Rudolf Carnap’s The Logical Structure of the World (Der logische Aufbau der Welt, 1928) is an explanation of how a logical system of concepts may be based on, or may be reducible to, what is immediately given by direct experience. Carnap’s logical empiricism asserts that all scientific statements may be reducible to structural statements about basic elements of experience. Structural statements may be logical propositions about the formal properties of objects and relations. The formal properties of objects and relations, and not their material properties, may determine their applicability to a logical construction of the world.

By the term "structure" (Aufbau), Carnap refers to all the formal properties of an object or relation. The formal properties of an object (or of a concept, statement, or relation) are those properties which define its logical structure, but not its material content. Scientific statements may describe the structural properties of objects or relations, and may take the form of either property descriptions or relation descriptions. A property description may be concerned with the formal properties of an object or relation. A relation description may be concerned with the relations which may occur between objects, or with the relations which may occur between other relations. A relation description may also take the form of a structure description, which may indicate the relations which are sufficient to determine the structure of an object or the relations which are sufficient to determine the structure of other relations.

Carnap defines a constructional system of objects as a system in which the objects of each level are constructed from objects of more elementary levels of construction. The most elementary level of a constructional system is the level of basic objects, which include basic elements and basic relations. Carnap describes the basic elements of a constructional system as "elementary experiences," which are not constructed but which are immediately given as formal objects.

According to Carnap, the basic objects of a constructional system may be either "autopsychological" (eigenpsychisch) or "heteropsychological" (Frempsychisch). "Autopsychological" objects are objects of a person’s own experience, while "heteropsychological" objects are objects of others' experience. Autopsychological and heteropsychological objects may be objects of subjective experience, but if their formal properties are investigated, then they may also become objects of intersubjective experience. Thus, scientific investigation of the formal properties of objects and relations may transform subjective experience into intersubjective experience, and may transform intersubjective experience into objective knowledge.

Carnap explains that intersubjective correspondence of autopsychological and heteropsychological objects may occur if the objects of a person’s own experience correspond to the objects of others’ experience. Thus, the intersubjective object domain is a unified domain of the autopsychological and the heteropsychological. This unity of the object domain is an important aspect of the logical unity of a constructional system of reality.

Because scientific statements about the structure of objects may be empirically verified, there may be intersubjective agreement about the properties and relations of the objects of a constructional system. Thus, Carnap describes how construction of a logical system of physical or psychological objects may provide knowledge of the intersubjective reality of the objective world.

Two problems which may need to be solved in order to better understand the relations of objects in a constructional system are described by Carnap as the "correlation problem" and the “essence problem.” The "correlation problem" is the problem of determining which objects are involved in a given relation, while the "essence problem" is the problem of determining what relation holds between related objects. According to Carnap, the "correlation problem" may be a scientific problem, while the "essence problem" may be a metaphysical problem.

Another problem which may need to be considered is described by Carnap as the "psychophysical problem." The "psychophysical problem" is the problem of what constitutes the nature of the "psychophysical relation." The "psychophysical relation" is described by Carnap as the relation between a psychological process and a corresponding physical process (e.g. the relation between a sensation and the corresponding neurophysiologic process). Carnap argues that the "psychophysical problem" may be an "essence problem."¹ The essence of the "psychophysical relation" may be a problem for metaphysical inquiry, and may not be a problem which can be answered scientifically.

According to Carnap, the types of objects which may be found in a constructional system include physical, psychological, and cultural objects. Physical and psychological objects may be reducible to each other, and may occur at multiple constructional levels. Cultural objects may be constructed from, and may be reducible to, psychological objects. The mutual reducibility of physical and psychological objects is defined by the fact that statements about physical objects may be transformed into statements about psychological objects, and by the fact that statements about psychological objects may be transformed into statements about physical objects. Physical and psychological objects may be connected by the "psychophysical relation" (whereby a psychological event is related to a corresponding physical event), or may be connected by the "expression relation" (whereby a physical event expresses a psychological event). Other types of objects which may be found in a constructional system include logical, mathematical, and spatial-configurational objects.

Carnap explains that objects may be "autonomous" if they may each have their own sphere. The "sphere" of an object may be defined as the class of objects which are permissible arguments for the same argument-position as that object in any propositional function.² A propositional function may be defined as an incomplete statement which is lacking one or more arguments from its argument-positions. If the names of objects are inserted into the argument-positions of a propositional function, then the propositional function may become a complete statement. According to Carnap, a propositional function which contains only one argument-position may define a property. A propositional function which contains more than one argument-position may define a relation. Objects may be "isogenous" if they are permissible arguments for the same argument-position in a propositional function.³ "Isogenous" (sphärenverwandt) objects share the same object-sphere, but "allogeneous" (sphärenfremd) objects do not. Thus, any differences in the spheres to which allogeneous objects belong must be recognized if logical error is to be avoided.

Carnap maintains that the basic elements of a constructional system cannot be analyzed into their proper constituents. "Elementary experiences" are unanalyzable, because they are not constructed and because they are immediately given to consciousness as the basic elements of a constructional system of reality. Thus, the basic elements of a constructional system of reality cannot be given property descriptions, and can only be given relation descriptions.⁴ The basic elements of a constructional system of reality may not be accessible to proper analysis, but may only be accessible to quasi-analysis, which may reveal their quasi-constituents. Objects at higher levels of construction may be analyzed, but proper analysis of these objects may only proceed until their basic elements have been identified, and further analysis may then be only a quasi-analysis.

Carnap argues that application of the rules of a constructional system may be useful for resolving many philosophical problems. For example, the rules of a constructional system may resolve the problem of what constitutes the essence of an object by clarifying the difference between constructional essence and metaphysical essence. While the constructional essence of an object may be defined by how the object is constructed from basic elements or relations, the metaphysical essence of an object may be defined by the inherent being of the object or by what it is as an object-in-itself.⁵

Carnap explains that the rules of a constructional system may also clarify the problem of whether or not the mind and body are two different substances. According to construction theory, physical and psychological objects are reducible to the same basic elements and relations, and thus they do not arise from different domains. Carnap says that construction theory may also clarify the problem of what defines the nature of the self, in that the self may be defined as a unified expression of elementary experiences.⁶ Construction theory may also clarify the problem of what defines the nature of intentionality, in that the intention relation may not be a unique relation which refers to something outside of itself, but may be a subclass of relations between a given experience and an experiential structure in which that given experience is included.⁷

Carnap argues that construction theory is based on the empirical reality of physical or psychological objects rather than on their metaphysical reality. Construction theory does not assert that physical or psychological objects have an objective reality which is independent of their being recognized as objects of consciousness. If physical or psychological objects had this kind of non-empirical reality, then their reality would not be constructed by cognition and could not be empirically verified. However, construction theory agrees with epistemological realism in asserting that real experiences are objectively different from unreal experiences, and that experiences can become objects of knowledge only insofar as they are real.⁸

According to Carnap, construction theory agrees with transcendental idealism in asserting that empirical objects may be constructed as concepts, and in asserting that only as constructed concepts can physical or psychological objects be integrated into a system of knowledge.⁹ Construction theory also agrees with phenomenalism in asserting that empirical objects are logical constructions which are based on elementary experiences, and in asserting that objective knowledge is limited to what can be constructed from elementary experiences of the world. Thus, Carnap asserts that construction theory does not contradict the epistemological claims of realism, transcendental idealism, and phenomenalism.¹⁰ However, he also emphasizes that construction theory does not support any of the conflicting metaphysical claims of these different schools of thought.

¹Rudolf Carnap, The Logical Structure of the World & Pseudoprolems in Philosophy, translated by Rolf A. George (Berkeley: University of California Press, 1969), p. 37.
²Ibid., p. 52.
³Ibid., pp. 51-2.
⁴Ibid., p. 111.
⁵Ibid., p. 256.
⁶Ibid., p. 260.
⁷Ibid., p. 299.
⁸Ibid., p. 284.
⁹Ibid., p. 285.
¹⁰Ibid., p.284.

Carnap, Rudolf. The Logical Structure of the World & Pseudoproblems in Philosophy. Translated by Rolf A. George. Berkeley: University of California Press, 1967.