Husserl and Carnap on regions and formal categories

HUSSERL AND CARNAP ON REGIONS AND FORMAL CATEGORIES ANSTEN KLEV Abstract. Husserl, in his doctrine of categories, distinguishes what he calls regions from what he calls formal categories. The former are most general domains, while the latter are topic-neutral concepts that apply across all domains. Husserl’s understanding of these notions of category is here discussed in detail. It is, moreover, argued that similar notions of category may be recognized in Carnap’s Der logische Aufbau der Welt. As conceived of in the Ideas,1 phenomenology is what Husserl calls an eidetic science: it deals not with matters of fact, but with Wesen or eidē, what in the English literature on Husserl are usually called essences. Clarification of the nature of phenomenology therefore requires clarification of what is understood by such essences, something Husserl sets out to provide in the first section of the Ideas, constructively in its first chapter (§§ 1–17) and critically in its second chapter (§§ 18–26). In the course of that constructive clarification Husserl introduces the distinction between regions and formal categories. The distinction is meant to capture the different senses that the word ‘category’ has when one speaks on the one hand about the categories of the physical and the mental and on the other hand about the categories of individual and property: the former are most general domains, most general topics, while the latter are topic-neutral concepts that apply across all domains. In the words of Ryle (1954, p. 116), who coined the term ‘topicneutral’, regions may be said to provide “the fat and the lean,” and formal categories the “joints and tendons,” of thought. In the following pages I wish to take a closer look at this distinction, concentrating on how Husserl understood it around the time of the Ideas and on how Rudolf Carnap in his Der logische Aufbau der Welt (Carnap, 1928) may have understood it. To deal with categories in an anthology on the philosophy of logic and mathematics in Husserl is justified not only on the grounds that Husserl appears to have regarded the general theory of categories as belonging to logic,2 but also on the grounds of the close ties that have existed between logic and the doctrine of categories throughout the history of philosophy. Although Aristotle may not have 1 That is the abbreviation used here for Ideen zu einer reinen Phänomenologie und phänomenologische Philosophie (Husserl, 1913). References to this work are of the form Ideen + paragraph number. References to the two other books of the Ideas, (Husserl, 1952a) and (Husserl, 1952b), not published during Husserl’s lifetime, are of the form Ideen + book number + paragraph number. References to the Logische Untersuchungen (Husserl, 1901) are of the form LU + investigation number + paragraph number. Its first volume, Prolegomena zur reinen Logik (Husserl, 1900), is abbreviated Prolegomena. 2 See the title of Ideen § 17 and also Prolegomena § 67. Husserl included a general discussion of regions and formal categories in his lectures on the theory of science; see Husserl (1996, pp. 274–286). 1 2 ANSTEN KLEV regarded the piece of writing now known as his Categories as belonging to logic, his ancient commentators since Andronicus of Rhodes in the 1st century bc did so regard it.3 The reason given for this, for instance by the commentator Simplicius (6th century ad), is that the Categories deals with the doctrine of terms, which— since syllogisms are composed of judgements, and judgements of terms—has to be taught as the first part of logic.4 Kant’s doctrine of categories falls under his socalled transcendental logic, and is intrinsically tied to the notion of judgement in general and to the so-called forms of judgement in traditional logic in particular.5 That type theory, a cornerstone of modern logic, may be regarded as a doctrine of categories was noted already by Ryle (1938, p. 189). I shall concentrate on the general theory of regions and formal categories, and hence avoid questions about the specific nature of the various regions and formal categories that come up for discussion in Husserl’s work. Such questions would be proper to a different kind of study, dealing for instance with the notions of nature and spirit (Geist) in Husserl’s work.6 The distinction between regions and formal categories is not intrinsically tied up with phenomenology or Husserlian doctrine; indeed, I think it is of use to anyone reflecting on the notion of category. The second part of this paper will investigate how the distinction can be understood in the context of simple type theory. This is where Carnap’s Aufbau enters the picture, since that work can be seen as suggesting one way in which regions can be mapped onto a simple type hierarchy. Carnap attended Husserl’s advanced seminar Phänomenologische Übungungen für Fortgeschrittene in the winter semester of 1923/24,7 and the influence of Husserl on Carnap’s dissertation, Der Raum (Carnap, 1922), is obvious.8 Husserl’s influence on the Aufbau is more difficult to assess. Mayer (1991) argues for “numerous systematical and terminological parallels” between the Aufbau and the Ideas. According to Roy (2004), Carnap regarded the Aufbau as a realization of Husserl’s idea of a mathesis of experience, an axiomatic counterpart to phenomenology (cf. Ideen §§ 71–75). Rosado Haddock (2008) likewise claims that Husserl’s influence on the Aufbau was decisive. The understanding of an important aspect of Carnap’s Aufbau in terms of a distinction from Husserl’s Ideas suggested in the present paper can indeed be taken as an indication of the influence of the latter on the former. In 3 It was Andronicus who placed the Categories first in the Organon and the Organon first in the list of Aristotle’s works (cf. Gottschalk, 1990, p. 66). 4 For a critical reading of Simplicius’s argument, see Morrison (2005). 5 For the background of Kant’s table of judgements in traditional logic, see Tonelli (1966). 6 A good place to begin such a study is the Einleitung des Herasugebers in (Husserl, 2001c). 7 This is clear from Carnap’s diaries of this period: on 21.11.1923 Carnap reports that Husserl has allowed him to participate in his seminar, meeting at 11.00 every Wednesday (cf. Schumann, 1977, p. 273); after that date and until the end of February 1924 Carnap regularly mentions ‘Husserl’ on Wednesdays. What the topic of the seminar was, I do not know. On 13.11.1923 Carnap attended Husserl’s class on Erste Philosophie; Husserl’s notes for the lecture that day (cf. Schumann, 1977, p. 275) can be found in (Husserl, 1956, pp. 44–51). In his diary Carnap writes ‘nicht sehr gefallen’. Landgrebe reported in 1976 to Schumann that Carnap followed Husserl’s seminars “SS 1924–SS 1925” (Schumann, 1977, p. 281). By considering Carnap’s diary entries on Wednesdays during that year—when, as in the previous years, the seminar met—one sees that this cannot be correct. 8 For more details, see especially Stone (2010), but also Sarkar (2003) and Rosado Haddock (2008, ch. 1). HUSSERL AND CARNAP 3 the final section of this paper I shall nevertheless express some reservations against making too much of the proposed parallels between these works. 1. Husserl on regions and formal categories 1.1. Region. It is a fundamental philosophical problem, according to Husserl, both to find out what regions there are (Ideen § 17) and to understand the nature of a given region and the interdependence of various regions on each other (ibid. § 152). Husserl is, as far as I have seen, never quite definite on what regions he takes there to be. It is clear that he regards physical or material nature and (pure) consciousness as two regions. An individual falling under the first of these is a physical thing and an individual falling under the second is an experience (Erlebnis), hence Husserl also speaks of these regions as the regions of physical thing and experience, respectively. Other regions Husserl mentions in the three books known as the Ideas include the region of the body (cf. Ideen III §§ 2–3), living nature (animalische Natur ), and the region of society and culture (die Geistige Welt). But it is not clear from the discussion in those works whether these are all distinct, nor whether any of them encompasses several regions. Is the region of the body separate from the region of living nature? Persons, which Husserl distinguishes from living human beings, are individuals of the region of culture and society, as are institutions and nations, and also works of art; should not these be taken to belong to separate regions? It lies outside the scope of this paper to discuss these questions as well as the question of how the region of pure consciousness relates to the other regions. Before considering Husserl’s rather technical definition of the notion of region, let us look at three important characteristics he takes regions to have. Especially important is the connection Husserl sees between regions and modes of original awareness of objects. For each region there is an original mode of awareness of objects of that region, a type of act in which items of that region are, as Husserl would say, “self-given.” There is, in other words, for each region a mode of consciousness in which one has direct access to objects of that region. This connection is stated especially succinctly in Experience and Judgement § 4: every kind of object has its kind of being self-given.9 Similar formulations are found at many other places (e.g. Ideen §§ 1, 138). That Husserl assumes this connection is also clear from the individual discussions of the various regions, since he there typically states what is the mode of access to the region in question. We access the region of nature through ordinary perception (e.g. loc. cit.). Such perception is in fact the paradigmatic instance of a mode of original awareness, and other original modes of awareness may by analogy be called perception of objects of the kind in question. Being an original mode of awareness, perception contrasts with, for instance, remembrance and phantasy, in which the object is not present before one. The original mode of awareness of experiences, i.e., the objects of the region of pure consciousness, is phenomenological reflection (ibid. §§ 77–78). That this reflection is qualified as phenomenological means that it involves the phenomenological reduction; only when the reduction has been carried out can pure consciousness be disclosed to us (ibid. § 50). One becomes originally 9 Husserl (1939, p. 12): “jede Art der Gegenständen hat ihre Art der Selbstgebung.” 4 ANSTEN KLEV aware of the body in what Husserl calls bodily apprehension (Ideen II § 36; Ideen III § 2). The individuals in the region of the body are localized sensations, namely sensations localized in the body (Husserl calls such sensations “Empfindnisse”). In order to apprehend these sensations a special form of apprehension is required, since usually sensations are apprehended as things in the outer world.10 I touch this table; I then speak of the sensations in my fingers on the basis of bodily sensations, but of the surface of the table on the basis of a perceptive apprehension. It is in the former sort of apprehension that I am aware of the body as a region. For the region of living beings, and that of society and culture, empathy (Einfühlung) plays an important role, but it is not clear to me whether Husserl regards empathy as an original mode of awareness; the question need not be settled here. A region is, furthermore, said to prescribe a rule for how we may vary an individual of that region in imagination so that it still remains an individual, in other words, so that we still have a unitary course of experience of an individual (Ideen §§ 142, 149, 150; Ideen III § 7). Less general concepts, for instance the concept of a diamond, may also be regarded as prescribing a rule for the course of experience, for instance that the thing posited as a diamond does not bounce back in our hands in the manner of a bouncy ball when we let it fall to the ground. But we can still imagine a continuous transformation of the diamond into a bouncy ball without our experience falling apart into a series of disconnected appearances; in fact we can imagine the diamond being continuously transformed into any other physical thing, namely so long as we remain inside the region of material nature. Husserl’s discussion of imaginative variation in the cited paragraphs relies on the region in question being that of nature, but he appears to have thought that the discussion would generalize to other regions.11 A third characteristic of regions concern their relation to sciences. A region gives rise to several “ontologies,” that is, to eidetic sciences of concepts that compose the region (Ideen §§ 9, 16). In the case of nature, there is for instance geometry as the ontology of space, and there should likewise be ontologies of time (pure chronology), of movement (pure phoronomy), and of matter, since space, time, and matter are all involved in the constitution of physical objects. As a matter of fact, most ontologies have not been developed in any systematic fashion, but such developments are in principle possible. Indeed, ontologies are indispensable to the foundations of empirical sciences: any such science studies objects of some region, and so assumes the results of the ontologies associated with that region. Natural science, for instance, assumes the results of geometry and of all the other ontologies of nature (ibid. §§ 8, 9). Let us now consider Husserl’s technical definition of the notion of a region (Ideen I § 16): 10 This is the so-called content/apprehension scheme; see Klev (2013) for more details. The so-called method of eidetic variation is discussed in more detail by Husserl in lecture notes from 1925 (Husserl, 1968, 69–87). Husserl notes there how the notion of genus is reached through such variation (ibid. 81–84). 11 HUSSERL AND CARNAP 5 A region is nothing but the total highest genus-unity belonging to a concretum, that is, the essential unity of the highest genera to which the lowest differentiae within the concretum belongs.12 Several glosses are needed in order to make sense of this.13 In particular, it must be clarified what is here meant by a highest genus, a lowest differentiae, a concretum, and by the belonging of lowest differentiae to a concretum. For the purposes of this paper we may think of Husserlian essences as objectified concepts. Essences, according to Husserl, fall into an ordering of genera and species (ibid. § 12); thus, one essence is a genus of another essence if it is more general than it; it is the species of another if it is more specific than it. That concepts, or terms, may be ordered in this way is a traditional idea, found already in Aristotle’s Topics and often associated with the philosopher Porphyry (3rd century ad), who in his so-called Isagoge remarked that14 Substance is itself a genus. Under it is body, and under body animate body, under which is animal; under animal is rational animal, under which is man; and under man are Socrates and Plato and particular men. Another, related, traditional doctrine in the logic of concepts is that of the content and extension of a concept: the content of a concept are all the various concepts that compose it, its marks (Merkmale); by the extension of a concept C one understood either all concepts of which C is a mark or all individuals falling under C.15 Husserl takes over this doctrine as well. Thus, an essence is said to contain all essences that are marks of it (Ideen § 12); as we shall see in more detail below, the use of the verb ‘to belong’ in Husserl’s definition of region refers to this notion of essence containment. Among the marks of an essence are its genera; hence an essence contains all of its genera.16 Not all essences contained in an essence are genera of it, 12 Husserl (1976, p. 36): “Region is nichts anderes als die g e s a m t e z u e i n e m K o n k r e t u m g e h ö r i g e o b e r s t e G a t t u n g s e i n h e i t, also die weseneinheitliche Verknüpfung der obersten Gattungen, die den niedersten Differenzen innerhalb des Konkretums zugehören.” 13 The only extended discussion of Husserl’s definition of region of which I am aware is Stone (2000, pp. 97–131). A brief discussion of Husserl’s technical definition can also be found in Null (1989, pp. 93–95). 14 The translation is taken from Barnes (2003, p. 6). 15The doctrine is found, for instance, in the Port-Royal Logique (I.vii): J’appelle comprehension de l’idée, les attributs qu’elle enferme en soi, & qu’on ne lui peut ôter sans la détruire, comme la comprehension de l’idée du triangle enferme extension, figure, trois lignes, trois angles, & l’égalité de ces trois angles à deux droits, &c. J’appelle étendue de l’idée, les sujets à qui cette idée convenient, ce qu’on appelle les inferieurs d’un terme general, qui à leur égard est appelleé superieur, comme l’idée du triangle en general s’étend à toutes les diverses especes de triangles. Here extension appears to be understood in the first sense. Leibniz considered extension also in the second sense (cf. Kauppi, 1971). The doctrine seems to be have been much discussed by German logicians in the 19th century and was well known to Husserl; it is, for instance, taken for granted in (Husserl, 1891a) and it plays an important role in his 1896 logic lecture notes (Husserl, 2001b). 16This doctrine can be found in Aristotle; see Metaphysics ∆ 25, 1023b 24: “the genus is called a part of the species.” 6 ANSTEN KLEV however; in Husserl’s terminology, these are the differentiae of the essence.17 Quite in line with the tradition, Husserl further distinguishes two notions of extension of an essence (Ideen § 13). The eidetical extension of an essence g is the collection of all the essences of which g is a genus. The other notion of extension—which Husserl does not give a name—is the collection of all possible instances—be they existent or not—of the essence, the collection of all the various “thisnesses” (Diesheiten) that instantiate the essence.18 Thus, a particular human being instantiates the essence human being, and a particular green inhering in the cover of a particular copy of a book instantiates the essence green. A lowest species in the ordering of genera and species is called an eidetic singularity by Husserl. Let s be an eidetic singularity falling under the essence g; calling s an eidetic singularity is motivated by the fact that any two instances of s are essentially identical g’s.19 For instance, if s is an eidetic singularity falling under the essence colour, then any two instances of s are essentially identical colours. An eidetic singularity s is either dependent or independent (LU III §§ 13, 21; Ideen § 15). It is dependent if there is another essence s′ , not contained in s, such that an instance of s cannot exist without an instance of s′ .20 For instance, the shape of this table cannot exist without some colour, that is without an instance of the essence colour. It is also true that this table itself cannot exist without some colour, but the essence colour is contained in the essence table, hence that fact does not make an eidetic singularity falling under the essence table dependent. An eidetic singularity is independent if it is not dependent. An independent essence is called a concretum and a dependent essence an abstractum.21 An instance of an abstractum is thus what is often called a trope in the contemporary literature.22 Husserl defines an individual to be the instance of a concretum (Ideen § 15). An abstractum may be said to have several instances, differentiated by what they inhere in. Thus, a most specific shade of green has an instance in the cover of two books on my desk, and these instances, although they are essentially identical colours, differ in that they inhere in different books. Since an instance of a concretum does not inhere in anything else, it is unique: it cannot be differentiated from some other instance of the same concretum by reference to the individual it inheres in. Thus, to each individual there is associated a concretum that is unique to it, 17 In traditional terms, these are the so-called constitutive, rather than the divisive, differentiae of the essence in question. This distinction seems to have been introduced by Porphyry. 18Instead of ‘thisness’ Husserl more frequently (Ideen § 14) employs ‘this-here’ (Dies-da), which he takes as a translation of Aristotle’s tode ti. ‘Thisness’ has the advantage of allowing a plural form. The distinction between thisnesses and essences is discussed in several research manuscripts from 1917/18, in particular in (Husserl, 2001a, Texte Nr. 16–17) and (Husserl, 2012, pp. 112–154). 19The assertion that there are concepts under which at most one object fall (which does not have to be an individual) can be found already in Husserl’s 1896 logic lecture notes (Husserl, 2001b, 124). On this topic, see also the texts cited in the previous footnote 18. 20This definition is adapted from LU III §§ 13, 21. The requirement that s′ not be contained in s is not stated by Husserl, but Simons (1982, p. 125) states something like it in his gloss on the definition of the related notion of foundation from LU III § 14. The definition given at Ideen § 15 is that s is dependent when it founds together with another essence s′ “the unity of one essence”; I shall not discuss the relation of this definition to the ones found in LU III. 21 This terminology was introduced in LU III § 17. For Husserl’s use of the word ‘abstract’ see also LU II §§ 40–42. 22 The use of the term ‘trope’ in this sense originates in (Williams, 1953); Stout (1923) had spoken about the same things as ‘abstract particulars’, in line with Husserl’s use of the word ‘abstract’. HUSSERL AND CARNAP 7 and which may be identified with the essence of that individual. Because of the potential infinity of individuals, there are also potentially infinite eidetic singularities. At this point Husserl is in disagreement with the tradition, since according to it the “division” of a concept into species should be dichotomous or at least finite,23 while the potential infinity of lowest species requires that at least one division in the ordering be potentially infinite. A differentia is itself an essence, hence it itself falls into an ordering of genera and species; whence it makes sense to speak of lowest differentiae contained in a concretum: these are differentiae that within their respective genus/species-orderings are lowest species. To each aspect of an individual there is a differentia contained in the concretum c that the individual instantiates. Under this differentia d there falls a lowest species s, which also must be contained in the concretum c, since it is only by virtue of c’s containing s that it contains d. For instance, any physical thing is coloured, whence any concretum instantiated by a physical thing contains the essence colour; but since the physical thing is coloured only by virtue of having some specific colour, the concretum also contains an eidetic singularity falling under the essence colour. Thus a concretum may be thought of as a union of lowest differentiae, each such differentia corresponding to a specific characteristic of the individual that instantiates the concretum. Husserl appears to assume that if the essence m is a characteristic mark of the essence s, and the essence m′ a genus of m, then m′ is also a characteristic mark of s. In terms of essence containment that is to say that, if m is contained in s and if m′ is a genus of m, then m′ is contained in s. Hence, the highest genus of a lowest differentia contained in a concretum is itself contained in the concretum. We are now better equipped for understanding Husserl’s definition of region. It says that a region is the unification of all the highest genera contained in a concretum. A concretum contains all its characteristic marks; to each of these marks there is associated a highest genus, also contained in the concretum; the unification of all of these highest genera is a region. Husserl is unclear whether the unification of highest genera making up a region is itself an essence—that is, whether the region itself is an essence—but he appears to assume as much at least for the regions of nature and pure consciousness: the region of nature is associated with the essence of physical or material thing, while the region of pure consciousness is associated with the essence of experience (Erlebnis). If a region in general is itself an essence, then a region may simply be defined as the highest genus of a concretum, that is, as the highest genus of an independent eidetic singularity. In any event we can say that a region consists of several essences, each of which is the highest genus within their orderings, and each of which is a characteristic mark of that region.24 1.2. Formal category. Let us now move to the notion of a formal category. As an intuitive description of this notion we may say that it is the form of an object. An 23 See the citations and references provided by (Barnes, 2003, pp. 132–133). 24This idea is spelled out quite explicitly in a short research manuscript apparently written some time between 1924 and 1928 (Husserl, 2012, p. 254): “Jedes Konkrete steht unter einer konkreten “Kategorie”—das ist die “Region.” Jedes Abstrakte als reine Möglichkeit unter einer abstrakten Kategorie, unter einem reinen Wesensbegriff stehend, der Komponente ist der Region.” From elsewhere in the manuscript it is clear that what is here called categories are highest genera. 8 ANSTEN KLEV individual differs in form from a property; a property differs in form from a state of affairs; a state of affairs differs in form from a set. Individual, property, state of affairs, and set may themselves be thought of as forms of object. According to Husserl they are formal categories (e.g. Ideen § 10). Formal categories are topicneutral in the sense that they crosscut the regions, they apply across all regions; for instance, there are individuals and properties in all of the regions. Husserl’s official definition of the notion of formal category relies on the idea of a formal ontology. Formal ontology is the theory of topic-neutral concepts; in Husserl’s words, it is the theory of the notion of an object in general (Gegenstand überhaupt). It studies, for instance, the part-whole relation and the formation of objects by means of categorial forms. A regional ontology is, in contrast to formal ontology, tied to a specific region. A regional ontology is the most general theory of objects falling under a region. Thus, the regional ontology of nature is the most general theory of physical, or material, objects; as already noted, it includes geometry and what Husserl calls phoronomy, the theory of movement. A formal category is defined as a primitive concept of formal ontology (Prolegomena § 67; Ideen § 10). A material or regional category is defined as a primitive concept of a regional ontology (LU III § 11; Ideen § 16). I mention this latter notion here only in order to exhibit the parallel between its definition and that of a formal category. In Husserl’s discussions it features much less prominently than both the notion of region and the notion of formal category. Husserl thinks of an object as a form-matter composite, its material elements being provided by the regions and its formal elements by the formal categories. The picture suggested in the Ideas is that regions consist of certain urelements (Husserl calls them Urgegenständlichkeiten), namely the individuals of that region, together with derivations of those urelements, obtained by means of the formal categories, these derivations being called syntactical objects (ibid. § 11).25 The original mode of awareness associated with the regions, discussed in the previous subsection, are primarily modes of awareness of individuals, that is, of the urelements of the region. Thus, what we are aware of in ordinary perception are the individuals of nature. The syntactical, or categorially formed, objects of nature are not displayed in such acts. Husserl’s doctrine of categorial intuition, developed in the sixth Logical Investigation (LU VI §§ 40–66), is meant to explain how we are originally aware of categorially formed objects.26 There is, for instance, a way of forming, on the basis of a simple perception of a pine tree, a perception of the state of affairs that the pine tree is green (ibid. § 48). There is also a way of forming a perception of finite sets; indeed, the first part of the Philosophy of Arithmetic (Husserl, 1891b) is mainly concerned with describing the nature of such set perception (see also LU VI § 51). Husserl also regarded so-called eidetic intuition—acts in which one perceives, or otherwise intuits, an essence—as an instance of categorial intuition (ibid. § 52); accordingly, he appears to have regarded essence as a formal category (cf. Ideen § 13). 25Note that the Greek word suntaxis simply means a putting together of certain elements, be they words or soldiers or whatnot. 26Lohmar (2008) provides a helpful discussion. HUSSERL AND CARNAP 9 Regions and formal categories are highly general concepts; but they are general in different ways. Husserl captures this difference with his distinction between generalization and formalization: generalization stands to regions as formalization stands to formal categories. In generalization one passes from an essence to a genus of it; in formalization one passes from an object to its formal category. Continued generalization leads to a highest genus, that is, either a region (provided a region is itself an essence), or a highest genus contained in a region. Thus, from yellow we pass to colour and from there, perhaps via some further steps, to sense quality, which according to Husserl is a highest genus (Ideen § 13). The reverse process of generalization is specialization. Continued specialization leads to an eidetic singularity, which may be a concretum or an abstractum. Thus, from colour we pass to blue, and from there, perhaps via some further steps, to a most specific shade of blue. In formalization (Ideen § 13; cf. LU III § 24), or what Husserl also calls pure categorial abstraction (LU VI § 60), we pass from an object to its formal category purely as a form or schema. In formalization we thus replace the material elements of the object by “empty forms” (Leerformen). Perhaps the best illustration of this process is the passage from a presentation of geometry in which the primitive terms have their intuitive, geometrical meaning to a presentation in the style of Hilbert (1899), in which the primitive terms are replaced by variables and the theory becomes “schematic.”27 (Carnap 1922, 7–8 obtains his notion of formal space from the space of traditional Euclidean geometry precisely by this process.) The reverse operation of formalization, in which the empty forms are “filled” again, Husserl calls de-formalization (Entformalisierung) or materialization (Versachlichung). In the geometrical case this corresponds to the passage from the schematic theory to a “model” of it. Husserl also calls formal categories ‘analytic categories’ and material categories ‘synthetic categories’. This terminology derives from his definition of analytic and synthetic laws and propositions (LU III §§ 11–12).28 An analytic law is a true proposition (Satz ) composed only of formal categories (or of concepts signifying formal categories), while a synthetic law is a true proposition whose only material elements are highest genera (or concepts signifying highest genera). An analytic proposition is one that results from an analytic law by materialization, that is, by filling the “empty forms” signifying formal categories with matter; while a synthetic proposition is one that results from a synthetic law by specialization of the highest genera signified in a synthetic law. Husserl gives as an example of an analytic law the proposition that the existence of a whole implies the existence of its parts; an analytic proposition derived from this law is that the existence of a particular house 27Cf. the following remark of Hilbert from lecture notes dated 1894 (Hallett and Majer, 2004, p. 104): Unsere Theorie liefert nur das Schema der Begriffe, die durch die unabänderliche Gesetze der Logik mit einander verknüpft sind. Es bleibt dem menschlichen Verstande überlassen, wie er dieses Schema auf die Erscheinung anwendet, wie er es mit Stoff anfüllt. For more on the relation between Hilbert and Husserl, see Hartimo’s contribution to this volume. 28Husserl made significant revisions in these paragraphs in the second edition of the Logical Investigations, the relevant part of which was published in the same year as the Ideas. For the definition of analytic and synthetic, see also (Husserl, 1996, pp. 227–229). 10 ANSTEN KLEV implies the existence of its roof. An example of a synthetic law would perhaps be that a colour cannot exist without an extension; a synthetic proposition derived from this law is that the brown of this table top cannot exist without the extension of the table top. Among the more well-known definitions of analyticity29—Kant’s, Bolzano’s, Frege’s—Husserl’s is perhaps closest to the latter (cf. Frege, 1884, § 3), since both rest on the distinction between general logical laws and truths pertaining to a specific domain of knowledge, the notion of analyticity being related to the former and that of the synthetic to the latter. Husserl was dissatisfied with, and so tried to avoid, the terms ‘a priori’ and ‘a posteriori’ (cf. Ideen, Intro). According to a traditional interpretation Aristotle’s categories are highest genera.30 Kant’s categories, by contrast, are described as forms of thought (KrV B150, B305). Here we could thus speak of regions and formal categories respectively. It would be mistaken, however, to think that Husserl with his distinction of regions and formal categories synthesizes the doctrines of Aristotle and Kant. Firstly, none of Aristotle’s categories could be regarded as Husserlian regions. In the greater scheme of things Aristotle’s primary substances correspond to Husserlian individuals;31 hence the Aristotelian category of substance splits into all the various Husserlian regions, since these are precisely the highest genera under which individuals fall. The Aristotelian category of quality would presumably be divided between the regions of nature and consciousness. Number is in the Aristotelian category of quantity (Categories, 4b 22), but for Husserl it is a formal category. Secondly, the role categories play in Kant’s philosophy differs from the role formal categories play in Husserl’s philosophy.32 For Kant the categories are concepts of “pure synthesis” (KrV A78/B104). For Husserl, as well, the formal categories are concepts of synthesis. The synthesis corresponding to Husserl’s formal categories, however, has a much narrower scope than the synthesis corresponding to Kant’s categories. The latter is involved in any act; in order, for instance, to perceive objects at all the mind must synthesize a “manifold of intuition,” namely by bringing it under the categories. According to Kant, the unity of an object does not lie in the object itself, to be extracted from it by perception, but is an “achievement of the understanding,” by virtue of which the object has unity in the first place.33 The synthesis corresponding to Husserl’s formal categories, by contrast, is involved only in acts whose objects are higher-level, such as sets and states of affairs. The mind is in general not active in bringing about the unity of objects. The colour and the spatial form of this table, for instance, are not connected by the mind, but are given to it already connected. Likewise, the many “snapshots” I make of the table as I regard it from different sides are not synthesized in the way higher-level objects are synthesized from other objects. We may think of the latter as an active form 29See Sundholm (2013) for a discussion of these. 30A critical discussion of this interpretation can be found in Klev (2014, pp. 15–28). 31Stone (2000, p. 129) accepts this identification. 32On this point, see De Palma (2010). 33E.g. KrV B134–135: “Verbindung liegt aber nicht in den Gegenständen, und kann von ihnen nicht etwa durch Wahrnehmung entlehnt und in den Verstand dadurch allererst aufgenommen werden, sondern ist allein eine Verrichtung des Verstandes, der selbst nichts weiter ist, als das Vermögen, a priori zu verbinden, und das Mannigfaltige gegebener Vorstellungen unter Einheit der Apperzeption zu bringen.” Cf. B129–130. HUSSERL AND CARNAP 11 of synthesis, while the former is passive (LU VI § 47; Ideen II § 9). Kant does not have this distinction between active and passive synthesis.34 He therefore regards all experience as categorially formed; for Husserl, by contrast, only the experience of higher-level objects is categorially formed. 2. Regions in type theory: Carnap’s Aufbau By a simple type hierarchy I shall understand a hierarchy of types or domains of entities of the following design. At the bottom of the hierarchy there are one or more types of individuals. At the next level there is for each natural number n > 0 a type of n-ary relations (a 1-ary relation is a class). Then comes n-ary relations between relations of individuals, and between relations of individuals and individuals, and so on. Such a hierarchy may be recognized in the ideography of Frege’s Grundgesetze der Arithmetik (Frege, 1893), but Frege there described only its first few levels without giving a general definition. It seems to have been Carnap who first provided such a general definition in his logic textbook, Abriss der Logistik (Carnap, 1929).35 Following Frege as well as Russell and Whitehead, who in their Principia Mathematica (Russell and Whitehead, 1910) had developed a more complicated type hierarchy nowadays known as a ramified type hierarchy, Carnap takes there to be only one domain of individuals, which we may denote by ι. The type of classes of individuals is denoted by (ι), that of binary relations of individuals by (ι, ι), the type of ternary relations of individuals by (ι, ι, ι), etc. The type of classes of classes of individuals is denoted by ((ι)), that of binary relations whose first place is a binary relation of individuals and whose second place is an individual is denoted by ((ι, ι), ι), etc. We get the following inductive definition: ι is a type; and if τ1 , . . . , τn are types, then (τ1 , . . . , τn ) is a type, namely the type of n-ary relations whose k-th place is of type τk . It requires little imagination to see that a hierarchy of types offers a system of categories in the sense of general domains of entities. Indeed, from the point of view of modern logic, with its basic form of proposition F (a)—function F applied to argument a—simple types are the first domains of entities one sees, namely as the objectual correlates of the categories of symbols employed in that logic: individual symbols, namely individual variables and constants, perhaps of different sorts; unary functors of individual symbols; binary functors of individual symbols; unary functors of unary functors of individual symbols; and so on.36 It is therefore natural to ask how the distinction between formal categories and regions can be understood against the backdrop of a simple type hierarchy. The related distinction between form and matter is not a part of the doctrine of types, just as it is not a part of the doctrine of modern logic in general. But the form/matter-distinction 34Cf. the criticism of Kant found already in the Philosophy of Arithmetic (Husserl, 1891b, 41): Kant übersah, daß viele inhaltliche Verbindungen uns gegeben sind, bei denen von einer synthetischen, die inhaltliche Verbundenheit schaffenden Tätigkeit nichts zu merken ist. 35Carnap’s role in the dissemination of the simple type hierarchy is discussed in Reck (2004, pp. 163–166). 36The meaning categories (Bedeutungskategorien) of Ajdukiewicz (1935) are of course just simple types. 12 ANSTEN KLEV does suggest a useful distinction between kinds of type hierarchy. Namely, a type hierarchy may be built over the “formal” ground type of individuals—that is, the only information provided about the elements of the ground type is that they are individuals; or it may be built over a “material” ground type, namely some specific domain, like the domain of natural numbers, or the domain of real numbers, or some empirical domain, like that of living beings—in this case more specific information is provided about the nature of the elements of the ground type or types. Distinguishing formal from material ground types is not yet to locate formal and material categories in simple type hierarchies. Husserl’s conception of a region as subsuming individuals together with derivations of these by means of formal categories is in fact readily adapted to the setting of simple types. Namely, we can simply identify a region with a simple type hierarchy built over a single material ground type; thus, each region will be its own type hierarchy. The ground type of each hierarchy is the type of individuals of the region. The higher types contain precisely all the various categorial derivations of the individuals. As formal categories we should therefore recognize ‘individual’ and the forms by means of which higher-type objects—that is, relations—are formed. Precisely which forms these are depends on technical details, but logical operators and an abstraction form, such as lambda-abstraction, will need to be among them. Carnap’s Der logische Aufbau der Welt (Carnap, 1928) suggests another way of mapping regions onto a simple type hierarchy. The stated goal of that work is to provide on the basis of a few primitive concepts a system of definitions of all scientific concepts (§ 1), where science is not to be equated with natural science, but must be taken to include the social sciences, including psychology, and the humanities (Geisteswissenschaften). Such a system of definitions is called a constitution system. Carnap sets out to construct, albeit only in outline, a constitution system by means of a simple type hierarchy with a material ground type. Two kinds of ground type are, according to Carnap, adequate for the task of yielding a constitution system, namely types whose elements are physical and types whose elements are psychological. As Carnap wishes the order of definitions in the constitution system to mirror the order of epistemic priority among concepts (§ 54), he settles on the latter kind of ground type (§ 64), and in particular on a ground type whose elements are my experiences (Erlebnisse) taken “in their totality and complete unity” (§ 67), what Carnap calls elementary experiences (Elementarerlebnisse). That these elements are experiences (in contrast to, say, electrons) and that they are my, the constitution-system-building subject’s, experiences can, however, be seen only after a significant portion of the system has been erected, namely when the domain of the physical has been been constituted, and my psyche has been distinguished from that of other subjects (§ 65). In order to be able to define objects in this type hierarchy one or more primitive relations must be given at the outset (§ 61). According to Carnap it is enough, at least for the outlines of a constitution system he sketches, to assume one such primitive relation, namely a binary relation over the ground type, holding between elementary experiences x and y if the recollection or retention of x is in part similar to y, that is, if a part of y is similar to a part of the recollection or retention of x (§ 78). From this relation, which is asymmetric and irreflexive, it is easy to HUSSERL AND CARNAP 13 define a relation that is symmetric and reflexive and that holds between elementary experiences x and y if these are in part similar to each other, that is, if a part of x is similar to a part of y (§ 77). With these two relations in hand Carnap goes on to define classes and relations of various types that are to serve as “rational reconstructions” of scientific concepts. The definitions quickly get complicated. So called quality classes are to serve as rational reconstructions of particular sense qualities, such as the sensation of a particular shade of red at a particular point in the visual field, or a particular tactile sensation at a particular point on the body. The definition of a quality class is one of the first provided (§ 112), but it already is rather complex and requires several pages of motivation (§ 81). Carnap then defines similarity between quality classes (§ 114) and obtains what he calls sense classes as the transitive closures of quality classes under similarity (§§ 85, 115): two quality classes belong to the same sense class if there is a path of similarity leading from the one to the other; there is, for instance, for any two colour sensations such a path between them. This definition may be straightforward enough, but in order to single out the various sense classes as the visual field, the tactile field, etc., Carnap must appeal to the technically non-trivial topological notion of (inductive) dimension (§§ 86, 115). It is in fact questionable whether all of these initial definitions capture what Carnap intends them to capture, as Goodman (1951, ch. V) noted. Our current interest in the Aufbau stems from the fact that Carnap there takes scientific concepts to be of different kinds, namely, he takes there to be different kinds of object (Gegenstandsarten) (§§ 17–25). These kinds of objects may in the greater scheme of things very well be regarded as regions more or less in the sense of Husserl. Indeed, the kinds of object that mainly concern Carnap are, in his terminology, the self-psychological (das Eigenpsychische), the physical, the otherpsychological (das Fremdpsychische), and the cultural and social (das Geistige), and these may well be taken to correspond to Husserl’s regions of consciousness, nature, living nature, and culture (die geistige Welt). In what follows I shall therefore also call Carnap’s kinds of object ‘regions’. According to Carnap an order of epistemic priority obtains between the various regions: the self-psychological is epistemically prior to the physical, the physical is epistemically prior to the otherpsychological, and the other-psychological is epistemically prior to the cultural and social (§ 58). The constitution system has to reflect this order. Hence we are to think of the regions as forming strata or segments within the type hierarchy. At the bottom of the hierarchy is the region of the self-psychological; then comes a segment with the physical, then a segment with the other-psychological, and finally a segment with the cultural and social region. The formal categories of the hierarchy will be the category of individuals together with the logical forms used in constructing objects of higher types. The latter include the Sheffer stroke, universal quantification over any type, and an abstraction form (§ 107); the abstraction form takes a propositional function ϕ(x) and yields, as the case may be, the proposition or propositional function x̂ϕ(x), where x is no longer free. These logical forms, or formal categories, Carnap calls the Stufenformen of his hierarchy (§ 26): “the recurring forms by which the passage from one level to the next is achieved.” 14 ANSTEN KLEV Let us now consider how the conception of regions as segments in the type hierarchy is to be made precise. It seems to me that in order for the described structure to be realized, the following two requirements must be met. (i) It need not, and usually will not, be the case that all elements of a type are used in a constitution system. That is, within any type, if it is employed at all in the system, there will, in general, be some objects that do serve and some that do not serve as rational reconstructions of concepts. Let us write u(τ ), the use of τ , for those elements of type τ that do in fact serve as rational reconstructions. The first requirement says that all elements of u(τ ) belong to the same region. This is a requirement of typical homogeneity: no type is to be separated by two regions. Let us, for instance, consider the type ((ι)) of classes of classes of elementary experiences. The so-called sense classes mentioned above belong to this type. Since sense classes serve as rational reconstructions of concepts from the self-psychological region, the requirement says that within the type ((ι)) there should not be another object that serves as the reconstruction of a concept belonging to some other region, for instance the region of the physical. If u(τ ) is non-empty, then let us say that the type τ is used. The main rationale for requirement (i) is that, provided it is met, we can define an order on used types as follows: σ ≤ τ if and only if no element of u(τ ) is epistemically prior to an element of u(σ). Thus, if requirement (i) is met, then the relation of epistemic priority among the four regions induces a partial order on used types. For instance, if the elements of u(σ) belong to the region of the physical and the elements of u(τ ) to the region of the other-psychological, then we have σ ≤ τ . If the elements of u(τ ) belong to the region of the self-psychological, however, then we have τ ≤ σ. (ii) Let us call the trace of a type the set of all types involved in its construction from the ground type. For instance, the types involved in the construction of the type ((ι)) are ι and (ι); these are, as it were, the building blocks of that type. The
types involved in the construction of the slightly more complicated type (((ι), ι), ι) are ((ι), ι), (ι), and ι. Continuing to employ ι as a name of the ground type, the trace tr(τ ) of a type τ can be defined inductively as follows: tr(ι) tr((τ1 , . . . , τn )) := := ∅ S {{τ1 , . . . , τn }, tr(τ1 ), . . . , tr(τn )} Thus the trace of a type (τ1 , . . . , τn ) is a set consisting of each of the types τ1 , . . . , τn together with the traces of each of these types. Employing the definition we find for instance that
tr (((ι), ι), ι) = {((ι), ι), (ι), ι}. Recall the order ≤, just defined, of epistemic priority among used types. The second requirement says that we should have σ ≤ τ for all used types σ in tr(τ ). Spelling out the definition of ≤, this is to say that, if σ ∈ tr(τ ), then the objects in u(τ ) are not to be epistemically prior to the objects in u(σ). This requirement gives mathematical expression to the idea that in the definition of an object a that is to serve as a rational reconstruction of some concept c we shall not need to refer to an object serving as the rational reconstruction of some concept c′ that, in view of its region, is epistemically posterior to c. No concept is built up from concepts epistemically posterior to it. HUSSERL AND CARNAP 15 Carnap does not spell out these requirements in the Aufbau. That he entertained a picture of the construction of the world in which they are met is, however, suggested by what he says about levels of constitution (§ 41). The level of constitution of a concept is the level in the type hierarchy at which a rational reconstruction of it is defined. Carnap had defined the notion of level in a simple type hierarchy in the Abriss.37 The level ℓ of the ground type is 0; the level of a higher type (τ1 , . . . , τn ) is defined by
ℓ (τ1 , . . . , τn ) := max{ℓ(τ1 ), . . . , ℓ(τn )} + 1 Those familiar with the cumulative hierarchy of sets will see the parallel to the notion of rank defined in that context. In the picture Carnap appears to entertain the regions respect levels: for used types, σ, τ , it holds that if ℓ(σ) < ℓ(τ ), then σ ≤ τ . We thus have a situation as in Figure 1. The first few levels make up the region Type hierarchy level k + l + m + n level k + l + m level k + l level k level 0 (ground domain) .. . — .. . — .. . — .. . — .. . Elementarerlebnisse Regions  ?  Culture  Other-psychological  Physical  Self-psychological Figure 1. Carnap’s construction of the world? of the self-psychological. The levels afterwards make up the region of the physical, the following levels make up the region of the other-psychological, and finally come the levels of the cultural and social. Whereas each region thus takes up only finitely many levels, the type hierarchy continues into infinity; at levels above those making up the region of culture the romantics among us can therefore imagine a region that is yet to be discovered. While Carnap structures his sketch of a constitution system in the Aufbau according to what he takes to be the regions the self-psychological, the physical, the other-psychological, and culture and society, he also maintains that the possibility of erecting a constitution system shows that there is fundamentally only one region (§ 4): “objects do not fall into different, unconnected domains, rather there is just one domain of objects.” Carnap seems to hold in particular that a constitution system with a self-psychological basis shows that the self-psychological region is, fundamentally, the only region. This view must be based on the assumption that if the ground type of a type hierarchy belongs to a given region, then the whole 37See Carnap (1929, p. 32). 16 ANSTEN KLEV hierarchy belongs to the same region; the region of any type is inherited from the region of the types out of which it is constructed and at the base there is only the one region of the self-psychological. There seems thus to be a tension between ideas such as those expressed in Figure 1 and what Carnap takes constitution theory to show, namely that there is just one region. To relieve this tension it seems to me best to distinguish between concepts before and after constitution. What Carnap calls rational reconstruction is a relation between between these, namely between ordinary scientific concepts on the one hand and relations in a certain type hierarchy on the other. The constituted concepts are ultimately to replace the ordinary scientific concepts, since only of the former do we know the precise definition in terms of elementary experiences (cf. § 179). Ultimately, therefore, it will be seen that there is only one region. For, while we can say of ordinary scientific concepts that they fall into different regions, we should not, according to Carnap, say the same about the constituted concepts. Figure 1 above thus does not show how regions actually live inside a constitution system; rather it shows the type hierarchy of a constitution system through the prism of a division into regions of ordinary scientific concepts; the order of epistemic priority holding between the regions is reflected by the order holding between the relations serving as rational reconstructions of the ordinary scientific concepts falling into those regions. 3. Carnap and Husserl Carnap had studied the Ideas thoroughly. That is clear from the detailed references to different sections of this work not only in the Aufbau but also in Carnap’s dissertation, Der Raum (Carnap, 1922).38 From references in the latter in particular one sees that Carnap was conversant with the distinction between regions and formal categories as well as with the related distinction between generalization and formalization, indeed with all the important notions from the first chapter of the first section of the Ideas.39 It is, however, difficult to say whether Carnap thought of what he called kinds of object (Gegenstandsarten) as Husserlian regions. In the Aufbau Carnap tends to be quite generous with references to the works of others, so if he had Husserlian regions in mind with his notion of kind of object, one would have expected some reference to Husserl at the relevant places, but that is not to be found. It has, however, been noted by Mayer (1991, p. 301, fn. 11), and with greater emphasis by Rosado Haddock (2008), that several apparently Husserlian influences are not indicated as such by Carnap. In § 25 of the Aufbau Carnap lists several kinds of object apart from those already discussed: logical objects, mathematical objects, spatial forms, colours, tones, biological objects, and ethical objects. Neither of these correspond to Husserlian regions (perhaps apart from the logical and 38Christian Damböck, who has studied Carnap’s reading lists, reported in a talk at the HOPOS 2014 meeting at Ghent, 4 July, 2014 that between 1920 and 1923 Carnap worked through the Ideas three times. 39See especially (Carnap, 1922, 60–61), where Carnap compares the relation between the geometries related to the three kinds of space he has been studying with the relation between formal ontology, regional ontology, and factual science (Tatsachenwissenschaft), and where he also employs the distinction between formalization and generalization. The Husserlian notions of essence and eidetic intuition are fundamental to Carnap’s treatment of what he calls intuitive space (ibid. 22–31). HUSSERL AND CARNAP 17 the mathematical objects, which Husserl sometimes (e.g. Ideen § 11) says belong to a formal region), a fact which suggests that Carnap’s notion of kind of object is independent of Husserl’s notion of region; but spatial form, colour, and tone are all essences in the region of nature, which Husserl discusses in the first chapter of the Ideas, so Carnap may have drawn inspiration from those discussions. One should in any event be careful not to make too much of the parallels between the Aufbau and the Ideas. A proper assessment of the relation between these works would require more space than what I have available here, but it should be clear, I think, that the Aufbau in no way can be regarded as a work in phenomenology.40 Carnap’s conception of what he calls constitution is telling. It is not unlikely that he had the term ‘constitution’ from Husserl,41 but his understanding of it is very far from Husserl’s. For Carnap ‘constitution’ means the definition of an object in the simple type hierarchy in terms of others (§ 38). For Husserl, however, ‘constitution’ indicates how an object presents itself to consciousness;42 to describe the constitution of material individuals, for instance, means to describe the various components, or layers, that make up our experience of such objects (cf. Ideen II §§ 12–17). An object in Carnap’s constitution system is to serve as a rational reconstruction of a concept. Carnap emphasizes that the constitution system need not reflect “the syntheses and formations of knowledge as they actually occur in the process of knowledge” (§ 54); rational reconstructions are to preserve only the “logical value” of the original concepts, they need not preserve their “cognitive value” (Erkenntniswert), not their sense (§§ 50–51). One of the more important methods of the Aufbau is called quasi -analysis and the result of an instance of quasi-analysis is said to be a formaler Ersatz for the components that a proper (eigentliche) analysis would yield (§§ 69–71). Such ideas are of course quite foreign to phenomenology, with its emphasis on giving a true description of experience and what is experienced, on merely explicating what originally gives itself in eidetic intuition. References Ajdukiewicz, K. (1935). Die syntaktische Konnexität. Studia Philosophica, 1:1–27. Arnauld, A. and Nicole, P. (1662/1683). La Logique, ou l’art de penser. Iaen Guignart/Guillame Desprez, Paris. Critical edition: Vrin, Paris, 1981. Barnes, J., editor (1984). The Complete Works of Aristotle. Revised Oxford Translations. Princeton University Press, Princeton. Barnes, J. (2003). Porphyry. Introduction. Translated with an Introduction and Commentary. Clarendon Later Ancient Philosophers. Oxford University Press, Oxford. Brockhaus, K. (1976). Konstitution. III. Neuzeit. In Gründer, K. et al., editors, Historisches Wörterbuch der Philosophie, volume 4, pages 997–1004. Schwabe, Basel. 40I take Roy (2004) and Ryckman (2007, pp. 95–98) to argue for the same stance. 41In Kant it is the adjective ‘constitutive’ rather than the noun ‘constitution’ that is prominent (cf. Brockhaus, 1976); ‘constitution’ is apparently employed by the Marburger neo-Kantians Cohen and Natorp (ibid. 1002–1003); but Carnap distances his use of ‘constitution’ from Marburgerschool doctrine in § 5 of the Aufbau. The word features prominently in the Ideas, especially in its final sections, and it may very well have come up in the Husserl seminar Carnap attended; Carnap may also have been familiar, through Ludwig Landgrebe, with the contents of the second book of the Ideas (cf. 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