Rudolf Carnap’s The Logical Structure of the World is a work of technical philosophy first written in German in the 1920s and later translated into English. It sets out to do something unusually concrete for a book of theory: to actually build, step by step, the whole conceptual vocabulary of science out of a single, minimal foundation. Rather than arguing in general terms that knowledge rests on experience, Carnap attempts to demonstrate it by constructing a formal system in which every concept—colors, physical bodies, other minds, cultural objects—is defined through chains of logical operations from the immediately given.
“The senses provide the material of cognition, reason synthesizes the material so as to produce an organized system of knowledge.”
The book grew out of work Carnap drafted between 1922 and 1925, and it belongs to the ferment of interwar Vienna, where he was a central figure in the circle around Moritz Schlick. Its intellectual debts are explicit: Gottlob Frege, Carnap’s teacher at Jena, and Bertrand Russell supplied the modern logic of relations that makes the whole project conceivable, while Ernst Mach and Richard Avenarius supplied the empiricist impulse to reduce “reality” to the “given.” Carnap’s aim, as he later described it, was not more general argument but the actual formulation of a conceptual system—choosing simple basic concepts and defining everything else from them.
The Ambition of a Constructional System
Carnap’s guiding idea is that a theory is fully axiomatized only when its statements form a deductive system grounded in axioms and its concepts form a constructional system grounded in fundamental concepts. He observes that deduction from axioms has received far more attention than the methodology of systematically constructing concepts, and it is the latter that concerns him here. Only a unified system of all concepts, he argues, can overcome the fragmentation of unified science into unrelated special sciences. Although all knowledge subjectively originates in contents of experience, the constructional system is meant to show how we can advance to an intersubjective, objective world—conceptually comprehensible and identical for all observers.
The method joins two branches that had been treated separately: symbolic logic, which Russell and Whitehead developed into a theory of relations capable of handling pure ordering, and the reduction of reality to the given pursued by Mach, Avenarius, Poincaré, and others. Carnap applies the theory of relations to the analysis of reality, formulates the logical requirements for a constructional system, clarifies its basis, and then demonstrates by actually producing such a system—at least in outline—that it can be constructed. He quotes Russell’s maxim approvingly: “Wherever possible, logical constructions are to be substituted for inferred entities,” and employs it more radically than Russell himself, constructing the unseen from the seen and other minds from one’s own.
The 1961 Preface and the Shape of the Project
Carnap opens the second edition by recalling that the Aufbau was his first large book, drafted between 1922 and 1925, and he still stands by its problems and its method. The central task is the rational reconstruction of the concepts of every field of knowledge out of concepts referring to the immediately given—finding new definitions for old concepts that are clearer, more exact, and fit into a systematic structure, a procedure he links to what he later called explication. Empiricists and rationalists agree that concepts and judgments arise from the cooperation of experience and reason, though they weight the two factors differently; traditional empiricism rightly stressed the senses but missed logical and mathematical form, while rationalism saw the form but wrongly thought reason could produce new content a priori. Frege, his teacher at Jena, and Russell showed him the purely logical, formal character of mathematics. Later the Vienna Circle around Schlick and Wittgenstein’s ideas shaped logical empiricism.
The book’s aim, he insists, was not more general argument but the actual formulation of a conceptual system: choosing simple basic concepts—sensory qualities and relations—and defining the rest, which required a logic of relations superior to tradition. The system takes elementary experiences as basic elements and a single basic relation, recollection of similarity; senses, visual field places, spatial relations, and colors are defined on that basis. Carnap now finds the single-basic-concept restriction too artificial, would prefer several basic concepts, and would choose as elements something like Mach’s elements—a red of a certain type at a certain place at a given time—with relations of earlier-than, spatial proximity, and qualitative similarity. He now favors a physical basis over the autopsychological one, for the intersubjective agreement it offers, a position he developed with Neurath as physicalism. He concedes that reduction cannot always take explicit-definition form, that definability and translatability into sense-data statements must be given up, and that the thesis that all statements are extensional is incorrect; the weaker claim, that every nonextensional statement can be translated into an equivalent extensional one, remains a conjecture. He surveys the literature—Goodman’s Structure of Appearance, Kraft, Jørgensen, Barone, Stegmüller—and notes that Pseudoproblems in Philosophy, written in his first Vienna year, is more radical than the Aufbau, condemning all theses about metaphysical reality as pseudostatements. The book had been unavailable since the war; he thanks Felix Meiner for reissuing it.
Axioms, Constructions, and the Unity of Science
A theory is axiomatized when its statements form a deductive system grounded in axioms and its concepts form a constructional system grounded in fundamental concepts. Deduction from axioms has drawn far more attention than the methodology of systematically constructing concepts, which is the present concern, applied to the conceptual system of unified science. Only a unified system of all concepts can overcome the separation of science into unrelated special disciplines. Although all knowledge subjectively originates in contents of experience, the constructional system will show how to advance to an intersubjective, objective world identical for all observers.
The method joins two branches: logistics, which Russell and Whitehead brought to a theory of relations capable of handling pure ordering, and the reduction of reality to the given pursued by Avenarius, Mach, Poincaré, Külpe, Ziehen, and Driesch. Russell’s maxim—wherever possible, logical constructions are to be substituted for inferred entities—is employed more radically here, on an autopsychological basis, constructing the unseen from the seen. If such a system is possible, there is only one domain of objects and one science; types of objects differ only by level of construction. Higher-level objects are logical complexes, not sums: an object state is constructed from psychological processes but is not their sum, and all statements about a complex transform into statements about its elements. Synthetic geometry serves as the analogy—it starts from points and lines, builds higher complexes in steps, yet every statement about the constructs is ultimately about the elements.
Every concept has exactly one object, and the borderline between general and individual concepts can shift; whether a sign denotes concept or object makes no logical difference, only a psychological one. Construction theory therefore speaks indifferently of constructed objects or concepts, employing a neutral language in which objects are neither created nor apprehended but constructed, so the realist-idealism controversy becomes an idle linguistic dispute. Object and concept are one and the same—a functionalization of the object, not a reification of the concept.
The Plan of the Work
Part II is preparatory. Chapter A explains structure, the purely formal aspect of a relation’s extension, showing that all objects can in principle be characterized by structural properties alone and all scientific statements transformed into purely structural statements.
Cardinal Numbers and Relation Extensions as Quasi Objects
Carnap begins with the class definition of cardinal numbers: two classes are equinumerous when a one-to-one correspondence can be set up between them, and the cardinal number 5 is simply the class of all five-element classes. Formally this is unobjectionable, yet it offends intuition, since the class of all five-object classes looks boundless beside the crisp arithmetical entity 5. The illusion, he argues, comes from substituting a class for a corresponding whole: the class of my right hand’s fingers is not the hand itself. Such a class is a quasi object, an autonomous complex whose symbol lets us make statements about its elements without enumerating them. The number 5 is likewise a quasi object; the sign “5” only states what all possible five-object classes share. Frege gets credit for the definition, Russell for rediscovering it independently in 1901; Hausdorff, Koenig, and Fraenkel raised objections, and Weyl endorses Carnap’s conception. Fractions follow the same pattern, definable as relation extensions—2/3 as the class of pairs (x, y) where 3x = 2y.
Constructional Levels, Being and Holding
Step-by-step construction from basic objects through class and relation formation yields constructional levels: stratified object spheres, each a domain of quasi objects relative to the one before. This reconciles the unity of the object domain with the multiplicity of independent object types—logically science concerns one domain, practically its statements concern many allogeneous constructed entities. The “modes of being” reflect these sphere differences: a quasi object “holds” for its elements, which “have being,” and the relationship repeats level to level, so being and holding are relative. Classes hold for things, cardinal numbers for classes, fractions for cardinal numbers, real numbers for fractions, complex numbers for real numbers—six modes in all.
The Extensionality Thesis
Constructional definitions define concepts only extensionally, though traditional logic rejects the thesis of extensionality. Carnap traces the extensional and intensional traditions through Boole, Venn, Schröder, Frege, Russell, and Wittgenstein’s attack, and promises to vindicate extensionality. A statement is extensional if any coextensive propositional function can replace another salva veritate: “x is a man” and “x is a rational animal” are coextensive, so the implication about mortality transforms into a class statement. “I believe that…” seems a counter-example. Frege’s triad of sign, sense, and nominatum resolves it: “7,” “VII,” and “5 + 2” differ as signs, (7) = (VII) but not (5 + 2), while [7] = [VII] = [5 + 2]. Sentences have thoughts as sense and truth values as nominatum. Since so-called intensional statements actually concern sense rather than the function, there are no intensional statements—all are extensional, and the extensional method is justified.
System Form, Indicators, and Epistemic Value
Order depends on reducibility, rendered logistically: “If somebody is a Negro, then he is also a man” becomes “(x): x ∈ Negro. ⊃ . x ∈ man.” Reducibility is restated through states of affairs and necessary and sufficient conditions, each object having a fundamental propositional function whose condition serves as definiens—temperature equilibrium, for instance, defined via bodies in contact showing no temperature change. An indicator is a sufficient condition ordinarily used to identify a state of affairs, as a barometer reading indicates air pressure; in principle indicators exist for all scientific states of affairs, including an infallible, always-present one. The rattlesnake is defined as the animal carrying rattles at the end of its body, and empathy in the cultural sciences is justified only where rational indicators can in principle be produced. Constructional transformation preserves logical value—extension and truth value—but not epistemic value; it is purely logical, not psychological, so “this animal, which carries rattles…, is a rattlesnake” turns tautological.
Anger, Neutrality, and the Order of Objects
Another person’s anger is defined constructionally as a bodily state characterized by physical processes or dispositions to react, the process type characterized via processes of my own body when angry. The realist objects that behavior is merely an indicator, demanding a separate symbol F for the anger itself; Carnap answers that every scientific statement about F transforms into statements about the indicator K with the same logical value, and since K and F satisfy the same propositional functions they are identical as far as logical value goes. Realistic and constructional languages carry the same meaning and stay neutral between realism and idealism; constructional language expresses epistemic-logical relations, not metaphysical doctrines, and “quasi object” names a relation, not a denial of reality.
Time, Place, and Colour from a Single Relation
Carnap asks whether temporal order needs its own basic relation. It does not: recollection of similarity already carries it, since if x is remembered as similar to y then x is earlier. This settles order only for part-similar pairs, but transitivity stretches it across the field. Because near experiences tend to be part-similar, the result is a preliminary order only—an unbroken sequence must wait for the regularities of physical processes, which is exactly how time perception actually works, completed by inference.
The visual sense is picked out by its dimension number of five, yet neither the colour solid nor the two-dimensional visual field falls out of similarity alone. Place identity must be derived instead: qualities occupying the same place can never appear in one elementary experience, which is expressed as mutual exclusivity. Exclusivity is necessary but not sufficient, so similarity circles are formed over it by quasi analysis, and the wanted place classes are identical with or subclasses of these. A footnote records that the first German edition said “abstraction classes”; the change follows Goodman’s observation that exclusivity is non-transitive, so no such class exists. Proximate places, where a quality of one place resembles one of another, ground spatial order, and the field’s two-dimensionality is a formal property of that relation. Colour order then needs nothing new: colour identity in proximate places, chained together, yields colours as abstraction classes, and the colour solid’s three dimensions are again formal. One might object that the place/colour difference is essential rather than formal, but the difference concerns pairs of qualities, not elementary experiences, so it must be derived anyway—location serving as the principle of individuation. The method is not unique; kinesthetic sensations or focus alone would serve, all yielding two dimensions first, later explained by light rays forming a bundle of the second degree.
Sensations, Fictions, and the Four Languages
A sensation is an ordered pair of an elementary experience and a quality class; simultaneity means the same experience. Qualities come first, sensations are built from them—an isolated experience is unanalyzable. Three-dimensional visual space, visual things, my body, and other minds all follow without new basic relations. Four languages do the work: logistics as the basic tongue, word-language paraphrase, realistic language for testing content, and fictitious constructive operations for testing formal correctness. The fictions include separating the raw material temporally from acting upon it, the retainability of the given, and supplying subject A with operating rules. Rational reconstruction mirrors intuitive object formation—the house, the plant—separating the given from synthesis by abstraction.
The Fiction of Retention and the Pair List
Subject A absorbs the given in the first part of life, then synthesizes the retained material in the second, without absorbing more. The fiction of retainability departs from reality, where much is forgotten and what survives is usually already synthesized. Construction postulates only the minimum of relations needed to build reality in principle; each construction means the object can be built this way given sufficient supply. Every elementary experience gets a permanent token, a number, so it can be used more than once. A may even be given only a pair list of experiences under the basic relation—an inventory of number pairs—and nothing else. Constructions that cannot be expressed as operational rules are thereby excluded; this is the regulative value of the fiction. Since the system reconstructs a cognition whose results we already know, we can guide A while remaining ignorant of his particular experiences. Each construction becomes a rule producing inventory lists, supplemented by object descriptions that accumulate further properties—definite description and characterization in realistic language. Operativeness is easily met in logistic language, where definitions take extensional form.
Building Similarity Circles and Quality Classes
Similarity circles over part-similarity are formed by quasi analysis. Realistically one takes the largest class of mutually proximate qualities; fictitiously, A lists all classes of part-similar experiences, starting from unit classes, then pairs, then triples, erasing subclasses of other listed classes, and numbering the remainder. A quality class is a class totally contained in each similarity circle containing at least half of it, with no outside element in every such circle—realistically, the largest classes left undivided by partial overlapping. A class is not the collection of its elements; a quality class is a quasi object standing for what its members share. A forms intersections and remainders until no further division occurs, and numbers the results. We know these are visual qualities, tones, fragrances; A cannot yet be told which is which, though the central thesis requires that eventually he can.
Part identity holds when a quality class contains both experiences; similarity between quality classes when every element of one is part similar to every element of the other. Sense classes are abstraction classes of the similarity chain; sight is the class whose dimension number is five, the visual field two-dimensional. A sensation pairs an experience with a quality class; division classes of the first type are abstraction classes of simultaneity.
Reports and the Weight of Meaning
Carnap turns to how whole sentences, not just single words, get their meaning. A sign-production that designates a state of affairs he calls a “report,” and the reporting relation must be built alongside the sign-production relation, each propping up the other. Take a bare three-word sentence—”Karl hits Fritz”—and the meaning is the state of affairs carrying the greatest total weight relative to that report. Weight factors attach to each position: the first object against the first word, the relation against the second, the third object against the third, plus a heavier fourth factor that peaks when the state of affairs actually obtains and shrinks as conditions go unfulfilled. Meaning is secure just insofar as the total weight outruns the rival states of affairs. These correlations then feed back into fixing which object a word designates, which is why “context” carries such value for meaning.
Intuition and the Logical Function
Construction, he insists, is a rational reconstruction of cognition’s formal structure, not a transcript of how anyone actually thinks. A child learns meanings associatively, by intuition, not by ratiocination; reading a face is even more purely intuitive. With sentences we can afterward recall the parts and check the whole, but facial expressions leave only the apprehended meaning behind. Still, a dependency holds throughout: all grasp of heteropsychological phenomena runs through some sign-production or expressive motion, and meaning is a function—in the mathematical sense—of the utterance’s physical properties. The construction states that function without pretending the process is discursive; the fiction of rationality lives only in the language of constructive operations. This holds for every construction, which bears the neutral character of a logical function.
Reports as a Resource, and the World of the Other
Reliable reports do double duty: they inform me of a state of affairs and tell me that another knows it. Reliability is tested against established facts and laws and against the author’s discovered trustworthiness, and testing is presupposed done. Reports enormously enrich what can be constructed—the physical, heteropsychological, and cultural domains rest almost entirely on them—yet no level introduces anything fundamentally new, only a reorganization of given elements. Another person M’s experiences are built through expression and reporting relations, fewer and less variegated than my own but obeying the same forms, now with subscripted symbols. “M’s world” is a branch within the one system, mirroring mine by analogy and called “of M” because it is tied to M’s body. Agreement is far-reaching but incomplete: my body and M’s body agree as physical things yet differ in hair color, and elsewhere a one-to-one correspondence between spatiotemporal world points, which Carnap calls intersubjective correspondence, does the work of “the same” object.
Foundedness and the Elimination of Basic Relations
The concept of “foundedness” resists definition—it cannot be derived from constructed concepts or from ordinary logical basics, yet belongs to no extralogical domain. Since his characterization of basic relations as founded relation-extensions holds for any constructional system whatever, Carnap treats foundedness as a basic concept of logic, alongside generality, and defines the basic relation as the only founded relation-extension from which a sufficiently high-level object with certain empirical traits can be built. Choosing the three-dimensionality of the color solid as his theorem, he writes the definition in purely logical symbols, achieving complete formalization—while conceding the unresolved presupposition that foundedness is logical. The theses follow: elements of one type, order through relation-extensions, a small number of basic relations, conjecturally just one (recollection of similarity), and objects arrayed from quality classes up through intersubjective objects. Earlier category tables seem “too rich” only because their tools were poor.
Essence, Dualism, and the Self
Indicating an object’s essence means giving truth criteria for sentences containing its sign; the constructional essence is the construction formula translating those sentences down to the basic relation. “Essential relations” cannot enter the system—unverifiable, they belong to metaphysics. Against mind-body dualism, Carnap replies that “object types” is a concession to realistic language; what matters is the uniformity of basic elements, so physical and psychological become order forms of one domain of propertyless elements, and dualism gives way to a pluralism of unlimited aspects. The self is the class of elementary experiences, a unit rather than a bundle, constructed late, mainly to mark it off from others; the Cartesian dictum thins to the tautology “this experience; therefore this experience is.”
Intention, Causality, and the Psychophysical Problem
Intention links a content-bearing process to its content—my representation of the cathedral—regardless of whether the intended object is real; the intended object is an ordering of experiences.
Words, Concepts, and the Limits of Science
A word does not become a concept merely by being used. Carnap insists that words function as signs of concepts only when they are defined or can be located within an experiential constructional system, and he cites Petzold to reinforce the point. From here he turns to labels. The view that science can handle any object and never meets an in-principle unanswerable question is sometimes called “rationalism,” but the tag misleads: in the old opposition of rationalism and empiricism it does not fit, because on construction theory every scientific statement is at bottom about relations among elementary experiences, so every substantive insight traces back to experience. “Empiricism” is the more justified name, though not a raw empiricism, given the weight construction theory places on form. In its modern sense, opposed to irrationalism, the word is rejected too: it names persuasions that give reason a leading role in life as a whole, a tendency absent here.
The proud thesis that no question is in principle unsolvable for science sits alongside a humble insight: even after all questions are answered, the problem life poses is not solved. Cognition is a definite, well-circumscribed task within life, and mastering life requires all our powers, not conceptual thinking alone. There is no “Ignorabimus,” yet there may be unsolvable riddles of life—no contradiction, since riddles of life are practical situations, not questions. The “riddle of death” is the shock at a fellow man’s death or fear of one’s own, not biological questions about death, which could in principle be answered but do not help a grieved person; the riddle is the task of getting over the situation. Wittgenstein is credited with formulating both the proud thesis and the humble insight, and his difficult, little-known treatise is praised as valuable.
The Summary Restated
The closing summary gathers the threads: individual and general concepts are not essentially different kinds; identity and synonymy; essence as constructional; mind-body dualism as two forms of order of one kind of basic element; the self as a class of experiences; intention as a special case; causality as functional dependency holding only in physics. The psychophysical problem concerns parallelism, observable only between autopsychological events and my own brain processes. Empirical reality is distinguished from metaphysical reality—”independence from the cognizing consciousness”—which is meaningless for science and replaced by the “objectivism” of lawlike regularities. Science aims at finding and ordering true propositions; no question is unanswerable in principle; faith and intuition in the nonrational sense do not belong to theory. Rationality is demanded only for science, with nonrational spheres acknowledged for practical life.
Pseudo-Problems and Rational Reconstruction
An appended section treats epistemology’s aim as formulating a method for justifying cognitions, relative justification by reduction, distinguished from logic and from psychological origin; the concept of implication is fundamental. Leibniz and Newton could answer derivative questions without defining “derivative,” using pseudo-concepts like “infinitesimally small magnitude” until a proper limit definition arrived. Epistemological analysis similarly possesses answers without questions. Rational reconstruction, sufficient and dispensable constituents, overdeterminateness, nucleus and secondary part, justification and the possibility of error are developed, then applied to heteropsychological cognition: its epistemological nucleus consists of perception of physical phenomena, the heteropsychological being only a secondary part of the physical, via reports, expressive motions, and character plus external conditions.
The Baby-Objection and the Stratified System
An infant may react to its mother’s joyful or sad countenance before learning what such expressions mean. Child psychology has not settled this, and the result stands regardless: even if an adult could recognize a heteropsychological occurrence without prior experience, knowledge would still require prior experiences. Perceiving a knit brow together with fear of rage is not yet knowledge that “A is in a rage” unless prior experiences let the perceiver know such an appearance warrants expecting rage—paralleling recognition of purely physical occurrences. Rational reconstruction does not claim that in actual experience the psychological is inferred from the physical; it claims only a logical dependency, provable because the psychological can afterward be derived by inference from the physical plus prior knowledge.
In all three ways—reports, expressive motions, character plus circumstances—the perception of the physical is epistemologically sufficient and the idea of the heteropsychological dispensable: the physical is the nucleus, the psychological the secondary part. Two criteria apply: justification of the psychological on the basis of the physical, and the possibility of error when the physical is given. A psychologist must state which way his knowledge was obtained; in reports he must cite words heard or read; in expressive motions he must describe observed acts; in the third case he describes perceived circumstances and the subject’s known character. Error is always possible—lies, pretense, play-acting—so the nucleus contains nothing but perceptions of physical events.
Structure, Quasi Objects, and the Neutral Language
Several ideas cut across the whole book and give it its distinctive shape. The first is the distinction between structure and content. Carnap argues that every scientific statement can in principle be replaced by a structural definite description of its object, and since there is only one object domain, every scientific statement can be transformed into a pure structure statement. This transformation is not merely possible but imperative, because science speaks of the objective, while whatever is material—pointable out in ostensive definition—is subjective. Physics, he notes, is almost wholly desubjectivized. Since each subject’s stream of experience differs, agreement can be achieved only through formal description of structure, not content; how uniform construction rules yield entities with the same structure for all subjects is the problem of intersubjective reality.
The second is the machinery of quasi objects and constructional levels. Step-by-step construction from basic objects via class and relation construction yields stratified levels, each a domain of quasi objects relative to the preceding. This reconciles the unity of the object domain with the multiplicity of independent object types: logically science concerns one domain, but practically its statements concern many allogeneous constructed entities. A quasi object “holds” for its elements, which “have being,” and this relationship repeats level to level—classes hold for things, cardinal numbers for classes, fractions for cardinal numbers, real numbers for fractions, complex numbers for real numbers. Being and holding are relative.
The third is the neutrality of constructional language. Carnap insists that constructional definitions can be formed by translating indicator-statements from realistic language, and once the two languages are seen as expressing the same state of affairs, most epistemological disputes become pointless. Realistic and constructional languages have the same meaning and are both neutral on realism versus idealism. “Quasi object” designates a relation, not a denial of metaphysical reality. The controversy over whether objects are “created” or “apprehended” is, in his bold formulation, an idle linguistic dispute: object and concept are one and the same—not a reification of the concept but a “functionalization” of the object.
The Given, the Self, and the Autopsychological Basis
Carnap’s choice of basis is among the book’s most debated moves. He selects “my experiences”—elementary experiences taken in their total, undivided unity—as basic elements, an autopsychological basis. He argues that choosing psychological atoms, simple sensations in Mach’s manner, would take abstractions rather than the given as basic; to agree with the epistemic order, we must proceed from experiences in their totality, with constituents derived by abstraction. This aligns him with the Gestalt theorists and with Schlick’s view that every state of consciousness is a unit, not strictly analyzable.
The egocentric starting point seems to threaten subjectivism, and Carnap confronts the worry directly. Calling an experience “egocentric” only makes sense once we speak of others’ experiences constructed from “mine.” Any duality in basic experience—a correlation between object and subject—must be denied; the self-object division, he suggests, results from a synthesis carried out in analogy to spatial ordering in visual impressions, and the blind, from tactile impressions, do not arrive at subject-object dualism at all. Objectivity, in the sense of independence from the judging subject, is then secured through structure: certain structural properties are analogous for all streams of experience, and science must restrict itself to statements about structures.
Because basic elements are unanalyzable units, construction can never be analytic; it is always synthetic. To construct the constituents of experience anyway, Carnap introduces quasi analysis, derived from the Frege-Russell principle of abstraction: unanalyzable units, given “only in point form,” are handled synthetically so that the results formally substitute for proper analysis. His example is a chord: the chord c-e-g is a uniform totality, not composed of parts, yet it belongs to three chord classes because it is tone-akin to all chords containing c, e, or g—the impression of tripartition is an intuitively performed quasi analysis. From a single basic relation, the recollection of similarity, he derives quality classes, sense modalities, the visual sense (identified as the sense class whose similarity order has dimension number five), the spatial order of the visual field, the color solid, and a preliminary time order.
Reception, Revision, and Legacy
Carnap returned to the book decades later with unusual candor. In the 1961 preface to the second edition he reaffirms its philosophical orientation—especially its problems and method—while conceding that the restriction to a single basic concept was “too artificial”; he would now prefer several basic concepts, and would choose as basic elements something like Mach’s elements, such as “a red of a certain type at a certain visual field place at a given time.” He also reports favoring a basis of physical things with observable properties over the autopsychological one, offering greater intersubjective agreement and suitability for reconstructing empirical science—a shift developed with Otto Neurath under the name “physicalism.” He gives up the thesis that every concept is explicitly definable in sense-data terms, proposing instead “reduction sentences” for dispositional concepts and, later, postulates and correspondence rules for theoretical concepts. He is no longer satisfied with the book’s treatment of extensionality, proposing a weaker conjecture in its place.
The book’s influence registered through later work: Nelson Goodman’s Structure of Appearance offered a thorough exposition and critique along with a system of his own, and Victor Kraft and Jørgen Jørgensen discussed it in connection with the Vienna Circle. Its companion piece, “Pseudoproblems in Philosophy,” written at the end of 1927, pushed further—condemning all theses about metaphysical reality as pseudostatements, more radical than the Aufbau itself. The Aufbau had been unavailable since the war, its copies and plates destroyed, and its reissue in the 1960s brought a foundational text of logical empiricism back into circulation at the moment when its central ambitions were being scrutinized most closely. What remains instructive is less the finished system than the seriousness of the attempt: a philosopher who insisted that if knowledge really does rest on experience, one ought to be able to show exactly how, concept by concept, the edifice is built.
