | q defined by the following truth-table. p q p|q t t f t f t t f t f f t CARNAP ON UNIFIED SCIENCE 9 and abstraction (cf. § 107).34 In accordance with Carnap’s view of logic as being without objects, neither universal quantification nor the Sheffer stroke belong to the type hierarchy E —had they done so, logic would have had objects after all. Thus we should presumably not think of the logical operators as functions, for as functions they would belong to a type hierarchy. Perhaps we should rather think of them as forms or “syncategoremata” of some kind, on a par with abstraction, which as a rule must be considered as a syncategorema or a form, even when the logical operators are treated as functions. A new relation is typically introduced into the constitution system as follows. From relations already at our disposal we construct by means of the Sheffer stroke and universal quantification a propositional function φ(x1 , . . . , xn ).35 By means of abstraction ˆ· on the free variables x1 , . . . , xn we thence obtain an n-ary relation x̂1 . . . x̂n φ(x1 , . . . , xn ). In a nominal definition this relation receives a new name, A say: A ≡ x̂1 . . . x̂n φ(x1 , . . . , xn ). The type of the relation A is determined by the types of the variables x1 , . . . , xn . Namely, if αi is the type of xi , then (α1 , . . . , αn ) is the type of A. In the setting of arithmetic, for instance, we may define the less-than-or-equal relation ≤ as follows: ≤ ≡ x̂ŷ ∃z(x + z = y) It is assumed that addition + is available. Thus we may form the formula ∃z(x+z = y), and thence abstract on its free variables x and y. Since we assume x and y to range over the natural numbers N, the type of ≤ is (N, N). The primitive relation of recollection of similarity together with the logical notions assumed do not by themselves determine the constitution system: the constitution system does not consist of all classes and relations definable by those means. Only the relations that the constructor of the constitution system believes can function as rational reconstructions of scientific concepts are singled out and given their own names in nominal definitions of the above form. An instance of rational reconstruction may be thought of as a relation obtaining between a relation R of E and a scientific concept C; we express that the relation obtains by saying that R is a rational reconstruction of C. The basis of a belief that such and such a relation in E can function as a rational reconstruction of a certain scientific concept C is knowledge about C and about the concepts involved in C (§ 179). That R is a rational reconstruction of C is typically suggested by the name given to R in a 34 Abstraction is not listed as a primitive by Carnap, but he avails himself of it constantly, as he indeed must do if he is to construct higher-order objects. He takes identity between individuals to be definable as indiscernibility, thus x = y is defined by the second-order formula ∀P (P x ⇐⇒ P y) (cf. Aufbau § 159). 35Carnap speaks of the definition of a propositional function as a “definition in use” (Aufbau § 39). This must be regarded as a misunderstanding of the term ‘definition in use’ as introduced by Russell and Whitehead (1910, p. 66) for the form of definition required in the case of what they call an incomplete symbol (of which definite description is a main example). In the context of the Aufbau one could say that definition in use is the kind of definition required of non-primitive logical constants. For instance, the definition of negation in terms of the Sheffer stroke could not take the form ‘¬ ≡ . . .’ since negation, as a logical constant, does not signify an object. This appears to be in line with Carnap’s later terminology: according to (Carnap, 1936b, pp. 62–63) the definition of a propositional function is an explicit definition and the definition of the existential quantifier in terms of the universal quantifier and negation is a definition in use. 10 ANSTEN KLEV nominal definition. For instance, by giving R the name sight the constructor of the constitution system suggests that R is a rational reconstruction of the concept of the visual field (cf. § 115). A nominal definition in a constitution system may thus be thought of as making an assertion, namely the assertion that “a certain familiar object as far is its rational concept is concerned can be derived in such and such a way from the primitive concepts” (§ 98). Once a constitution system is in place this system itself becomes the system of scientific concepts. Although an element of convention is involved in rational reconstruction, once a decision has been made, the reconstruction is to replace the original concept, at least for logical and epistemological purposes. One can perhaps not expect that an experimental psychologist will abandon his concept of the visual field and take up the rational reconstruction sight instead. But for someone interested in the logical and epistemological basis of the concept of the visual field only sight will do (provided one has settled on this rational reconstruction). In fact, according to Aufbau § 179, only of the rational reconstruction do we know that it is rooted in experience. By unfolding the definition introducing the rational reconstruction—that is, by continuously replacing defined terms by their definientia—we eventually get a name containing, besides logical terms, only variables ranging over some type in E and the primitive non-logical term of recollection of similarity (cf. § 119), and these (it is assumed) are rooted in experience. Sentences built up only from elements of E thus have what Carnap calls a “verifiable sense” (verifizierbarer Sinn) (§ 179). On the other hand, if we cannot reduce the nonlogical components of a relation to elements of experience, we cannot be certain that its name has sense (ibid.). Carnap assumes that the existence of a constitution system implies that there is only one domain of objects.36 This assumption may be divided into two parts: i) a constitution system is to comprehend all concepts of science; ii) all elements of the constitution system belong to one domain. We have just commented on part i), but a comment on part ii) is also in order. Carnap must here be relying on a certain conception of how the notion of a kind of object behaves within a type hierarchy: if the individuals in a simple type hierarchy are all of kind K, then all elements of the hierarchy are of kind K. The conception is thus that the kind of the ground type is inherited by all other types in the hierarchy. Assuming that the elements of the ground type of E fall into the self-psychological domain, it follows therefore that all elements of E fall into this domain. This is not to say that with the construction of a constitution system we no longer have any means of classifying concepts (§ 41): we can distinguish elements of a constitution system according to the “spheres of objects” (Gegenstandssphären) to which they belong (§§ 29–30), that is, according to which type in E they belong to. But although there is an indefinite number of such types, there is only one kind of object in the constitution system.37 36Aufbau § 4: “If a constitution system [. . . ] of the kind indicated is possible, then it follows: the objects do not fall apart into distinct, disconnected domains, rather there is just one domain of objects and therefore just one science.” 37Sauer (1987) maintains that the constitution system in the Aufbau provides the theoretical basis for the distinction of domains of objects, and that one therefore cannot think of Aufbau as arguing for the unity of science. It seems to me that he then confuses the distinction between type and kind of object. CARNAP ON UNIFIED SCIENCE 11 Formulation (1) of the thesis of unified science reads: (1) All concepts of science can be explicitly defined from a handful of primitive relations within a simple type hierarchy whose base type consists of “elementary experiences”. That Carnap in the Aufbau would accept this as the formulation of the thesis of unified science seems to me clear in light of what he there says about the relation between constitution theory and unified science (esp. §§ 2, 4, 179). Science is unified if there is only one domain of objects for science to investigate. That there is only one such domain is to follow from the existence of a constitution system. Hence the thesis of unified science will be established once a constitution system is in place. The particular constitution system that Carnap develops in the Aufbau is based on the type hierarchy E , built over a ground type of elementary experiences and one primitive relation within it. The thesis of unified science defended in the Aufbau is thus the thesis that this constitution system has been erected, which is in effect the content of formulation (1). 3. Unified science in the syntactic period Since the constitution system sketched by Carnap in the Aufbau is based on elementary experiences of a given subject, the question arises how from it one can attain an intersubjective world. In Aufbau § 66 Carnap phrases this question as the question of how constitution theory can guarantee the objectivity of knowledge, where objectivity is understood as “independence from the judging subject”, or as “validity also for other subjects” (ibid.). In the Aufbau Carnap provides two not obviously compatible answers to this question.38 The first answer assumes a perspective internal to a given constitution system. Within E one can describe an entity called the intersubjective world, as follows. Other subjects are constituted within E as their own inner constitution systems (§ 145). Namely, for each subject M a certain relation RM is introduced that inside E models M ’s relation of recollection of similarity. A constitution system is then built up inside E using RM instead of the original relation of recollection of similarity. By means of what Carnap calls the world of physics (die physikalische Welt) an element within E can be recognized as “the same object” as an element within such an inner constitution system (§§ 146–147). The intersubjective world consists of all the equivalence classes of the relation of being the same object as understood in this way (§ 148).39 The subject attains an intersubjective world by constituting these equivalence classes. The second answer assumes a perspective external to any one constitution system. Each subject has its own elementary experiences and therefore its own constitution system (within each of which one finds an intersubjective world as described by the first answer). The question is, How do these different constitution systems 38How this came to be is one of the main questions of Richardson (1998). His answer (given ibid. ch. 8) is that Carnap was torn between two conceptions of epistemology: as an empirical science, whose concepts—including objectivity—are to be rationally constituted; or rather as a formal science. 39It is not clear from Carnap’s discussion whether he thinks of the intersubjective world itself as an element of E . 12 ANSTEN KLEV communicate with each other? Carnap holds that whereas “the material of individual streams of consciousness are altogether different from each other” the structural properties of individual streams of consciousness are shared and therefore intersubjective (§ 66; likewise § 16). For Carnap, as for Schlick before him,40 this leads to the view that “science is essentially structural science” (ibid.), it deals only with structure in the sense of the formal scaffolding of experience. What is required for intersubjectivity is therefore formalization of each constitution system in the sense of a “de-materialization” of it, represented by letting the ground type of E and the primitive relation of recollection of similarity be replaced by variables.41 Thus the subject attains an intersubjective world by considering the formal structure of its constitution system. At the latest around 1930 Carnap must have become dissatisfied with these accounts of intersubjectivity. In the abstract to a lecture he gave to the Verein Ernst Mach that year,42 Einheitswissenschaft auf physischer Basis, one reads:43 But how is “unified science” possible? If the sentences of science are to be intersubjectively communicable, physical concepts must be taken as basic concepts. All other concepts of science are derivable from these. In the Aufbau Carnap had argued that a constitution system with a physical basis was possible, but he had preferred a system with psychological basis, since only such a system would reflect the epistemic priority among scientific concepts. The sketch of this constitution system was accompanied by accounts of the objectivity of science as just spelled out above. Now, however, Carnap argues that only by starting from physical concepts can one show that science is unified while simultaneously securing the objectivity of knowledge. Carnap thus in effect renounces his previous attempt—still defended in the Vienna Circle manifesto (1929)—at erecting a constitution system with a basis in the self-psychological domain on the grounds that such a system does not secure the objectivity of knowledge. Carnap thereby also renounces his account of the objectivity of knowledge in the Aufbau: neither the constitution of the so-called intersubjective world nor the formalization of the constitution system secures objectivity; what is required for objectivity is the employment of physical concepts. Although both Wittgenstein and Heinrich Neider—a student member of the Vienna Circle—may have played a role in convincing Carnap of the virtues of physicalism,44 Carnap in his writings portrays Neurath as the torch-bearer of physicalism within the Vienna Circle.45 Neurath was also an important force in bringing about 40 See e.g. Schlick (1926), who notes the similarity to Carnap (ibid. p. 150). 41For more discussion of this response to the problem of objectivity, see Friedman (1999, ch. 5). 42The lecture was given on 10.5.1930; see Carnap’s diary entry on that day (Carnap, 1930a). 43Carnap (1930e): “Wie aber ist “Einheitswissenschaft” möglich? Damit die Sätze der Wissen- schaft intersubjektiv übertragbar sind, müssen als Grundbegriffe die physikalischen Begriffe genommen werden. Alle andern Wissenschaftsbegriffe sind aus diesen ableitbar.” 44See Uebel (1995) for a general overview of this and related priority disputes. For more details on Wittgenstein, see e.g. Hintikka (1993) and Stern (2007). Neider’s report can be found in (Neider, 1977, pp. 29–30), further discussion of which are found in Uebel (2007, pp. 128–137). 45See Carnap (1932b, p. 452), quoted below, as well as Syntax § 82 (pp. 248–249) and Carnap (1963a, pp. 51–53). CARNAP ON UNIFIED SCIENCE 13 what may be called Carnap’s linguistic turn. In a footnote in Universalsprache Carnap remarks that46 Neurath has, as the first in the discussions of the Vienna Circle and then resolutely in the aforementioned article [Neurath (1932a)], required that one should no longer speak about “the contents of experience” or about the comparison between the sentence and “reality”, but only about sentences; he has moreover put forward the thesis of physicalism in its most radical form. The “aforementioned article” (Neurath, 1932a) contains the following passage, which must be among the ones Carnap has in mind:47 Statements are compared with statements, not with “experiences”, not with a “world”, nor with anything else. All these nonsensical duplications belong to a more or less refined metaphysics and are therefore to be rejected. Science must remain at the level of language; to try to the assess its sentences against experience or reality is to engage in metaphysics and is therefore to be avoided. The constitution system Carnap developed in the Aufbau was, however, predicated on the belief that the assessment of sentences against experience was in fact possible; indeed, a sentence was there deemed to be nonsensical if it was not possible to assess it against elementary experiences.48 In fact, as late as 1930 Carnap says in an unpublished manuscript:49 In order to verify a sentence p, I have to compare p with the state of affairs that p expresses. Carnap then goes on to say that this comparison amounts to the comparison of a certain other, equipollent sentence p′ , speaking about the contents of experience, with an experiential state of affairs (Erlebnissachverhalt). It is precisely the notion of verification—and by the verifiability criterion of meaning, the notion of meaningfulness—presupposed here that Neurath challenges in the quoted passage.50 Carnap’s response to this challenge in Universalsprache § 3 is to abandon elementary experiences in all contexts except unofficial, heuristic ones and replace them in official contexts by certain linguistic entities he calls protocol sentences, sentences that report about “the given” (cf. Psychologie p. 108). Thus the notions of verification and meaningfulness are officially no longer to be based on the notion of an elementary experience, but rather on the notion of a protocol sentence. It is not unreasonable to call this a linguistic turn. Precisely which role the notion 46Carnap (Universalsprache, p. 452): “Neurath hat als erster in den Diskussionen des Wiener Kreises und dann in dem genannten Aufsatz mit Entschiedenheit gefordert, man solle nicht mehr von “Erlebnisinhalten” und vom Vergleich zwischen Satz und “Wirklichkeit”, sondern nur von den Sätzen sprechen; ferner hat er die These des Physikalismus in der radikalsten Form aufgestellt.” 47Neurath (1932a, p. 403): “A u s s a g e n w e r d e n m i t A u s s a g e n verglichen, nicht mit “Erlebnissen”, nicht mit einer “Welt”, noch mit sonst etwas. Alle diese sinnleeren V e r d o p p e l u n g e n gehören einer mehr oder minder verfeinerten Metaphysik an und sind deshalb abzulehnen.” 48See Aufbau §§ 179, 180 and the definition of Sachhaltigkeit in (Carnap, 1928b, § 7). 49Carnap (1930c, p. 9): “Um einen Satz p zu verifizieren, muss ich p mit dem Sachverhalt vergleichen, den p besagt.” 50This challenge is part of an ongoing discussion between Neurath and Carnap at the time, the details of which are presented and discussed in (Uebel, 2007, chs. 6–7). 14 ANSTEN KLEV of a protocol sentence plays in the formulation of the thesis of unified science will become clear later when we consider the notion of translation. That protocol sentences rather than protocol words signifying elementary experiences and relations between elementary experiences replace the basis elements of the Aufbau’s constitution system points to another aspect of Carnap’s linguistic turn: the sentence rather than the concept has become the primary object of logical analysis. According to traditional, Aristotelian logic the concept is prior to the judgement, which in turn is prior to the inference.51 A reversal of the order of the first two of these has been recognized in the works of Kant, Frege, and others.52 Carnap can with his formulation (2) of the thesis of unified science be said to follow suit, for now the sentences of science, rather than its concepts, are the objects of the unification of science. (2) Every sentence of science can be translated into the language of physics, a certain higher-order language containing variables ranging over real numbers. That this is the formulation of the thesis of unified science defended in Universalsprache and Syntax seems to me uncontroversial (cf. Universalsprache pp. 437, 448, 462 and Syntax § 82). In the terminology introduced above the objects of the unification of science according to this formulation are sentences; its means is translation; and its target is the language of physics. I take the notion of sentence to be clear enough, so it remains to explain what is meant by translation and what is meant by the language of physics. I begin with the latter. In accordance with Carnap’s motivation for adopting physicalism everything expressible in the language of physics is to be intersubjectively accessible. In Universalsprache § 4 Carnap argues that intersubjectivity can be guaranteed only by a purely quantitative language. A quantitative language of physics is a language whose atomic sentences assign values of “physical state quantities” (physikalische Zustandsgrößen) to space-time points or sets of space-time points. As spelled out in Syntax §§ 40, 82, the language Φ of physics may be described as follows. It is a higher-order language built around a simple type hierarchy whose ground type is the type of real numbers.53 In addition to logico-mathematical expressions it contains what Carnap calls descriptive expressions.54 These are names of physical state quantities. Since space-time points are represented by quadruples of real numbers, physical state quantities become functions whose arguments are of either of two types: (i) quadruples of real numbers or (ii) predicates of quadruples of real numbers, representing space-time regions; and whose values are real numbers or n-tuples of real numbers. That these functions are not logico-mathematical means that in order to determine their value it is required, for at least some admissible 51The earliest statement of this order of priority that I am aware of is in Ammonius’s commentary on Aristotle’s Categories; see (Cohen and Matthews, 1991, p. 13). 52See Heis (2014) for a recent discussion. 53With second-order quantifiers present the real numbers can be defined from the natural numbers (as Carnap does in Syntax § 39); but it seems more natural in the current setting to take the real numbers as basic. 54In the case of the language of physics the descriptive expressions are given by enumeration, hence there is no need to rely on the general definition of this notion in Syntax § 50, which MacLane (1938, pp. 173–174) showed to be faulty. CARNAP ON UNIFIED SCIENCE 15 arguments, to make empirical observations of some kind. The descriptive functions of Φ will, however, show regularity in their behaviour, in the sense that if the value at such and such a point is such and such, then the value at certain other points will be such and such. This regularity is captured by means of non-logico-mathematical axioms in Φ, what Carnap calls P-determinations (§ 51). The language Φ of physics may be regarded as the language of what Carnap in the Aufbau called the world of physics. And the role played by the world of physics in Carnap’s account of intersubjectivity in the Aufbau is similar to the role played by the language of physics in Carnap’s account of intersubjectivity in Universalsprache: just as the world of physics is used in correlating an object of E with “the same object” within some inner constitution system in E , so Φ is used in correlating protocol sentences with each other that concern the same experiment. This correlation of protocol sentences is in effect a two-step translation: first into and then out of the physical language. The contents of our experience, thus Carnap (Universalsprache pp. 445–447), shows regularity (eine gewisse Ordnungsbeschaffenheit) to such an extent that physical state-quantities can be postulated that will vary in accordance with the qualitative characters of the contents of experience; thus one can translate protocol sentences, phrased in qualitative language, into the language of physics, which is purely quantitative.55 From the physical language one can, on the other hand, pass to the protocol language by recording which protocol sentences a given subject reacts with when the values of the state quantities are such and such. Thus, via Φ one can translate a protocol sentence concerning a certain experiment that one subject accepts to a protocol sentence concerning the same experiment that some other subject accepts (Universalsprache §§ 4, 6). From this possibilty it follows that the physical language is intersubjective: each subject can “interpret” the atomic sentences of the physical language by means of protocol sentences and moreover recognize the interpretation another subject gives to the same atomic sentences. Let us now take up the question of what is meant by the translation of a sentence into the language of physics. We should first note the difference between definition and translation (cf. Universalsprache p. 435). While definition is intra-lingual, a relation within a single language, translation is inter-lingual, a relation between two languages. Moreover, a definition involves an extension of a given language with new vocabulary, while no such extension takes place in a translation. Unification of science by means of definition, as in the Aufbau, thus means extending a certain base language with more and more defined terms so that in the end a language of unified science results. Unification of science by means of translation, as in formulation (2), rather means showing that any given language of any given special science can be translated into a base language, which is taken to be fixed. According to formulation (2) of the thesis of unified science this base language is the language Φ of physics. Carnap devotes a whole paper, Psychologie, to the question of whether the language of psychology is translatable into the language of physics. It is therefore natural to investigate the notion of translation assumed in formulation (2) on the 55The relation between the purely quantitative notions of physics and the qualitative nature of subjective experience is central already in Carnap (1923b). It is, in effect, the main topic of Carnap (1926). 16 ANSTEN KLEV basis of this case. We must then assume that there is a language Ψ of psychology determined by formation and transformation rules. Although Carnap operates with the notion of translation in both Universalsprache and Psychologie, it is only in Syntax § 61 that it receives a precise definition.56 A translation of Ψ into Φ is a mapping tr : Ψ → Φ from Ψ into Φ that preserves the consequence relation. Thus, if the sentence ψ is a consequence of the set of sentences Γ in Ψ, then tr(ψ) is to be a consequence of tr[Γ] = {tr(γ) | γ ∈ Γ}. In mathematical terminology this is to say that tr is to be a homomorphism with respect to the consequence relation. Carnap emphasizes that the consequence relation in a language L need not coincide with the relation of derivability in L (Syntax § 48). Unlike the relation of derivability, the relation of consequence is in general not defined on the basis of the transformation rules of L. For instance, in Carnap’s so-called Language I, a certain infinitary rule must be added to the transformation rules in order for the relation of consequence to be defined (Syntax § 14); and in the definition of consequence for the so-called Language II the transformation rules play no role at all (Syntax § 34).57 For the definition of translation from Ψ to Φ above to make sense, we must therefore assume that in addition to the transformation rules a consequence relation has been determined for each of Φ and Ψ.58 According to the definition of tr, its domain and range consist of sentences. At several places in Universalsprache and Psychologie Carnap seems, however, to have in mind a translation of terms or symbols rather than of sentences. The domain and range of tr should accordingly be the terms or symbols, respectively, of Ψ and Φ. Carnap considers translations of this kind in his technical discussion of translation in Syntax § 61; they are there called term- and symbol-wise translations, respectively. A term- or symbol-wise translation will, however, induce a sentence-wise translation by means of the formation rules of the languages in question. For instance, let us say that we translate, symbol-wise, the constant symbol 2 by 2∗ , the function symbol s by s∗ , and the predicate symbol P by P ∗ . Then s∗ (2∗ ) is a translation of the complex term s(2), and P ∗ (s∗ (2∗ )) a translation of the sentence P (s(2)). The notion of sentence-wise translation differs from the notions of term- and symbolwise translation in not requiring there to be a correspondence between the terms or symbols, respectively, of the languages in question. The notion of sentence-wise translation is thus simply a more general notion of translation. Whatever general conclusion we reach about the notion of sentence-wise translation will therefore also apply to the notions of symbol-wise and term-wise translation. A number of complications come to light when one looks closer at this notion of translation and its role in the unification of science. Carnap does not note these 56There seems to have been a gradual development in Carnap’s conception of translation from what is in effect an identification of translation and definition in (Carnap, 1930d, pp. 4–5) to the abstract mathematical conception of translation found in Syntax § 61. In Universalsprache and Psychologie Carnap’s discussion at times assumes a conception closer to the first and at other times a conception closer to the latter. 57Carnap’s definition was only reported on in Syntax § 34, details being given in (Carnap, 1935a); it was included in § 34 of the English translation of Syntax (Carnap, 1937a). 58Carnap’s definition of consequence II in Language II can be extended to a definition of consequence Φ in Φ provided we regard Φ as obtained from Language II simply by the addition of certain axioms (“the laws of physics”). Let F be these axioms. We define: Γ Φ φ if and only if F ∪ Γ II φ. CARNAP ON UNIFIED SCIENCE 17 complications in print, though awareness of some of them may be one of the factors that led him finally to discard formulation (2) of the thesis of unified science. I wish next to go through these complications and suggest solutions to them. In the end there will, however, remain one difficulty that I do not see how to get around. The difficulty arises from Carnap’s assumption that the protocol language is disjoint at least from the language Φ of physics. As will be seen in more detail below, this assumption is no longer made in formulation (3) of the thesis of unified science. From the requirement that the translation-mapping preserve the consequence relation it follows that the axioms of Ψ must translate to so-called valid sentences in Φ. A sentence is said to be valid if it is a consequence of the empty class of sentences (Syntax § 48).59 An axiom is valid, hence if λ is an axiom of Ψ, then tr(λ) will have to be a consequence of the empty set of sentences, that is, it will have to be valid in Φ. It is reasonable to regard the axioms of Ψ and Φ as basic laws of psychology and physics, respectively. Hence, basic laws of psychology will have to translate into valid sentences of physics, and thus be reducible, in the appropriate sense, to the laws of physics. Carnap is, however, explicit that the unification of science does not require the reduction of all scientific laws to the laws of physics (Universalsprache p. 449; Psychologie p. 109).60 We should, accordingly, allow that the translation tr(λ) of a law λ of psychology need not be a valid sentence of Φ. On the other hand, for tr to be a translation from Ψ to Φ, tr(λ) must be a valid sentence of Φ. I suggest solving this dilemma by altering Φ so that tr(λ) is an axiom of Φ whenever λ is an axiom of Ψ. The language Φ that interests us is therefore, in effect, the language of physics extended with axioms tr(λ), where λ is a basic law of psychology. A deeper problem arises from a requirement Carnap places on the translation postulated to exist by formulation (2) of the thesis of unified science. From the discussion of the notion of translation in Psychologie (pp. 108–109) and from Carnap’s explicit statement in Syntax § 82 one sees that Carnap requires this translation to be what he calls ‘content-preserving’ (gehalttreu).61 Thus, in the latter place one reads:62 The thesis of physicalism maintains that the language of physics is a universal language of science, that is, that every language of any sub-domain of science can be translated in a content-preserving manner into the physical language. The notion of a content-preserving translation is defined by Carnap in his technical discussion of translation in Syntax § 61 as follows. A translation tr : Ψ → Φ is content-preserving if the sentence ψ of Ψ and its translation tr(ψ) in Φ have the same content (Gehalt).63 The content of a sentence—described by Carnap (1934c, 59For a sentence of Φ to be analytic in the sense of Syntax § 52 it must be valid already on the basis of the logico-mathematical fragment of Φ. 60Likewise, in Carnap (1938, pp. 60–62), written after the syntactic period. 61‘Content-preserving’ seems to me preferable to the translation ‘equipollent’ in (Carnap, 1937a). 62Syntax § 82: “Die These des P h y s i k a l i s m u s besagt, daß die physikalische Sprache eine Universalsprache der Wissenschaft ist, d. h. daß jede Sprache irgendeines Teilgebietes der Wissenschaft gehalttreu in die physikalische Sprache übersetzt werden kann.” 63In Psychologie pp. 108–109 Carnap says that a sentence s is translatable into a sentence s′ if there are general rules by which s′ follows from s and s from s′ . Carnap must have regarded this 18 ANSTEN KLEV p. 12) as the main concept of the logic of science—is the class of all non-valid consequences of the sentence (Syntax § 49). Thus, the content of a sentence s is the set of all sentences that are consequences of s but are not already consequences of the empty class. We shall denote the content of a sentence s by G(s) (‘G’ for Gehalt). No translation tr : Ψ → Φ can, however, be content-preserving in this sense. Since Ψ and Φ are disjoint, the content of any sentence of Ψ will be disjoint from the content of any sentence of Φ, whence G(ψ) can never be equal to G(tr(ψ)). The problem that arises from the requirement that tr be content-preserving is how to amend the notion of content-preservation so that it can serve Carnap’s purposes. What we need, in effect, is a notion of a sentence of Ψ having the same content as a sentence of Φ. Once such a notion is found we can say that tr is content-preserving if ψ and tr(ψ) have the same content in this revised sense. It will now be useful to turn to the protocol language. Protocol sentences are in a sense the points of contact between language and experience, hence according to the logical empiricist theory of meaning (however that is spelled out more precisely), it is primarily by virtue of them that language has content. The essential part of the content G(s) of a sentence s should therefore be the set of protocol sentences in G(s). Carnap seems to assume something along these lines in the following passage from Psychologie (p. 108):64 The verification of system sentences by a subject S takes place thus, that from these sentences sentences of S’s protocol language are derived and compared with the sentences of S’s own protocol. The possibility of such derivations of protocol-language sentences makes up the content [Gehalt] of a sentence. Carnap goes on to say that if no such derivations can be given, then the sentence is without content;65 he thereby seems to identify the content of a sentence s with the protocol sentences in G(s). This notion of content can, however, not be used in the definition of a contentpreserving translation when the protocol language is assumed to be disjoint from at least one of the languages involved in the translation. The content in this revised sense of a sentence in a language disjoint from the protocol language will of course be the empty set. It is clear that the protocol language, containing qualitative predicates, cannot be part of the physical language Φ described in Syntax. The language Φ contains descriptive functions, but these have as domain and range real numbers or tuples of real numbers, hence they are purely quantitative. In fact, both in Universalsprache and in Psychologie Carnap explicitly assumes that the formulation as equivalent to the formulation involving content-preservation, for he takes it to be obvious (Syntax §§ 14, 49) that s and s′ have the same content if and only if each follows from the other. 64“Die Nachprüfung (Verifikation) von Systemsätzen durch ein Subjekt S geschieht dadurch, daß aus diesen Sätzen Sätze der Protokollsprache des S abgeleitet und mit den Sätzen des Protokolls des S verglichen werden. Die Möglichkeit derartiger Ableitungen von Sätzen der Protokollsprache macht den Gehalt eines Satzes aus.” 65In the Überwindung der Metaphysik (1932a) Carnap takes the opposite relation between system sentences and protocol sentences to be the criterion of meaningfulness: a sentence is meaningful if and only if it is derivable from protocol sentences (ibid. pp. 221–224). Carnap must have realized when thinking the matter through more carefully that this criterion is too strong. CARNAP ON UNIFIED SCIENCE 19 protocol language is disjoint from what he there calls the system language, namely the language of a given science. Although it would be enough for my purposes to assume that the protocol language is disjoint only from Φ, I shall therefore assume that it also is disjoint from Ψ. There are thus no protocol sentences in the content G(s) of any sentence s of Φ or Ψ. There may, however, be translations of protocol sentences in G(s). Indeed, we have already seen that Carnap takes the protocol language to be translatable into the physical language and vice versa—the possibility of these translations is what allows us to say that the language of physics is intersubjective (Universalsprache § 6). Carnap does, as far as I know, not discuss whether the protocol language is translatable into the language Ψ of psychology, but I assume that he thinks it is. In fact, in his paper Über Protokollsätze (1932d) Carnap explicitly takes it for granted that if the protocol language is separate from a given system language, then there are rules for translating the former into the latter.66 Hence we may assume that we have translations of protocol sentences both in Φ and in Ψ. In particular, we have a subset Φprot ⊂ Φ consisting of the translations of protocol sentences into the language of physics, and likewise a subset Ψprot ⊂ Ψ consisting of the translations of protocol sentences into the language of psychology. We have thereby reached a revised notion of content suitable for our purposes: we may think of the content of a sentence ψ of Ψ as the set of sentences G(ψ) ∩ Ψprot , and of the content of a sentence φ of Φ as the set of sentences G(φ) ∩ Φprot . That a sentence ψ of Ψ and a sentence φ of Φ have the same content in this revised sense must then mean that any protocol sentence that is translated by a sentence in G(ψ) ∩ Ψprot is also translated by a sentence in G(φ) ∩ Φprot , and vice versa. For the translation tr : Ψ → Φ to be content-preserving in the revised sense it is thus required that for each ψ ∈ Ψ the elements of G(ψ) ∩ Ψprot and the elements of G(tr(ψ)) ∩ Φprot are translations of precisely the same protocol sentences.67 We can express this requirement in mathematical terms as follows. Let Π be the protocol language and let πΦ : Π → Φ and πΨ : Π → Ψ be the translations of the protocol language into Φ and Ψ, respectively, assumed by Carnap to exist. The translation tr : Ψ → Φ is content-preserving in the revised sense if for each ψ ∈ Ψ we have −1 −1 (G(tr(ψ)) ∩ Φprot ). (G(ψ) ∩ Ψprot ) = πΦ πΨ The sets here flanking the identity sign are subsets of Π, the domain of both mappings πΨ and πΦ . The set on the left-hand side contains just the protocol sentences translated by the sentences in G(ψ) ∩ Ψprot and the set on the right-hand side just the protocol sentences translated by the sentences in G(tr(ψ)) ∩ Φprot . Hence, if these sets are equal we may say, metaphorically, that G(ψ) and G(tr(ψ)) contain the same protocol sentences. This account seems to me the best way of amending the notion of a contentpreserving translation to a notion that both sustains formulation (2) of the thesis of unified science and is consonant with Carnap’s remarks on translation and on the relation between the physical language and the protocol langauge. The account 66Cf. Carnap (1932d, p. 215): “first method: protocol sentences outside the system language; [. . . ]; specific rules for the translation of protocol sentences into system sentences are provided.” 67Carnap appears to assume precisely this notion of translation at Universalsprache pp. 462–463. 20 ANSTEN KLEV does, however, leave one with the difficulty of how to understand the translations πΦ and πΨ of the protocol language into the physical language and the psychological language, respectively. We had to introduce these mappings in order to define the revised notion of content-preservation. But how do we know that these translations are good, or faithful, translations? The revised notion of content-preservation just defined cannot be applied to them, since that definition rests on the assumption that the translations πΦ and πΨ are good translations. Formulation (2) therefore rests on the assumption that we understand how to translate the protocol language into the languages of physics and psychology. This perhaps problematic assumption would be avoided by letting go of Carnap’s assumption that the system languages are separate from the protocol language. For if the protocol language is part of Ψ as well as of Φ, then we can speak without qualification of G(ψ) and G(tr(ψ)) containing the same protocol sentences. Formulation (3) of the thesis unified science—to be discussed in the next section—assumes, mutatis mutandis, that the protocol language is in fact part of the system language. It can thus be seen as motivated by the problem of understanding what a faithful translation is of the protocol language into a system language. Before turning to that formulation, however, I should like to make a remark regarding the distinction between the formal and the material mode of speech— another outcome of Carnap’s linguistic turn introduced in Universalsprache—in relation to the thesis of unified science. In the formal mode of speech one speaks only of expressions and the forms of expressions; in the material mode of speech one speaks also of objects, states of affairs, meanings, etc.68 While the material mode of speech is justified, and indeed required, in the empirical sciences, in philosophy it leads to pseudo-problems, or obscurity and confusion more generally, and is therefore best avoided (Syntax §§ 74–81). Formulation (2) of the thesis of unified science, accordingly, speaks only of sentences and languages, where these terms can be understood in the appropriate, formal way. The formulation says, in effect, that the language of physics is what Carnap calls a universal language (Universalsprache § 5): a language into which any sentence of any science can be translated. Since the language of physics is the target of the translation thus postulated, this is a thesis of physicalism. It seems to me that the corresponding more general thesis of unified science cannot easily be phrased in the formal mode of speech. The more general thesis would say that there is some language of science into which any sentence of science is translatable. That there is a language into which both Φ and Ψ are translatable is, however, a trivial fact: just take as the target language 68In mediaeval semantics a similar distinction was drawn between formal and material supposition, but here the roles of ‘formal’ and ‘material’ are inverted; cf. the following passage from William of Sherwood’s introduction to logic (Kretzmann, 1966, p. 107): Supposition, then, is on the one hand material, on the other hand formal. It is called material when a word itself supposits either for the very utterance itself or for the word itself, composed of the utterance and the signification—as if we were to say, ‘man is a monosyllable’ or ‘man is a name’. It is formal when a word supposits what it signifies. Carnap’s original German uses ‘inhaltlich’ rather than ‘material’, and is thus less likely to confuse the student of the history of logic; but ‘inhaltlich’ has no natural English translation, and ‘material’ is perhaps as good a choice as any. CARNAP ON UNIFIED SCIENCE 21 some amalgamation of these two languages. What seems to be required in a nontrivial statement of the general thesis of unified science is that the target language be homogenous in some sense. In the material mode of speech this homogeneity could be said—as in Carnap’s intuitive conception of unified science—to consist in the homogeneity of the objects in the domain of the first-order quantifiers of the language (space-time points in the case of physics, elementary experiences in the case of introspective psychology). In the formal mode of speech it is, however, not easy to see how the required notion of homogeneity can be articulated. One could require that the target language be a one-sorted language; but it is a wellknown theorem that any many-sorted language can be translated into a one-sorted language.69 As long as one remains, as Carnap does, with the thesis of physicalism, or some other X-ism, this problem of formulation does, however, not arise, since in that case the target language is already specified. 4. Unified science in Testability and meaning Carnap (1932d) took the main point of criticism made by Neurath (1932b) against the version of physicalism articulated in Universalsprache to be that one should not separate, as Carnap there did, the protocol language from the system languages of science: the protocol sentences must be part and parcel of the language of science. Carnap (ibid.) accepted this criticism and came to regard a language including the protocol sentences as “the most appropriate among the the forms of scientific languages currently defended in the theory of science”.70 According to Carnap’s conception, the protocol language contains qualitative predicates, while the physical language is purely quantitative. That the language of science is to include the protocol language from the outset therefore calls for a conception of unified science quite different from that defended in Universalsprache, where the physical language is the target of the unification. In Testability and meaning Carnap no longer takes a quantitative, but rather a qualitative, language as basic for his account of unified science. He calls this language the thing language, and introduces it by the following description: “the language which we use in every-day life in speaking about the perceptible things surrounding us” (Testability I p. 466). The thing language is, however, not altogether free of idealizations, since its quantifiers are taken to range over space-time points (ibid. p. 433), rather than “the perceptible things surrounding us”. While the previous formulations (1) and (2) of the thesis of unified science rested on higherorder languages, Carnap now rests content with first-order quantification. Indeed, he now even considers restricting the number of quantifier interchanges, that is, he considers restricting the language to formulas of Σn - or Πn -form for some specific natural number n.71 On the grounds that Π2 seems to be needed for physics and 69A theorem to this effect is stated by (Herbrand, 1930, p. 64), a work Carnap cites in Syntax. 70Carnap (1932d, p. 228): “die zweckmäßigste unter den gegenwärtig in der Wissenschaftslehre vertretenen Formen der Wissenschaftssprache” 71Let φ be a formula without quantifiers. The formula ∀xφ is said to be of Π -form, as is ∀x∀yφ, 1 and more generally ∀x1 . . . ∀xn φ. Formulas of the form ∃x1 . . . ∃xn φ are of Σ1 -form. A formula of the form ∀x1 . . . ∀xn ∃y1 . . . ∃yn φ is Π2 , while a formula of the form ∃y1 . . . ∃yn ∀x1 . . . ∀xn φ is Σ2 . Thus, for each new quantifier interchange we increase the index n. If the outermost quantifier is ∀ the formula is Πn , and if it is ∃ the formula is Σn . Carnap writes Un for what is here written 22 ANSTEN KLEV that making a cut above that level seems arbitrary, he opts for the full first-order language (Testability II, pp. 27–28). The thing language is thus a full first-order language whose variables range over space-time points. The predicates of the thing language are required to be what Carnap calls observable predicates.72 A predicate P is observable for a subject if for some arguments, among them, say, a, the subject “is able under suitable circumstances to come to a decision with the help of a few observations about a full sentence, P (a), i.e. to a confirmation of either P (a) or ¬P (a)” (Testability I, p. 455). This explanation of the notion of an observable predicate does not provide it with clear-cut application criteria, but it does place a constraint on the decision of which predicates to take as basic in the thing language: provided one is suitably located only a few observations should be necessary in order to decide whether the predicate is true or not of a given space-time point. For a subject with ordinary sensory capacities ‘red’ and ‘blue’ are therefore observable predicates, as are ‘hot’ and ‘cold’ and ‘heavy’ and ‘light’. I can determine that ‘red’ is true of a certain space-time point by looking at the cover of a book in front of me; taking a piece of paper in my hand I can determine that ‘light’ is true of a certain space-time point. Temperature—Carnap’s standard example of a physical state quantity—is not observable, since it requires measurement by an instrument, and the use of instruments requires that we have made preliminary observations. For the same reason, neither is ‘weight’ an observable predicate (Carnap, 1938, pp. 52–53). The requirement of observability thus implies that the predicates of the thing language are qualitative; their being qualitative is also the reason why the thing language itself may be called a qualitative language. At Universalsprache p. 439 Carnap lists three answers to the question of what can be regarded as the given, or the immediate contents of experience.73 The first answer is the answer of classical positivism, according to which sense data constitute the given; the second answer is the answer of the Aufbau, according to which elementary experiences constitute the given; according to the third answer ordinary things as such constitute the given. For each answer there is a corresponding protocol language, namely a language that speaks about the given in the appropriate sense. Carnap notes (ibid.) that the third answer “does not have many defenders nowadays,” but that various things speaks for it and that it would deserve closer investigation. To my mind, we should regard the thing language described in Testability as the protocol language corresponding to the conception of the given as ordinary things as such. The thing language is, after all, precisely a language that speaks about the ordinary things we perceive around us. As we shall see in more detail shortly, the language of unified science is, according to Carnap’s view in Testability, built on the basis of the thing language, hence the thing language is there included in the language of unified science. The language of science thus includes, from the outset, the protocol language in the form of the thing language. Πn and En for Σn . The use of Π and Σ in this context appears to have originated in Warsaw in the late 1950’s; see Addison (1959, pp. 126–127). I am grateful to Stefan Roski for bringing this paper to my attention. 72As Carnap (Testability II, p. 13) notes, the atomic sentences of the thing language are similar to the “basic sentences” (Basissätze) of Popper (1935). A basic sentence expresses that an observable event takes place at a certain space-time region (cf. ibid. § 28). 73Likewise at (Carnap, 1932a, pp. 222–223). CARNAP ON UNIFIED SCIENCE 23 There is no longer any need to postulate the translations πΦ and πΨ from the protocol language into the language of physics and psychology, respectively. In fact, the notion of translation will not have to be called upon at all: instead of translating the protocol language and other languages into the language of physics, Carnap now aims in effect to build the language of science from the protocol language by means of explicit definition and what he calls reduction sentences. The formulation of the thesis of unified science defended in Testability and related publications is (3) All predicates of science can be either explicitly defined from or “reduced to” observable predicates. This formulation can be found e.g. at Testability I, p. 467 and it is implicit in the discussion of (Carnap, 1938). It is worth noting the commonalities between the project suggested by this formulation and the project of the Aufbau. As in the Aufbau, unified science is to be built on the basis of the given. The notion of the given assumed here is, however, different from that assumed in the Aufbau: not elementary experiences, but ordinary things are here taken to constitute the given. Considerations of intersubjectivity had led Carnap around 1930 to abandon the project of building unified science on the basis of elementary experiences. The rather extreme view defended in Universalsprache is that only a quantitative language, such as the language of physics, can be intersubjective.74 Perhaps influenced by Neurath’s criticism of this view (cf. Neurath, 1932b, pp. 211ff.), Carnap admits that also the thing language is intersubjective (Testability II, p. 12). Formulations (1) and (3) of the thesis of unified science thus agree in taking the target of the unification of science to be the given, although the notion of the given is different in each case. The formulations also agree, mutatis mutandis, in what are taken to be the objects of the unification of science. In formulation (1) the objects of the unification are concepts: the concepts of science are to be explicitly defined by means of type theory from relations defined over elementary experiences. After Carnap’s linguistic turn protocol sentences came to play the role of elementary experiences, and formulation (2) of the thesis of unified science says that the sentences of science are to be translated into the language of physics. A more conservative linguistic turn would have replaced the relations defined over elementary experiences by predicates, the linguistic counterpart of concepts. In formulation (3) predicates are indeed the objects of the unification of science. What is essentially new in formulation (3)—what cannot be explained as a modification of formulation (1) required by considerations of intersubjectivity or the linguistic turn—is the notion of reduction.75 Carnap (e.g. 1936b, pp. 63–65) motivates the need for this notion by considering how to account for disposition concepts. 74In Universalsprache (p. 448) Carnap claims, writing in German (italicization as in the origi- nal): “Außer der physikalischen Sprache (und ihre Teilsprachen) ist keine intersubjektive Sprache bekannt.” [“Besides the physical language (and its sublanguages), no intersubjective language is known.”] 75Carnap’s terminology here is quite unfortunate, since we naturally use ‘reduction’ for many kinds of relation between terms or theories, not only for the very specific kind of relation that Carnap has in mind. 24 ANSTEN KLEV In an ordinary first-order language without an abstraction operator an explicit definition has the form ∀x̄(Rx̄ ⇐⇒ φ(x̄)), where ⇐⇒ is the ordinary material bi-implication and x̄ is a sequence of variables. For instance, in arithmetic the less-than-or-equal relation may have the following definition ∀xy(x ≤ y ⇐⇒ ∃z(x + z = y)). The concept ‘soluble in water’, which is true of a thing if when placed in water it dissolves, is an example of a disposition concept. If S is the corresponding predicate in the thing language, then the open sentence S(x) may be read either as ‘the spacetime point x is soluble in water’ or as ‘the thing at space-time point x is soluble in water’. The first reading accords with Carnap’s decision to let the variables of the thing language range over space-time points, while the second reading accords more with common sense and will be preferred here. A natural suggestion for an explicit definition of S is ∀x(S(x) ⇐⇒ (W (x) ⊃ D(x))), where W (x) is read ‘the thing at space-time point x is in water’ and D(x) is read ‘the thing at space-time point x dissolves’. From this definition it follows, however, that, since my computer is not soluble in water, it is presently in water, which it is not.76 The counterexample can no longer be constructed if we introduce the predicate S by postulating that the following sentence is true ∀x(W (x) ⊃ (S(x) ⇐⇒ D(x))). This sentence may be read ‘for all space-time points x: if the thing at x is put in water, then it is soluble in water if and only if it dissolves’. From the truth of this sentence it does not follow that my computer is presently in water (W (c), say), even if it is not soluble (¬S(c)). Carnap (Testability I, p. 443) calls a sentence of the form ∀x̄(χ(x̄) ⊃ (R(x̄) ⇐⇒ φ(x̄))) a bilateral reduction sentence for R. A reduction pair (ibid. p. 442) for R is a pair of sentences of the form ∀x̄(χ1 (x̄) ⊃ (φ1 (x̄) ⊃ R(x̄))) ∀x̄(χ2 (x̄) ⊃ (φ2 (x̄)) ⊃ ¬R(x̄)). A bilateral reduction sentence may be regarded as a special case of a reduction pair, since if χ1 = χ2 and φ2 = ¬φ1 , the reduction pair for R is equivalent to a bilateral reduction sentence. Whereas Carnap in the Aufbau had required that all new concepts be introduced by explicit definition, he now finds it necessary, for instance in light of the consideration of disposition concepts, to allow that a new predicate R may be introduced also by postulating that each member of a set of reduction pairs 76Carnap had discussed disposition concepts in Psychologie § 3. In the manuscript that formed the basis for this paper (Carnap, 1930d) Carnap makes the explicit suggestion that a disposition concept is to be defined by a disjunction of conditional sentences (ibid. p. 11), thus e.g. as ∀x(S(x) ⇐⇒ (A(x) ⊃ B(x)) ∨ (C(x) ⊃ D(x))) The counterexample arises on this account as well. CARNAP ON UNIFIED SCIENCE 25 for R is true.77 An R introduced by a reduction pair as above is said to be reduced to χ1 , χ2 , φ1 , φ2 . While an explicit definition of R determines the meaning of R for all of its admissible arguments, a reduction pair does so only for the space-time points x for which either χ1 (x) ∧ φ1 (x) or χ2 (x) ∧ φ2 (x) is true. This means that R is not in general eliminable: there is no general principle allowing us to replace it by some combination of the predicates χ1 , χ2 , φ1 , φ2 to which it is reduced. Thus reduction differs from explicit definition, which guarantees substitutability of the definiens for the definiendum. Elimination of a predicate R introduced by a set of reduction pairs is guaranteed only if it is everywhere determined. Determination everywhere can of course be achieved by sheer postulation, namely, by postulating that R is true or that it is false of the points for which R until now was undetermined; but such postulation, as Carnap notes (Testability I, pp. 448–449), does not conform with the practice of scientists. We may now describe how the language of unified science is to be built up from the thing language. The thing language is not the language of physics, but Carnap (Testability I, p. 467) takes it for granted that the language of physics can be constructed from the thing language ∆ (delta for ‘Ding’) by means of explicit definitions and reduction pairs. That is, from ∆ we obtain successive extensions ∆′ , ∆′′ , . . . , Φ as follows. From the language L the extended language L′ is obtained by adding • to the vocabulary of L a new predicate R; • to the axioms of L either an explicit definition of R or a set of reduction pairs for R. Let Φ be a language containing all the predicates needed in a language of physics. It may be that Φ is not itself a language of physics, as it may not contain all the laws of physics; these should then be added to Φ so that a language of physics results. Carnap (Testability I, pp. 459–461) argues, however, that each natural law can be given in the form of a reduction pair. If that is true, then by choosing the right set of reduction pairs for suitable R’s when adding them to the thing language, Φ will already be a language of physics, containing not only the predicates needed, but also the natural laws. The language of unified science is obtained by continuing this process of adding new predicates and, possibly, new laws, to the language obtained so far, first through the rest of the natural sciences, then through psychology, then through the social sciences and the humanities. 5. Unified science in Carnap’s later works While unified science is an ongoing concern for Carnap until the late 1930’s, it disappears from the compass of most of his later work. The only writings after (Carnap, 1938) that to my mind are of relevance to the topic are two papers outlining a new conception of the language of physics (Carnap, 1956, 1959) as well as two short discussions of physicalism, namely Carnap’s response to Feigl (1963) in the Schilpp-volume (Carnap, 1963b, pp. 882–886) and an unpublished discussion 77For a single reduction pair it must be required that there is no space-time point x of which all of χ1 , χ2 , φ1 , φ2 are true, for should such an x exist, then R(x) ∧ ¬R(x) would follow from the reduction pair. For a set of reduction pairs a similar, but more complicated, requirement must be laid down. 26 ANSTEN KLEV note (Carnap, 1955). It is clear from these writings that Carnap still subscribes to the thesis of unified science. He emphasizes that there is no difference in kind between organisms and non-organisms, nor between different organisms, such as man and other animals (Carnap, 1963b, p. 884).78 We may here recognize the thesis, explicitly defended by Carnap in his earlier work, that there is fundamentally only one domain of objects for science to investigate. Carnap moreover holds that the prospect of our being able to define all theoretical terms, and derive all scientific laws, from those of physics “seems today much more probable and much less remote in time than it appeared even thirty years ago” (Carnap, 1956, p. 75).79 Thus Carnap would seem to think that the thesis of physicalism is better supported by the science of the period in which he is writing this—the mid-1950’s—than it was when he and other members of the Vienna Circle first advanced the thesis around 1930. What is lacking from Carnap’s later work is a systematic account of ‘the total language of science’ (die Gesamtsprache der Wissenschaft, cf. Carnap 1959, p. 236), in particular an account of the relation between the languages of psychology and physics. Since Carnap in his later work revises the account of the language of physics given in Testability to something closer to the account given in Syntax, it is clear that he can no longer subscribe to the account of the total language science defended in Testability. Carnap’s new conception of the language Φ of physics— foreshadowed already in (Carnap, 1939, § 24), but developed in more detail only in (Carnap, 1956)—may be briefly described as follows. It is a higher-order language, allowing quantification over any type, with the natural numbers forming the ground type. The terms of Φ are not, as in Testability, to be obtained by explicit definition and reduction sentences from the thing language; rather, its primitive terms are introduced through postulates (in effect, physical laws). The meaningfulness of the primitive terms and terms explicitly defined from primitive terms is gauged by the impact of sentences these occur in on the so-called observation language. The variables of this observation language are taken to range over “observable events (including thing-moments)” (Carnap, 1956, p. 40) and its predicates to designate observable properties of, or observable relations between, observable events (ibid. p. 41). The observation language is thus a qualitative language playing a role in this new conception similar to that played by the protocol language in the conception of the syntactic period. We saw that in order to specify what is the content G(φ) of a sentence φ of Φ in the sense of Syntax we had to assume there to be a translation πΦ of the protocol language into Φ. In Carnap’s new conception the assumption of such a translation is no longer implicit, but is made explicit in the form of the postulation of so-called correspondence rules, certain sentences containing terms from Φ as well as from the observation language (cf. Carnap, 1956, pp. 47–49). Just as with the translation πΦ , the correspondence rules are to allow for the derivation of sentences of the observation language from sentences of Φ (within some amalgamation of these two languages). 78See also Carnap (1955, pp. 5–8). The context of these parallel remarks is a criticism of the so-called emergentism discussed by Meehl and Sellars (1956). 79A similar statement is found in Carnap (1963b, p. 883). CARNAP ON UNIFIED SCIENCE 27 Carnap (1956, pp. 69–75) argues that the language Ψ of psychology is best understood along similar lines; in particular, that its primitive terms are best thought of as introduced via postulates and as gaining their meaning through the effect they have on the observation language. But Carnap says nothing or little about how the language Ψ of psychology and the language Φ of physics are to relate to each other. Physicalism decrees that Ψ should in some sense be reducible to Φ; but, as we have seen in the course of this paper, reduction in this sense can mean many different things: explicit definition in Φ of the primitive terms of Ψ; introduction of the primitive terms of Ψ through reduction sentences in Φ; a global translation of Ψ into Φ; and, probably, much more besides. In his response to Feigl (1963), Carnap (1963b, p. 885) says that he agrees with Feigl’s so-called identity theory.80 The most natural way of interpreting the identity theory in the current setting is as the thesis that the primitive terms of Ψ are explicitly definable from terms of Φ; an explicit definition is, after all, an identification in some sense. Whether a definition of a term of Ψ from terms of Φ is adequate may be judged on the basis of the sentences of the observation language derivable from Φ extended by this definition. The relevant sentences of the observation language should, presumably, concern behaviour. Hence, we may need to add to the observation language new predicates for kinds of behaviour as well as new correspondence principles. In comparison with the accounts of the relation between Φ and Ψ during the syntactic period and the period of Testability the resulting account is relatively simple: Ψ is obtained from Φ via explicit definitions. Carnap (1956, p. 67) does, however, suggest that new terms of Φ may be obtained not only through explicit definitions but also through reduction sentences. Once that is admitted there is little reason not to hold that also terms of Ψ may be introduced from terms of Φ through reduction sentences. The resulting view of the relation between the language Ψ of psychology and the language Φ of physics would thus be that the former is obtained from the latter by means of explicit definitions and reduction sentences. This view may be regarded as a synthesis of the views of Syntax and Testability: on the one hand, the quantitative language of physics is taken as basis, the meaning of the non-logical terms of which is to be gauged by their impact on the observation—in effect, the protocol—language; on the other hand, the terms of psychology—and, let us assume, all other sciences—are to be introduced into the physical language by means of definition and reduction. But whether Carnap entertained such a synthesizing vision of physicalism and unified science in his later works will have to be left for speculation. Acknowledgements. The research on which this paper is based was instigated by a kind invitation from Michel Bourdeau to speak on Carnap at the conference 1935–2015: 80 ans de philosophie scientifique at Cerisy in July 2015. Comments 80See, for instance, (Feigl, 1958, pp. 438–465) and (Feigl, 1963, pp. 255-267). Carnap (1956, p. 75) says that this latter paper “explains” his “recent views on the question of physicalism”, though he notes at (Carnap, 1963b, pp. 885–886) that he has “some doubts about his [Feigl’s] way of formulating” this question: from Feigl’s formulation it seems that the question of physicalism is “a factual question about the world” rather than “a question concerning the choice of a language form”. 28 ANSTEN KLEV from Stefan Roski as well as critical remarks and constructive suggestions from two referees led to significant improvements of the paper. References Addison, J. W. (1959). Separation principles in the hierarchies of classical and effective descriptive set theory. Fundamenta Mathematicae, 46:123–135. Barnes, J. (1993). Aristotle. Posterior Analytics. Translated with a Commentary. Clarendon Press, Oxford, 2nd. edition. Betti, A. and de Jong, W. R. (2010). The Classical Model of Science: A millenia-old model of scientific rationality. Synthese, 174:185–203. Carnap, R. (1922). Der Raum. Reuther & Reichard, Berlin. Carnap, R. (1923a). Diary 1923. RC 025-72-02. Transcription available at https://homepage. univie.ac.at/christian.damboeck/carnap_diaries_2015-2018/index.html. Carnap, R. (1923b). Über die Aufgabe der Physik. Kant-Studien, 28:90–107. Carnap, R. (1924). Diary 1924. RC 025-72-03. Transcription available at https://homepage. univie.ac.at/christian.damboeck/carnap_diaries_2015-2018/index.html. Carnap, R. (1926). Physikalische Begriffsbildung. G. Braun, Karlsruhe. Carnap, R. (1927). Eigentliche und uneigentliche Begriffe. Symposion, 1:355–374. Carnap, R. (1928a). Der logische Aufbau der Welt. Weltkreis Verlag, Berlin. Carnap, R. (1928b). Scheinprobleme in der Philosophie. Weltkreis Verlag, Berlin. Carnap, R. (1929). Abriss der Logistik. Springer, Vienna. Carnap, R. (1930a). Diary 1930. RC 025-73-04. Transcription available at https://homepage. univie.ac.at/christian.damboeck/carnap_diaries_2015-2018/index.html. Carnap, R. (1930b). Die alte und die neue Logik. Erkenntnis, 1:12–26. Carnap, R. (1930c). Die physikalische Sprache als Universalsprache der Wissenschaft. Unpublished manuscript. RC 110-03-22. Carnap, R. (1930d). Die psychologie in physikalischer Sprache. Unpublished manuscript. RC 110-03-36. Carnap, R. (1930e). Einheitswissenschaft auf physischer Basis. Erkenntnis, 1:77. Abstract of a lecture given in the Verein Ernst Mach. Carnap, R. (1931). Die logizistische Grundlegung der Mathematik. Erkenntnis, 2:91–105. Carnap, R. (1932a). Überwindung der Metaphysik durch logische Analyse der Sprache. Erkenntnis, 2:219–241. Carnap, R. (1932b). Die physikalische Sprache als Universalsprache der Wissenschaft. Erkenntnis, 2:432–465. Reprinted in Stöltzner and Uebel (2006). Carnap, R. (1932c). Psychologie in physikalischer Sprache. Erkenntnis, 3:107–142. Carnap, R. (1932d). Über Protokollsätze. Erkenntnis, 3:215–228. Reprinted in Stöltzner and Uebel (2006). Carnap, R. (1934a). Aufgabe der Wissenschaftslogik. Einheitswissenschaft. Gerold, Vienna. Cited from Schulte and McGuinness (1992). Carnap, R. (1934b). Logische Syntax der Sprache. Julius Springer, Vienna. Carnap, R. (1934c). On the character of philosophic problems. Philosophy of Science, 1:5–19. The original German manuscript is published in Carnap (2004). Carnap, R. (1935a). Ein Gültigkeitskriterium für die Sätze der klassischen Mathematik. Monatshefte für Mathematik und Physik, 42:163–190. Carnap, R. (1935b). Formalwissenschaft und Realwissenschaft. Erkenntnis, 5:30–37. Carnap, R. (1936a). Testability and meaning. Philosophy of Science, 3:419–471. Carnap, R. (1936b). Über die Einheitssprache der Wissenschaft. Logische Bemerkungen zum Projekt einer Enzyklopädie. In Actes du Congrès International de Philosophie Scientifique, Sorbonne, Paris 1935. II Unité de la science, pages 60–70. Hermann, Paris. Carnap, R. (1937a). Logical Syntax of Language. Routledge & Kegan Paul, London. Translation and slight extension of Carnap (1934b). Carnap, R. (1937b). Testability and meaning—continued. Philosophy of Science, 4:1–40. CARNAP ON UNIFIED SCIENCE 29 Carnap, R. (1938). Logical foundations of the unity of science. In Neurath, O., editor, Encyclopedia and Unified Science, International Encyclopedia of Unified Science, pages 42–62. The Univeristy of Chicago Press, Chicago. Carnap, R. (1939). Foundations of Logic and Mathematics. International Encyclopedia of Unified Science. The Univeristy of Chicago Press, Chicago. Carnap, R. (1942). Scientific empiricism; Unity of Science Movement. In Runes, D., editor, Dictionary of Philosophy, pages 285–286. Philosophical Library, New York. Carnap, R. (1955). Remarks on physicalism and related topics: Discussions with Wilfrid Sellars, December 1954. Unpublished manuscript. RC 86-06-01. Carnap, R. (1956). The methodological character of theoretical concepts. In Feigl, H. and Scriven, M., editors, The Foundations of Science and the Concepts of Psychology and Psychoanalysis, Minnesota Studies in the Philosophy of Science, pages 38–76. University of Minnesota Press, Minneapolis. Carnap, R. (1959). Beobachtungssprache und theoretische Sprache. Dialectica, 12:236–248. Carnap, R. (1963a). Intellectal autobiography. In Schilpp, P. A., editor, The Philosophy of Rudolf Carnap, The Library of Living Philosophers, pages 3–84. Open Court, Chicago. Carnap, R. (1963b). Replies and systematic expositions. In Schilpp, P. A., editor, The Philosophy of Rudolf Carnap, The Library of Living Philosophers, pages 859–1013. Open Court, La Salle, Illinois. Carnap, R. (2004). Scheinprobleme in der Philosophie und andere metaphysikkritische Schriften. Felix Meiner Verlag, Hamburg. Church, A. (1976). Comparison of Russell’s resolution of the semantical antinomies with that of Tarski. Journal of Symbolic Logic, 41:747–760. Clauberg, K. W. and Dubislav, W. (1923). Systematisches Wörterbuch der Philosophie. Felix Meiner Verlag, Leipzig. Cohen, M. and Matthews, G. (1991). Ammonius. On Aristotle Categories. Ancient Commentators on Aristotle. Duckworth, London. Creath, R. (1996). The unity of science: Carnap, Neurath, and beyond. In Galison, P. and Stump, D., editors, The Disunity of Science, pages 158–169. Stanford University Press, Stanford. Dahms, H.-J. (2005). Die “Encyclopedia of Unified Science” (IEUS). Ihre Vorgeschichte und ihre Bedeutung für den logischen Empirismus. In Nemeth, E. and Roudet, N., editors, Paris – Wien. Enzyklopädien im Vergleich, pages 105–120. Springer, Vienna. Damböck, C. (2012). Rudolf Carnap and Wilhelm Dilthey: “German” empiricism in the Aufbau. In Creath, R., editor, Rudolf Carnap and the Legacy of Logical Empiricism, pages 67–88. Springer, Dordrecht. Diemer, A. (1974). Geisteswissenschaften. In Ritter, J. et al., editors, Historisches Wörterbuch der Philosophie, volume 3, pages 211–215. Schwabe, Basel. Feigl, H. (1958). The “mental” and the “physical”. In Feigl, H., Scriven, M., and Maxwell, G., editors, Concepts, Theories, and the Mind-Body Problem, Minnesota Studies in the Philosophy of Science, pages 370–497. University of Minnesota Press, Minneapolis. Feigl, H. (1963). Physicalism, unity of science and the foundations of psychology. In Schilpp, P. A., editor, The Philosophy of Rudolf Carnap, The Library of Living Philosophers, pages 227–267. Open Court, La Salle, Illinois. Frege, G. (1891). Funktion und Begriff. Hermann Pohle, Jena. Friedman, M. (1999). Reconsidering Logical Positivism. Cambridge University Press, Cambridge. Frost-Arnold, G. (2005). The large scale structure of Logical Empiricism: Unity of science and the elimination of metaphysics. Philosophy of Science, 72:826–838. Gabriel, G. (2004). Introduction: Carnap brought home. In Awodey, S. and Klein, C., editors, Carnap Brought Home: The View from Jena, pages 3–23. Open Court, Chicago. Goldfarb, W. (1996). The philosophy of mathematics in early positivism. In Giere, R. and Richardson, A., editors, Origins of Logical Empiricism, pages 213–230. University of Minnesota Press, Minnesota. Goodman, N. (1951). The Structure of Appearance. Harvard University Press, Cambridge, MA. Hahn, H. (1929). Empirismus, Mathematik, Logik. Forschungen und Fortschritte, 5:409–410. Hahn, H. (1933). Logik, Mathematik, Naturerkennen. Einheitswissenschaft. Gerold, Vienna. 30 ANSTEN KLEV Heis, J. (2014). The priority principle from Kant to Frege. Nous, 48:268–297. Herbrand, J. (1930). Recherches sur la theorie de la démonstration. Doctoral thesis, University of Paris. Hintikka, J. (1993). Ludwig’s apple tree: on the philosophical relations between Wittgenstein and the Vienna Circle. In Stadler, F., editor, Scientific Philosophy: Origins and Developments, pages 27–46. Kluwer, Dordrecht. Husserl, E. (1913). Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie. Erstes Buch. Max Niemeyer, Halle. Kant, I. (1781/1787). Kritik der Reinen Vernunft. Johann Friedrich Hartknoch, Riga. Kretzmann, N. (1966). William of Sherwood’s Introduction to Logic. Translated with an introduction and notes. University of Minnesota Press, Minneapolis. Lewin, K. (1925). Über Idee und Aufgabe der vergleichenden Wissenschaftlehre. Symposium, 1:61–93. Cited from Milkov (2015). MacLane, S. (1938). Carnap on logical syntax. Bulletin of the American Mathematical Society, 44:171–176. Meehl, P. E. and Sellars, W. (1956). The concept of emergence. In Feigl, H. and Scriven, M., editors, The Foundations of Science and the Concepts of Psychology and Psychoanalysis, Minnesota Studies in the Philosophy of Science, pages 239–252. University of Minnesota Press, Minneapolis. Milkov, N., editor (2015). Die Berliner Gruppe. Felix Meiner Verlag, Hamburg. Morris, C. (1960). On the history of the International Encyclopedia of Unified Science. Synthese, 12:517–521. Neider, H. (1977). Persönliche Erinnerungen an den Wiener Kreis. In Marek, J. C. et al., editors, Österreichische Philosophen und ihr Einfluss auf die analytische Philosophie der Gegenwart, pages 21–42. Josef Zelger, Innsbruck. Neurath, O. (1932a). Soziologie im Physikalismus. Erkenntnis, 2:393–431. Reprinted in Stöltzner and Uebel (2006). Neurath, O. (1932b). Protokollsätze. Erkenntnis, 3:204–214. Reprinted in Stöltzner and Uebel (2006). Neurath, O. (1933). Einheitswissenschaft und Psychologie. Einheitswissenschaft. Gerold, Vienna. Neurath, O. (1935). Einheit der Wissenschaft als Aufgabe. Erkenntnis, 5:16–22. Reprinted in Stöltzner and Uebel (2006). Neurath, O. (1936). L’encyclopédie comme “modèle”. Revue de Synthese, 2:187–201. German translation in Stöltzner and Uebel (2006). Neurath, O. (1938). Unified science as encyclopedic integration. In Neurath, O., editor, Encyclopedia and Unified Science, International Encyclopedia of Unified Science, pages 1–27. University of Chicago Press, Chicago. Oppenheim, P. and Putnam, H. (1958). Unity of science as a working hypothesis. In Feigl, H., Scriven, M., and Maxwell, G., editors, Concepts, Theories, and the Mind-Body Problem, Minnesota Studies in the Philosophy of Science, pages 3–36. University of Minnesota Press, Minnesota. Oppenheimer, F. (1919). Theorie der reinen und politischen Ökonomie. Fischer, Jena. Ouelbani, M. (2005). Carnap und die Einheit der Wissenschaft. In Nemeth, E. and Roudet, N., editors, Paris – Wien. Enzyklopädien im Vergleich, pages 205–219. Springer, Vienna. Pincock, C. (2003). Carnap and the unity of science: 1921–1928. In Bonk, T., editor, Language, Truth and Knoweldge. Contributions to the Philosophy of Rudolf Carnap, pages 87–96. Kluwer, Dordrecht. Popper, K. (1935). Logik der Forschung. Springer, Vienna. Reck, E. H. (2004). From Frege and Russell to Carnap: Logic and logicism in the 1920’s. In Awodey, S. and Klein, C., editors, Carnap Brought Home: The View from Jena, pages 151– 180. Open Court, Chicago. Reisch, G. A. (1994). Planning science: Otto Neurath and the “International Encyclopedia of Unified Science”. British Journal for the History of Science, 27:153–175. Richardson, A. (1998). Carnap’s Construction of the World. Cambridge University Press, Cambridge. CARNAP ON UNIFIED SCIENCE 31 Russell, B. and Whitehead, A. N. (1910). Principia Mathematica, volume 1. Cambridge University Press, Cambridge. Sauer, W. (1987). Carnaps Konstitutionstheorie und das Programm der Einheitswissenschaft des Wiener Kreises. Conceptus, 21:233–245. Schlick, M. (1926). Erleben, Erkennen, Metaphysik. Kant-Studien, 31:146–158. Scholz, H. (1930). Die Axiomatik der Alten. Blättern für deutsche Philosophie, 4:259–278. Cited from Scholz (1961). Scholz, H. (1961). Mathesis Universalis. Abhandlungen zur Philosophie als strenger Wissenschaft. Benno Schwabe & Co Verlag, Basel. Schulte, J. and McGuinness, B., editors (1992). Einheitswissenschaft. Suhrkamp. Schumann, K. (1977). Husserl-Chronik. Martinus Nijhoff, The Hague. Stadler, F. (1997). Studien zum Wiener Kreis. Suhrkamp. Stern, D. (2007). Wittgenstein, the Vienna Circle, and physicalism. In Richardson, A. and Uebel, T., editors, The Cambridge Companion to Logical Empiricism, pages 305–331. Cambridge University Press, Cambridge. Stöltzner, M. and Uebel, T., editors (2006). Wiener Kreis. Felix Meiner Verlag, Hamburg. Uebel, T. (1995). Physicalism in Wittgenstein and the Vienna Circle. In Gavroglu, K., Stachel, J., and Wartofsky, M., editors, Physics, Philosophy, and the Scientific Community, pages 327–356. Kluwer, Dordrecht. Uebel, T. (2007). Empiricism at the Crossroads. Open Court, Chicago. Der Wiener Kreis (1929). Wissenschaftlicher Weltauffassung. Artur Wolf Verlag. Reprinted in Stöltzner and Uebel (2006). Windelband, W. (1894). Geschichte und Naturwissenschaft. Heitz, Strasbourg.