Eidetic description of consciousness, or consciousness explained in its own right

In the context of «reassessing the relationship between explanation and phenomenology», the paper discusses the question in what ways Husserlian phenomenology as a descriptive science of consciousness has an explanatory potential in consciousness studies. It takes a very limited approach to the wide-ranging themes that may come to mind on this topic. At the center is an exploration of consciousness as an explanandum in its own right, building on Husserl's reflective-eidetic analyses of conscious experiences. It will concentrate on explicating acts of intuitive representification ( anschauliche Vergegenwärtigungen) as intentional modifications of perception, making up higher, radical novel levels of intentionality. Acts of remembering, imagining, depicting something, as well as iterations and combinations of such acts, will serve as examples. A formal notation will be used with the intention to make the reflection-based theoretical language of phenomenology more precise and easier to survey.

of consciousness as an explanandum in its own right, building on Husserl's reflective-eidetic analyses of consciousness. 1 I will focus in particular on the crucial discovery of the phenomena of "intentional implication" and/or "intentional modification" which obtain in acts of representification (Vergegenwärtigung) and in their relations to the basic form of perceptual consciousness. To be sure, in his reflective intentional analyses, Husserl also unfolds implications already at the level of presentifying (gegenwärtigende) perceptual acts, for example, in the context of the analysis of time-consciousness and, especially, of the consciousness of inner and outer horizons belonging to every act of consciousness. In what follows, however, I will concentrate on explicating acts of intuitive (anschauliche) representification as intentional modifications of perception. Acts of remembering, imagining, depicting something, as well as iterations and combinations of such acts, will serve as examples. To give a hint at what is at stake with these phenomena of consciousness, think of an episodic recollection or of a simple imagination of something as they readily may occur in daily life. Such experiences are intentionally directed at something not really presently given. Reflective analysis, as will be discussed, reveals complex forms of referring to something absent (past, imagined, depicted, etc.) to be described in terms of acts which imply other acts and thereby modify their qualities in one way or another, making up novel unities of intentionality compared with the basic act of perceiving something in its presence here and now.
Phenomena of intentional implication and modification in the life of consciousness offer a good way to explore the question of the explanatory potential of Husserl's descriptive method of analyzing conscious experiences. First, as I will argue in the following, there is such a potential already within pure phenomenology itself with its descriptive analyses of eidetic structures or forms of representifying consciousness and of their lawful inner relationships. Second, for Husserl there obviously is an additional explanatory potential in applying eidetic cognition and eidetic laws to studies of consciousness in various empirical sciences, as I will only very briefly comment at the end of the present paper.

A brief guide through the following discussion
Notice in advance that the following discussion is restricted to static descriptive eidetic phenomenology which Husserl considered systematically to be the first task of pure phenomenology, only to be followed in a second step by a genetic analysis of constitution. In static phenomenology, it will be question of analyzing the streaming life of consciousness in a, as it were, cross-sectional view, defining multiple eidetic structures or forms of intentional conscious experiences as consciousness of something, with all their necessary and sufficient constituents that can be distinguished in reflection, regardless of the way they have become what they are. Husserl's goal within static phenomenology was to describe the essential features making up a unified intentional conscious experience of one kind or another at any moment of its being experienced as such.
In Section 2, I briefly address basic methodological issues. First I lay out how I understand and will make use of Husserl's phenomenological reflection, taking a clue from a text written in the 1920ties where Husserl is clearly aware that reflection presupposes representifications of experiences and thus cannot work as immanent perception. Second, I draw attention to the shift from the natural to the phenomenological attitude which is crucial in relation to the method of the phenomenological reduction. I sketch the turn from objects simpliciter to noemas as correlates of noeses. In connection with the correlational view of the noema, I highlight the importance of Husserl's methodological idea of the noematic guide for uncovering structures of the intentional acts on the noetic side, and I point out that in this view everything objective is dealt with as something objective of consciousness.
In Section 3, I point out that, once the phenomenological reduction is established, i.e. the method of suspending the natural empirical apperception of consciousness in order to study pure consciousness, and given the "Heraclitean flux" of conscious experiences, Husserl emphasized that descriptive scientific statements can only be made by a descriptive science of essences, that is, by an eidetics (Eidetik) of consciousness. I briefly document what I take to be the crucial task of this eidetics in Husserl's writings and I take up further methodological clarifications from the work of Kern (1975).
In Sects. 4 and 5, I delve further into the eidetic analysis of conscious experiences of representification, recalling first a sharp criticism of the inability of empirical psychology to do justice to cardinal distinctions between presentification and various modes of representification which Husserl repeatedly expressed on the basis of his refined intentional analyses under the titles of "intentional implication" and "intentional modification". Taking up the gist of the foregoing sections in support of the argument, I present a descriptive reflective analysis of the eidetic moments of an act of representification, namely of a simple act of imagination as a case of modified perception. By pointing out eidetic connexions and their lawfulness within and across conscious experiences, I aim at providing evidence for the claim that consciousness as such is well suited for being explained in its own right.
In view of corroborating, in Section 6, what I try to argue for, I somewhat didactically make use at this point of a phenomenological notation as first presented in detail in Marbach (1993;see also 2007, 2010. The notation is intended to make the theoretical language of phenomenology more precise and easier to survey when applied to representing (darstellen) the eidetic findings obtained from reflection on structures of conscious experiences.
In Section 7, I further explicate the issue of eidetic connexions and their lawfulness, arguing that making explicit the hidden a priori lawfulness in the cognition of eidetic connexions among the constitutive moments of conscious experiences goes beyond describing structures and provides explanations of consciousness taken as an explanandum in its own right.
In the final Section 8, I briefly raise the issue of the explanatory potential in applying eidetic cognition and laws in empirical sciences. Elsewhere, over many years, I explored the matter which Husserl referred to as "empirical phenomenology" or "applied phenomenology" in more detail; but there is still much work to do. "Any knowledge that doesn't lead to new questions quickly dies out: it fails to maintain the temperature required for sustaining life" (Wislawa Szymborska).

Some basic methodological issues
Before entering into details, let me say something concerning phenomenological reflection and the fundamental shift from the natural attitude towards the world in which we live to the phenomenological attitude which comes about with the method of phenomenological reduction. I deem it quite important to take account of these methodological basics for doing justice to the point of view of Husserlian pure phenomenology and the issue of its potential explanatory power -especially in the context of present-day proposals of 'naturalizing' phenomenology.
Recall, quite generally, that in his fundamental work Ideas for a Pure Phenomenology and Phenomenological Philosophy (Ideas I, 1913), Husserl speaks of the "universal methodological function" of reflection and he states that "the phenomenological method moves entirely in acts of reflection" ( §77), or that "reflection is, as we may also put it, the name for consciousness' method of knowing consciousness at all" ( §78; also §79). In Ideas I, as already in earlier texts, he misleadingly tends to characterize reflection as immediate (schlichterfassend) "inner" or "immanent perception" (e.g. § §38, 45, 78, et passim). In the present context, however, I would like to refer to a text from the 1920ties. Here, Husserl clearly points out that for something to be given as object at all, synthetic identifying performances made possible by representifications (Vergegenwärtigungen) are presupposed. And he goes on to say that this applies to "every kind of object, also to the noetic and noematic structures of the intuitive experiences which for us became scientific objects in our phenomenological investigation". It seems like an ironic self-criticism when he at once declares: "We, sure, quite obviously (ja selbstverständlich) obtained all our findings < … > on the basis of reproductions < i.e. representifications of experiences > : we typically compared a manifold of perceptions of the same content (Sinnesgehalt), but this we could only do in strings of recollections, relative to elapsed experiences, by means of repeated passing through and identifying of what they have in common". And a few lines later, looking back to studies of perception and remembering, Husserl notes "that we could obtain all cognition of what lies in perceptions only on the basis of rememberings and analyses on the basis of remembered perceptions. (Also our cognitions about rememberings necessitated that we not only remembered but that we performed reiterated experiences of remembering and brought them themselves in the remembering to analytic cognition and comparison" (Hua XI, 327 and 328). So much, to hint at least at the fact that the practice of the phenomenological method of reflection cannot get going by means of immanent perception. Rather, reflection is a retrospectively thematizing attitude in a second, higher-order act, presupposing representifications (e.g., rememberings, imaginings) of conscious experiences and their correlates, involving intentional implications of consciousness 'within' consciousness of various complexity (cf. Kern, 2021, 133ff.).
In Husserl's conception of pure phenomenology to be carried out on the basis of the phenomenological reduction which he had first introduced in lectures during the winter term of 1906/07 (Hua 24), reflection takes place upon a fundamental shift of attitude (Einstellungsänderung) towards things, events, in short, the world. When we are doing phenomenology on the basis of reflection upon the various conscious experiences or intentional acts which are directed at objects in the world -be it in the real world in its presence or absence or in some fictional world, etc.-we have to do, as Husserl put it in Ideas I (1913) "not with objects simpliciter in an unmodified sense, but with noemas as correlates of noeses". In other words, we have to turn away from dealing straightforwardly (geradehin) with the objects simpliciter (Gegenstände schlechthin) in order to study these objects in the modified sense of "noemas", that is, "as correlates of noeses". (Hua III/1, §133). In connection with this correlational view of the noema, often also simply called the correlate of consciousness (Bewusstseinskorrelat), let me stress Husserl's methodological idea of the noematic guide (Leitfaden) for uncovering the eidetic structures or forms of the intentional acts on the noetic side of the correlation. Taken as correlates of noeses the objects with their properties, components, and structures guide us 'noematically' in the reflective noetic analysis of the conscious acts, because so viewed they are, precisely, the noematic objects. In Ideas I, Husserl put the idea thus: "We can designate all those noetic components only by appealing to the noematic object and its moments: thus saying, for example, consciousness, more particularly, perceptual consciousness, of a tree trunk, of the color of the trunk, etc." (Hua III/1, §97: 204; emphasis EM).
Based on noetic-noematic reflections, everything objective is dealt with "as something objective of consciousness" (als Objektives des Bewusstseins) and as presenting itself in subjective modes (cf. Hua VII, 49f.). In the noematic perspective, the object in its objective How of being intended as X (α, β, γ, …) is a 'carrier' (Träger) of various characters, called noematic characters, some of which always attach to the X (α, β, γ..). There are many dimensions of such characterizations of modes in which an object determined as such and so is subjectively given (cf. Hua III/1, § §99ff.). In the present context, the most relevant ones to be considered concern distinctions between something objective being given either 'originarily' (originär), as it is the case, e.g., in actually perceiving something in its presence, or being given 'non-originarily' ('reproductively'), as in one or another variety of representification (Vergegenwärtigung), such as remembering, imagining, depicting, merely thinking about, etc., and on the other hand, between varieties of positional characters (Setzungscharaktere), such as being given as 'actually being' or 'actually having been' in contrast to, e.g., being given as 'imaginary' or 'pictorial', or 'neutrally'. Crucially, so far, we would not yet be engaged in a reflective phenomenological analysis of the acts of consciousness proper, i.e. in the reflective analysis of 'noetic' intentionality, which for Husserl is intentionality "properly so dubbed" (Hua III/1, §104: 241; E: 207). Picking up the idea of the noematic guide for investigating noetic intentionality in what follows, it is important to notice that there are relations of mirroring between noematic and noetic components: the "noetic 'characterizations' are mirrored in the noematic ones" (Hua III/1, §98; cf. §104).

Descriptive eidetics of consciousness
Now, in order to know what is essential about conscious experiences, Husserl argued that the phenomena themselves as they occur in our conscious life, "abstracted from the empirical apperceptions", 2 have to be submitted to a differentiating reflective analysis. Such an analysis for him was the task of "a description (a description not at all appreciated for its true importance and difficulty)" (Hua XXIII, p. 13; E: 12). However, based on the foundation of the phenomenological reduction and given the "Heraclitean flux" of consciousness, descriptive scientific statements regarding individual factual pure phenomena of consciousness can only be made by way of "a descriptive science of essences" (Ideas I, § 75). As late as the Krisis, Husserl still maintained with respect to the individual factual case of this or that phenomenologically reduced experience which must serve as a basis for the reflective eidetic analysis: "The fact is here as that of its essence and determinable only through its essence and in no way to be empirically documented through inductive empirical evidence in an analogous sense like in the objective sphere (Objektivität)." (Hua VI, §52, 182; E: 178).
Eidetic phenomenology strives to determine the essence or eidos of experiences of consciousness by defining what belongs to, for example, "perception as such", to possible perception in general, and, mutatis mutandis, to possible recollections, phantasies, expectations, image consciousness, experiences of thinking of any kind, of feeling and willing, and combinations and iterations thereof in general. Crucially, "the individual intuition (Anschauung) turns itself < … > into eidetic intuition (Wesensanschauung), that is, into the attitude of the thinking which, based on the intuition < Intuition > , is grasping essential relationships in pure eidetic concepts and expressing them" (Hua V, §8, 40f.; E: 35). The question, whenever we are dealing with the eidos, the essence, of a conscious experience of one kind or another is always what belongs to them essentially, and what do they demand according to their essence as necessarily belonging to them (ibid.). Or, as Husserl pertinently put it in 1907: "We do not ask how Experience (Erfahrung) arises (namely as sum total of psychological experiences (Erlebnisse) < … > but what 'resides' in it < … > The conditions of the 'possibility of Experience' are the first. Conditions of the possibility of Experience signify, and may signify, here, however, nothing else than all that resides immanently in the essence of Experience, in its essentia, and thereby belongs to it irrevocably. The essence of Experience, which is what is investigated in the phenomenological analysis of Experience, is the same as the possibility of Experience, and everything established about the essence, about the possibility of Experience, is eo ipso a condition of the possibility of Experience." (Hua XVI, §40, 141f.; E: 118f.) When one is studying Husserl's extensive, sometimes diffusive or redundant but always fascinating writings and manuscripts about consciousness, one may occasionally feel somewhat lost. The results of his profound analytical investigations of our conscious life according to his own methodological requirements are very often not placed close to each other, or succinctly summarized, in his texts. At this point I want to take up methodological clarifications concerning eidetic cognition of consciousness from Iso Kern's seminal work, Idee und Methode der Philosophie. Leitgedanken für eine Theorie der Vernunft (1975). In Kern's book you find a very clear but in part also sharply critical rethinking of central themes and methods of phenomenological philosophy which remained very important for his own philosophical standpoint, of which he says that it "owes almost everything to Husserl's theory of consciousness" (loc. cit., 124). At any rate, the book opened my eyes and helped me make use of the eidetics of consciousness in a more systematic way when studying Husserl anew, and it encouraged me eventually to design the beginnings of a phenomenological notation for representing (darstellen) eidetically distinct kinds of intuitive consciousness.
For the reflective elaboration of eidetic determinations of a conscious activity, the following conception by Iso Kern seems to me decisive, when he explains that we have cognition of an eidetic form of a conscious experience of one kind or another, of what it is as such, only "when we grasp it as a necessary unity, more precisely, as a multiplicity within a necessary unity. Only when we analytically distinguish different moments and recognize them synthetically as a necessary connected unity (Einheitszusammenhang)" (ibid., 275). Kern clarifies the unity by insisting that the 'band' (Band, vinculum) which constitutes the firm and 'permanent' unity of an essence, an eidos, "is no phenomenal spatial or temporal connection partes extra partes, < it is > rather the necessary connexion (Zusammenhang) of moments of an analytical unity < that is > only grasped by the understanding (Verstand)" (Kern, 1975, p. 288).
What sounds rather abstract is made comprehensible by Kern's analysis of an intuitive representification (Vergegenwärtigung), namely remembering or recollecting, whose moments make up an eidetic structure or form. The analysis leads straightaway back to the phenomena of intentional implication and modification, summarizing the moments as follows: "The act of remembering, an intentionally implied past perception, objective identity as objective unity of these acts, subjective, egoical (ichlich) unity of these acts and finally an immediate consciousness (perception or sensation), simultaneous with the act of remembering, founding the latter". (ibid., 275) Discussing Kern's subtle and detailed reasoning that and how it is that these moments form a "necessary connexion of unity" (Einheitszusammenhang) (ibid., 275-301) would lead us too far. Two points should still be mentioned, though. First, remembering (or recollecting) as such -and mutatis mutandis any form of intuitive representification, such as imagination, image consciousness, combinations or reiterations thereof which will be presented below -is "only possible if all these listed moments are present; all these moments are constitutive for the recollection, they are its necessary conditions of possibility. Moreover, they together are also the sufficient conditions: when they are present together, there eo ipso also exists the recollection" (ibid., 275). Second, "only for such unities in which certain (einzelne) analytical moments require all the other moments as necessary conditions of their possibility can we speak of a necessary unity or, in the recognition of their existing together (Zusammensein), of an analytically necessary synthesis". (ibid., 276) As Kern explains, the act of remembering cannot be without the intentionally implied act of perceiving, nor without the objective identity, the egoical unity, and the founding perceptual act. Similarly for the intentionally implied act of perceiving, the objective identity and the egoical unity: for these moments, all the other moments, thus the entire connexion of unity of remembering are mutually necessary conditions of their possibility. By contrast, the simultaneous act of perceiving which founds the act of remembering, while thus being required by all the other moments, is itself conceivable independently of all the other moments of the representifying act (ibid. 276).

Empirical psychology's inability rigorously to describe cardinal distinctions between presentification and modes of representification
Bringing the previous remarks together, let me now recall a sharp criticism of the empirical psychology of Husserl's time as expressed by him in a text from 1912. In the section on "The significance of phenomenological descriptions for the realm of experience (Erfahrung)", Husserl addresses points that lead to the core of what I wish to argue for in the following sections: Whoever is phenomenologically skilled sees right away that all the well-meaning descriptions of psychology scarcely scratch the surface and are essentially wrong even for the surface. One only needs <…> to look at the inability of the usual descriptions to understand and to describe in rigorous concepts such cardinal distinctions as those between presentification (Gegenwärtigung) and the various modes of representification (Vergegenwärtigung), e.g., between material perception, corresponding imagination, remembering, expectation, pictorial intuition, as well as the inability of realizing thereby that in every representification, in the simplest imagination, a higher level of intentionality, and a radically novel one, is already present (Ideas III, Hua V, §9,54f.; E: 47, amended. See also Krisis, §71, 253; E: 249).
In this passage Husserl thinks of his work in the years shortly before and after Ideas I (1913) during which he crucially refined the intentional analysis of conscious experiences under the titles of "intentional implication" and "intentional modification". It is interesting to note that in 1917/18, while he was working in Bernau, Husserl himself characterized this finding as "most peculiar intentionality of the 'modifications'" brought forward in Ideas and several years earlier in lecture courses "for clarification of different basic kinds of the modification as of all kinds of 'representification'" (Hua 33, Nr. 9, 176). 3 As he explains there: Each 'modification' is characterized in that in it itself the relation to another consciousness, of which it is said to be modification, is contained, a consciousness which is not really (wirklich) contained in it and yet is graspable for a suitably directed reflection. Each modification has thus the peculiarity (das Eigene) that it admits not only the kind of reflection which belongs to every intentional experience, and by which it <the experience> itself gets grasped as unity of the inner consciousness, but even a second reflection by which the modified consciousness comes into view. And with this hang together still other peculiar reflections upon the corresponding act-correlates. Thus in the imagination, e.g. etc. <sic!> Or in the recollection, since by this internal reflection which draws the view back from the remembered it makes visible the former perceiving with the former aspects etc. which come to intuitive givenness, but in the modified character of the 'reproduction' (ibid.).
As Husserl, based on the eidetic attitude, described acts of presentification (Gegenwärtigung) and acts of representification (Vergegenwärtigung), he pointed out "cardinal distinctions" between them, e.g., between a perception of a material thing and the corresponding imagination or recollection, etc. of this thing. What does he have in mind when, in contrast to a perception of a material thing, he writes that "already in the simplest imagination, a higher level of intentionality, and a radically novel one is present"? I want to argue that what he emphasizes here in a critical intention directed at contemporary psychology refers precisely to the phenomenological-reflective finding of radically modified acts of perceiving a thing as soon as they are intentionally implied in corresponding acts of referring to the thing in question in acts of intuitive representification, such as already "in the simplest imagination".

A descriptive reflective analysis of the eidetic moments of an act of representification
To support my claim, let us take up Husserl's reflective noetic-noematic approach, the idea of the noematic guide, and follow Kern's conception of determining an eidetic structure or form as an "analytically necessary synthesis" of its moments. Be the experiential basis an instance of a simple act of intuitively (anschaulich) imagining something, say, I imagine an elephant flying over a cottage. Of such an activity, I am conscious while I am actually performing it in everyday life, that is, I 'know' that I am engaged in imagining something and not, for example, in remembering or merely thinking of a flying elephant, but, as long as I do not reflect upon the act of imagining, I know only implicitly, what it is as such to imagine something. In particular, while I am imagining the flying elephant in everyday life, I am pre-reflectively, i.e., without performing a higher-order reflection on the act of imagining itself, living through an experience of only 'seeing as it were' the flying elephant, not really, actually seeing the elephant, though. I may also indulge in more or less attentively focusing one or another detail of the scene while I am imagining. Doing so would occur while I would live in the imagined scene, visually exploring it from an imaginary point of view and thereby all the while remaining pre-reflectively conscious of imagining the scene.
In order reflectively to analyze the eidetic structure of such a simple act of imagining something, I must stop being actually engaged in imagining. Instead, I must turn the act of imagining into the theme for the higher-order reflective analysis which is based on an act of remembering (or of another act of representifying -see methodological section, above) to have been imagining something. In phenomenological reflection, I now think of this something, say, the elephant flying over a cottage, being aware that it is the object of a representified (remembered or imagined, etc.) act of imagining, that is, the noematic object of a corresponding noetic act. Put another way, in reflecting on the act of imagining I am now actually intentionally referring to something, say, to the flying elephant, taken as object of a merely representified act of imagining. The act of imagining is itself intentionally implied and modified as no longer actually, really ('reell', as Husserl would say) being performed in my now actually reflecting on this act and its intentional object. I still think of the flying elephant: I representify the elephant over the cottage which I was previously actually imagining, but without actually imagining the elephant now as I had done before reflection set in. The next move to make in reflecting is to take the noematic object with its objective properties, the X (α, β,γ …) (form, color, spatial position in its surroundings, etc.…), as guide for grasping the essence (eidos) of the correlatively representified noetic activity. This operation amounts to displaying the multiple constitutive moments required as the conditions of the possibility of the intentional activity in question, or of the modes of the subjective givenness of its object. To do so, one must proceed step by step, asking oneself, either in noematically oriented reflection, how the imagined object is given to me as such, or, in noetically oriented reflection, what enables me intentionally to refer to the imagined object as such. Either way, one has to pay particular attention to the noematic characters attaching to the intended noematic object X (α, β, γ, …) and to display the relevant relations of mirroring between noematic and noetic components.
Starting the analysis proper of the eidetic moments contained in the structure of the example of intuitively imagining an elephant flying over a cottage, we can describe or characterize the following reflectively highlighted moments which together constitute an "analytically necessary synthesis": The whole setting intentionally referred to in the example of actually imagining something is noematically characterized as non-originarily given to me, in stark contrast to something originarily given in my actually belief-bestowed perceiving it. In other words, the imagined object referred to is characterized as not actually being present in the sense of actually appearing here and now, relative to the presently occupied perceptual point of view of mine. However, the object is not merely signified or emptily referred to by means of signs without any intuitive content. Rather, it is given as being imagined with a certain content of appearance (visual, tactual, etc.), but without belief in the object's existence. Such ways of being subjectively given mirror a corresponding act of intuitively representifying the object by way of an innerly representified or reproduced 4 perceiving of the object. This innerly reproduced perceiving is consciously lived through in such a way that it only is as if I were seeing the elephant flying over a cottage, i.e., as if the elephant etc. were given, or appearing, in a spatial orientation and at some distance relative to a more or less indeterminate quasi-perceptual point of view of mine. The phrases 'as if', 'as it were', or 'quasi-perceptual' are indicative of a radical modification of one's activity of perceiving, to the effect that one's normally belief-bestowed perceptual referring to something in its present actuality is no longer experienced as such. In one's intuitive representifyingly referring to something imagined, perceiving is at the very same time intentionally implied or contained as merely representified, or as innerly reproductively modified perceiving. Moreover, in the case of imagining something, the reproductively modified perceiving which is implied in one's intentionally referring to the imagined scene is not believed to be an actually occurring perceiving and, mirroring the imagined scene's positional character (Setzungscharakter) of being given neutrally, it is a thetically neutral perceiving, i.e., a perceiving which neither posits nor denies the existence of the imagined scene but rather withholds from taking position.
It appears, then, that somehow, even in such a simple act of imagining something, at least two acts are involved as conditions of the possibility of my imaginatively representifying in the intuitive manner: the actually performed representifying act of imagining and the thereby intentionally implied or reproductively modified act of quasi-perceiving intentionally converge upon one identical object: the scene of the elephant flying over a cottage. As I understand the phenomenon of intuitively imagining the scene, I have an experience of actually referring to an elephant, i.e. to something objectively identical in the following sense: I am intentionally referring to the one that I am seeing as it were flying over a cottage, and not, for instance, the one which in another act of imagining I could be seeing-as-if standing on the ground in front of the cottage, etc.
A further condition of the possibility of intentionally referring to an imaginary object appears to be this: The various moments descriptively highlighted so far are united in the subject who performs the act of representifying something in imagination. Put another way, an act of representifying X (α, β, γ, …) does not consist of multiple fragmented intentional components. Quite to the contrary, such an act is at any moment experienced as a unity of consciousness, a unity of performance, in virtue of which intentional reference to an objective something is established. The complexity of the components or moments of a representifying act is simultaneously unified in a subjective I-consciousness. The unification of temporally and spatially discontinuous moments takes place in an I-consciousness: I am aware of being more or less lively or attentively representifying X (α, β, γ, …). I experience myself as being as it were "there and then", either appearing myself as part of the imagined scene, or only as seeing as it were the scene from a representified perceptual point of view, while simultaneously, albeit less lively, being conscious of presentifying my actual surroundings, thus of being "here and now" (e.g., at my desk). For the person engaged in imagining, there is an immediate consciousness (perception or sensation) of the actual surroundings, simultaneous with the ongoing representifying act of imagining a flying elephant.
Why, one may ask, is all this an "analytically necessary synthesis"? It may seem that such a more or less tortuous enumeration of distinct structural moments, based on reflection, presents in a way only a description of the essence or the eidos (Wesensbeschreibung) of the act, without as such establishing anything to be necessarily existing together or being lawfully involved in the unity of the act in question (see above, Kern (1975)). Note that in a text from 1912 Husserl himself said about the significance of description in physics and in psychology or phenomenology, respectively: "Description of essence yields per se < an sich > no eidetic law yet." But, crucially, in the very same context, with regard to psychology or phenomenology, Husserl pointed out that "the rigorous shaping of the description however requires phenomenological analysis; the concepts are only scientific if their pure essences are grasped and rigorously separated and differentiated in their essential connexion" (Wesenszusammenhang)". And just after stating that eidetic description does not per se yield an eidetic law, Husserl continued thus: "On the other hand, however, to the description of essence (namely, grasping of essences in intuition and conceptual fixation of them) there attaches itself immediately the cognition of eidetic connexions, and in each < scil., eidetic connexion > there lies per se already concealed a lawfulness (Gesetzlichkeit) of an a priori sort". And indeed, suitable reflections on the relations among the "rigorously separated and differentiated" eidetic moments of the acts make them intelligible as "essential connexions" or as "necessarily occurring together", exhibiting thereby the lawfulness of eidetic connexions (see Hua V, §11, 59-70; quotes from 68f.; E: 59f. -emphasis EM; Kern,loc.cit.,275ff.). In my understanding, such reflective findings of eidetic connexions within and across conscious experiences precisely provide evidence for the fact that consciousness as such is well suited -given appropriate methodologies -for being explained in its own right and for fulfilling an explanatory function in applications in the empirical sciences.

Using the phenomenological notation in reflection-based analyses of acts of representification
As announced above, let me now turn to the phenomenological notation. The notation can be helpful to represent (darstellen) the eidetic findings of the easily divagating reflective attitude in a more condensed and better surveyable manner than it is possible with descriptions in one or another natural language. It may thus be apt to corroborate what I try to argue for. The formulae of the notation can be considered as models of the reflectively described eidetic structures of conscious experiences. They must therefore be read and interpreted on the basis of actually reflecting oneself on an example of the kind of experience in question. Only then can the non-phonetic formulae be understood as referring to the solely reflectively obtainable findings of which the formulae are intended to be models. Perhaps, keeping in mind the indispensable role of active reflection for phenomenological analyses, the prescientific concept of a model formulated by Marvin L. Minsky is quite appropriate for the phenomenological notation as well: "For an observer B an object A* is a model for an object A to the extent that B can use A* for answering questions relative to A which are of interest to him" (Minsky, 1968). 5 Famously, Frege already concluded his very thoughtful short paper "Über die wissenschaftliche Berechtigung einer Begriffsschrift» thus: «… at any rate an intuitive representation of forms of thought (anschauliche Darstellung der Denkformen) has an importance reaching beyond mathematics. May therefore philosophers, too, pay some attention to the matter!" (1882b, [56], 114). Well, despite the obviously different goals of Frege's new script in his Begriffsschrift (1879), modelled on the language of arithmetic, his intention seems to me particularly relevant, indeed, to aim at "expressing a content by means of written signs in a way that is more precise and easier to survey than it would be possible by means of words." (Frege, 1882a, [1], 97). The phenomenological notation should also help "to avoid misunderstandings by others and at the same time mistakes in one's own thinking" (Frege, 1882b, p. [48], 106). Moreover, with regard to his Begriffsschrift, Frege (1882b) pertinently pointed out in a passage about the "advantage of the written" as opposed to the "restless flow of our actual thought movement (dem restlosen Fliessen unserer wirklichen Gedankenbewegung)": The script provides the possibility of keeping a lot present at the same time, and even if we can only fix our eyes upon a small part of it at any given moment, we nonetheless retain a general impression also from the rest, which is, whenever we need it, at once at our disposal. (1882b, [53], 111) In the following I present a couple of examples of formulae of the phenomenological notation, relevant in the present context, going about this somewhat didactically. 6 To begin with, instead of directly writing the full formula for the reflectively analyzed moments contained in the 'simple' eidetic structure of the example used above of imaginatively representifying something, I try graphically to suggest how one can proceed (here, and mutatis mutandis in other examples; but note that one may just as well proceed by going more or less back and forth) step by step, so to speak, 'back' from the noematic side to the noetic analysis of the activity, as Husserl himself suggested it, e.g., in his lectures of 1925. 7 Be the example again 'I imagine an elephant flying over a cottage' (note that for simplicity the intentional objects are designated by 'x' in the formulae), and the question now is: 6 At the workshop on "Reassessing the relationship between explanation and phenomenology", convened at the University of Leipzig by Heath Williams and Kristina Musholt (4-7 october 2021), I referred to the notation only cursorily at the end of my talk.-Michela Summa, in her comment on the paper, said that with the notation "we gain more clarity in the construction of what may be called phenomenological explanatory models", but she quite aptly also asked whether "besides gaining something by translating a phenomenological explanatory model into a formal notation, don't we also lose something?", having in mind a "quest for a theory that aims also to account for the concrete diversity of experience, and even the diversity of approaches within psychology, not all of which may be persuaded by a formal notation. I am particularly thinking of qualitative research". I can only agree, being myself acutely aware of the limitations of the notation as it stands. -Then again, another exchange, with Oliver Casper and Philip Haueis, motivated me to make use of the notation in the present thoroughly overhauled and in content modified paper again. 7 Hua IX, §3c, 28f.; E: 20f.; see also the 'Noetic-Noematic Table' in Appendix 1, and 'A brief survey of the elements of the notation', Appendix 2, below.
2: in the How of its objective determining content (animal, flying, cottage, surroundings, etc.):

X )
3: in the How of the subjective modes of givenness, i.e., in the noematic characters, attached , however not as real predicates of X: to be representified, more specifically, to be imagined without belief 4: a correlated intentional act or experience on the noetic side, mirroring the noematic characters: 1: A determinable X, i.e., the noematic object simpliciter: In the notation, as mentioned, a few non-phonetic signs for designating crucial aspects of the noetic intentionality will be used (see Appendix 2, below): Most importantly, (a) pairs of '(….)'-parentheses for designating the encompassing intentional correlation between an actually performed act and its intentional object; (b) pairs of square brackets, '[]', in given cases reiterated pairs, '[… […]]', to designate the occurrence of intentionally implied and modified conscious acts within (a), that is, within the encompassing unmodified representifying act; c) a horizontal stroke, '______', I call the foundation-stroke; d) a sign of the form 'Ͱ'and another sign of the form '-' serve as 'belief-stroke' and 'neutrality stroke', respectively, put in front of the corresponding conscious acts and of their correlates; e) the temporal aspect of intentionally implied acts will be marked by the subscript letter 'p' and 'f' for 'past' and 'future', respectively; f) the lower-case letter 'i', written at the very left of the compound expressions designates the 'I-awareness' contained in the activity of representification under study. Several of these signs appear to be apt, as Frege had pointed out, "to express a fact" "directly", "without mediation of the sound" (1882b, [54], 113). As I see it, the absence of pronunciation is convenient for expressing intentional properties and relations in concise ways. In sum, I deem formulae with the various types of parentheses and brackets together with the various strokes particularly well suited to designate "rigorously separated and differentiated" eidetic moments within the phenomena of intentional implication and modification quite "directly" (unmittelbar) or, as Frege also had it, "to being united with a content in the most intimate way" (1882b, [55],113).
The formula for the phenomenological eidetic structure or form of imagining something {IMA} x, described above for the example of imagining a flying elephant looks like this: Actually imagining, i.e. visualizing, object or event x: (IMA) x reflectively analyzed, yields, starting at the noematic side of the intentional correlation by asking yourself how the object is given to you or appears to you: i.e. some fictional object or event x is given to me, i, in correlation with my actually representifying x by means of a reproductively modified thetically neutral perceiving of x while simultaneously the surroundings s are correlated with my actually experienced bodily presentification of s.
To bring back to mind right away the finding of "a higher level of intentionality, and a radically novel one" said to be present in every representification, already in the simplest imagination, contrast formula (1), containing a reproductively modified perception, [PER], with formula (2) for the simple, unmodified or really (reell) experienced act of perceiving a material thing in its surroundings: {PER} x: Actually simply perceiving object x: reflectively yields: (2) (PER) x i.e., x is given in correlation with an actual perceiving of x; or: x is given by means of actually perceiving (seeing, touching, etc.) x itself. Now recall Husserl's critical reflective observation regarding "cardinal distinctions" between "presentification (Gegenwärtigung) and the various modes of representification (Vergegenwärtigung). In my understanding, the pair of square brackets containing the reproductively modified perception, '[PER]', in formula (1), is precisely meant to capture the phenomenological fact of a "higher level of intentionality and a radically novel one". The square brackets, '[…]', highlight the crucial moment of representifying acts quite generally, i.e. from the simplest to ever so complex higher order representational acts: that they contain intentionally implied and reproductively modified acts within the actually, 'really' performed, itself unmodified, unifying act surrounded by the '(…)'-parentheses, and it seems to me that the parentheses and brackets are thus "united" with the content, "in the most intimate way".
To illustrate, look at the formulae for more complex structures of representifying something, for example, by way of (3) imagining having imagined something, and by way of (4) remembering a depiction seen in a museum. (3) and (4) are distinctly different experiences of an actually representifying act containing in itself a reproductively modified representifying act -in (3), of an object or event itself, in (4), of a depicted real or fictional object or event.
Within the scope of the paper, these examples of using the notation just serve to give a glimpse of its potential for handling higher-order forms of intentionality, i.e. forms of "consciousness of consciousness of something". By the way, keep in mind, what Husserl pointed out in Ideas I: "Thus, 'consciousness of something' is something readily intelligible (sehr Selbstverständliches) and yet at the same time something supremely unintelligible (höchst Unverständliches). < … > If one has acquired the right attitude and fortified it through practice < … > to heed the clear instances of essential givenness, then firm results (feste Resultate) will promptly arise and the same ones with everyone in the same attitude; there arise firm possibilities of communicating to others what one has seen oneself, checking their descriptions, bringing out the unnoticed intrusions of empty verbal meanings, making known and eradicating, through subsequent measuring (Nachmessung) in the intuition (Intuition), errors that are possible here as they are in every sphere of validation. But now", as Husserl adds, "zu den Sachen" ( §87, 201; E: 173). Husserl (1980) gives a nice example for an iterated imagination of this sort: "I live in the imagining of a centaur. I imagine that I am carrying out this imagining. For example, I phantasy myself into the following situation: I am travelling in Africa; I rest from my march and give myself up to my phantasies; I think of centaurs and water nymphs in the world of the Greek gods." And he comments as follows: "These phantasies are not taken as present phantasies but as phantasies that are themselves phantasied. Within the phantasy, a distinction is again made between reality and dreams (phantasy)" (Hua XXIII, Text No. 2b, around 1905,183;E: 220).

Cognition of eidetic connexions and their explanatory potential
Let me return to the issue of eidetic connexions within and across conscious experiences (see above, p. 11) and further explicate this point. As I understand the matter, reflectively making explicit the hidden a priori lawfulness in the cognition of eidetic connections among the constitutive moments of conscious experiences goes beyond describing the structures and provides explanations of consciousness taken as an explanandum in its own right. Notice, for example, that a reflective-eidetic description of the phenomena of the intentional implication and modification of consciousness within consciousness of representification has to be formulated step by step by determining which of the reflectively separated and differentiated individual moments is connected with which other moment(s), and in what way(s) these moments are necessarily, or lawfully, connected together and are together sufficient for constituting the conscious act as such. As Husserl pointed out in the text from 1912 quoted above (Section 5), making such distinctions "can only succeed if the experience to be considered is subjected to modifications of the essence which set its various sides and components in motion, or, if it < the experience > is compared with various other possible experiences which contain similar sides or components in another function". Moreover, one has to recognize "the necessity of performing innumerable variations in the manifestation of the intentionality and reflections on the manner of the manifestation" (ibid.). From all this, Husserl concludes that "it is clear that any description confining itself to the single experiences (Erlebnisse) given in the actual Experience (Erfahrung) cannot in any way deliver valuable and binding results." (Hua V,§11,69;E: 59).
Reflecting on the eidetic structures or forms of somewhat more complicated phenomenologically described representifying acts on the basis of the stable formulae in the notation carries the potential for discovering lawful explanations of various possibilities and limits of the relationships between the constitutive moments. I am thinking of, for example, "phenomena of the overlapping and mixing of intuitions (Deckung und Durchsetzung von Anschauungen) and the experiences of agreement, conflict, and the modes of position taking belonging to them" of which Husserl said that they "must be studied in detail, since otherwise one easily goes astray" (Hua XXIII, Appendix L, around 1912: 479). Consider, for example, conflicts of attention in the various possible directions of engaging in the representifications and/or in the simultaneous founding bodily presentification of one's actual surroundings. Or think of limits regarding possibilities of mentally situating oneself simultaneously at various actual or representified bodily positions, causing different modalityspecific interferences. Moreover, consider possibilities of various reflections 'within' the representifying acts, permitting, e.g., to explore ways of appearing of representifed things from a simultaneously representified correlative point of view. Having recourse to the stable notations for the complicated structures, which permit to keep a lot present at the same time, may then facilitate the task of surveying and comparing the various constitutive moments of complex distinctly different eidetic structures in view of formulating explanations of lawful relations and dependencies among the moments of the acts. 8

Explanatory potential in applying eidetic cognition and eidetic laws in empirical sciences
To be sure, I am aware of the fact that one can make good use of Husserl's work in the context of empirical, scientific studies of consciousness based on his own proposal of phenomenological psychology without adopting the point of view of pure transcendental phenomenology which becomes a stumbling block for the naturalization of consciousness., 9,10 However, I remain intrigued by the observation many 8 In Marbach (1993), especially in Chapter 6, "Reiterations, Transformations, and Combinations of Purely Mental and Pictorial Representations" (147-174), I explored related issues, using an earlier version of the notation. 9 See, e.g., the recent impressive study Mechanism and Consciousness: Integrating Phenomenology with Cognitive Science by Marek Pokropski, Taylor and Francis Group, 2021, which presents a detailed overview and an illuminating discussion of various views on the naturalization of phenomenology, of models of explanation in cognitive science and of types of phenomenological explanation and phenomenological understanding, arguing throughout the book in favor of an integration of phenomenology with multilevel mechanistic explanation. I have learned a lot from this book and sense a, as it were, cautious affinity to many points in the discussion, not least to the general proposal summarized in the "Conclusion: Toward Methodologically Guided Mutual Constraints" between phenomenology and cognitive (neuro-) science. I am most grateful to Heath Williams for drawing my attention to this work. 10 In earlier work, I discussed the question of applying eidetic phenomenology within the framework of Husserl's distinction between "a priori first philosophy" and "second philosophy", also called "empirical phenomenology" or "applied phenomenology", in explicit analogy to the application of pure a priori mathematics to the empirical physical sciences. This applied phenomenology was conceived by Husserl as a "transcendental science of facts" in the sense of a "phenomenological transformation" or a "phenomenological interpretation" of the empirical sciences of facts, a transformation made possible by a priori, i.e. eidetic phenomenology (Hua III/1, 134; Hua VII, 188; Hua VIII, 361; see Marbach 1977Marbach , 1987  times expressed throughout Husserl's work that what belongs to the essential or eidetic structures of conscious experiences of one kind or another as revealed by phenomenological reflection on pure consciousness invariably belongs to them. For instance, in Ideas I, § 84 Intentionality as the main theme of phenomenology, he refers back to the "preparatory eidetic analyses (Wesensanalysen) < … > about consciousness in general", presented before introducing the method of the reduction. In those analyses "it was already necessary for us < … > to work out a series of the most general determinations regarding intentionality in general < … > Of these < determinations of intentionality > we continued to make use, and it was legitimate for us to do so, although the original analyses had not yet been implemented under the explicit norm of the phenomenological reduction. For they concerned the pure essence proper to experiences, hence they could not be affected by the suspension of the psychological apperception and < psychological > positingof-being (Seinssetzung)", which occurs with the phenomenological reduction (Hua III/1, 187f.; E: 161; emphasis mine). And again in Ideas III on Phenomenology and the Foundations of the Sciences, Husserl said "the pure experience with its whole essence enters in the psychic state and only undergoes an apperception which does not change it itself but instead peculiarly apprehends it" (Hua V, §12; similarly §8).
If so, what could a naturalization of consciousness contribute to cognition of consciousness as such, in its own right? The empirical sciences of consciousness are indispensable, however, as Husserl himself clearly pointed out, in order to determine "how such experiences < perceptions, etc. > occur in human beings and animals, under what real conditions and with what consequences, according to what general or specific laws of nature, that can and must be established according to the methods of the empirical sciences, by means of observation and experiment" (ibid., §8). As is well known, Husserl liked to make an analogy between pure, a priori and applied mathematics, on the one hand and, on the other, between pure, a priori phenomenology and applied or empirical psychological phenomenology. Thus, he writes in the context referred to above (Section 5): " < … > the recognition is necessary that the total domain of the phenomenological a priori, the total manifold of essences and eidetic laws, must be systematically worked out, and, to be sure, in the interest of empirical psychology itself. In this regard < … > the analogy holds: one does not study the figures of the material bodies by description in Experience, but rather at first a priori, as geometric ones. All study of the figures of factual bodies is application of geometric knowledge, and has to be. That is the only correct method. < … > And it's precisely just the same relationship between phenomenology and natural-scientific psychology" (Hua V, §11, 70; cf. 69; E: 60; cf. 59). Biological, causal, mechanistic, neurocognitive etc. explanations of empirical findings concerning facts of consciousness would have to be put in relation to detailed structurally defined reflective eidetic findings in order to decide Husserl's "decisive question"raised in the conviction that "there are essential laws of consciousness"-to what extent "what is essential about consciousness assigns limits to the conceivable possibilities" (see above). A description of the consciously experienced mental reality in purely neurobiological or neuroscientific and ultimately physical language cannot reflection, it will become clear that x's and y's are parts of s's singled out in one way or another by activities of PRE or REP.
A pair of curly brackets, '{…..}', serves to designate the very theme of a reflective analysis. Thus, expressions like {REM x}, {IMA IMA x}, {REM PIC x}, etc. are meant to indicate that the mental acts mentioned inside the curly brackets are to be submitted to reflective analysis in order to determine their phenomenological forms.
A pair of parentheses, '(……)' together with 'x', 'a', etc., is used to designate the reflective finding of the intentional correlation between an actually occurring mental act as a whole and its object(s). Thus expressions such as '(PER)x', '(IMA)a', etc. designate the fact that an actually occurring perception, imagination, etc. has x, or a, etc. as its intentional object or correlate. These act-wholes or act-unities are to be reflectively analyzed in terms of phenomenological forms or structures of presentifying and representifying the intentional object. Putting the '(….)'-parentheses around the expressions for the multiple components of the act, rather than around the expression for the intentional correlate, is precisely meant intuitively to capture the unity of an act as a whole.
Pairs of square brackets, '[…..]', surrounding expressions for mental activities and put inside the expressions for the act as a whole surrounded by parentheses, designate the reflective finding of an occurrence of an intentional implication or modification of a mental activity contained within another activity. Crucially, the expression of an activity surrounded by such brackets is meant to be indicative of the fact that such an intentionally implied activity is involved in the mode of non-actuality; it is no longer actually performed but is, precisely, experienced as being only representified (vergegenwärtigt in Husserl's sense of reproduction of acts in inner consciousness) in one way or another in one's actually representifyingly (vergegenwärtigend) referring to an object. Thus, the expression.
designates the reflective finding that the actually occurring representifying act in its intentionally referring to x implies within itself a non-actual activity of perceiving x. Forms of representifying experiences, (REP)x, relevant in the present context are IMA, REM, PIC, and combinations thereof; they all intentionally imply an activity of perceiving, or more than one, in ways further to be specified.
The correlates of the act and its components are written outside the parentheses and brackets, simply as x, y, s, a. It is true, however, that the expressions for the objects could also be put within parentheses or brackets of their own, possibly doing better justice to Husserl's method of the transcendental phenomenological reduction according to which objects are sometimes said to be "put within parentheses", thus in the notation as (x), (y), (s), (a) next to expressions surrounded by '(….)' and '[…]', respectively.
A horizontal stroke, '______', called "foundation-stroke", serves to account for the reflective finding that all representifying experiences involve a simultaneously occurring presentifying experience on the basis of, and in contrast to, which one's intentionally referring to something representified takes place; the compound expression is set in subscript position: In addition, this stroke also serves in cases where a representifying experience involves a simultaneously physically present or representified carrier or foundation for the representifying function, such as in cases of depicting something. Thus, an expression such as designates part of the form of the mental activity of pictorially representifying some x that is grounded in a simultaneous perceiving of the picture (carrier) y, in which x appears. The vertical stroke '|' between 'x' and 'x over y' is used to capture the finding that, with (PIC) x, intentional reference is made to a peculiar "double object" (i.e., the depicted real or fictional x just in so far as x appears in the physical picture y as pictorial or image object 'x over y').
A sign of the form 'Ͱ ', called "belief-stroke", when put in front of a pair of brackets serves for expressing the fact that a given representified mental activity is experienced with the force of "belief" (or "positionality"), 'Ͱ […..]', and, when put in front of the symbol for the intentional correlate, that this is taken for something in the real world.
On the other hand, a sign of the form '-', called "neutrality-stroke", when put in front of a pair of brackets and/or in front of the symbol for the intentional correlate, serves for indicating the property of being thetically neutral, either with regard to a representified activity or to an intentional object.
Written in subscript position, the letter 'p' serves as a temporal index for 'past', and where necessary, the letter 'i' will be written at the very beginning of a formula to designate the I-consciousness that is involved as subjective unity in representifying experiences.
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