Rudolf Carnap

First published Mon Feb 24, 2020; substantive revision Tue May 5, 2020

Rudolf Carnap (1891–1970) was one of the best-known philosophersof the twentieth century. Notorious as one of the founders, andperhaps the leading philosophical representative, of the movementknown as logical positivism or logical empiricism, he was one of theoriginators of the new field of philosophy of science and later aleading contributor to semantics and inductive logic. Though his viewsunderwent significant changes at various points, he continued toreaffirm the basic tenets of logical empiricism, and is stillidentified with it. His influence declined, therefore, when logicalempiricism lost its dominance in the 1950s and 60s, even though manyof the efforts of the next philosophical generation (such asQuine’s) may be understood as responses to Carnap. Beginning inthe 1980s, a reassessment set in that has resulted in a much morenuanced and complex picture of his philosophy and its development. Theliterature on him is now enormous and still growing rapidly, and hisideas are presently enjoying a major revival in various areas ofphilosophy.

1. General Characterization of Carnap’s Philosophy

1.1 Rational Reconstruction and Explication

Carnap differed fundamentally from the western philosophical traditionin his conception of philosophy and his attitude toward philosophicalproblems. These supposed problems, he thought, were largely artifactsof our inadequate tools—they originate in confusions due to thelanguages our species has evolved over millennia to deal with thepractical problems of a pre-scientific and pre-technological everydaylife. These primitive tools leave us unequipped even to express, letalone to address, the traditional problems of philosophy coherently;our inherited languages distort the picture too badly, and to seethings more adequately we need to devise new concepts and organize ourthoughts in less parochial categories. Just as we have devised newconcepts and vocabularies to find out about the world in systematicscientific inquiry, so we have to leave behind our traditional ways ofarticulating how everything fits together, how we should understandour place in the world, and how we should shape our lives inresponse.

So philosophical inquiry became, for Carnap, a kind of“conceptual engineering” (see Creath 1990, Flockeforthcoming-b) rather than a form of inquiry or search for knowledge.It did not ask how things are, in Carnap’s view, but ratherhow—within the constraints of our available tools and theknowledge available from the sciences—wewant things tobe. This form of “voluntarism” (Jeffrey 1992) lies at thebasis of Carnap’s philosophy from beginning to end.

Carnap applied this voluntaristic conceptual engineering in manydifferent ways to many different problems, at different levels and ondifferent scales. He applied it both within science and to largerproblemsabout science (e.g., scientific language), or aboutthe place of science in our lives. He applied it both to localreconstructions or explications of particular concepts (e.g.,confirmation), and more globally, to entire language frameworks (seesection 1.2 below). And he wanted the local and global to fit together; precisedefinitions of explicated concepts were to be situated within suchlarger frameworks.

The terminology evolved over the years. Carnap tended to think of hisfirst engineering projects as “rational reconstruction”;later he favored the term “explication”. Both refer to thereconstruction or replacement of particular terms or concepts withinour more primitive ordinary languages (or vestiges of them inscientific languages) rather than to the design and development ofentire languages or language frameworks. There was a progressivechange of emphasis over the course of Carnap’s career in thegoals and the scope of this reconstructive engineering. In the earlyyears Carnap (along with most of his colleagues in the 1920s ViennaCircle) saw these engineering projects in much the same light as theeighteenth-centuryEncyclopédistes andnineteenth-century positivists had seen them. Ordinary language andtraditional concepts were to beovercome; they were to bereplaced by better and more scientific ones. Later,Carnap’s view became more pluralistic and dialectical (Stein1992); he increasingly recognized the practical nature of conceptualengineering and allowed more room for the standpoint of the languageuser, as well as the differing priorities and value systems involvedin the choice of language frameworks or explications. Recently,Carnap’s idea of explication has attracted a good deal ofattention (Maher 2007; Kitcher 2008; Carus 2007a; Dutilh Novaes &Reck 2017; Brun 2016; several papers in Wagner 2012), particularlyamong authors seeking to define the proper role of the newsubdiscipline of experimental philosophy (Justus 2012; Shepherd &Justus 2015; Schupbach 2017) or of the methodology of mathematicalphilosophy (Leitgeb 2013). More details are to be found in thesupplement onMethodology. (For more on conceptual engineering more generally, see, e.g.,Cappelen 2018.)

1.2 Frameworks

Explications or rational reconstructions were envisaged by Carnap assituated (where possible) in larger linguistic or conceptualframeworks, constructed object languages with a hierarchy ofmetalanguages in which to define and explore truth, analyticity,synonymity, designation and other semantic resources of the objectlanguage, and of the object language with respect to itsextra-linguistic environment.

Frameworks always involve logical consequence relation(s), theirdefinition(s) of what follows from what logically. But this need notalways mean that frameworks have purely logical object languages thatare then provided with empirical interpretations. Other modes ofinference employed in existing scientific disciplines, includingconceptual inference, experimental procedures, and the reasoning fromthese, can also be reconstructed in or by frameworks. Carnap continuedto hope that all of them could, eventually, be understood in morestraightforwardly logical terms, but he realized that this was along-term program and not immediately on the horizon. In particular,the framework could also come equipped with an inductive logic, wherethe deductive consequence relation for the object language isaugmented by a numerical degree-of-confirmation assignment thatsatisfies the axioms of probability. In any case, Carnapian languageor framework go beyond what we now mean by a formal language: they donot just involve a syntactic vocabulary and syntactic formation rules.From the modern logical point of view, a Carnapian framework is closeto a logic or a formal theory (but perhaps with an interpretation),while from the philosophy of science point of view, a Carnapianframework is meant to reconstruct the conceptual and inferentialpresuppositions of a scientific theory rather than a scientific theoryitself.

Carnap’s earliest attempts to develop frameworks, which soughtto encompass the conceptual resources of all empirical knowledge, canbe found inDer logische Aufbau der Welt (1928a,TheLogical Construction of the World), commonly referred to as theAufbau, its abbreviated original German title. Carnap therefocused on sketching a phenomenalist framework in which scientificconcepts could be constructed from pure observation. The idea was tohave a single framework relative to which any scientific sentencewhatsoever (other than purely logical or mathematical ones) could bejudged to be cashable or not cashable in empirical, observationalterms. However, as Carnap soon realized, the framework failed toaddress theoretical scientific concepts, disposition concepts, orprobabilistic concepts, among much else.

The frameworks on which Carnap worked after this were less specific toparticular epistemological problems, and more abstract and general. Inhis view, the specification of a framework was a prerequisite for anyrational reconstruction of rational discourse whatsoever. As we willdiscuss in more detail below, hisLogische Syntax der Sprache(1934, translated asThe Logical Syntax of Language, 1937,hereafter LSS) worked out two different frameworks for mathematics(and physics) and developed a corresponding account of philosophy asthe logical syntax of the language of science. Soon after, Carnapfollowed Alfred Tarski in making the basic concept of“truth” language-relative; and in 1950 he applied the sameidea more explicitly to the basic concept of “existence”.It only made sense to speak of something “existing”relative to a framework (i.e., one could only speak of“existence” asinternal to a framework), he said,not in any general sense (external to any frameworkwhatever). This deflationary conception of truth and existence (andmany other previously metaphysical concepts) again reflectsCarnap’s resistance to the suggestive traps set by ordinarylanguage and the philosophical tradition that has been too ready tofall into these traps.

In his later work, Carnap extended his construction of semanticframeworks by developing frameworks in which probabilistic relationsplay a central role, including eventually frameworks for rationaldecision and action (decision theory). The specific details ofCarnap’s various linguistic frameworks are discussed in thefollowing supplements:Aufbau (Section 1),Logical Syntax of Language,Semantics,The Reconstruction of Scientific Theories, andInductive Logic.

1.3 Pluralism and Tolerance

Carnap differed from the philosophical tradition not only in hissuspicion of ordinary language and its potentially misleading“philosophical” artifacts, and in his engineering impulseto replace our inherited languages by better-constructed and moreprecise constructed linguistic frameworks, but also in hisincreasingly pronounced pluralism among frameworks. In theAufbau, Carnap had already discussed the availability ofdifferent frameworks (phenomenalist, physicalist, and more), and howthey were more or less suitable for different purposes (see thesupplement onAufbau). But these frameworks still differed only in the choice of non-logicalprimitives and in the definition of non-primitive terms—theframeworks were still based on the same syntactic formation rules andon one and the same logical system. As far as the explicit endorsementof syntactic and logical pluralism and tolerance is concerned, theturning point came in 1932, while Carnap was writing his book (nowoften considered his masterpiece)Logical Syntax of Language.The starting point of that book, as we will see in more detail insection 4 below, had been strongly motivated by the search for a singlestandard language of science. But this was now combined withCarnap’s new idea that, for philosophical statementsabout science, the standard of communicative acceptabilityshould not (as in Wittgenstein’sTractatus) be that ithavemeaning (that it picture some state of affairs), butthat it be translatable into the “formal mode of speech”.His criterion for the scientific (non-metaphysical) status of aphilosophical statement, that is, had shifted from the reducibility ofa sentence to “atomic” observation sentences to itsexpressibility as a statement solely about linguistic artifacts(rather than about the supposed things and processes they refer to).But Carnap had still thought, until late 1932, that a single standardlanguage for logical syntax could be found, and had invested a lot oftime in devising such a language system. At that point, however, twosets of controversies attracted attention: the so-called“protocol sentence debate” about the correct form ofobservation sentences (and by implication, the role of observation inscience), and the dispute about the foundations of mathematics amongthe three schools of logicism, intuitionism, and formalism. Both thesecontroversies came to seem to Carnap, after years of involvement ineach of them, to stumble over artifacts of inherited language justlike the old philosophical problems the Vienna Circle thought it hadswept away. He came to regard the different positions in these debatesnot as potentially “right” or “correct” (or“wrong” or “incorrect”) but as differentproposals for language frameworks in which to frame the questions,different ways of articulating the problems surrounding empiricalevidence and the nature of mathematics, respectively. And it seemed tohim that these proposals were mostly not mutually exclusive; on thecontrary, he came to think that many different alternative languagesshould be pursued and developed to see how well they perform indifferent contexts. He saw them as motivated by different needs andrequirements, perhaps by different ultimate values, and he thought thediscussion of values should not be confused with the study anddevelopment of the language frameworks themselves: “inlogic”, he famously wrote in theSyntax (LSS:§17), “there are no morals”.

This new pluralism undermined the initial premise of theSyntax book on which he was working then, but Carnapnonetheless took it on board. The language he had initially beenintending to propose as the single standard language of science wasnow used simply as an example, and to be sure that it wasn’ttaken too prescriptively Carnap also developed another language(Dr.-Seuss-like, he called them “Language I” and“Language II”), and stressed that both were acceptable,though each had its strengths and weaknesses for different purposes.The new linguistic pluralism was stated as the

principle of tolerance: we are not in the business of setting upprohibitions but of arriving at conventions…In logicthere are no morals. Everyone is welcome to set up his logic,i.e., his form of language, as he pleases. If he wants to discuss itwith us, though, he needs to state his intentions clearly, and givesyntactical specifications rather than philosophical debates. (LSS:§17)

This principle would remain a permanent, indeed the dominant,component of Carnap’s philosophy for the rest of his career. Formore details on Carnapian tolerance, see the supplementTolerance, Metaphysics, and Meta-Ontology (Sections 1 and 2).

1.4 Metaphysics

Why, under this pluralism, should some statements and expressionsstill be excluded, asnot having any content, asnotconveying anything but as being just empty verbiage that purports tosay something significant? Why, that is, should“metaphysics” still be excluded, as Carnap notoriouslyinsisted? Surely the metaphysician is as free as anyone else to chooseher language?

These questions take us back to the engineering ethos described insection 1.1 above, about explication and rational reconstruction. Languagechoice, for Carnap, was not an end in itself but was rather in theservice of freeing ourselves from the distorted perspective on theworld imposed on us by our inherited natural languages. Theselanguages had not evolved to optimize the transparent representationof knowledge, but for very different, primitive practical purposes.For the pursuit of knowledge, and insight into the human condition inthe light of that knowledge, better languages are needed. What makes alanguage “better”? In principle Carnap leaves that open.Everyone has their own values about what they want languages to do forthem, and will choose accordingly. But Carnap’s own values werethose of the Enlightenment. His value hierarchy placed the value ofescaping from the complacent, passive acceptance of authority, or oftraditional or folk ideas—and finding something objectivelybetter—near the top. The replacement of knowledge acceptedpassively from authority or tradition by objective knowledge was hisgoal just as it had been the goal of theEncyclopédistes. And by “objective”knowledge, Carnap meant essentially scientific and practicalknowledge, just as they did.

This did not mean a rejection of the humanistic tradition, or ofdimensions to values other than the scientific andengineering-oriented. Carnap took entirely for granted (so deeply thathe hardly ever bothered to make it explicit) that literature, art, andmusic shaped people’s values and were closely connected withthem. But these were for individuals to negotiate. Since hisexperience of the First World War, he had realized that the Germanintelligentsia’s political indifference, its overindulgence inhumanistic individual values, had been partly to blame for the war. Hehad resolved, therefore, to attend more to the framework that allhumans shared, and that formed the basis for their social andpolitical cohabitation. Objective knowledge was, to him as to theEnlightenment, at the core of this shared framework. Practical(especially political) decisions should beinformed ones,arrived at in the light of the best possible knowledge about theavailable choices and their consequences.

Metaphysics was, in his view, a distraction from this program.Metaphysics was a kind of failed art form masquerading as knowledge,so it was both fake artand fake knowledge. Unlike a logicalor mathematical proof or the confirmation of a scientific theory,metaphysical proposals are unable to command widespread agreement;even the criteria by which they should be judged are often indispute.

On the other hand, all of Carnap’s repeated attempts, overseveral decades, to give a precise delineation—to explicate thedistinction—between scientific (or meaningful or communicativelyadequate) statements and metaphysical (non-scientific, non-meaningful)ones failed. He therefore became more liberal and less exacting aboutwhat was to be regarded as metaphysical. He was willing to allow thatmany metaphysical theories of past philosophers (he cites Aristotle,Leibniz, Kant, Peirce, and Whitehead, among others) could be regardedas useful steps toward the construction of “the most generalframeworks containing categorial concepts which are fundamental forthe representation of all knowledge”, and moreover that hehimself regarded this task as among “the most important problemsof philosophy” (Carnap 1963b: 862). See the supplementTolerance, Metaphysics, and Meta-Ontology (Section 2 and 3) for further detail.

1.5 Verification and Confirmation

Carnap’s life-long quest to explicate the distinction betweenstatements that genuinely convey something and empty verbiage thatonly purports to say something (metaphysics) began withWittgenstein’sTractatus, the Vienna Circle’sprovisional starting point. The Circle interpreted Wittgenstein asrequiring what Carnap later called a “molecular” language,by which he meant a language that permitted only finitely restrictedquantification. This posed an obvious problem in that scientifictheories, the very paradigm of what the Circle regarded as proper(non-metaphysical) knowledge, nearly all contain unrestricteduniversal quantifiers and thus range, in principle, over an infinitenumber of instances. As Carnap already acknowledged in his firstwritings on the subject, well before Popper appeared on the scene,this meant that theories could not, strictly speaking, be verified;they could only be confirmed up to a certain confidence level, ordisconfirmed (e.g., Carnap 1926: 7–9).

As we will see insection 5 below, this and related problems constituted a large part of theCircle’s agenda during the late 1920s and early 1930s. Theimportant thing to keep in mind through all this is that “theverification principle” in its crude form was never advocated byCarnap or any other major figure in the Circle. (More detail on thisin the supplement onThe Reconstruction of Scientific Theories (Section 1).) In theAufbau, Carnap had, it is true, worked out afinitist, “molecular” phenomenalist language and advocatedthe epistemological benefits of reconstructing scientific concepts onits basis. During this period, he was attracted to a form of radicalpositivism that played down theories as mere auxiliary devices for theprediction of observations. The observations that confirm theories, inthis view, was really all there was to science, in what amounted to akind of instrumentalism about theories, as it would later becalled.

But soon afterwards, in hisLogical Syntax, and moreexplicitly when he published “Testability and Meaning” in1936–37, Carnap decisively distanced himself from suchdoctrines. In the light of the new principle of tolerance, theobsession with just one standard language form seemed unnecessarily“absolutist” and rigid. In “Testability andMeaning” it is stressed that many different language forms arepossible in science and should be investigated, and that none is“correct” or uniquely acceptable for the purposes ofscientific confirmation. The point is to devise languages that meetcertain goals of inquiry better than others, in the awareness thatsome languages may be better for the pursuit of one goal, while otherlanguages are preferable for other goals. This is perhaps the firstfully explicit expression of the engineering ethos described insection 1.1 above.

This period also marks a return to the recognition that radicalpositivism of the “molecular” orTractatus sorthardly does justice to actual science—so Carnap returns now toscience as it actually is done rather than an idealized, purelyfactual science. This meant, once again, an acceptance thattheoretical vocabulary needed to be accounted for in one’sconception of science. Another kind of concept characteristic ofactually practiced science that gets special attention in“Testability and Meaning” is disposition concepts (e.g.,“soluble” or “refrangible”; more ondisposition concepts in the supplementThe Reconstruction of Scientific Theories (Section 2)). Probabilistic concepts would soon come into focus as well as asignificant preoccupation.

1.6 Theory Reconstruction and Inductive Logic

From this period, then, Carnap once again focused on scientifictheories, and on theoretical languages as not fully reducible toempirical observation sentences. While he had given up the effort toreduce theories to observations, he remained preoccupied withthe complementary problems of how a theory can beconfirmedby observations, and how the empiricalcontent of a theorycan be determined. Both of these problems were articulated, and seenas interrelated, in “Testability and Meaning”, butthereafter they took separate paths. The first of these problems wascentral to Carnap’s preoccupation with inductive logic fromabout 1942, though he was never able to develop it to the point whereit could be applied to the confirmation oftheoreticalsentences (as opposed to mere empirical generalizations). The secondproblem was the focus of significant attention to the nature oftheoretical languages and the degree to which theories are constrainedby evidence, as well as the problem how to identify the analytic andsynthetic parts of a theoretical hypothesis or a theory, i.e., todistinguish what components of it come with the language framework inwhich it is expressed, and what components contain actual informationabout the world. See sections8.1 and8.3 below on Carnap’s further pursuit of both problems and hiscontroversies and interactions with Popper, Hempel, and others onthese issues. The supplementThe Reconstruction of Scientific Theories (Sections 3 and 4) deals in more detail with Carnap’s distinction betweenobservation language and theoretical language in science, and withCarnap’s reconstruction of scientific theories and theoreticalterms by means of Ramsey sentences and related logical resources.

His own primary attention during the later years of his career was toinductive logic, where he began by distinguishing two fundamentallydifferent explicanda of the concept “probability”: (i) theidea of probability asrelative frequency of some occurrencein a series of events or in a population, which he regarded as alegitimate and entirely empirical matter. He contrasted it with (ii)probability understood as anepistemic measure of ourcertainty or uncertainty about the empirical truth or adequacy of astatement. The latter was Carnap’s focus; at the outset heworked out a structural and logical conception of epistemicprobability, influenced by Waismann and Keynes, as further explainedin the supplementInductive Logic, and progressed over the years toward a more “personalist”view, though never giving up the logical conception entirely. Heworked closely with various students and associates on these problems,especially Richard Jeffrey, Yehoshua Bar-Hillel, and John Kemeny. Seesection 8.2 below, see the supplementInductive Logic for the details of his structural account of probability, and see thesupplementMethodology (Section 1) for his probabilistic explication(s) of inductive confirmation. RayJ. Solomonoff’s work on universal inductive inference was alsotriggered by Carnap’s inductive logic. (Solomonoff studied withCarnap in Chicago. See Sterkenburg 2018 for a discussion andevaluation.)

1.7 Structuralism

Another strand of Carnap’s indifference to ontology was hislifelong focus onstructures as the main objects ofknowledge. Even as early as 1922, Carnap had thought that mathematics,correctly understood, is not so much the study of quantity and numberas the study of structures; Kant’s dictum that something isscientific just insofar as it is mathematical was now superseded, hethought, by his new dictum that something is scientific just insofaras it isstructural (Carnap 1922b: p. cl[r], translated andquoted in Carus 2007a: 163). And if the object of our knowledge is notthe particular or the qualitative but the structural, then, as HermannWeyl had said, “A science can determine its subject matter onlyup to an isomorphic representation”.

In particular, it is altogether indifferent toward the“essence” of its objects of study…It is mysticismto expect of scientific knowledge that it reveal—toacquaintance—a deeper essence than that openly available toacquaintance. The conception of isomorphism pinpoints theunquestionable and ineluctable limit to knowledge. (Weyl 1926: 22[1947: 25–26])

Weyl speaks here in the language of axiomatic systems and theirstructurally identical—isomorphic—models, a languagelargely articulated at the beginning of the twentieth century by DavidHilbert. But Hilbert had only made more precise the notions ofstructuralism that went further back and had animated a great deal ofnineteenth-century mathematics (see Schiemer 2013), culminating in thegroup-theoretic (algebraic) understanding of the new non-Euclideangeometries and Felix Klein’s celebrated “ErlangerProgramm” for the unification of geometry by this means, whichalso inspired the early Bertrand Russell. Russell himself, and beforehim Gottlob Frege and Richard Dedekind, had given“top-down” definitions of structural concepts by means ofhigher-order logical quantifiers (as in Frege’s 1879 famousdefinition of the ancestral of a relation in hisBegriffsschrift, or in Dedekind’s 1888 definition ofsimply infinite system in hisWas sind und was sollen dieZahlen?, or in Whitehead and Russell’s 1910–1913Principia Mathematica), all of which influenced Carnapsignificantly. An equally important influence, at about the same timeas Klein, was the epistemological structuralism of Hermann vonHelmholtz. Carnap was clearly inspired by these ideas, not only in hisearliest work, but all through his career, even into his work onprobability and induction, as we will see below (section 8).

Carnap is best known, though, for his application of structuralismfirst to epistemology, in theAufbau, and then to mathematicsitself, in theSyntax and later work, as well as tomathematically formulated scientific theories. The frameworksdiscussed in section 1.2 above were always structural ones, in whichCarnap invariably abstracted from the actual instantiation of thestructures in question in actual languages or conceptual systems, withthe result that even some of his closest allies and associatesmisunderstood him, including (among others) Russell, Neurath, Popper,and Quine (seesections 3 through 8 below for details). The articulation of these structuralframeworks is discussed in the supplementsAufbau,Logical Syntax of Language,Semantics, andReconstruction of Scientific Theories.

Carnap’s structuralism about mathematics also points forward, inits anticipation, for instance, of Tarski’s structuraldelimitation of logic modeled on the Erlanger Programm (Tarski 1986,Sher 1991), and has recently been seen as a precursor of a new form ofmathematical structuralism based on homotopy type theory in itsemphasis on invariance (Awodey 2017).

From theAufbau (see the supplementAufbau (Section 2) on Carnap’s early structuralism) to his mature reconstructionof scientific theories (see the supplementThe Reconstruction of Scientific Theories (Section 6) on Carnap’s later structuralism), Carnap sought to articulatean innovative type ofconceptual orlinguisticstructuralism about science that is metaphysically neutral and whichresembles modern versions of structuralism about mathematics: thecognitive content of what can be asserted precisely and meaningfullyin science can be reconstructed as a structural constraint onempirical content, and one should aim at such structuralreconstructions as they enhance the objectivity of science. Whilestructural properties are expressed using logical concepts usuallydiscussed in the context ofdeductive logic, Carnap’slater work oninductive logic considers probability measuresthat are logical or structural in the analogous sense, i.e., whereprobabilities remain invariant under isomorphisms. This“inductive structuralism” is discussed in supplementInductive Logic.

1.8 Values

Carnap is not generally known for his (very sparse) publications aboutvalues, but what he did publish is sufficient (in conjunction withrecently published texts) to yield a fairly accurate insight into histhinking, which turns out to be sufficiently original to havesignificant potential for further development. Carnap’s mainpublication on values is the final (and longest) chapter of hisreplies to critics in the Schilpp volume (the Reply to Kaplan, Carnap1963b). On the basis of this text, Carnap has generally beenclassified simply as an (ethical) non-cognitivist. And there is aclose resemblance between Carnap’s proposed logic of normativestatements (“optatives”, Carnap calls them) and that ofRichard Hare (1954) published at about the time Carnap’s replywas written (though it was not published until 1963). The term“non-cognitivist” to describe the view that normativestatements cannot be true or false (and that therefore no“ought” can be derived from an “is”, as Humehad put it), was, in fact, proposed by Carnap—one of his morewidely-accepted (if low-profile) coinages.

However, it had been assumed that since Carnap required a framework tobe in place for any kind of rational discourse to be possible, thechoice of frameworks itself must be simply a matter of personal whim,at the level of Hume’s declaration that there is no rationalargument for me to prefer the relief of a pain in my little toe to theprevention of some world-engulfing catastrophe. This problem of theirrationality of framework choice (George 2012) or—put anotherway—the supposed infinite regress in the selection ofmeta-frameworks for the choice of framework (Richardson 2007;Steinberger 2016; Carus 2017) has been discussed recently from variousangles. It is a special case, in the way Carnap is still usually seen,of the supposedly more general impossibility, for Carnap, of bringingreason to bear on normative choices, since in his view all reasoningseems to presuppose internality to a framework.

But from an interpretive viewpoint, this was clearly an unsatisfactoryposition, since Carnap had in fact from his earliest days usedreasoning to argue for normative positions, and continued to do so allhis life. So there seemed to be a tension, at such a basic level thatone would surely think Carnap must or should have been aware of it. Infact, there is no tension, as it turns out that Carnap (at least inhis later years and probably for much of his career) held aquasi-Kantian view whereby the logical reasoning we employ inmathematics, logic, and science (including inductive logic anddecision theory) is conceived as subordinate to (and narrower in scopethan) a purely normative form of reasoning—in Kantian terms,Verstand (understanding) is subordinate to (and narrowerthan)Vernunft (reason). So at least it appears from arecently published fragmentary draft Carnap wrote in 1958 of acontinuation of or sequel to the reply to Kaplan about values that hadappeared in the Schilpp volume (Carnap 2017); see the supplementTolerance, Metaphysics, and Meta-Ontology for further discussion.

More recent forms of normative non-cognitivism have recast theirdoctrines somewhat to describe them as “expressivist”(Blackburn 1993; Gibbard 1990). From this starting point Huw Price(1988) has sought to generalize expressivism to include not onlynormative language but other kinds as well. In some more recentexpositions of this proposed globalized expressivism or“functional pluralism” (Price 1997; see also Creath 1994on the sense on which Carnap’s view can be called“functionalist”), he invokes Carnap’s conception ofmathematics as the exemplar on which he proposes to model his approachto all sectors of language; he calls this the “Carnapthesis”, and assigns it fundamental importance in thedevelopment of a new “global expressivism” as he alsocalls his position (Price 2013, 2018). In view of the discussionabove, it would seem that Carnap himself had already generalized hisfunctionalist “Carnap thesis” regarding mathematics to atleast values and possibly also to other sectors of language (Carus2018; Price 2018). This is also consistent with the new-found interestin Carnap’s “inferentialism” (Peregrin 2011,forthcoming; Chalmers 2012), discussed further insection 5 below. Perhaps, in some respects, current philosophy is beginning tocatch up to Carnap.

(General surveys of Carnap’s work can be found in, e.g., Mormann2000, Friedman and Creath 2007.)

2. Toward theAufbau

2.1 Beginnings

Carnap was born on 18 May 1891 in the small town of Ronsdorf, now partof Wuppertal, an industrial city near the Ruhr area of northwesternGermany. His mother was a schoolteacher, and her father, FriedrichWilhelm Dörpfeld (1824–93), had been a leading educator andeducational thinker in the Herbartian tradition. Carnap washome-schooled by his mother until secondary school, and brought upreligious, but the emphasis was on the ethical, rather than thedoctrinal, dimensions of religious life. As a result, Carnap said, hehad no crisis of conscience when he later abandoned any belief in Godor the supernatural. In 1908 the family moved to Jena, into the houseof another famous relative, Carnap’s maternal uncle WilhelmDörpfeld (son of Friedrich Wilhelm), a well-known and highlyinfluential archaeologist. Carnap made trips to Greece with his uncleduring this time. He subsequently finished secondary school in Jenaand enrolled in the university there, studying philosophy, physics,and mathematics, vaguely intending to become a high-school scienceteacher.

At the University of Jena he soon encountered the “SeraCircle”, an offshoot of the Youth Movement that swept Germany inthe years before World War I. He became enthralled with the idea, ashe later said, that social forms and behavioral standards did not haveto be assimilated uncritically from the surrounding society, or fromtradition, but could be freely invented. The “voluntarism”that suffuses every phase of his later philosophical career (Jeffrey1992) seems to have had its origins here. He became not only anenthusiastic participant in the Youth Movement but also a leader,representing the Jena branch at the climactic national meeting oflocal Youth Movement groups at the Hoher Meißner in 1913 (Werner2003).

Carnap’s first exposure to logic came from an obscure andreclusive professor of mathematics at Jena, Gottlob Frege. Carnap wasso fascinated that he took every course Frege offered (including twocourses on Frege’s Begriffsschrift and a course on Logic inMathematics). His resulting shorthand notes are sufficiently detailedto permit a reconstruction of Frege’s response after the systemof theGrundgesetze had been undermined by Russell’sparadox (Reck & Awodey 2005). It would be another decade, though,before Carnap came to see Frege’s logic as the key to a new wayof doing philosophy. Carnap also studied with neo-Kantians andLebensphilosophen, including Bruno Bauch (whose course onKant’s First Critique left a lasting impression), Herman Nohl (astudent of Dilthey) and—while in Freiburg for asemester—Heinrich Rickert, whose lectures Carnap wasparticularly enthusiastic about.

The war interrupted this development. Carnap and his Youth Movementfriends, though hardly enthralled, felt they could not shirk theirduty to serve. Carnap spent most of 1914–17 at the front (firstthe eastern, then the western), and took part in some of the bloodiestengagements. In 1917 he was wounded, awarded the Iron Cross, and spentthe remainder of the war at a radio research facility in Berlin. Healso became politically active: he joined the (by then anti-war)Independent Socialist Party, circulated excerpts from the world press,mostly critical of the German government, to friends with his comments(Werner 2015), and participated in the transformation of the YouthMovement (or parts of it) into a political force. He teamed up withKarl Bittel, another Youth Movement leader, to start the undergroundPolitical Circular, a newsletter for university YouthMovement adherents that appeared irregularly during the monthsimmediately preceding the German Revolution of 1918. In the firstissue, Carnap reviewed two books on proposals for worldwide politicalunion (Carnap 1918a). He also prepared for publication a much longerand more detailed analysis of the entire political situation followingGermany’s military defeat, but the Revolution occurred just asit was to be published, and it never appeared. (See the editors’introduction to Carnap 2019; it has now been published, along withother early Carnap manuscripts, in Damböck, Sandner, & Wernerforthcoming.)

Carnap’s newfound political orientation was a non-Marxistlibertarian socialism of a kind represented by Gustav Landauer(1870–1919), a writer much admired by both Bittel and Carnap(Carnap 1919: 124, as described in Carus 2007a: 59). What is moststriking about Carnap’s unpublished analysis of the Germansituation after the defeat, though, is howunpolitical itremains, in any literal sense. He certainly deplores the unwillingnessof educated Germans to dirty their hands with politics, and urges afundamental change in attitude, balancing the exclusive Germanemphasis on the contemplative life with greater involvement in theactive life. However, what Carnap calls “politics” in thisanalysis is “everything… that has some connection withthe public social life of people”—which, as he makes quiteexplicit, includes practically all human activities, including somevery ivory-tower ones. Indeed, the key to his advocacy of greater“political involvement” is that he assigns intellectualwork a central and indispensable role in arriving at the “formof community [Gemeinschaftsgestalt]” that could serveto coordinate the vast and heterogeneous multitude of tasks and jobsthat have “some connection with the public social life ofpeople”. Only by virtue of such a “form ofcommunity” can we hope to remove this otherwise anarchic hive ofactivities “from the realm of chaotic whim and subordinate themto goal-oriented reason” [“der choatischenWillkür zu entziehen und der zielbewußten Vernunft zuunterwerfen”] (Carnap 1918b: 17–18, translated andquoted in Carus 2007a: 63).

2.2Der Raum

For Carnap the basis for “goal-oriented reason” could onlybe a comprehensive system of knowledge, and this exhortation to removethe design of our system of the sciences “from the realm ofchaotic whim”, and to “subordinate” it to“goal-oriented reason” reverberates throughout his earlyphilosophical papers (e.g., Carnap 1923: 107), which have now beenpublished together with English translations in Carnap (2019). In theeditors’ introduction to this new edition it is argued that thisprogram was not just a momentary response to a particular crisis, butcontinued to inform the architectonic of Carnap’s philosophythroughout its development. This is hardly disputed with respect tothe immediately following stages of Carnap’s career, addressingthe nature and design of the system of knowledge—hisdissertation on philosophical problems of space and geometry,DerRaum (1922a) and other early papers.Der Raum[Space] prefigures later works in its effort to disentanglevarious meanings of the word “space” and to show thatphilosophical confusion had resulted from the failure to distinguishthem clearly. In this case, Carnap distinguishes “formal”,“intuitive”, and “physical” space. The firstwas a purely logical or set-theoretic construction of space; thesecond was built up from a version of Hilbert’s axiomsrestricted to a local, subjective space; the third was the space ofphysics. In each case, by separate arguments, Carnap reaches theconclusion that the space we must assume as the precondition for anyknowledge is not Euclidean space, as Kant had argued (and someKantians such as Natorp were still arguing), nor even any metricspace, but topological space of arbitrarily many dimensions. Whilethis represents a form of (neo-)Kantianism Carnap would soon leavebehind, it was tempered by the critical role of the “factualbasis [Tatbestand]” in deciding among mathematicallypossible kinds of physical space. The factual basis was determinedonly up to the topological relations among its elements;Carnap’s residual Kantianism is expressed in the topologically“necessary form” (not reaching to metrical relations) ourperception imposes on its elements (see Heis 2011 on the neo-Kantianbackground in the philosophy of geometry).

2.3 TheAufbau Program

A series of notes taken during this period exhibit Carnap’spreoccupation with the question how the system of knowledge could,unlike the proposals of Diderot and d’Alembert in theEncyclopédie and those in its wake such asComte’s and Ostwald’s (1914a, 1914b), be unifieddeductively, as Leibniz—and Frege—had envisaged(on Ostwald as a starting point for Carnap during this period, seeDahms 2016). What especially preoccupied the young Carnap was thechallenge of giving the system empiricist underpinnings, i.e., findingdeductive relations between sense perceptions and the abstractconcepts of the advanced sciences. For a year or two he struggled withthis problem without success, until finally, in early 1922, justbefore the publication ofDer Raum, Carnap read BertrandRussell’sOur Knowledge of the External World (1914).Here he found his answer—the concepts were to be derived not byanalysis of experience, and deduction from the resultingelements, but byconstruction, using a “principle ofabstraction” (Russell 1914a: 44–45; see also Pincock2002). Experiences could be gathered into equivalence classes, and forpurposes of constructing a “real” world, each such classcan be regarded as a concept, defined by its extension. Immediate,momentary experience—the basis for knowledge among positivists,phenomenologists, as well as fictionalists such as the Germanphilosopher Hans Vaihinger—need not be transcended in such aconstruction. The hitherto insurmountable problem of forcing the fluidcharacter of lived experience into the straitjacket of deductiverelations disappears.

This move also overcame another traditional positivist andphenomenological obstacle to Carnap’s project of a Leibnizian,deductive system of knowledge, formulated most drastically by HansVaihinger (who influenced Carnap in this regard): the“chaos” of subjective experience, as we immediatelyexperience it, has no structure whatever. Nothing is really“given” but the undifferentiated chaos itself. Nodistinguishable “elements” present themselves as naturallyisolable from it or as inherently available, without externallyimposed fictions. Russell’s principle of abstraction—hismethod of substituting “logical constructions for inferredentities” (such as qualities)—solved this problem, butwith the addition of a small but indispensable contribution fromphenomenology. What enabled Carnap to obtain the elements he soughtwithout isolating identifiable elements within theundifferentiated “chaos” was a single act ofphenomenological discernment: a partition of the entire“chaos” into just two sectors, which he called the“living” and “dead” components of experience.This one distinction allowed Carnap to arrange experiences into atemporal sequence (“dead” experience is past;“living” experience present), making it possible toidentify holistic temporal cross-sections of experience, in which thetotal experience of a given specious present remains intact as amomentary whole. This chronological sequence of experientialtime-slices now gave Carnap the basic framework he needed foridentifying qualities as cross-temporal equivalence classes ofdiscernable persistences across series of adjacent specious presents.These holistic time-slices did not need to beanalysed.Qualities and qualitative relations could, rather, beconstructed as something like equivalence classes ofsufficiently “similar” persistences across a series ofadjacent time-slices (up to any desired degree of precision in“similarity”). The result was that what empiricists suchas Hume or Mach had always hoped to achieve by “analysis of thesensations” could be achievedwithout analysis. Carnapcalled it “quasianalysis” (which is explained in moredetail in the supplementMethodology (Section 3)). Physical objects could be constructed as connected classes ofqualities, and from objects the path to a “reality” seemedclear.

In this early stage of what became theAufbau project, Carnapstill followed Vaihinger in distinguishing sharply between the direct,genuine, first-hand knowledge of the “chaos” and thefictive, constructed nature of “reality”. But he put theboundary between them in a different place. This was becauseHusserl’s phenomenology offered an escape route fromVaihinger’s completely undifferentiated chaos. It yieldedcertain distinctionswithin the chaos (e.g., between“living” and “dead” experience) that couldclaim a degree of objectivity. These distinctions, Carnap thenthought, werenot fictional, but actually extended the rangeof what could be genuinelyknown, even without fictions, justfrom the chaos itself. So Carnap’s boundary between theimmediately knownprimary world (of sensory“chaos” plus a minimal, phenomenologically extrapolatedstructure) and a fictivesecondary world of“reality” included more in the “primary”sector than Vaihinger’s. Carnap thought he could show onphenomenological grounds that the primary world is two-dimensional inall sense modalities (Carnap 1924). So the boundary between the fixedprimary world and the freely choosable secondary worlds(“realities”) was located at the ascent from two to threedimensions. Within the primary world, the construction proceededentirely by explicit definition, beginning from the qualities obtainedby quasianalysis. Secondary worlds, by contrast, are not uniquelydetermined. The construction of a secondary world proceeds, rather, byoptimizing its fit to whichever fictions are chosen to guide theconstruction, subject to the constraint of the (fixed) primaryworld.

Carnap remained as radically pragmatist about the choice amongfictions to guide this ascent as Vaihinger; the choice of fictions wasentirely practical and purpose-relative. (For more onVaihinger’s account of fictions, see, e.g., Chapter 1 of Appiah2017.) To obtain thescientific secondary world, Carnapmaintained, we need only two fictions, corresponding roughly toKant’s categories of cause and substance: a principle ofinduction (or uniformity of nature) and a principle of“continuity” (as Mach had called it), requiring certainclusters of perceptions, such as those grouped into a “physicalobject”, to remain constant, under certain conditions, while weare not perceiving them.

Sometime during 1924, theAufbau project changed coursedrastically, and arrived at essentially its later published form(Carus 2016). The phenomenological approach to the basis was dropped;a fixed “primary world” was no longer to be distinguishedby phenomenological intimation from the various “secondaryworlds” built upon it. Russell’s “constructionprinciple”, as Carnap called it, came to dominate the project,and would become the book’s epigraph:

The supreme maxim in scientific philosophizing is this: Whereverpossible, logical constructions are to be substituted for inferredentities. (B. Russell 1914a: 155)

So now the two-dimensionality of perceptual space, for instance, is nolonger obtainable from phenomenological discernment, but becomes asmuch a logical construction as everything else (Aufbau:§§89, 117, 124). And in a talk Carnap gave about theAufbau project in Vienna in January 1925, we find a newguiding principle: “Overcoming subjectivity” (Carnap1925a, 1925b, as quoted in Carus 2007a: 168; 2016).

2.4 Vienna and Wittgenstein

After completing theAufbau first draft in late 1925, alongthese new lines, Carnap left for Vienna, where he became a lecturer[Privatdozent] and submitted theAufbau manuscriptto Moritz Schlick as hisHabilitationsschrift. He immediatelybecame an active participant in Schlick’s weekly Circle, whichwas embarking just then on yet another careful re-reading ofWittgenstein’sTractatus. This group would soon (due toOtto Neurath’s effective propaganda) become known to the worldas the “Vienna Circle”, the fount of a new(anti-)philosophy known as “logical positivism”—aterm Carnap never liked.

Like others in the Vienna Circle, Carnap saw theTractatus asa basis for solving the perennial problem of accommodating the truthsof logic and mathematics to empiricism. Wittgenstein was noempiricist, but his characterization of logical truth as a pureartifact of representation, empty of empirical significance, gave theVienna Circle what they needed. Their logicism extendedWittgenstein’s truth-functional conception of logic to the wholeof mathematics, and their empiricism interpreted Wittgenstein’satomic sentences as sense perceptions, along the lines of theElementarerlebnisse at the basis of Carnap’sAufbau. This version of Wittgenstein made mathematicsconsistent with empiricism. However, its weaknesses were obvious evento the Circle: First, from the empiricist perspective of the ViennaCircle, Wittgenstein’s truth-functional conception of logicseemed to require finitism; even the most abstract theories of physicscould then employ only restricted, finitary quantification rather thanunrestricted quantification over a potentially infinite number ofobservations (Aufbau: §180; Carnap 1936–37:§23). And second, Wittgenstein’s exclusion of“elucidations” (meta-sentences about the object sentencesframed in the language of science) was not only paradoxical (it madeall statement and discussion of logical principles meaningless) butseemed at odds with recent developments in the foundations ofmathematics, especially Hilbert’s metamathematics, and thebrilliant use made of this approach by Skolem, Tarski, and by one ofCarnap’s own students, Kurt Gödel. (In turn,Gödel’s arithmetization of syntax and his incompletenesstheorems would have an enormous impact on Carnap’sLogicalSyntax of Language just a few years later—see thesupplement onLogical Syntax of Language for more details.)

Carnap set to work, after his arrival in Vienna, to solve these twoproblems. He embarked on a major project to explore “generalaxiomatics”, in which he sought to show that Hilbertianaxiomatics could be accommodated within the Wittgensteinianrepresentational framework—i.e., he sought to show that theHilbertian “method of bifurcation” (into metalanguage andobject language), while mathematically useful, could ultimately bereduced to a Wittgensteinian single language. The immediate goal wasto prove a fundamental completeness theorem, purporting to show that aconsistent axiom system is categorical just in case it is decidable(Awodey & Carus 2001). After three years of concentrated work onthis project (a substantial manuscript of several hundred pagessurvives in Carnap’s papers), Alfred Tarski convinced him thatthis theorem was defective, and that Carnap’s attempt to workwithin a single language failed to capture the metamathematicalconcepts fully (but see Schiemer 2013). And late in 1930, Gödelactually showed that an important special case of Carnap’stheorem was false: second-order arithmetic, though categorical, is notdecidable. This famous result put an end to Carnap’s project offusing Hilbert and Wittgenstein.

3. TheAufbau

3.1 Main Point and Motivation of theAufbau

As we saw insection 2 above, theAufbau project began as a continuation of theencyclopedic ambitions of the Enlightenment, in response to thecatastrophe of the war and the hopes inspired by the Germanrevolution—only that in contrast to the eighteenth-centuryEncyclopédistes, and to similar projects since then,Carnap conceived the idea of a system of knowledge as adeductive system, under the influence of his teacherFrege.

By the time of the book’s publication the emphasis had shifted,but the idea of bringing all concepts into a single deductive systemsurvives. In a lecture given to a general audience in Vienna in 1929,Carnap explains the point of his book by telling a dialectical storyof human history as a struggle between “criticalintellect” and “imagination”. At first imaginationruled the day, but then in antiquity, critical intellect made adiscovery that enabled it to put strict limits on imagination’sclaims:

That is the discovery ofone [single]comprehensivespace. All things are in space; any two things are alwaysspatially related to each other. So there is also a path from me toany [given] thing.

So existence claims could now be subjected to a simple test:

Every thing is accessible. If someone now claims that a thingof a particular kind exists, I can demand of him that he show me thepath from me to the claimed thing.

Imagination responds by relocating its gods and gremlins to remote orinaccessible locations, but as humankind explores more of the earth,this stops working. So imagination “goes for a really radicaloption; it evacuates its creations to the non-spatial, the‘trans-spatial’”, which is plausible since we quitelegitimately refer to things that are not physical objects, so notlocatable in space. Feelings, mental images, and thoughts, forinstance, are non-spatial. So instead of situating its gods in aphysical location such as Mount Olympus, Carnap explained,

the putative God was removed from space into the realm of the spirits.God was regarded now as aspiritual being without a body.

But people starting noticing “that something isn’t quiteright with that sort of claim, that there is something rather odd,something problematic about it”. So imagination went further andreplaced theology with metaphysics.

Here the concept of God no longer has anything physical or anythingphysically rooted about it… The flight from the grasp ofcritical reason with its spatial system appears to have beencompletely successful.

But critical intellect now has an answer: theAufbausystem—“now a system is discovered that comprehends notjust [corporeal] things, but everything thinkable, all concepts,whether thing-like or not”. This system is the natural successorand generalization, in Carnap’s dialectical drama, of physicallyall-encompassing space:

In space all things have spatial relations to each other, and therehas to be a path of access from me to each thing. In the same way, onthe basis of the concept-system, an all-comprehending conceptualspace, so to speak, all concepts have relations to each other (in thiscase logical, conceptual relations). And here there has to be aconnecting path to each concept from the contents of my experience,e.g., from my perceptions. Everything of which I can speak has to betraceable back to things experienced by me. All knowledge I can haverelates either to my own feelings, mental images, thoughts, etc. orcan be derived from my perceptions…

Though Carnap had redesigned the system in 1924 to dispense with thephenomenological development of the “primary world” fromwhich the “realities” or “secondary worlds” ofscience and everyday reality were constructed, it could be said thathe adopted Husserl’s method of “bracketing” thesupposed external reality to which our subjective world appears torefer—and that he adopted it more radically and strictly thanHusserl himself. For Carnap bracketed not just the external realitybut also the internal subjectivity, leaving only the bare logicalstructure of the constitution system unbracketed (Carus 2016).

3.2 Significant Aspects of the PublishedAufbau

In the publishedAufbau this abstemious bracketing policy isapplied very strictly. Carnap adopts a principle of extensionalitythat does not exclude the use of intensional languages in auxiliaryroles, but denies them any ultimate significance. Fregean“Sinn” (sense) is specifically excluded as merelypsychological (§44), having only “epistemic value”but not “logical value” (§50), which is limited tothe extensional meaning of an expression. Each step in the spelled-outconstitution of the subjective (“autopsychological”) worldis explained not only in logical symbols but also in a simpleparaphrase, then in “realistic language” (as ordinarilyused in science) and finally in a language of “fictiveconstruction”. But Carnap makes clear that this is solely forconvenience and to make the steps more transparent to readers. Thefour languages may differ not only in form but in their“Sinn”, their epistemic value (the different mental imagesthey elicit), he says, though their logical value is always identicaland is expressed most neutrally and clearly in the symbolic language(§95); for more detail, see the supplementAufbau.

Behind this radical extensionalism lies precisely the new strictnesswith which Carnap applied the Husserlian “bracketing”strategy in 1924—ironically just at the time he abandoned thephenomenological development of the constitutional basis. (Moredetails on Carnap’s extensionalism are to be found in thesupplementSemantics (Section 2).) The most direct expression of this was a more thoroughgoing andself-conscious rejection of ontology. In the final chapter of theAufbau, which addresses some philosophical problems to whichthe constitutional system can be applied, the overriding theme is theirrelevance of ontological questions to the actual constitutionalsystem (Friedman 2007). And in the same year as theAufbauCarnap published a pamphlet onPseudo-problems in Philosophy(Carnap 1928b) in which the “problem of realism” is themost prominent example of such pseudo-problems.

The actual detailed construction of the autopsychological realmoccupies only a small part of the book. The first sections focuslargely on what Carnap would later call “clarification of theexplicandum” (seesection 1.1 above). Carnap considers various options for the choice ofbasicelements (the elements or building blocks of which everything isto be constructed) andbasic relations (the relations betweenand among these building blocks that is to effect the construction).The radicalism of Carnap’s push for simplification is expressedby his choice of only asingle kind of basic elements,“elementary experiences”, and asingle basicrelation, “recollection of similarity”. The elementaryexperiences were not isolated “sense data” of traditionalempiricism (the isolated pitch and timbre of momentary sounds orcolored points of the visual field that we find in Hume or Mach), butholistic time slices of total experience, from which nothing has yetbeen abstracted; Carnap was here attempting to do justice to thepsychology courses he had taken as an undergraduate, where he hadlearned about the new directions taken inGestalt psychologyby Köhler, Koffka, and others. By quasianalysis, an abstractiontechnique formalizing Russell’s “principle ofabstraction”, (see the supplementMethodology (Section 3)) the similarities among these time-slices could retrospectively begrouped (by repeated application of the basic relation, recollectionof similarity) into something like equivalence classes of, say, acertain color or a certain smell that were sufficiently similar. Bythis means Carnap constructs the subjective cognitive world of asingle mind in some detail, up to the point where, on that basis, athree-dimensional objective world of space-time can be constructed(see the supplementAufbau (Section 2) for more detail concerning some of these constructions).

At this crucial point of theAufbau(§§125–7), the ascent from two to three dimensions,where Carnap stops spelling out the steps in detail, he also suspendsthe explicit definition applied up to there, and instead resorts to aninformally described optimization approach, whereby certain fairlyobvious desiderata (continuity of motions, temporal continuity ofobjects and processes, etc.) are to be maximized subject to certain(again fairly obvious) constraints (see the supplementAufbau (Section 3) for further details). The construction of the physical realm and thefurther realms on its basis (the heteropsychological, social,cultural, and value realms) are sketched very sparsely. The book endswith a final section discussing some philosophical consequences of theconstitution system, addressing (though only obliquely, and hardly byname) both phenomenology and various forms of realism.

3.3 Later Discussion of theAufbau

When the book was published in 1928, it was widely discussed and,along with Wittgenstein’sTractatus, became one of theclassic texts of the Vienna Circle. Its effect was amplified in theEnglish-speaking world by A.J. Ayer’s acknowledgement of Carnapas the philosopher to whom he “owe[s] most” in hisbest-sellingLanguage, Truth, and Logic (Ayer 1936), whichwas understood as an accessible summary exposition of the supposedphenomenalism of theAufbau, but misrepresented the bookquite seriously. This misrepresentation contributed to the laterneglect of the book among Anglo-American philosophers, which even thesophisticated discussion, critique, and further development by NelsonGoodman (1951) or the belated English translation (1967) could hardlybudge. It also allowed many preconceptions about the book to continuecirculating almost through the end of the twentieth century.

Only toward the end of that century did a revaluation set in,initiated by Michael Friedman, who took issue, in a series of papers(later collected in Friedman 1999), with the entire English-speakingtradition (going back to Ayer) of seeing theAufbau as aphenomenalist project of reducing all knowledge to sense impressionson the model of Hume or Mach. Instead, Friedman pointed out, we shouldsee it in the context of its neo-Kantian origins. From thatperspective, theAufbau is better understood as seeking a newbasis of scientific objectivity—achieving objective knowledgedespite the subjective starting point of individual perception, andthe structuralism discussed above (section 3.2). On the basis of Friedman’s discussions, many others have sincecontributed to the revaluation of theAufbau (Richardson1998; Mormann 2000; Pincock 2005, 2009; the papers collected inDamböck 2016.)

This new interpretive interest in theAufbau and itsphilosophical context has also led to renewed efforts to reconstructtheAufbau’s constitution system with new tools.Goodman’s 1951 critique of quasianalysis has finally foundresponses and repairs from Mormann (1994, 1997, 2009) and Leitgeb(2007); Leitgeb (2011) goes further and argues that if the goals oftheAufbau strategy are limited in certain ways,Goodman’s and Quine’s critiques no longer apply (see thesupplementAufbau (Sections 3 and 4)). Chalmers (2012) suggests a much more drasticrationalisticrevision of theAufbau; where Carnap thought it would bepossible, in principle, to derive all true scientific sentenceswhatsoever from basic true sentences in an “empiricisticallyacceptable” constitution system just by means of thesystem’s definitions, Chalmers drops any empiricist ambitionsand replaces the role of definitions by that ofa prioriknowledge, includingsynthetic a priori knowledge (whoseexistence Carnap of course denied).

4. The Road toSyntax

The Wittgensteinian program favored by the Vienna Circle (section 2.4 above) had collapsed in 1930. But Carnap soon recovered, and during asleepless night on 21 January 1931, conceived of an entirely new basisfor the Vienna Circle’s characteristic doctrines (Awodey &Carus 2009). Instead of trying to fuse Hilbert and Wittgenstein,Carnap now dropped Wittgenstein altogether and pursued a Hilbertianapproach. “Meaning” was no longer rooted in thecorrespondence between configurations of elementary facts and theirlinguistic representations. In fact, meaning was banished altogether,at least in our statementsabout the language of science (ourmetalinguistic “elucidations” such as those in theTractatus itself or theAufbau). The scientificlanguage itself had empirical meaning, but how this was to beunderstood became a matter of dispute (the famous“protocol-sentence debate”) within the Vienna Circle (thesentences recording observations were calledProtokollsätze by the Circle, which became“protocol sentences” in English). This brought abouta split in the Circle between a more realistic “rightwing” (who adhered to something closer to Wittgenstein’spicture theory and held that once a state of affairs was“registered [konstatiert]” by an observer therecould be no further doubt) and the “left wing” whofollowed Carnap in his new reference-avoiding syntax program (seeUebel 2007 on this debate). In any case our elucidations of the objectlanguage remain, in the new syntax framework, entirely within thelinguistic realm; we are talking always and only about language. Inlogical syntax, we should be careful not to talk about“facts” or “things” but instead only aboutsentences or thing-names. We should restrict ourselves in principle tothe “formal mode of speech” (sentences and names),employing the “material mode of speech” (facts and things)only for convenience, and when we are sure we can translate it intothe formal mode. The (meta-)mathematical methods of Hilbert, Tarski,and Gödel were, in other words, to be extended to the whole ofknowledge.

Carnap’s immediate task was to create a canonical language forthe formal mode of speech. Taking his cue from Hilbert’smetamathematics, he began by stripping this language down to barebones, eliminating all problematic assumptions. It would consistsimply of strings of dots on a page, and the basic laws of arithmeticwould arise unambiguously in the metalanguage from the immediatelyevident patterns of dots (e.g., the commutative law from theperceptibly equivalent number of dots counted from the left and fromthe right). Carnap soon found he could not express certain essentialconcepts in this limited language, and turned instead to a more usualaxiomatized arithmetic. This also had the advantage that, by usingGödel’s new trick of arithmetizing syntax, Carnap could nowmore easily express the syntax of the language (i.e., its logic) inthe language itself. So the syntactic metalanguage collapses into theobject language, and there is, as before, only a single language. Thecanonical language for the formal mode of speech seemed within hisgrasp.

This idea also gave Carnap a new route to the elimination ofmetaphysics, superseding the Wittgensteinian strategy with its meaningcriterion. The new criterion dispensed with meaning. It required thatany statement either be at the object level (straightforwardlyfactual) or translatable into the formal mode of speech—i.e.,into the canonical language or an equivalent. Carnap assumed that hiscanonical language, once fully worked out, could express the entirelanguage of physics, as well as containing its own metalanguage. Sincethe Vienna Circle’s “unity of science” program heldthat all knowledge was expressible in the language of physics, Carnapproposed his canonical language as auniversal language forall knowledge (Carnap 1932b). Another way of expressing the newcriterion, then, was that any acceptable statement must be phrased inthe language of physics. The new idea of January 1931 flowed intoCarnap’s discussions with Neurath and others to produce the newdoctrine of physicalism (Uebel 2007, 2018).

But the demands on the “correct” language for the formalmode of speech were exorbitant. Carnap had originally wanted to keepit weak and uncontroversial, but it had to be capable of expressingall the mathematics needed for physics. On the other hand, itsarithmetized syntax had to be capable of expressing the basic conceptof “analytic truth”, or it would be impossible todetermine when a formal-mode statement “holds”. Before1930, it had been assumed that provability was the standard ofmathematical truth, but now Gödel had shown that for eachconsistent and recursively axiomatized system that included enougharithmetic, some true sentences are not provable in the system. So adifferent criterion was needed, but one that would still—likeprovability—pick out the logically true sentences solely bymeans of the formation and transformation rules of the language.Carnap did attempt such a criterion for “analyticity” inthe first draft of his syntax book (entitledMetalogic),written in late 1931 and the spring of 1932. He sent the typescript toGödel, who pointed out that the new criterion was defective. Infact, he added, it isimpossible to define analyticity orlogical truth inany metalanguage that can be faithfullyrepresented in the object language (e.g., by arithmetization); this isnow familiar to us as Tarski’s theorem on the indefinability oftruth. So Carnap’s single-language approach fails after all(Awodey & Carus 2007, 2009).

And without the single canonical language containing its ownmetalanguage, there is no longer any reason to regard any particularmetalanguage as more “suitable” or “natural”than any other. One option may turn out to be moreusefulthan another for particular purposes, but this is no reason toprivilege it as uniquely “correct” (or canonical). WithGödel’s assistance, Carnap developed a new definition ofanalyticity, but it hardly seemed to matter any more; thelanguagerelativity of any definition of truth or analyticity moved to thecenter of attention. The disputes about protocol sentences within theVienna Circle merged in Carnap’s mind with the disputes amongintuitionists, logicists, and formalists in the philosophy ofmathematics.

All these disputes, he realized in the autumn of 1932, concerned thequestion of how to set up a language, which has no right or wronganswers. One could only try out different ways, and see which onesworked better. This new attitude, which first appeared inCarnap’s reply to Neurath about protocol sentences (Carnap1932b), received its definitive statement in the “principle oftolerance” quoted in1c. above, enunciated in theLogical Syntax of Language (LSS: §17). In thisprinciple, the voluntarist and utopian convictions of his youth,partially submerged during theAufbau period, finally foundadequatephilosophical expression. He spent the remainder ofhis career absorbing the consequences of this breakthrough, andworking on a vast number of language projects within the new freedomit afforded.

5.Logical Syntax of Language

TheSyntax is probably Carnap’s best-known book, andhas attracted much of the renewed attention to Carnap in recent years.At the time of its publication, the Vienna Circle was disintegrating,its members were fleeing from political persecution, and philosophicalcommunication was disrupted. Its English translation, published 1937,lacked context and was almost uniformly misunderstood by nearlyeveryone, with the partial exception of Quine, whose later work inlogic, the philosophy of logic, and logic-based philosophy wasinspired by—though sometimes opposed to—theLogicalSyntax. Through Quine, some of Carnap’s ideas eventuallyalso found their way into the logic education of many philosophydepartments in the US. On the other hand, what Quine understood, as isevident from his 1934 Harvard Lectures, immediately after thebook’s publication (reprinted in Creath 1990), was thefirstdraft of theLogical Syntax, in which the principle oftolerance was still absent. So evenhis comprehension of theSyntax was partial and one-sided (Creath 1987, Friedman2006). In any case, the book was widely assumed to have beensuperseded by the time the translation appeared, now that Carnap hadmeanwhile embraced semantics and dropped his insistence on the“formal mode of speech” (above,section 1.3). Only recently, therefore, has theSyntax come to beappreciated in its full radicalism.

In this recent work, the principle of tolerance has attracted the mostattention. Previously, the rejection of meaning and insistence on theformal, rather than the material, mode of speech had been in theforeground since, after all, the entire philosophical Part V of thebook had been devoted to it, and Quine had reinforced that emphasis.It is fair to say that the principle of tolerance taken byitself—unlike the notion of analyticity or theses ofconventionalism (see the supplementCarnap vs Quine on the Analytic-Synthetic Distinction)—was hardly discussed before its present, belated reception in the Carnapliterature. It is a new idea on the philosophical scene today, whoseconsequences are still being digested.

It certainly has lost none of its explosive revolutionary force as aradical program for philosophy (Creath 2009), and this is what hasmost divided commentators. Like most revolutionary ideas, it hasencountered steadfast and vocal resistance. Most commentators havebeen concerned to limit the scope of the principle of tolerance, todilute it or trivialize it, while the appreciative minority has mostlyremained defensive. Much of the literature, therefore, is devoted toclarification and the correction of misunderstandings (e.g., Goldfarb& Ricketts 1992; Ricketts 1994; Goldfarb 1995), rather thanpositive explorations of the principle of tolerance and itsconsequences (with a few exceptions: Carus 2017, Kitcher 2008, Creath2009, Kutz, Mossakowski, and Lücke 2010, Justus 2012). Thus theremainder of this section will, after a brief exposition of thebook’s contents, focus on these recent discussions andclarifications. Carnap’s principle of tolerance is discussed inmore detail in section 1 of the supplementTolerance, Metaphysics, and Meta-Ontology, and theLogical Syntax more generally in the supplementLogical Syntax of Language.

5.1 Brief Exposition ofLogical Syntax

The stated aim of the book is to show that logic is syntactical, i.e.,that it consists in formal theories of linguistic symbols—atheory is “formal”, Carnap says (LSS [1937: 1]) when

no reference is made in it to either the meaning of the symbols (e.g.,the words) or to the sense of the expressions (e.g., the sentences),but simply and solely to the kinds and order of the symbols from whichthe expressions are constructed.

The idea had of course been suggested by Hilbert’s “methodof bifurcation [Methode der Zweiteilung]” as Carnap hadcalled it, distinguishing a meta-mathematics with concrete meaning, onthe one hand, from mathematics proper, on the other, which was to beregarded as purely formal, and the formal properties of which (e.g.,consistency) Hilbert had aimed to study and prove inmeta-mathematics—a method which Carnap sought to extend frommathematics to the whole of knowledge. The “chief motivation formy development of the syntactical method”, Carnap later wrote,was this:

In our discussions in the Vienna Circle it had turned out that anyattempt at formulating more precisely the philosophical problems inwhich we were interested ended up with problems of the logicalanalysis of language. Since in our view the issue in philosophicalproblems concerned the language, not the world, these problems shouldbe formulated, not in the object language, but in the metalanguage.Therefore it seemed to me that the development of a suitablemetalanguage would essentially contribute toward greater clarity inthe formulation of philosophical problems and greater fruitfulness intheir discussions. (Carnap 1963a: 55)

That the main concepts of deductive logic (“e.g., provability,derivability from given premises, logical independence, etc”.)are purely syntactical was argued primarily by showing how they couldbe defined in two exemplary languages without reference to themeanings of any terms. Language I is a form of primitive recursivearithmetic, and was intended to exemplify a constructivist kind oflanguage, while Language II contains classical mathematics. (In modernterminology, both of these “languages” are reallytheories.) Of the book’s five parts, the first three are takenup with the development of these two languages. In part IV, Carnapgoes beyond the treatment of specific languages to sketch a templatefor “general syntax”; he tries to give a framework for thesyntactical development or description of any language whatever. Heabstracts from the syntactical categories of the particular languageunder consideration, and does not even assume he is given its set ofvariables, the distinction between its logical and descriptivevocabulary, its negation symbol, or any other syntactic property.Instead, all these sets and concepts are to be defined solely from thetransformation (inference) rules of the language (see§46–47); Carnap is developing here what we would now call aversion of “proof-theoretic semantics” or “logicalinferentialism” (see the supplementLogical Syntax of Language for further details). Throughout all parts of theLogicalSyntax, Carnap distinguishes between the “d-terms”specifiable this way (derivable, proof, demonstrable, refutable,decidable) from the “c-terms” (consequence, valid,contravalid, determinate, incompatible, content, synonymous). Thoughboth are considered to be “syntactic” terms by Carnap, thec-terms seem closer to what we would now call “semantic”.This raises the question, for the modern reader, what Carnap actuallymeans by “syntactic” (or “formal”) here; andit turns out (as Carnap himself later recognized) that“syntax” includes much of what he would later call“semantics”. Indeed we find (Wagner 2009: 22) thatlanguages I and II are not actually “formal” in our senseat all; they are interpreted languages. While the syntactic method, asCarnap here conceives of it, requires that the interpretations bedisregarded, a particular fixed interpretation implicitly remains inplace. Carnap often refers to the import of some syntactic result orattribute “in material interpretation [bei inhaltlicherDeutung]” (e.g., LSS: 30), and the material interpretationsometimes slips in to play a role in the argument. Accordingly, Tarski(1936 [2002]: §2) characterizes Carnap’s definition ofconsequence for Language II in theLogical Syntax assemantic, acknowledges that “The first attempt at theformulation of a precise definition for the proper concept offollowing comes from R. Carnap” (in theLogicalSyntax), and regards his own model-theoretic definition oflogical consequence as essentially equivalent to Carnap’s(though applicable to a broader range of formalized languages thanjust to Language-II-like languages; see the supplementLogical Syntax of Language). This character of theLogical Syntax as a transitional workbetween syntax and semantics raises many subtle interpretative andhistorical issues that require distillation of the actual argumentfrom the (often newly-invented) terminology in which it is embedded.Fortunately, Pierre Wagner’s (2009) excellent handbook on theLogical Syntax provides the reader with a guide.

For all the technical apparatus, Carnap later acknowledged that“the investigation of philosophical problems was originally themain reason for the development of syntax” (Carnap 1963a: 55),and the final Part V of the book is devoted to these. The focus,however, is on the “syntax” idea itself, not on the othermain idea, the principle of tolerance. There is a simple reason forthis: Part V was almost entirely written before Carnap arrived at theprinciple of tolerance in late 1932, and when the book went to thepublisher it had to be cut (the definition of“analyticity” for Language II (§ 34d), for instance,was not even included in the original book, only in the 1937 Englishtranslation). And Part V is devoted to a sustained argument forsticking to the “formal mode of speech” and avoiding the“material mode of speech” unless it is translatable intothe formal mode. So it is hardly surprising that philosophers (see forinstance Woleński 2003) took this to be the book’s mainphilosophical point and thought Carnap had left it behind after theembrace of semantics in 1935.

5.2 Recent Discussion and Commentary

Much of the recent discussion surrounding theSyntax,especially the principle of tolerance, was inspired byGödel’s critique of Carnap, unpublished until 1995, thatwas originally intended for the Schilpp (1963) volume on Carnap in theLibrary of Living Philosophers. Gödel withdrew hispaper, but six successive drafts of it were found in hisNachlass, of which several have now been published(Gödel 1995). It appears, from its title (“Is MathematicsSyntax of Language?”) and much of the exposition, to focusspecifically on the “syntax” thesis, or more generally onthe “linguistic” accounts of the foundations ofmathematics deriving from Wittgenstein’sTractatus(Goldfarb 1995: 325). However, Gödel himself understood thatCarnap had meanwhile left behind that view (in itsLogicalSyntax form), and recent commentary has focused on the principleof tolerance (see section 1 of the supplementTolerance, Metaphysics, and Meta-Ontology for the details of Gödel’s criticism).

Carnap’s early-1930s syntactical method of avoiding referencefor terms in the philosophical metalanguage has recently beenidentified as the first self-consciously worked-out program of what isnow often called “inferentialism” (Peregrin forthcoming),a different form of which is especially championed by Robert Brandom(1994, 2000), and has been found attractive by others (e.g., Price2013). Though Carnap’s inferentialism had different motivationsfrom Brandom’s program of “reference explained away”(Brandom 1984), there is clearly at least an analogous strategy atwork. While Carnap himself left the syntax program in its originalform behind when he went on to incorporate semantics into his overallprogram for scientific languages, the syntax episode with itsexplicitly inferentialist agenda is now viewed by some (e.g., Chalmers2012, Peregrin forthcoming) an important innovation in its own right.Some of these commentators thus regard Carnap’s later embrace ofsemantics as a step backwards. That had also been the view of Neurathat the time (Uebel 2007, Mormann 1999, Carus 2019), and of Quine andothers later (e.g., Goldfarb & Ricketts 1992; Ricketts 1996;Goldfarb 1997). These criticisms are at least partly due to aperception that Carnapreturned to a substantive conceptionof meaning such as the Wittgensteinian one he had dropped in 1931, butactually his conception of reference and meaning remained minimalistand schematic, much to the frustration of, e.g., Russell (1940; seePincock 2007), who sought a substantive account of the intrinsicnature of reference (see the supplementSemantics for further discussion).

6. Semantics and Modality

6.1 From Syntax to Semantics

Carnap had moved to Prague in late 1931, where he became a fullprofessor at the German University, and wrote both drafts of theLogical Syntax of Language. The published book had tried tofuse the three major ideas of 1931–2. First, in January 1931,had come the rejection of Wittgenstein’s picture theory ofmeaning and its replacement by Hilbert’s sharp distinctionbetween a language (a calculus, a purely formal symbol system) and itsinterpretation, with the requirement that a language be entirelyspecified by explicit rules. Closely bound up with this was the secondidea, the insistence on the “formal mode of speech” andthe avoidance of talk of meaning in the metalanguage. And third, latein 1932, had come the principle of tolerance: no language isdefinitive or “correct”, there is no logical“reality” for a language to “correspond to”.But within a year of the book’s publication, the second idea hadbeen dropped; Carnap incorporated Tarski’s new semanticalaccounts of designation and truth, and extended his view of languageaccordingly. The first and third ideas, however, survived for the restof Carnap’s career. What did not survive was the overreactionagainst “meaning” that accompanied the original insight ofJanuary 1931—the exclusive emphasis on the “formal mode ofspeech” in meta-discourse. In distinguishing between a languageand its interpretation, Carnap’s first response had been torestrict extra-linguistic interpretation to the object language (andthere to one particular—physicalistic—interpretation) anddispense with it entirely in the “elucidatory”metalanguage. But this restriction was loosened when Tarski convincedhim in 1935 that interpretation could be completely specified byexplicit rules governing satisfaction, designation, and truth.

By this time, the storm clouds gathering in Europe were obvious forall to see, and like many of the Vienna Circle, Carnap sought anappointment in North America. In 1936 he landed at the University ofChicago, where he would stay for nearly twenty years, longer than hespent anywhere else. While he felt personally and intellectuallycomfortable in the United States, his written prose was never aselegant or forceful in English as it had been in German, and hispublications were mostly quite technical. The larger context of hisphilosophy was of course unknown to most colleagues and students, andremained obscure to the larger public. This decontextualization oflogical empiricism was reinforced by political factors. As newimmigrants, Carnap and his Vienna Circle friends felt vulnerable inthe United States, and many of them, having previously supportedsocialist causes in Europe, were kept under observation by the FBI,including Carnap himself (Reisch 2005). It was thus in their interestto play down the larger significance of their philosophicalpreoccupations, and to pose as narrow specialists in technicalsubjects.

Carnap’s first major publication in English, soon after hisarrival in the United States, was “Testability andMeaning” (1936–37), discussed insections 1.5–6 above, the first in a series of attempts to explicate“empirical content” or “empiricalreducibility” more loosely than the strict reducibilityenvisaged in theAufbau. By the late 1930s, Carnap waswilling to countenance a theoretical language whose primitive termsare not constructed bottom-up from observation sentences at all butentirely top-down, “floating in the air, so to speak” sothat these basic theoretical terms can have “only anindirect interpretation, which is incomplete in a certainsense” (Carnap 1939: 65). With these steps, Carnap began hisreturn to a consideration of the theoretical language, which he hadleft behind during the Vienna years. But his main focus, after“Testability and Meaning”, was the semantic frameworkitself. In the slim volume onFoundations of Logic andMathematics for the Encyclopedia of Unified Science (1939), thetripartite classification of linguistic theory into syntax, semantics,and pragmatics was first laid out. A five-volume series ofStudiesin Semantics was projected, of which the first two volumes,Introduction to Semantics andFormalization of Logicwere published in 1942–3. Carnap then pursued a long-standinginterest in modal logic and intensional languages, and published“Modalities and Quantification” in 1946,Meaning andNecessity in 1947. More details on Carnap’s work insemantics can be found in the supplementSemantics.

Carnap had embraced semantics in 1935 because Tarski had convinced himthat designation and truth could be described and discussed in anentirely schematic and objective way, free from any psychological,subjective, or epistemological entanglements or commitments (Carnap1936). As we have seen, the return to a schematic form of“meaning” led many to regardLogical Syntax asoutdated. Carnap himself (e.g., 1942: §39) was careful to denythis, but probably didn’t emphasize enough that the return of“meaning” did not mean a return to anexplanatoryconception of meaning like Russell’s multiple relation theory ofbelief or Wittgenstein’s picture theory. This abstract andschematic approach to meaning disturbed many empiricists, giving themthe impression that Carnap had no interest in what actually underlaymeaning, i.e., wherein the relation between predicate and property(cf. Wilson 1982) actually consists. As B. Russell (1940: 314)complained, for instance, Carnap ignored “certain priorquestions to be considered” before “the relation ofempirical knowledge to non-linguistic occurrences” could be“properly understood”. But these “priorquestions” were just the ones Carnap had put aside in 1931(Pincock 2007). In this respect there is a seamless continuity inCarnap’s “minimalism” with respect to language; evenwith the embrace of semantics in 1935, these questions remainedabsent, and only began to make a rather shadowy reappearance withCarnap’s (1939) addition ofpragmatics (the study oflanguage in use) to his conception of language. Semantics abstractsfrom use and focuses only on the expressions themselves and theirdesignata, while syntax abstracts from designata as well (1939:3–4; 1942: 9).

In Carnap’s work after 1935, it is important to distinguishbetween two different parts of the semantic enterprise. On the onehand, there are the repeated attempts to pin down the inferentialrelations between observation-statements and more general oneswithin the general framework of semantics. In this work,meaning and reference are considered particularly as they concern theempirical content (or meaning) of general statements, whetherempirical generalizations or theories of more universal scope. Thisincludes “Testability and Meaning” (Carnap 1936–37),the later work on the theoretical language (Carnap 1956a, 1959a), andmuch of the work on inductive logic (seesection 8 below). On the other hand, there is the construction of the semanticframework itself, its logical delineation and development; even ifthis was in principle to serve the first purpose, it became in effecta distinct project. This includes theStudies in Semantics,the modal logic systems (Carnap 1946), and the later version of hislogic textbook,Einführung in die symbolische Logik(Carnap 1968b). We discuss this second component insection 6.2, immediately following, and the first component insection 8 below.

6.2 Carnap’s New Priorities

There are two main changes leading from the linguistic frameworks oftheLogical Syntax to the “semantic systems” ofMeaning and Necessity: Carnap took the semantic turn,allowing for a relation of reference or designation; and beyond thathe allowed for intensional operators which he supplied with a newintensional semantics.

FromFoundations of Logic and Mathematics (1939) (andIntroduction to Semantics, 1942) Carnap had taken upTarski’s conception of semantic truth. The principle oftolerance in theLogical Syntax remained intact, but in thefollowing refined form: the syntactic rules of formation can be chosenfreely; if the syntactical rules of transformation (derivation,inference) are determined prior to the semantic rules, they may bedetermined freely as well, but the semantic rules will have to beselected such that the transformation rules are sound with respect tothem;vice versa, if the semantic rules are chosen prior tothe transformation rules, the former may be determined freely, inwhich case the latter will need to match the former by being soundwith respect to them (see, e.g., section 12 of Carnap 1939).Completely new questions arose, e.g., whether the rules of inferenceof classical propositional logic would determine the semantics of thestandard logical connectivesuniquely (given certainconstraints): this novel type of categoricity question was answered inthenegative by Carnap (1943). (In recent years, this part ofCarnap’s work has sparked a lively debate: see, e.g.,Raatikainen 2008, Murzi & Hjortland 2009.) Semantics became justas important in Carnap’s work for the construction of formallanguages as syntax had been in theLogical Syntax.

Secondly, Carnap extended Tarski’s extensional semantics by anew intensional one, in which the truth values of sentences withoperators creating intensional contexts (such as a sentential operatorfor necessity) can also be determined compositionally. Carnap’sinvention of what would become “possible worldssemantics,” which he showed one could spell out in anextensional metalanguage, had a decisive influence on the developmentof modal logic and intensional semantics. Even though there aresignificant differences between modern “Kripke semantics”(which is rightly associated with Saul Kripke’s work),Carnap’s intensional semantics is still a possible worldssemantics in the sense that it evaluates formulas at possible worlds(“state-descriptions” in Carnap’s terminology), andthe semantic rule for Carnap’s operator ‘N’for (logical) necessity invokes universal quantification over worlds:\(N(A)\) holds in state-descriptions if and only ifA holds in every state-description (see §41 ofMeaning and Necessity; the differences and similarities toKripke semantics are explained in detail in the supplementSemantics (Section 1)). On the side of theoretical linguistics, Richard Montague’slater intensional semantics for natural language built onCarnap’s semantics (see Partee 2011).

As discussed in the supplementSemantics (Section 2), he partially weakened his early radical thesis of extensionality bythe time ofMeaning and Necessity.

6.3 Intensional Semantics

The languages to which Tarski’s semantics applied wereextensional; Carnap’s semantics extends Tarski’s byassigning compositionally to each singular term, each predicate, andeach sentenceboth an intensionand an extension.The intension of an expression explicates what we understand when weunderstand it, and Carnap’s treatment of this is again“minimalist” in the sense that nothing subjective orpsychological is involved; “understanding” is entirelyschematic, i.e., determined solely by semantic rules. The extension ofan expression at a state-description is determined by applying thesemantic rules (or the expression’s intension) to thestate-description. In the words of David Lewis (1970: 23):

The plan to construe intensions as extension-determining functionsoriginated with Carnap… Accordingly, let us call such functionsCarnapian intensions.

A state-description (an idea that derives from the“Spielräume” in Wittgenstein’sTractatus, and more distantly from Leibniz’s idea ofpossible worlds) is simply a setX of sentences for which thefollowing is the case: for each atomic sentence in the objectlanguage, either the sentence or its negation is a member ofX, but not both; andX only includes atomicsentences or negations of atomic sentences. One state-descriptiondescribes the “actual state of the universe” (Carnap 1947:§2), and how a linguistic expression is evaluated at thatstate-description recovers the Tarskian extension of the expression.Intensions are assigned to linguistic expressions by evaluating thematarbitrary state-descriptions.

According to Carnap’s setup, two sentencesA andB have the same intension if and only if the equivalence \(A\leftrightarrow B\) isL-true. A sentence isL-true(logically true) just in case it holds in in every state-description.For Carnap this definition ofL-truth explicates the informalidea that a sentence is logically true if it is true in virtue ofsemantic rules alone without reference to empirical facts. Later,Carnap introduced the idea of “meaning postulates” thatcould restrict the range of state-descriptions (Carnap 1952) andadopted Quine’s terminology by which only those sentences are“logically true” whose truth is evident from the logicalparticles alone, while the larger class of sentences true in allstate-descriptions are called “analytic”.

Carnap (1946, 1947) worked out an intensional semantics for necessityand possibility operators for different example languages, and for themodal logic S5 that C.I. Lewis (1944) had previously discussed (seethe supplementSemantics (Section 1) for the details). He also started exploring areas that are presentlyof special interest, such as “hyperintensional” semantics(see, e.g., Yablo 2014): In the context of addressing the paradox ofanalysis, he found that a stronger or finer-grained notion of synonymywas needed than identity of intension, i.e.,L-equivalence,and he defined a relation called “intensionally isomorphicto” for that purpose. In response to critiques by Benson Matesand Leonard Linsky (1949), who pointed out instances of apparentsynonymity that were not intensionally isomorphic by Carnap’sdefinition, Carnap replied that this just showed that theordinary-language conception of “synonymity” is vague, andthat actually it conceals a number, perhaps a range, of explicanda;for certain purposes, he agreed, a still stronger (or finer-grained)conception of intensionality (and thus synonymity) might be required(Carnap 1949).

Alonzo Church used Carnap’s concept of intensional isomorphismin his reconstruction of Frege’s notions of sense and reference,“A formulation of the logic of sense and denotation”(Church 1951), and later also addressed a critique to Carnap directly(Church 1954), to which Carnap (1954b) replied. John Myhill (1958) ina critique of Church’s reconstruction, re-discovered a paradoxfirst spelled out by Russell in Appendix B ofPrinciples thatraises precisely the same issue about individuating intensions, andsince then the study of Russellian intensional logic, andfiner-grained versions of intensional identity, has continued (Church1976, 1985; Linsky 1988; Anderson 1989; Cantini 2004; Deutsch2014).

Carnap argues inMeaning and Necessity (especially §30)that his method of extension and intension is an improvement overFrege’s method of reference and sense, because it preserves theextension and intension of a linguistic expression across contexts(i.e., regardless of whether they are extensional or intensionalcontexts), while Frege’s method does not. Before MichaelDummett’s work on Frege, Carnap’s detailed criticalengagement with Frege’s theory of sense and reference in thisbook probably did more to establish Frege as a classic of analyticphilosophy than any other single impulse. Not only Church, but manyothers were inspired not only to reconstruct Frege’s originalview in a more rigorous way, but to do so in the light ofCarnap’s challenge and his critique of those views from a modernpoint of view. Carnap’s intensional semantics is discussed inmore detail in the supplementSemantics (Section 1).

7. Quine and “Empiricism, Semantics, and Ontology”

The best-known aspect of Carnap’s reflections on semantics,however, concern his various controversies with Quine, which addresseda broad range of issues, two of which have aroused particularinterest: ontology and “the” analytic-syntheticdistinction. For many years after Quine launched his critique ofCarnap, in the 1950s, it was widely agreed that Quine had“won”, and for several decades his paper “Two Dogmasof Empiricism” (Quine 1951) became perhaps the best-known andmost widely cited paper in all analytic philosophy. However, since therevival of Carnap studies in the 1980s and 90s, the picture looksrather different, and if there is a mainstream opinion on theCarnap-Quine debates now, it would probably be something like theposition articulated in a series of papers by Richard Creath (1987,1990, 1991, 1994, 2007, 2009) to the effect that Quine at leastpartially misunderstood Carnap and that the two philosophers werelargely talking past each other (while of course trying hard notto).

With respect to reductionism (the second dogma of empiricism inQuine’s 1951), Quine rightly criticized the viability ofCarnap’s radical reductionism in theAufbau—which, however, Carnap himself gave up soonafter theAufbau’s publication. It is much less clearwhether Quine is right to attribute a weaker form of reductionism tothe later Carnap, since it was inLogical Syntax andafterwards that he regarded the confirmation of scientific hypothesesto be holistic and theory-relative. This is discussed in more detailin the supplementThe Reconstruction of Scientific Theories (Section 1).

The other “dogma of empiricism” that Quine discerned inCarnap was his adherence to “the” analytic-syntheticdistinction. Unlike Quine, though, Carnap was not primarily interestedin defining analyticity for natural language, but rather in theconstruction of linguistic frameworks for which a coherent notion ofanalyticity could be defined in precise terms. Nor did Carnap imaginethat there was a single unique such distinction; he thought ratherthat any such distinction had to be language-relative and himselfconstructed precise definitions of analyticity for a number oflinguistic frameworks with different applications. True, Carnap alsoattempted inSyntax to give ageneral definition of“analytic” that would apply toall languages, butdid not think even at the time that he had succeeded. He went ontrying to find one, but never seriously proposed a solution. SoQuine’s criticism of Carnap’s lack of definition of‘analytic-in-language-L’ withvariable‘L’ was definitely sound, but it ran in open doors, asCarnap had never claimed to have supplied such a definition even tohis own satisfaction. It is a matter of ongoing debate, though,whether Quine’s concerns somehow undermined Carnap’sdefinitions of analyticity forparticular formal frameworksand whether these constructed and language-relative notions ofanalyticity (the existence of which was of course acknowledged byQuine) satisfied the conceptual role that Carnap ascribed to them. Inany case, Carnap himself did not think that every language had to haveanalytic sentences. Most sophisticated language frameworks, especiallythose equipped for scientific statements, would need them, since theanalytic sentences are just those that “come with” theframework (by being provable by the rules of the framework withoutfurther assumptions), but it is possible, Carnap thought, to design alanguage that has no analytic sentences. (In terms of a modernanalogy: there are systems of non-classical logic, such asthree-valued Strong-Kleene logic, which include an interesting andwell-defined logical consequence relation, but where the set oflogically true statements is empty.) He did not think this worthpursuing, though, since to him it was obvious that such a languagewould not be scientifically useful. He often cited Einstein’s(1921) insistence that without Hilbert’s strict distinctionbetween physical geometry and mathematical “purelyaxiomatic” geometry (the latter of which was regarded asanalytic by Carnap), Einstein could never have formulated the theoryof relativity.

The debate between Carnap and Quine about analytic and synthetic hasproduced a flood of commentary, which is still being added to (see,e.g., Juhl & Loomis 2010 or Ebbs 2017 for recent discussions,Proust 1986 [1989] for a broader historical perspective). The mainpoints of the controversy, the main commentators, and Carnap’sown view of the matter are discussed in more detail inCarnap vs Quine on the Analytic-Synthetic Distinction.

On the subject of ontology, Quine criticized Carnap’s use ofquantifiers over intensional entities in Carnap’s intensionalsemantics. Closely related criticisms were voiced by many others,especially including Carnap’s own former Vienna colleague OttoNeurath and the Oxford philosopher Gilbert Ryle, whose review ofMeaning and Necessity (Ryle 1949) was perhaps the nastiestand most vituperative review ever written of anything Carnap wrote.Carnap responded (calmly) with his well-known paper “Empiricism,Semantics, and Ontology” (1950a), in which he distinguishedbetween two understandings of “existence” attributions,internal and external.Internal ones are framework-relative;they specify a language framework before claiming or denying orquestioning the existence of a thing.External existenceclaims or questions lack such a relativization to a framework. ForCarnap only internal questions make sense, if you take them literally.Thus “are there infinitely many numbers?” makes sense ifyou relativize it to a framework such as, for instance,Zermelo-Frankel set theory—which has an axiom of infinity, sothe answer is (trivially) yes. But without such a relativization thequestion makes no sense to Carnap—unless, that is, youreinterpret it as apractical (normative) question ofdeciding among frameworks or explications. All of this applies, inparticular, to the quantification over abstract entities in aframework for semantics, such as intensional semantics. In turn, Quinerejected Carnap’s internal/external distinction, which for Quinerelied on the analytic/synthetic distinction, as accepting a frameworkwould consist in accepting the sentences that are analytic in theframework. Whether the ontological internal/external distinction needsto build on the semantic analytic/synthetic distinction has itselfbecome a topic in recent philosophical work on metaphysicaldeflationism about existence questions, which takes Carnap’smetaontological views as its historical starting point (see, e.g.,Thomasson 2014; see the supplementTolerance, Metaphysics, and Meta-Ontology (Sections 2 and 3) for further discussion).

8. Inductive Logic and the Re-Emergence of the Theoretical Language

8.1 Confirmation

Carnap’s first sketch of a linguistic framework (that of theAufbau) envisaged complete reducibility of all concepts byexplicit definition, at least in principle. By the time of“Testability and Meaning” (1936–37), as we sawabove, Carnap had conceded that such definitional reducibility is notalways possible, and suggested various forms of incompletereducibility that, while not employing only explicit definitions, atleast required of empirically meaningful sentences a clear groundingin observation. He considers verifiability as a criterion forempirical content or meaning, and rejects it for essentially the samereason as he had a decade previously (in Carnap 1926: 7–9). Healso considers Popper’s falsifiability criterion, and rejects itbecause only sentences of a very particular logical form arefalsifiable at all (such as, e.g., “all swans are white”).Indeed, most scientific theories (all theories that use limitconcepts, for instance) have to be stated using unbounded multiplemixed quantifiers, e.g., “for allx there is ay such that \((\ldots x \ldots y\ldots)\)”, and thereare instances of such sentences which can neither be verifiednorfalsified by a single observational counter-instance. Inparticular, to falsify such a statement there would have to be acounter-instancex to falsify an unbounded existentiallyquantified (empirical) sentence, which (as Popper himselfacknowledged) is not generally possible. So in these cases, typical oftheoretical science, falsifiability has no advantage oververifiability. (For a more precise discussion of falsifiability, seeSchurz & Dorn 1988.)

Carnap therefore opts neither for verification nor for falsification,but for a form ofpartial verification that he calls“confirmation”:

If in the continued series of such testing experiments no negativeinstance is found but the number of positive instances increases, thenour confidence in the law will grow step by step. Thus, instead ofverification, we may speak of gradually increasingconfirmation of the law. (TM1: 425)

The acceptance or rejection of a scientific hypothesis becomespartially a practical matter, and to some degree a matter ofconvention. Carnap speaks in this connection of the “degree ofconfirmation” but means this not in a quantitative but merely“topological” (what he would later call“comparative”) sense. He specifically rejectsReichenbach’s proposal to equate degree of confirmation to“the degree of probability in the strict sense which thisconcept has in the calculus of probability, i.e., as the limit ofrelative frequency” (TM1: 427). Five years later Carnap wouldrealize that the probability calculus could be given a different,epistemic interpretation as had been done historically by Bayes,Laplace, Pearson, and Keynes, and was now continued by HaroldJeffreys—and he would make that interpretation the basis of hisremaining life’s work of developingquantitativeexplications of “degree of confirmation”. (For moredetails on Carnap’s work on confirmation and inductive logic,see the supplementInductive Logic.)

8.2 Inductive Logic

Why did Carnap decide to change directions so radically, at the age of52? This is unusual in a philosopher, especially as in Carnap’scase it involved reading his way into a whole new field of inquiry, aswell as learning a whole new branch of mathematics. We know that theidea of a “degree of confirmation” had interested himsince at least the time of “Testability and Meaning”. Atthis time, as we saw insection 8.1 above, he thought it could be defined only comparatively, since herejected Reichenbach’s conflation of truth-value with frequencyas well as his identification of relative frequency and confirmation(Carnap 1935b, 1936–37). And it had been the accepted wisdom inthe Vienna Circle that the classical (epistemic) interpretation ofprobability had been entirely superseded by the frequencyinterpretation, partly because the former relied on Laplace’smuch-criticized principle of indifference, which they classified asmetaphysical. Even Keynes (1921) had given insufficiently cleararguments and his axioms were defective, they thought, but there wasinterest in Wittgenstein’s logical (purely analytic) conceptionof probability, suggested in theTractatus, and developed inmore detail by Waismann (1930).

Then in 1937, right after “Testability and Meaning”,Carnap was sent the typescript of Reichenbach’sExperienceand Prediction for evaluation by the University of Chicago Press.In a long letter to Reichenbach he takes him to task for exaggeratingthe drawbacks of what Reichenbach chastises as the “disparityconception” of probability, whereby the “weight” (or“degree of confirmation” as Carnap also calls it) andprobability (understood as relative frequency) are two separate(disparate) things. Reichenbach had gone so far in his submitteddraft, apparently, as to claim that the disparity conception was notonly the root of all philosophical error, but a form of metaphysics.Carnap says that he himself is not sure what side he is on regardingthe disparity conception (and there is no reason to doubt this, in1937, as far as we know), but he thinks both its acceptance and itsrejection are perfectly compatible with empiricism, and advisesReichenbach to tone down his rhetoric.

Though he was open-minded about the “disparity conception”during this period, it was only in the spring of 1941, according toCarnap’s autobiography, that he “began to reconsider thewhole problem of probability” (1963a: 72). He re-readKeynes’s book more carefully, and found it very enlightening(ibid.). He began to develop a new conception of confirmation,influenced by both Waismann and Keynes:

But I tried a new approach. I believed that the logical concept ofprobability should supply an exact quantitative explication of aconcept which is basic in the methodology of empirical science, viz.the concept of the confirmation of a hypothesis. (1963a: 72)

The starting point of Carnap’s new inductive logic was, first ofall, precisely Reichenbach’s “disparityconception”—i.e., to distinguish very clearly between twodifferent explicata of the ordinary-language word“probability”. One was relative frequency, which is anempirical matter, and was held up as theonly acceptableinterpretation of the Kolmogorov probability calculus by frequentistssuch as von Mises, Reichenbach, and (classically) Ronald Fisher. Theother was epistemic probability, which Keynes and Harold Jeffreys heldto be theonly acceptable interpretation. Carnap called them“probability₂” and“probability₁” respectively, and set aboutclearing the ground for an explication of the latter, without castingany doubt on the legitimacy of “probability₂”as an empirical tool. This distinction was the main focus ofCarnap’s first article on inductive logic (Carnap 1945a).

The conception he developed in his next article (Carnap 1945b) wasindeed logical in the Wittgenstein-Waismann sense, in that therelation between observation sentences and hypothesis was purelylogical and analytic. To achieve this, a relativized principle ofindifference was needed; unlike that of Laplace or Keynes,Carnap’s was entirely language-relative (framework-relative); itwas no longer a quasi-metaphysical assertion about the nature ofdistributions, let alone about the statistical nature of the world,but a matter of constitutive definition. As in any other area ofknowledge, Carnap thought it essential to define the framework beforemaking assertions, so that we are all on the same page. (This logicalor “structural” conception of probability and therelativized principle of indifference are explained in concrete detailin the supplementInductive Logic.) This means that the value of a confirmation measure as applied to ahypothesis and the evidence for or against it is an analyticalconsequence (in the chosen language framework) of the logical andinductive method given by the framework.

In 1950, Carnap published what would be longest book of his career byfar, theLogical Foundations of Probability, into which heworked these two papers (much expanded) and several others, and alsowent into great detail to bring a number of perspectives to bear onthe clarification of the explicanda of “probability” and“confirmation” (both in the sense ofprobability₁). He also goes into detail to discuss ways ofarriving at axioms, and to motivate the choices he ends up with. Inthe course of these clarifications he addresses a number ofphilosophical issues surrounding induction, confirmation, andscientific inference. A simpler exposition than Carnap himself gave ofhis inductive logic project was given later by Kemeny (1963). See thesupplementInductive Logic for further details.

Carnap’s inductive logic encountered a wide range of criticisms,e.g., that of Hilary Putnam, whose philosophical development had beenstrongly influenced by regular meetings with Carnap at Princeton inthe 1950s. Putnam criticized the general idea of an algorithmicaccount of the inductive confirmation of scientific hypothesis byevidence (as exemplified by the special confirmation measure \(c^*\)that is described in the appendix of Carnap 1950b), while at the sametime laying the foundations of what would becomeformal learningtheory (see Putnam 1963 and the concluding section of thesupplementInductive Logic). But perhaps the biggest obstacle to a better and more widespreadunderstanding of Carnap’s inductive logic was the memorablecaricature of Carnap’s whole enterprise by Karl Popper in hisattacks on Carnap during the 1950s and 1960s (e.g., Popper 1963).These were so convincing that the philosophical public retained onlythe caricature and hardly bothered to consult the original. In otherwords, the same pattern repeated itself that we have already seen withrespect to the Quine-Carnap controversies of the 1950s and 60s (section 7 above)—for a long time, the general philosophical publicretained only one side of the debate, influenced mainly byQuine’s (and then Popper’s) superior rhetorical skills, asa result of which both Quine and Popper were much more widely readthan Carnap (though Quine’s proximity to traditional Americanpragmatism surely also played a role). The difference between thesecases is that Popper, unlike Quine, actually misrepresentedCarnap’s position quite blatantly, as Carnap’s supporters(e.g., Bar-Hillel 1955, 1956; Kemeny 1955, 1963) were quick to pointout. (Michalos 1971 gives a well-informed, brief, but balanced surveyof the Popper-Carnap controversy.)

Statisticians (and statistically literate philosophers) have beenquicker to acknowledge not only the continuity between Carnap’sinductive logic and the present-day renaissance of Bayesianstatistical inference, but Carnap’s role in bringing epistemicprobability back from the dead and ensuring that it was takenseriously again (e.g., Leblanc 1962; Skyrms 1996; Zabell 2007, 2011).Many of the standard features of current Bayesianism were firstformulated in Carnap’sLogical Foundations and in hissubsequent work. Carnap went on working on inductive logic for another20 years afterLogical Foundations; his final statement (the“Basic System”), in which prior probabilities depended ongeometrical “quality space” features of the givenframework, appeared after his death in two long installments, editedby his friend and associate Richard Jeffrey (Carnap 1971a, 1980; foran extensive discussion of the “Basic System”, seeHilpinen 1973, Sznajder 2017). His later work appeared to move in amore “personalist” direction (though see Sznajder 2018),but Carnap continued to insist that the prior probability from which astatistical inference proceeds be motivated rationally (byconsiderations of symmetry) andnot be merely subjective;here he stuck to his original idea of the relation between evidenceand hypothesis being purely analytic and thus framework-relative.Though this distinguishes his standpoint from current subjectiveBayesians, there are and have been many other kinds of Bayesians thatare reasonably close to Carnap’s views, including“objective” Bayesians (e.g., Jaynes 1968, J. Williamson2010). (For more on Carnap’s relation to current Bayesianism andvarious discussions of it today, see the supplementInductive Logic.) As one prominent Bayesian pointed out in 1971, one can distinguish atleast 46,656 possible varieties of Bayesians (Good 1971), and Zabell(a later prominent Bayesian) thinks Carnap would surely qualify forinclusion among these. Zabell also cites a characteristicallyconciliatory passage from Carnap’s posthumous “BasicSystem” that sums up Carnap’s appraisal of thesituation:

I think there need not be a controversy between the objectivist pointof view and the subjectivist or personalist point of view. Both have alegitimate place in the context of our work, that is, the constructionof a set of rules for determining probability values with respect topossible evidence. At each step in the construction, a choice is to bemade; the choice is not completely free but is restricted by certainboundaries. Basically there is merely a difference in attitude oremphasis between the subjectivist tendency to emphasize the existingfreedom of choice, and the objectivist tendency to stress theexistence of limitations. (Carnap 1980: 119, quoted by Zabell 2007:294)

8.3 Return to the Theoretical Language

As we saw insection 6.1, by the late 1930s Carnap had returned to a consideration oftheoretical languages whose primitive terms are not constructedbottom-up from observation sentences at all but entirely top-down,“floating in the air, so to speak” so that these basictheoretical terms can have “only anindirectinterpretation, which is incomplete in a certain sense”(Carnap 1939: 65). In Carnap’s mind, the question ofconfirmation of theories and the question of the empirical content oftheories were directly and inseparably connected, as they had been in“Testability and Meaning”. In this subsequent work onthese two questions, however, they were pursued separately, and forall of Carnap’s efforts, the two strands could not be joined up.His inductive logic was never able to assign a degree of confirmationother than zero to unrestricted universally quantified theories, whichwas obviously a defect of the theory and was seized upon by Popper asdiscrediting the entire enterprise (e.g., Popper 1963). Carnap’sown way around the problem was to argue that scientists often regardthe degree by which a piece of evidenceE confirms auniversal law hypothesis \(\forall x P(x)\) to be given by the degreeto whichE confirms an “arbitrary” instance ofthe law \(P(a)\), wherea is an individual constant that doesnot occur inE: see Carnap (1945b: §14). Later authorstried to repair the defect in alternative ways, with varying degreesof success; see the supplementInductive Logic. On the other hand, though Carnap’s work on the empiricalcontent of sentences in a theoretical language often discusses therelations between observational language and theoretical language, hewas never quite able to spell out a criterion for empiricallymeaningful sentences in the theoretical language that did not fallprey to fairly straightforward criticism (e.g., Kaplan 1975). Thegrand design of connecting up the projects of explicating confirmationand of reconstructing scientific theoretical language remained adistant goal.

We have already surveyed the inductive-logic side in the previoussection 8.2. On the theoretical-language side, Carnap’s first major paperwas “The methodological character of theoretical concepts”(Carnap 1956a), followed by “Observation language andtheoretical language” (Carnap 1958) and “Theoreticalconcepts in science” (1959a). Carnap also touches on theoreticallanguages in several parts of the Schilpp volume (1963).Philosophical Foundations of Physics (1966), finally, is aredaction by Martin Gardner of a class Carnap gave at UCLA in the late1950s, presented as an introductory textbook in the philosophy ofscience. Among other things, it gives a lucid summary ofCarnap’s mature views on the reconstruction of scientifictheories. See the supplementThe Reconstruction of Scientific Theories (Sections 3–5) for details and criticism.

One common misunderstanding of Carnap’s work on the theoreticallanguage is an extension of the above-discussed misunderstandings oftheAufbau (section 3 above). TheAufbau was traditionally perceived as anexercise in providing phenomenalist or empiricist foundations forscientific sentences. Therefore, it was assumed, the later work onboth inductive logic and the theoretical language must be motivated bythe aim of providing empiricist foundations for scientific sentences,to distinguish them from non-scientific, i.e., metaphysical sentences.This was certainly Popper’s view, for instance, and largelyQuine’s, but they were not alone; it was widespread until the1990s, when the new and more careful scholarship about logicalempiricism began to take hold.

It is true, of course, that in Carnap’s later work on scientifictheories and theoretical languages, he distinguishes between atheoretical language and an observation language, and studied therelations between them. What is often overlooked, though, is that evenin theAufbau (and even in the earliest proto-Aufbaumanuscripts) Carnap was very clear that what we are to take as“the given” is not inherently fixed or givenbynature (as Aristotle would have put it), but something we have todecide on, something we have to specify provisionally in ourchosen form of rational reconstruction. Later Carnap became evenclearer that what we choose to regard as “observationsentences” is purpose-relative and can’t be decided oncefor all contexts, in the abstract. As early as “Testability andMeaning” (TM1: §16) Carnap was saying that “there canbe several and even mutually exclusive bases” for confirmationby observation. And in later work on the theoretical language thispluralism is extended; in “The methodological character oftheoretical concepts” he merely enumerates various possiblerequirements of different kinds and strengths that might be imposed onthe observation language.

In Carnap’s view, the choice of the theoretical language dependson the purpose. The boundary between “observational” and“theoretical” terms, likewise, is relative to the languagechosen and not fixed by nature:

no sharp boundary separates theO-terms from theT-terms. The choice of an exact dividing line is somewhatarbitrary. From a practical point of view, however, the distinction isusually evident. (Carnap 1966: 258)

Observational terms are assumed to be fully interpreted; theirspecification comes with an explicit link to observation (preciselydefined in some way), while theoretical terms are specifiedaxiomatically and are, in the first instance, uninterpreted or onlymathematically interpreted formulas. These formulas can then beendowed with physical (or chemical, or biological, or social)interpretations by means of correspondence rules, which logicallyrelate observation terms and theoretical terms.

Carnap’s views on the theoretical language during this perioddeveloped in response to critiques and commentaries from (as well aspersonal correspondence with) C.G. Hempel (1945, 1958, 1963). Oneresponse to these interactions was Carnap’s adoption of an ideafirst suggested by Frank Ramsey (1929) for the purpose of separatingthe theoretical from the empirical content of a theory; this ideafirst appeared in print in (the original German version of)Carnap’s paper “Observation language and theoreticallanguage” (1958). (This procedure is explained in detail in thesupplementThe Reconstruction of Scientific Theories (Sections 4–6).) The idea was that a theory could essentially be stated in such a waythat all the theoretical terms in it are eliminated, i.e., it could bestated solely in terms of its “empirical residue”. ButCarnap’s goal in adopting this method was not to suggest thatthe theoretical language was eliminable, that theoretical terms couldor should be eliminated (as some versions of traditional empiricismmight have liked). The point was rather to understand the empiricalcontent of theoretical claims, and its logical function withintheories. This leads to many complications, which are still very muchunder discussion (e.g., Demopoulos 2007, Friedman 2011, Schurz2005).

The Ramsey approach was adopted, following Carnap, by others, notablyDavid Lewis (1970), who put it to a rather different, moremetaphysical use that was later adopted by Frank Jackson and otheradvocates of the “Canberra Plan” of conceptual analysis.This was also Chalmers’s (2012) point of departure, in his moremetaphysical adaptation of theAufbau, mentioned above (section 3). See the supplementThe Reconstruction of Scientific Theories (Section 4).

9. Final Years and Legacy

In 1951, Herbert Feigl approached Paul Schilpp, the editor of theLibrary of Living Philosophers, about doing a volume not on aparticular philosopher, but on logical empiricism as a movement.Carnap and Reichenbach were to be in the foreground, as representativefigures for the movement as a whole. Schilpp was sufficientlyinterested that he persisted with the idea even afterReichenbach’s sudden death in 1953; the volume was now to befocused on Carnap alone. Carnap invested a great deal of time in theproject. He took the task of writing an autobiography seriously,reviewing many of his old papers, including his extensive diaries, inpreparation for it. The resulting autobiography was much too long, andhad to be cut by a third before publication. (The cut portions areavailable at the Young Research Library, University of California atLos Angeles, Special Collections, Collection 1029 (Rudolf Carnap), Box2, CM3, mostly in folder marked “M-A5”; extensivequotations and references can be found in Carus 2007a.)

Unfortunately, publication was delayed by a series of mishaps, andwhen the book finally appeared in 1963, logical empiricism was nolonger at the forefront of interest. Analytic philosophers had largelybeen swayed by Quine’s critique of Carnap over the past decade,and philosophers of science were captivated by Thomas Kuhn’sbookThe Structure of Scientific Revolutions, published theyear before in the International Encyclopedia of Unified Science,co-edited by Carnap. Logical empiricism no longer inspired passions,either for or against; it seemed to belong to the past. Carnap saw inthe anti-war and student movements of the 1960s an American version ofthe Youth Movement that had played such an important role in his owndevelopment half a century earlier, but insofar as the students of the1960s were interested in philosophy, it was not in logical empiricism.A few weeks before his death, Carnap prepared a report for an AmericanPhilosophical Association committee about his meeting in the summer of1970 with some philosophers imprisoned in Mexico. It illustrates hiscontinued interest in social and political matters and in his fellowphilosophers, and appeared posthumously, in December of that year, intheJournal of Philosophy. When Carnap died in Los Angeles in1970, the philosophical world at large (as opposed to the majorfigures whose views he had shaped, such as Quine, Goodman, Putnam,Jeffrey, or Stein) had lost interest in him. But half a century later,it is fair to say that Carnap’s work is as much in theforeground of philosophical discussion as it has ever been.

10. List of Supplements

Bibliography

Carnap’s Works

The two major collections of Carnap papers are at the Archive ofScientific Philosophy (Hillman Library, University of Pittsburgh) andat the Young Research Library (University of California at LosAngeles). Both of these collections have been used extensively in manyof the publications cited.

1918a [2019], “Völkerbund—Staatenbund”,Politische Rundbriefe, 1: 4 and 4: 15–16. Translatedinto English in Carnap 2019: 3–10. [Carnap 1918 available online]
1918b, “Deutschlands Niederlage: Sinnloses Schicksal oderSchuld?” (typed), 29 October 1918, Archives of ScientificPhilosophy, Hillman Library, University of Pittsburgh, Carnap Papers[089-72-04].
1919,Politischer Rundbrief of 1 April 1919.Recommendation of G. Landauer’s bookRevolution undSozialismus, p.124. Archives of Scientific Philosophy, HillmanLibrary, University of Pittsburgh, Carnap Papers [110-01-28].
1922a [2019],Der Raum: Ein Beitrag zurWissenschaftslehre, Kant-Studien Ergänzungshefte, Nr. 56,Berlin: Reuther & Reichard. Translated into English in Carnap2019: 21–208.
1922b, Three positions papers on: (a) Beziehungslehre undStrukturlehre; (b) Ansätze zur Charakterisierung von Strukturen(with Bernhard Merten); (c) Aufbau der Wirklichkeit (Strukturtheoriedes Erkenntnisgegenstandes) (carbons); late 1922. Archives ofScientific Philosophy, Hillman Library, University of Pittsburgh,Carnap Papers [091-17-12].
1923 [2019], “Über die Aufgabe der Physik und dieAnwendung des Grundsatzes der Einfachstheit”,Kant-Studien, 28: 90–107. Translated into English inCarnap 2019: 209–46.
1924 [2019], “Dreidimensionalität des Raumes undKausalität: Eine Untersuchung über den logischenZusammenhang zweier Fiktionen”,Annalen der Philosophie undphilosophischen Kritik, 4: 105–30. Translated into Englishin Carnap 2019: 247–298.
1925a, “Gedanken zum Kategorienproblem. Prolegomena zu einerKonstitutionstheorie (Vortrag Wien)” (shorthand), 21 January1925. Archives of Scientific Philosophy, Hillman Library, Universityof Pittsburgh, Carnap Papers [081-05-03].
1925b, “Entwurf einer Konstitutionstheorie derErkenntnisgegenstände” (typed), first sketch, 17 December1924; this version typed, 28 January 1925. Archives of ScientificPhilosophy, Hillman Library, University of Pittsburgh, Carnap Papers[081-05-02].
1926 [2019],Physikalische Begriffsbildung, Karlsruhe:Braun. Translated into English asPhysical Concept Formationin Carnap 2019: 339–440.
1927, “Eigentliche und uneigentliche Begriffe”,Symposion, 1: 355–374.
[Aufbau] 1928a [1967],Der logische Aufbau derWelt, Berlin: Weltkreis. Second edition, Hamburg: Meiner, 1961.Translated into English asThe Logical Structure of theWorld, Rolf A. George (trans.), Berkeley, CA: University ofCalifornia Press, 1967.
1928b,Scheinprobleme in der Philosophie, Berlin:Weltkreis.
1929,Abriß der Logistik, mit besondererBerücksichtigung der Relationstheorie und ihrer Anwendungen,Vienna: Springer.
1930a, “Die alte und die neue Logik”,Erkenntnis, 1: 12–26. doi:10.1007/BF00208606
1930b, “[Review of] Felix Kaufmann,Das Unendliche inder Mathematik und seine Ausschaltung”,DeutscheLiteraturzeitung, 51: cols. 1674–1678.
1930c, “Bericht über Untersuchungen zur allgemeinenAxiomatik”,Erkenntnis, 1: 303–307.doi:10.1007/BF00208622
1930d, “Review: Der logistische Neupositivismus: E. Kaila(1930)”,Erkenntnis, 2: 75–77.doi:10.1007/BF02028134
1930e, “Plan für Kaila-Aufsatz: Über dieErkenntnis des sog. ‘Nicht-Gegebenen’” (shorthand),2 November 1930; also an outline headed ‘Kaila-Aufsatz’ ona separate sheet dated 29 October 1930, Young Research Library,University of California at Los Angeles, Special Collections, CarnapPapers (Collection 1029) [UCLA Box4, CM13, item1].
1931, “Die logizistische Grundlegung der Mathematik”(The Logicist Foundations of Mathematics),Erkenntnis, 2:91–105. doi:10.1007/BF02028142
1932a, “Überwindung der Metaphysik durch logischeAnalyse der Sprache”,Erkenntnis, 2: 219–241.doi:10.1007/BF02028153
1932b [1934], “Die physikalische Sprache alsUniversalsprache der Wissenschaft”,Erkenntnis, 2:432–465. Translated into English asUnity of Science,Max Black (trans.), London: Kegan Paul, Trench & Co., 1934.doi:10.1007/BF02028172
1932c, “Psychologie in physikalischer Sprache”,Erkenntnis, 3: 107–142. doi:10.1007/BF01886414
1932d, “Erwiderung auf die vorstehenden Aufsätze von E.Zilsel und K. Duncker”,Erkenntnis, 3: 177–188.doi:10.1007/BF01886417
1932e [1987], “Über Protokollsätze”,Erkenntnis, 3: 215–228. Translated in 1987 as “OnProtocol Sentences”, Richard Creath and Richard Nollan (trans.),Noûs, 21(4): 457–470. doi:10.2307/2215667 (en)doi:10.1007/BF01886421 (de)
[LSS] 1934a [1937],Logische Syntax der Sprache, Vienna:Springer. Translated by Amethe Smeaton asThe Logical Syntax ofLanguage, London: Routledge, 1937.
1934b, “Theoretische Fragen und praktischeEntscheidungen”,Natur und Geist, 2:257–260.
1934c [1987],Die Aufgabe der Wissenschaftslogik, Vienna:Gerold. Translated as “The Task of the Logic of Science”,Hans Kaal (trans.), inUnified Science, Rainer Hegselmann andBrian McGuinness (eds.), Dordrecht: Reidel, 1987, 46–66.doi:10.1007/978-94-009-3865-6_3
1934d [2004], “On the Character of PhilosophicProblems”, W. M. Malisoff (trans.),Philosophy ofScience, 1(1): 5–19. German original “Über denCharakter philosophischer Probleme” published in R. CarnapScheinprobleme in der Philosophie und andere metaphysikkritischeSchriften, T. Mormann (ed.), Hamburg: Meiner, 2004,111–127. doi:10.1086/286302 (en)
1935a,Philosophy and Logical Syntax, London:Routledge.
1935b, “Review: Logik der Forschung. Zur Erkenntnistheorieder modernen Naturwissenschaft: Popper, Karl (1935)”,Erkenntnis, 5: 290–294. doi:10.1007/BF00172319
1936 [1949], “Wahrheit und Bewährung”, inActes du Congrès international de philosophie scientifique,Sorbonne, Paris 1935, fasc. 4.Unité de lascience, Paris: Hermann, pp. 18–23. A modified version istranslated as “Truth and Confirmation”, in Feigl andSellars 1949: 119–127.
[TM] 1936–37, “Testability and Meaning”,Philosophy of Science,
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1939,Foundations of Logic and Mathematics, Chicago:University of Chicago Press.
1942,Introduction to Semantics, Cambridge, MA: HarvardUniversity Press.
1943,Formalization of Logic, Cambridge, MA: HarvardUniversity Press.
1945a, “The Two Concepts of Probability: The Problem ofProbability”,Philosophy and Phenomenological Research,5(4): 513–532. doi:10.2307/2102817
1945b, “On Inductive Logic”,Philosophy ofScience, 12(2): 72–97. doi:10.1086/286851
1946, “Modalities and Quantification”,Journal ofSymbolic Logic, 11(2): 33–64. doi:10.2307/2268610
1947,Meaning and Necessity, Chicago: The University ofChicago Press; second edition: 1956.
1949, “A Reply to Leonard Linsky”,Philosophy ofScience, 16(4): 347–350. doi:10.1086/287056
[ESO] 1950a [1956], “Empiricism, Semantics, andOntology”,Revue Internationale de Philosophie, 4(11):20–40. Reprinted in Carnap 1956b: 205–221.
[LFP] 1950b,Logical Foundations of Probability, firstedition, Chicago: University of Chicago Press.
1952a [1956], “Meaning Postulates”,PhilosophicalStudies, 3(5): 65–73. Reprinted in Carnap 1956b:222–229. doi:10.1007/BF02350366
1952b,The Continuum of Inductive Methods, Chicago:University of Chicago Press.
1954a [1968],Einführung in die symbolische Logik, mitbesonderer Berücksichtigung ihrer Anwendungen, firstedition, Vienna: Springer; second edition, 1968.
1954b [1956], “On Belief Sentences: Reply to AlonzoChurch”, inPhilosophy and Analysis, Margaret MacDonald(ed.), Oxford: Blackwell, pp. 128–131. Reprinted in Carnap1956b: 230–232.
1955a [1956], “On Some Concepts of Pragmatics”,Philosophical Studies, 6(6): 89–91. Reprinted in Carnap1956b: 249–251. doi:10.1007/BF02341065
1955b [1956], “Meaning and Synonymy in NaturalLanguages”,Philosophical Studies, 6(3): 33–47.Reprinted in Carnap 1956b: 222–229. doi:10.1007/BF02330951
1956a, “The Methodological Character of TheoreticalConcepts”, inThe Foundations of Science and the Concepts ofPsychology and Psychoanalysis, Herbert Feigl and Michael Scriven(eds.), Minneapolis: University of Minnesota Press, pp. 38–76. [Carnap 1956a available online]
1956b [1947],Meaning and Necessity: A Study in Semantics andModal Logic, second edition, Chicago: University of ChicagoPress. (This is an enlarged version of 1947.)
1957, “How Can Induction Be Justified?” UnpublishedManuscript from the Carnap Papers at the Archives of ScientificPhilosophy, Hillman Library, University of Pittsburgh, cataloguenumber 082-01-01.
1958 [1975], “Beobachtungssprache und TheoretischeSprache”,Dialectica, 12(3–4): 236–248.Translated as “Observational Language and TheoreticalLanguage”, in Hintikka 1975: 75–85.doi:10.1111/j.1746-8361.1958.tb01461.x
1959a [2000], “Theoretical Concepts in Science”,unpublished lecture. Published in Stathis Psillos, 2000, “RudolfCarnap’s ‘Theoretical Concepts in Science’”,Studies in History and Philosophy of Science Part A, 31(1):151–172. doi:10.1016/S0039-3681(99)00031-X
1959b,Induktive Logik und Wahrscheinlichkeit (coauthor:Wolfgang Stegmüller), Vienna: Springer.doi:10.1007/978-3-7091-3142-8
1961a, “Vorwort zur zweiten Auflage” (introduction tosecond edition), inAufbau, second edition, Hamburg: Meiner,pp. X–XV.
1961b, “On the Use of Hilbert’s ε-Operator inScientific Theories”, inEssays on the Foundations ofMathematics, Y. Bar-Hillel et al. (eds.), Jerusalem: MagnesPress, pp. 154–64.
1962,Logical Foundations of Probability, second edition,Chicago: University of Chicago Press.
1963a, “Carnap’s Intellectual Autobiography”, inSchilpp 1963: 3–84.
1963b, “The Philosopher Replies”, in Schilpp 1963:859–1013.
1964, “Interview mit Rudolf Carnap”, inMein Wegin die Philosophie, Rudolf Carnap, interview with WillyHochkeppel, Stuttgart: Reclam, pp. 134–148.
1966,Philosophical Foundations of Physics: An Introduction tothe Philosophy of Science, New York: Basic Books.
1968a “Inductive Logic and Inductive Intuition”, inThe Problem of Inductive Logic, Imre Lakatos (ed.),Amsterdam: North-Holland, pp. 258–314.
1968b, “On Rules of Acceptance”, inThe Problem ofInductive Logic, Imre Lakatos (ed.), Amsterdam: North-Holland,pp. 146–50.
1971a, “A Basic System of Inductive Logic, Part I”, inCarnap (and Jeffrey) 1971c: 33–165.
1971b, “Inductive Logic and Rational Decisions”, inCarnap (and Jeffrey) 1971c: 5–31.
1971c,Studies in Inductive Logic and Probability, volume1, with Richard C. Jeffrey, Berkeley: University of California Press.See Jeffrey 1980 for volume 2.
1974,An Introduction to the Philosophy of Science, NewYork, Basic Books; second edition of Carnap 1966.
1980, “A Basic System of Inductive Logic, Part II”, inJeffrey 1980: 7–155.
2000,Untersuchungen zur allgemeinen Axiomatik, ThomasBonk and Jesús Mosterin (eds.), Darmstadt: WissenschaftlicheBuchgesellschaft.
2017, “Value Concepts (1958)”,Synthese,194(1): 185–194. doi:10.1007/s11229-015-0793-2
2019,Rudolf Carnap: Early Writings, A.W. Carus, MichaelFriedman, Wolfgang Kienzler, Alan Richardson, and Sven Schlotter(eds.), (The Collected Works of Rudolf Carnap, 1), New York: OxfordUniversity Press.

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