Husserl’s and Carnap’s Theories of Space

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2.3 The Aufbau75

I think that in order to accurately understand of theoretic-spatial position formulated in the Aufbau we need to assume few things. First we have to assume that we do not possess either an accurate experience of space76 or an eidetic insight into the spatial structure77. If we need to describe the physical space we have to use a precise model elaborated within formal sciences78. On the other hand geometry (here a sub-discipline of the relation theory) can be constructed on the grounds of logic79 being the primary science in the science system80. Second, when scrutinizing space we are interested only in its formal features and they are modeled by geometry.

Concerning the step from the ‘two-dimensional order of visual field’ to the ‘three-dimensional order of visual things’ (the step that is one of the most important ones within the construction of space procedure), the author of the Aufbau refers to different theoretical attitudes those of Russell’s and Husserl’s81. Conversely to the former he claims that he tends to gain the ‘whole visual world’ not a sphere of individual things and on the contrary to the latter Carnap does not assume the two-dimensional field as anything given but as something that must be introduced constructionally82. He asserts that we cannot treat the visual space, a space location, space configurations and spatiality of things as, so to speak, primary beings, but rather as objects subject to the construction83. The system of the Aufbau grasps only the structure of space. However, adds Carnap, the space constructed in it is not an abstract space in geometric sense (i.e. geometric manifold)84.
I have mentioned before about some interpretative difficulties that we encounter when attempting to univocally designate how one could accurately understand The Logical Building of the World anyway I shall try to recreate a compact image, trying to fulfill gaps in explanations that are present in Carnap’s book. We can distinguish generally two attitudes to the problems of space: physicalistic and epistemological ones85. The former is strictly connected with the construction of the ‘all-embracing’ structure of the world86, so only the latter should be connected with the autonomous constituting of the space. The former attitude refers to the theoretic-physical procedures elaborated by A. Eddington, Weyl and H. Minkowski. The space here should be conceived as one of the parameters constituting the reference system for physical events: 1) the relation between electrons, 2) set of relations within a four-dimensional continuum, 3) set of connections between the ‘world-points’ (i.e. elements of the ‘world-lines’ in Minkowskian sense)87. Such conceived the spatial structure of the world would be, as we can think accordingly to the main thesis of the Aufbau88, the fundamental reference system for any intra-world objects or events.

However Carnap points to that he would not like to prejudice which of the above mentioned models is the most adequate to the construction of the ‘world of science’89 and focuses more on epistemologically conceived the ‘constitution of space’. It is grounded upon an epistemico-logical procedure thanks to which there are constituted different levels of the visual space. Probably for Carnap the sensual-qualitative order is primary to any ‘actualization’ or ‘material fulfillment’ of our visual experience structures. The order determines the forming of the experience and those philosophical conceptions that inferred a sphere of the sense qualities out of that what is monosubjective were wrong. Hence we should reach the structure of the experience beginning from the structure of the world and not conversely90.

When building the ‘science system’ we should introduce some ontological and epistemological assumptions. First of all we have to assume that the objects of science are structures, i.e. that it deals only with formal features of objects and relations between the features91. In that manner we perform the first ontological reduction wherein an object is reduced to a web of its formal features. Next procedure consists in reducing the objects of science to the ‘sense qualities’92 or in other Carnapian words, to the ‘elements of our experience’93.

The level of those qualities we attain also by means of an epistemological reduction performed on a structure of our sensual experience. Performing the procedure we abstract from the entire ‘material contents’ of the experience, from its actual process and we have in effect an elementary form of the experience, the form that consists in a certain arrangement/configuration of ‘sense qualities’. Each of subjects of perception, Carnap maintains, has his own sequence of sensual experiences (Erlebnisstrom) and in order to reach a structural congruence with respect to the objects constructed on the grounds of those experiences, we have to refer either to formal features of the objects or to formal features of the experiences wherein the objects appear94. We assume in the same time95 that the subjects’ structures of experience are analogical i.e. that the subject S1 perceives outer objects similarly as S2 (the assumption seems to be necessary when speaking of the ‘science system’)96.

We can illustrate it so that each of subjects {S1, S2, …, Sn} deals with a certain set of physical objects97 {o1, o2, …, on} that are seen by him every day while the sets do not have to be extensionally equal. Moreover, the sets even do not have to have their intersection. Objects seen by me in my house might be never perceived by a subject Sx. In what manner is it possible any intersubjective communication with respect to objects of the world since every one of us possesses his own ‘set’ of them? Accordingly to Carnap we are allowed to do so by the language of science. It is referred to the ‘state of affairs’ (general and special ones)98 and gives us certain indexes99 (Kennzeichen) or more strictly describes us certain conditions that must be fulfilled to such and such state of affairs may occur. Those indexes allow us accurately identify a given object, i.e. the subject knows which states of affairs are to be anticipated in case of such and such objects (e.g. how to recognize ‘rattle-snakes’100). Hence each of subjects {S1, S2, …, Sn} can observe a different rattle-snake while the structural description of the reptile (intersubjectively communicated) would be structurally consistent with the states of affairs occurring within the experiences either of S1, of S2 or Sn. Beside in the science system the construction of some new objects is founded upon a procedure of giving certain conditions of appearing of those objects, of pointing to certain possible states of affairs that should occur if a given object is to be perceived by someone101.

In case of the space theory, accordingly to Carnap, we have to construct such model102 that would 1) conceive structural features of our visual perceptions (we assume that every subjects sees the world analogically i.e. three-dimensionally103), and simultaneously, 2) correspond with the physical objective image of the world. To the above mentioned construction is necessary a ‘visual reduction’ separating the entire and rich contents of our perceptions and founded upon formal features of visual experience (the features are conceived as they were topologico-geometric)104. The procedure performed such way allows us to reduce the visual qualities to certain ‘seen points’ and to submit all the ‘visual space’ to the formal space (elaborated in geometry).

Similarly as in the Chaos there is in the Aufbau a radically reduced sphere of experience. However this time though his use of the visual reduction Carnap claims that he performs also the phenomenological reduction which in his opinion leads to the field of logistico-eidetic researches on the structure of the pure experience105. We have to know that this procedure is not analogical as Husserl’s (i.e. leading to revealing the layer of the ‘pure phenomena of cognition’ and to the ‘pure, absolutely existing consciousness’) but is rather a way to reconstructing the constitutive, logical structure of pure (here: elementary) experience and to the logical structure of the world, or in other words the way to the pure space.

Carnap withholding the entire knowledge about the reality excludes also from the field of his researches the self-consciousness of a subject, asserting that its constitution is possible just after a fulfilling of certain conditions and for sure it cannot be the point of departure of the ‘science system’ that is build in the Aufbau. It allows Carnap to assume logistico-eidetic foundations and then to approach recreating/reconstructing fundamental levels of the reality and dependencies between them. Hence it allows him to perform implicitly something of the kind of the eidetic reduction affording possibilities for the insight into the essential states of affairs106.

The reduction of the monosubjective sphere and assuming a ‘constructionist’ attitude prove that – against Carnap’s declarations - we do not deal here with the phenomenological epoché. Since he wants his theory to be epistemologically neutral107 and refers to the conceptions that do not concern an active role of a subject in the process of perception108. „The given is subjectless”109, he claims referring to Mach, R. von Schubert-Soldern and F. Nietzsche; that means (when we construct space) we should assume that there is seeing (not I can see now)110. ‘I’ is to be constructed at the higher levels of the system.

Husserlian epoché leads to achieving the ‘ultra-cognition’, to the new conscious sight of that what occurs within e.g. our visual perception. In the Aufbau in turn we deal rather with an ‘operational’ use of another ‘ontologico-epistemological’ reduction conducted in order to build next stages of the ‘science system’, one of those is the constructed space. Carnapian epoché might be described as not the ‘stopping of the process of visual perceptions’111 but rather as a completely ‘turning off/extinguishing’ of the view, as an ‘annihilating’ of all the data as if we did not see anything112.

Obviously, in the physiological sense it is not possible (our visual field is always filled with certain ‘sense qualities’), but we can assume that we speak about an ‘empty’ or ‘potential’ visual field, namely about all that can be seen or will be seen (will be filled with our visual perceptions). Let us assume that it means the ‘area behind us’, the area behind our back. Let us assume also that we do not have any possibility to turn back and pointing our perceptions to the area. How can we describe it (structurally and in the connection with our possible experience)?

Not assuming at the beginning all the ‘thing-contents’ of the area we can assume only that this is a certain set of places to which we can match a certain ‘space’ that is in principle a set of points. If we assume that in the area there runs the time we can treat temporally113 (a la Minkowski) those presumed points and all of them comprehend as certain multidimensional continuum of the ‘world-points’114.

The space has to be structured in a way, that means it must be furnished with some complex of possible qualities (e.g. ‘shapeliness of something’, ‘colorfulness’, ‘closer location’, ‘further location’ etc.) that are ready to be visually grasped. However, in order to theoretically describe the entire perceptual situation we need to have a new reduced form of language. Hence Carnap introduces next reductional procedure, so to speak, conceptually-linguistic one, since he argues that we constructionally cannot recreate the structure of our visual experience by means of the natural language or a language of any science. We reduce the sphere of our concepts and of meanings of the language of science referring to the structure and contents of our experience. It is necessary to elaborate a new language not only in terminological respect but first of all in formal one. It has to be a precise and univocal language pointing only to those cognitive situations that are (or are to be) reconstructed within the field of theory of space for example.

We know, Carnap says, that our natural perceiving is done spontaneously and we can only try to reconstruct its formal structure referring to e.g. the phenomenological or psychological researches. We reconstruct and not analyze a process of eventual perceiving, for accordingly to Carnap, the elementary experiences are non-analyzable and non-constructible115. Quasi-analysis of perceptual contents that are present in our visual perceptions is in the same time their ‘linguistic synthesis’116. In other words we recreate the fundamental structure of visual perception by means of geometric and linguistic models. Both of the models (beside the physical one) constitute the foundations of Carnapian theory of cognitive assignments that is meant to explain the informative side of our outer perception.

In the Aufbau there is admitted the mathematic space i.e. the space of real numbers wherein distinguished are so-called world-points. To latter there are then assigned colors117 and then, Carnap adds, to the ‘world-points’ are assigned also the ‘quality classes’ and higher classes as e.g. ‘sense modalities’118. There is also a sequence of peculiar ‘world-points’ called here the ‘view-points’. Certain lines starting at a given ‘view-point’ constitute the ‘view-lines’119. To the ‘view-points’ are then assigned elementary experiences120 and to the ‘view-lines’ – certain ‘visual sensations’ respectively. Next a color apprehended by us within a visual sensation is assigned to a certain ‘world-point’ on a certain ‘view-line’. And in the manner mentioned above there reveal ‘color spots’ , ‘surfaces’ and at the end ‘color solids’ that are visual things (Sehdinge)121. We assume here that there exist a certain minimal changeability conditions that could occur in that visual field122 and possibility of connecting in the course of perception: that what is observed with that what is not observed by means of 1) a succeeding perceiving of a partly seen things or 2) observations of other subjects123.

Then, when some parameters remain still in the visual field, there starts the constitution/construction of a visual thing. We can call it the ‘solid body’ („starr”) if its metric relations remain still. The class of sensations which refer to certain seen points of the given thing is called the ‘aspect’ of the thing124.

There also exists a certain visual solid fulfilling some conditions that allow us name it my corporality (mein Leib). Each state of the thing is close to a certain point of view. My corporality constitutes an open surface when it is seen from a certain point of view. On this level, accordingly to Carnap, we need to construct a correlation between the ‘world-lines’ of my corporality and the qualities (or ‘quality classes’) of a certain sense, because in effect of adjoining of the ‘world-lines’ of mL with 1) other part of mL or 2) a different visual thing, there constitutes a ‘tactile quality’. Simultaneously there is constructed another correlation, that of certain movements of mL with qualities of a different ‘sense class’ called the kinesthetic sense125.

mL has other constructible features, i.e. 1) a still presence in the visual field, 2) an openness of a surface (mL is not seen wholly), 3) referring of the places on the surface of mL to the qualities grasped with the tactile sense, and 4) referring of the sense qualities received by the kinesthetic senses to the movements of mL126. My corporality hence is constructed as a thing specifically spatial for ‘tactilely-visual’ one127, Carnap concludes, adding then that just after, namely on the background of the above mentioned correlation between the sphere of qualities and the spatial sphere, we can talk about the construction of subject and so-called my consciousness128.

The ‘tactilely-visual’ things become ‘perceptible’ ones when we assign them sense qualities. The ‘world of perception’ in turn is constructed on the ground of analogical i.e. embracing all areas of things two postulates of causality and substantiality. Using of the postulates (the same as all epistemological construction procedures) is, accordingly to Carnap, based empirically, for these postulates have been abstracted from our experience129. We can use them in the procedure of joining seen ‘color-points’ with unseen ones and ‘touched points’ with untouched ones130. The full field of our perception (‘the world of perception’) is constituted on the ground of the assignment of the sense qualities to the ‘world-points’ (e.g. we can assign a green color to the leafage seen by us).

The omitting in the Aufbau the material contents of our visual perception is supposed to allow Carnap to analyze only its formal features131. The ‘world-points’ as we know from Minkowski’s theory picture some physical events while the ‘world-lines’ picture all sequences of those events i.e. ‘the history of a given objects’. Hence we can interpret the early thought of Carnap in a new manner (different than Goodman’s). We can epistemologically assume that the Aufbau ‘world-points’ are 1) formal pictures of ‘histories’ of certain quality areas of our sensual experience and/or 2) formal pictures or ‘histories’ of certain quality qualifications of a perceived object. (Those ‘world-points’ would be assigned under some conditions to some areas of the physical world)132.

A little enigmatic (and the same claims its discoverer from the Aufbau)133 seems to be so-called ‘physico-qualitatative’ correlation posed by Carnap as a fundamental step completing the construction of the world of physics134. It is to be consisted in that the ‘world-points’ of physics (i.e. certain events) are in one-one relation with the ‘world-points’ of the perception world. The author of the Chaos adds that the metric of the farmer world can differ from that of the latter (the first can be non-Euclidean) hence from the side of our visual experience (i.e. from the ‘sense qualities’) there would have to be one-many relation between the sense qualities and physical magnitudes135. Unfortunately here his description of the fundamental step connecting the sphere of perception with that of events in physics’ sense finishes136.

Carnap after all points to that the constructed full area of perception is not an important level of the ‘system of science’. The perceptual world is an occasional construct in the progress of our knowledge137 since the last level is the quality-free world of physics. Moreover, he argues, we cannot say about the objects located in the sphere of our perceptions that they are real in the same sense as the ‘reality’ is defined by science.

3. Terminological and methodological kinships between conceptions of early Carnap and Husserl.
I think that after the sketchy compilation of the opinions of the two philosophers we can speak of certain program concurrences that shortly could be expressed such: philosophy as a strict science, neutralisticly conceived epistemology, formal ontology as a theory that gives some conceptual grounds for the system of other scientific (non-philosophical) disciplines, logic as a meta-ontology. However, there are many divergences: absolutistic-maximalistic conception of phenomenology contradicts with the minimalistic-conventionalist and methodologically dogmatic the logistic conception of the constitution/construction theory. Moreover the author of the Ideen is interested in the ‘phenomenon of the world’ while the author of the Logical Building of the World focuses on the ‘fact of science’.

In both mentioned theories we can notice the terminological similarities (‘epoché’, Konstitution, ‘kinaesthesis’, ‘eidetic’, Körper, Erlebnisstrom, mein Leib, Retention etc.) and methodological ones (analysis of aprioric structure of experience, various reduction procedures, geometrizing analysis of perception and methododologically solipsistic perspective). At the same time Husserl and Carnap uses many different terms138 and methods and besides (in Carnap) there is a substantial modification of meanings of similarly sounding expressions (e.g. the Konstitution) and modificating of uses of certain philosophical procedures (e.g. ‘Wesensanschauung’ in the Raum, ‘phenomenological reduction’ in the Aufbau). First of all (and perhaps that is the point), Husserl treats space continually and Carnap conceives it as discrete (i.e. atomisticly)139.

Both of the philosophers maintain that the content of our perception is sensual qualities and at the lowest level of our perceiving of space is so-called two-dimensional visual field140. Though Husserl and Carnap disagree with the atomistic attitudes in the theory of outer perception, they many times say that the sensual stage/layer of our cognition is irreducible at all. The founder of phenomenological school considers sensual data as so-called ‘pre-objects’ and the author of The Logical Building of the World thinks of sensual qualities as fundamental, cognitive elements of an elementary scientific experience (in Carnapian sense). Despite their considering the sense qualities as ‘abstracted’ from the contents of perceiving both of them begin with the pure sensuous sphere when describing the building of our knowledge on spatial world – in Husserl we have ‘sensuous fields’ and in Carnap ‘sense classes’ that ‘activate’ the suitable sensual modalities in a subject’s cognitive apparatus.

In their descriptions and explanations of our seeing the spatial they use the method of geometrization of perception (it includes even the structure or contents of acts of perceiving). Whereas Husserl uses it in a special phenomenological manner, as it was mentioned earlier the author of the Logical Syntax having assumed geometry as a theory constructible with the tools of logic, he tries to use the formal (abstract) model of space even to reconstruct the structure of our visual perception or to construct the structure of the physical space141.

At the roots of the use of such procedure by Husserl and Carnap there is, I think, an obvious assumption that our world is three-dimensional, extending in three directions and filled with variously structured and shaped bodies. If we want to know its spatial layer we should use the theory of ‘pure spatial shapes’. However, both of them do not scrutinize in principle the seeing of depth i.e. that which way in different types of visual experiences the three-dimensionality of the world itself appears to us142. The author of the Ideas starts his researches from analyses of an isolated spatial object while the author of the Raum constructs the (empty at the beginning) ‘pure space of perception’ ex post constructing the physical space (he passes from one model to another). We do not have to add that the latter’s epistemology is anti-realistic143.

Meanwhile, I believe, at the beginning of theoretic-spatial research we should neither perform Husserlian visual isolation nor Carnapian visual reduction, but rather the ‘decentralization of our seeing’. Since our every glance is usually focused, namely it is concentrated on a certain object isolated from the surroundings then to the analysis of our visual perception we should elaborate the decentralized type of seeing wherein we apprehend only an aspect (some aspects) of the depth of all things seen at the moment. In that ‘ultra-cognitive’ look144 the solidity of physical objects is given to us simultaneously and multi-fariously; moreover it shows different features in the course of our stationary perception than when we perceive in our movement (or our being moved). The depth seen by us when we stand inside the church is ‘frozen’ or ‘ossified’ while the depths seen when we drive into the town is ‘plastic’, it is subject to the never-ending ‘metamorphoses’; the solidity of objects ‘bulges’ or ‘flattens’ (depending on our coming to them or driving away) and it also ‘opens’ and ‘bursts’ (if suddenly perpendicularly to the direction of our drive we can see a street debouching down with some new objects on the both sides of it. Certainly, the space seen that way, i.e. the ‘depth of the world’, is not a container for physical objects but rather their ‘multi-shape’ it is constituted by their structuring and their distributing (locations) – however we discover the space, it surprises us with its various formation. It is not a result of our intentional activity nor any construct within the domain of our visual perception.


The issue of meeting of those two thinkers on the theoretical ground is not so insignificant as Carnap wanted to see it after his leaving Europe and arriving to the USA. On the contrary it can be very fruitful in explaining the progress of almost whole the American philosophy of the first half of XX century145 which he was one of the most important members146. Certainly, Carnap did not follow Husserl, but something had to fascinate him since he wrote under the influence of Husserl as we saw. If somebody asked what was it? I would answer univocally: Husserlian conception of the constitution of space (and connected with it the constitution of the world), and perhaps the conception of philosophical researches introduced in the Logische Untersuchungen.

No doubt that the author of the Raum did not carry his own researches on perception processes; the evidence to it is the sketchiness of descriptions and explanations and the lack of any neither epistemological assumptions nor examples showing different perceptual situations. In the same time, as I showed, he referred to the solutions elaborated within the phenomenology of space, to its terminology and methodology; he did so selectively and modifying it using also the tools taken from formal sciences. All of that allows us, I believe, to name Carnap’s researches to the Aufbau an attempt of logistic criticism of Husserlian phenomenology of space or his phenomenology at all147.
Paweł Przywara, Ph. D.

The University of Information Technology and Management in Rzeszów, Poland

This article is strictly connected with the contents of my dissertation: Teoria przestrzeni Husserla i Carnapa. Analiza porównawczo-krytyczna (Husserl’s and Carnap’s Theories of Space. A Comparative-Critical Analysis), The Catholic University of Lublin, Lublin 2005 (Ph. D. diss., manuscript).

2 I would suggest to distinguish the following differences:

  1. The real space = space of the real world; space wherein we move and which is intersubjectively available for us; space around us; it is sometimes called (by naturalist philosophers) physical space, but we should remember that so-called physical space can be acknowledged only as an aspect of real space;

  2. The visual space = that one which is monosubjectively perceived by every one of us in the range delimited by our eventual somatic position and eventual set of physical objects, space around me; in other words, monosubjectively given real space;

  3. The physical „space-1” = posed by physical sciences; an abstract model of all physical phenomena;

  4. The phenomenal „space-2” (manifold-1) = monosubjective sphere of sensuous qualities accessible for us within our perceptual experience;

  5. The imaginative „space-3” (manifold -2) = mental sphere, sphere within our mind, wherein we intuit e.g. relationships between geometric objects;

  6. The „space-4” = geometric (abstract) model of space;

7) * the vision space = (optic) sphere of our sight.

3 Any movement is impossible here, any exchange of places as well, those objects are timeless.

4 Carnap (1928). Despite translating the Aufbau as The Logical Structure of the World (Carnap, 1967) I would suggest the above mentioned translation of the title. Furthermore in consideration of big terminological differences between the Aufbau from 1928 and that of 1967 I use the abbreviations Aufbau-1 and Aufbau-2 for the former and the latter respectively. If the differences are not so important I say simply about the Aufbau.

5 I mean the epoché (Carnap, Aufbau-1, p. 86), phenomenological terminology and especially a procedure of geometrization of perception introduced by Husserl (in his lectures from 1907 published as Husserl (1973b). An unconscious reader of the Aufbau could take the procedure as an original idea of Carnap. Husserl works were referred by his student Becker (Becker, 1923) whose paper is cited by Carnap in his theory of space. That means Carnap must have known about that kind of methodology in analyses of perception. Another problem is an issue of so-called geometry of the world used by Carnap in the Aufbau as well.

6 Carnap’s conceptions from the period the Raum - Aufbau-1 we should not treat as belonging to logical positivism. I do not agree with K. Popper and A. Ayer. In this paper I avoid discussing logical positivism and Carnap’s semantics (or his other conceptions).

7 A lack of any Carnap’s notes on Husserl was noted by B. Uhlemann from the Carnap’s Archives in Konstanz (private email). R. Creath claimed that in The Collected Works to be published in the following years, there are not any notes on Husserl (private email). It is worth to add that in 1935 the founder of the phenomenological school meets the author of the Aufbau (and some other members of the Vienna Circle) after his lecture in Prague (Husserl, 1968, p. 96).

8 I do not mean unimportant changes that happen when translating any philosophical book. George with Carnap changed fundamental terms, e.g. in the English version of the Aufbau the word Konstitution (and the concept of constitution respectively) used by Carnap in his original conception was converted with the word ‘construction’ (hence with the concept of construction).

9 I guess it is a precedent in history of philosophy when one work has two substantially different versions.

10 The philosophers surprised such connection were e.g. Creath, M. Friedman, P. Galison (private emails). Reasons to not mentioning it may be the following: 1) a general idiosyncrasy of analytic philosophers to Husserlian phenomenology, 2) the fact that the publication Husserl’s Ding und Raum (in English, of course) was in 1998 scarcely, and after reading it (if anyone wants to do so) you can find similarities between his phenomenology of space and Carnap’s early constructionism.

11 C. Glymour having fund out from me about Carnap’s attending Husserl’s seminars, answered that the former just wasted his time (private letter).

12 The groups from München, Getingen and Freiburg. Most of them are called the phenomenologists or connected with phenomenology, but it is worth to know that Husserl did not concern them as real phenomenologists at all (because of their treating of transcendental reduction).

13 Cf. Claesges (1964), Ströker (1977) and Drummond (1975).

14 Other conceptions with respect to the issue are: 1) radical realism (we perceive space), conceptualism (space is a structure within our mind or is a construct of our mind; we perceive it mentally, pure noeticly only), and nominalism (we do not perceive space, we just use the word ‘space’ to talk about some dependencies between physical objects).

15 Husserl analyzes in great detail e.g. so-called ‘visual field’, ‘visual coordinates’, ‘visual points’ and a changeability of appearing of spatial things in the visual field. He emphasizes a reversing of the appearances of things in our visual field in the course of perception.

16 The constituting of corporality manifests on three levels. One of them is the ground of the expanding of spectrum of movements of different perceptual organs, e.g. a spectrum ‘eyes-movements’ „demands” (because of limitations of a stable perception) an expanse for a spectrum of ‘head-movements’ as well as ‘upper-part-of-body-movements’. Any detailed description of Husserl’s phenomenology of corporality within his phenomenology of space is not an issue of my paper, however, I have to remind (writing on Carnap) that the author of the Ideas conceives subject’s corporality in the following aspects of: 1) visibility of it (it is present as a solid in the visual field), 2) being the Wahrnehmungsorgan (it helps a subject to perceive), 3) tactility and sensitivity of it (subject’s corporality has special properties: when being touched or being moved it gives to the subject peculiar sensations i.e. the ‘kinesthetic’ ones) and 4) movability of it (the subject can move his corporality using his free will).

17 I would prefer to say ‘sensings’ than ‘sensations’ when the latter have so long philosophical tradition and wide connotation. The sensings point to 1) constitutive role of subject’s corporality in perceiving spatiality and 2) the spatiality of subject’s body, for all the sensings are spatially localized, they are, so to speak, close to me, they let me talk about my corporality (mein Leib). I also prefer translating ‘mein Leib’ as ‘my corporality’ to ‘my body’ since the term ‘body’ has in English its special connotation that is far from Husserl’s phenomenological meaning. Hence I do not agree with R. Rojcewicz’s translation of Husserl’s Ding und Raum (Cf., Husserl, 1997).

18 Widely comprehended, because our perception grasps even objects of outer space or different states of our body.

19 Husserl (1973a).

20 It is impossible to epoché to take us back „in time” to that state of our perceptual apparatus that we had at the stage of our „first encounters with space”. However, it seems that those encounters could be conceived only as “possessing the space of our body” not as “learning outer spatiality”.

21 I want to clearly distinguish ‘meta-cognition’ i.e. in the sense of a reflection attendant upon our ordinary acts of cognition (formulated e.g. in the sentence ‘I cannot clearly see that picture on the wall’) from the ‘ultra-cognition’ as the effect of the transcendental reduction. The ultra-cognition is a peculiar intellectual look at the pure phenomena of cognition (in Husserl’s sense, of course). The ‘ultra’ prefix is to be characterizing a special type of our cognition i.e. 1) as transcending the ordinary type of cognition (here extraordinarity, originality) and 2) perfection of the phenomenological look (super-cognition, the highest type of reasoning perception or intuition). Cf. Husserl (1973a).

22 Husserl (1966, p. 145).

23 Cf. Drummond (1979-80). However, on the contrary to Drummond, in my phenomenological research and interpretation of Husserl’s conception I respect the epoché.

24 In Husserl (1973b) it is called the ‘objective space’.

25 It is not an analysis of perception more geometrico. We should remember that all ‘perceptual organs’ are treated by Husserl pure phenomenologically as well. One must not understand them physiologically at all.

26 At least two of them are constitutive to the phenomenon of space. Transformation (or ‘metamorphosis’) of the first level leads to multi-sided, three-dimensional presenting itself a given spatial thing and it is the transformation of different ‘surfaces’ given apparently into a apparently-full given solid. Transformation of the second level (founded upon the first one) turns ‘shallow’ (and moving together with a subject) ‘vision/sight spaces’ into the ‘full’ ‘space of sight’ that being intentionally fulfilled structurally overlaps the perceived space. The perceived space then is the correlate of the whole kinesthetic system (at the given moment), and is perceived by every subject monosubjectively and in the same time, structural analogically, i.e. as co-seen with spatial things.

27 I mean Husserl’s theory of space when writing the so-called Ideas I and II (at about 1912).

28 The moderate determinism of Husserl manifests in concerning a conditioning between e.g. 1) an objective placement (of a given thing) and a location of its appearance in our visual field, 2) an objective shape of a thing and its intra-perceptual quasi-figure, 3) an objective coloring of a thing and its quasi-coloring, 4) an objective temporality of a thing (persistence of it) and its quasi-temporality (persistence of its appearance or persistence of a continuum of appearances of the thing), 5) an objective spatiality of a thing and so-called quasi-rotation of its appearances in the course of moving perception (Husserl 1973b, pp. 198, 206, 215-216) and other correlations discovered by him when analyzing a phenomenon of space.

29 Carnap (1922), henceforth the Raum.

30 This arrangement is being done within an enigmatic understood the ‘theory of knowledge’. Carnap does not give any theoretical assumptions or clear criteria of his own treating of the issue. He tries to sketch some object domains and then assign them to different scientific and philosophical disciplines. However his research is not ‘methodologically neutral’ when he use methodological tools taken from different theories without checking if the tools are compatible each other even on the ground of research or its explanation.

31 Raum, 64. He refers to B. Riemann, H.v. Helmholtz, L. Couturat and H. Poincaré.

32 Some philosophical landmarks here are: Kantian philosophy of geometry, Husserlian early (up to his Ideen I theory of space, problem of different geometries and the problem of a structure of space itself (with respect to the discussions about Einstein’s theory).

33 Grünbaum (1963, p. 664).

34 Carnap’s use of the term ‘Anschauungsraum’ is not consistent with Husserl’s one. Husserl would say about the space of our outer perception as the Anschauungsraum (or perhaps about the „space” grasped by the acts of our imagination), but certainly he would not name the essence of space that way (the same as he would not say about the essence of color as if it were a color). It seems from Carnap’s remarks to his dissertation (Raum, 80) that he means a space “seen” by us in our geometric acts of cognition. Moreover he clearly distinguishes it from the physiologische Sehraum or space of sight, hence there is no doubt that the Anschauungsraum is meant here in a non-Husserlian way. Cf. Drummond (1984, p. 791).

35 Carnap, Raum, 63. A. Richardson maintains that it is something like a spatial formal minimum of appearing any visual experience (1997, p. 147), since Carnap (following Kant) conceives here space as a condition of possible experience adding at the same time that we have to concern which spatial relations we can reveal in every experience. We cannot use an induction here, continues Carnap, nor take into an account a quantity of experiences. So-called ‘factual content’ of our experience is always and necessarily spatially ordered but the relations within the factual material are topological only (Richardson, 1997, p. 145).

36 Carnap follows Reichenbach here (modificating Helmholtz’s and Poincaré’s conceptions of measure).

37 Carnap, Raum, p. 62. However, not all of them, adds Carnap. The synthetic apriori judgments are possible by the means of our insight into the aprioric structure of topological space (ibid p. 63). Grünbaum (1963, pp. 664-665).

38 This conception is characteristic to the whole thought of Carnap (1966, p. 168). Carnap (following Reichenbach) says that geometry becomes the theory of the space of physical world at the moment of fixing the rules of congruency (Schillp, 1951, pp. 50, 57). Grünbaum (1963, p. 672 (note 136) and p. 674).

39 Raum, pp. 61,65. The Anschauungsraum has some special formal features: it refers only to a delimited area (region) hence it can support (within our cognition) only spatial forms of delimited seize or magnitude (ibid p. 23). Cf. Richardson (1997, pp. 148, 154). However, in Carnap’s opinion, the Anschauungsraum is an irreducible chain between formal and physical space.

40 It is not explicitly said if he does it himself or under the influence of B. Bauch (his promoter).

41 Carnap, Raum, pp. 31, 61, 65. This is contradictory to Kant and neokantism too. Grünbaum says that we should connect it with Helmholtz’s conception (1963, p. 665). Cf. Richardson (1997, p. 141).

42 ibid p. 148.

43 ibid p. 154.

44 ibid.

45 Richardson says that Carnap follows Cassirer here Richardson (1997, p. 148).

46 Grünbaum (1973, p. 152).

47 Richardson, (1997, pp.156-158).

48 Carnap (1925) and (1926). Cf. (1924a), wherein Carnap thinks of passing from the primary ’sphere of sensations’ to the secondary ’ficticious world of physics’.

49 I mean also a personal context. Admittedly Carnap after his dissertation refers to Reichenbach’s and Schlick’s works but he gets to know with them personally at the first half of 20s and then they start and criticize his works in manuscripts.

50 He refers here to Herbart-Helmholtz-Mach’s conception of a ‘formalization’ of sensations, to Natorp and Whitehead (epistemological constructionism), to Russell (epistemological logicism) and to Husserl’s phenomenology of space (especially to his geometrization of perception).

51 Russell distinguished between three orderings of space yet in 1897. Cf. Wiener, in: . (Schillp, 1951, p. 273).

52 Cognition understood as ‘function’ was introduced by neokantians, see Kim, Paul Natorp, in: The Stanford Encyclopedia of Philosophy (Fall 2003 Edition), ed. Edward N. Zalta,
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