What divides the east-coasters and west-coasters is not the middle of the park but a dispute over the status of what Husserl calls the "noema"—what is thought about. West-coasters think that Husserl's noema is an intensional entity distinct from the intentional (intended) object (Føllesdal, 1969, 1990); Smith & McIntyre, 1984). Consequently, the phenomenological reduction is for the west-coasters a methodological device that transfers our refective gaze from worldly entities to intensional entities by virtue of which we intend those worldly entities, which might or might not exist. The east-coasters, by contrast, hold that the phenomenological reduction is a change in attitude. In other words, the east-coasters reject the idea that the reduction discloses an entity that is not manifest in ordinary, straightforward experience. The change in attitude is a shift in focus from the *object* as signifcant for us to the *signifcance* of the object for us. One object, one signifcance, but a shift of focus from the entity to its meaning as disclosed by subjects with an experiential history, particular interests and concerns, and a particular structure of embodiment—but, nevertheless, with shared traditions (Holmes, 1975; Sokolowski, 1984; Langsdorf, 1984; Bernet, 1989; Drummond, 1990, 2012).

Everyone in the park is also interested in more particular forms of intentionality. Consequently, people, even though partial to a particular part of the park, regularly move to and fro among the different areas. Since it's in the areas along the path between the lake and the pond that the more particular forms of intentionality get discussed by folks from both coasts, let's backtrack a bit and see what we fnd.

In the *nord du parc*, many conversations tend to revolve around the themes of subjectivity and intersubjectivity. These themes encompass the consciousness of inner-time, self-awareness, the self, the body, empathy, personal identity, weconsciousness, and ultimately, community—all those things that make us the kind of beings we are. The regulars in this area include John Brough (1972, 2008, 2011), Dan Zahavi (1999, 2008, 2014, 2015), Shaun Gallagher (2006, 2017; see also Gallagher and Zahavi 2020), Søren Overgaard (2017a, b; see also Krueger and Overgaard 2012; Overgaard and Michael 2015), Thomas Szanto (2018, 2020; see also Szanto and Krueger 2019; Szanto and Slaby 2020), Steven Crowell (2001, 2013, 2015), Komarine Romdenh-Romluc (2008, 2011, 2013), Sara Heinämaa (2010, 2017), Matthew Ratcliffe (2012), Jakub Čapek (2017, 2019a, b), Joona Taipale (2014, 2015, 2019; see also Taipale and Salice 2015), Rudolf Bernet (1993, 2020), Robert Sokolowski (1999, 2008), John Drummond (2006b, 2021), David Carr (1991, 1999, 2014), Daniel Dahlstrom (2000, 2003; see also Dahlstrom et al. 2015), Nicolas de Warren (2009), James Dodd (1997, 2005), Antonio Calcagno (2007, 2018), David Woodruff Smith (1986, 2005, 2011a), Ed Casey (2004), Hans Bernhard Schmid (2012, 2014a, b, 2018), Klaus Held (1966, 2000, 2007), James Jardine (2014, 2015; see also Jardine and Szanto 2017)), Donn Welton (2012), Sebastian Luft (2011), Hanne Jacobs (2014, 2016, 2021), and Dermot Moran (see Jensen and Moran 2012, Szanto and Moran 2015a, b). Quite a crowd, but this isn't even a complete list because it's impossible to talk about intentionality at all without talking about subjectivity and intersubjectivity.

Recent discussions here in the *nord du parc* have centered on conceptions of empathy, the "we," and community in Husserl, Edith Stein, Gerda Walther, Max Scheler, and similarly minded thinkers. In such a large group of people as mentioned in the previous paragraph, there are bound to be differences of opinion, but what is striking about the discussions of these issues is that there appears to be a unifed research program that continues to develop in cooperative and complementary work.

Heading over to Speakers' Corner, we fnd people focusing on language and knowledge claims, on emotions and their expressive character, on action, including moral action, and on religious beliefs and practices. Just about everyone we saw up at *nord du parc* will turn up here at some time or another as well. With respect to language, however, standing out is the work of Robert Sokolowski (1974, 1978), Lenore Langsdorf (1983; see also Angus and Langsdorf 1992), Andrew Inkpin (2016), and the young upstart Hayden Kee (2018, 2020); with respect to knowledge, the work of Walter Hopp (2009, 2011) comes immediately to mind; and with respect to Husserlian approaches to religion, I think of Anthony Steinbock (2007a, 2012), Crina Gschwandtner (2012, 2015, 2020), and Bruce Benson (2013; see also Benson and Wirzba 2005).

When we turn to emotional expression—more generally, our affective lives—the explosion of work over the last 30 years or so has been enormous. There are fssures in this work. Fundamental is the division between axiological realists and constructivists, that is, the division between early phenomenologists (e.g., Husserl, Stein, Scheler) who believed that values are disclosed in and by intentional feelings and emotions and a later generation of phenomenological constructivists who believe that values are constituted in our exercises of freedom (e.g., Sartre, Merleau-Ponty, Beauvoir). Then, among the feeling-axiologists, there is a division on the issue of realism and the relation between intentional feelings and cognition. Schelerians, for example, Anthony Steinbock (1994, 2007b, 2013, 2014; see also Steinbock and Depraz 2018) and Zachary Davis (2005, 2012; see also Davis and Steinbock 2019), are strong realists, claiming that intentional feelings grasp a priori values directly apart from any cognitive basis. The cognition of an object is only the occasion for the feeling's apprehension of the value and its recognition of the object as a bearer of the value. By contrast, those following Husserl's suggestions, for example, Íngrid Vendrell Ferran (2006, 2008, 2015a, b, 2018, 2020, 2021, forthcoming), Sonja Rinofner-Kreidl (2009, 2014a, b, 2016), and John Drummond (1995, 2006a, 2010, 2013, 2017, 2018, 2019, 2021; see also Drummond and Rinofner-Kreidl 2017, Drummond and Timmons 2021) might be called weak realists. They claim that the

axiological sense of the object—its value—is grounded in the non-axiological properties of the object. The sense of the object is given in a value-perception—an intentional feeling (or emotion) directed to the object as possessing the axiological attribute and the relevant non-axiological properties. This sense can be "perceptual," that is, pre-predicative rather than propositional, although some complex emotions, while involving perception, have a propositional sense. Another way to characterize this opposition is to say that the strong realists understand emotions to be responses to the felt value, whereas weak realists apprehend the value (of the particular thing) in a feeling- or emotion-response to the thing's non-axiological properties that are salient in the light of the subject's physical constitution, experiential history, interests, and commitments.

The group of phenomenologists working on the emotions is large. Just a few others that I see up here by Speakers' Corner, in addition to those already mentioned, are Sara Heinämaa (2020), Anne Ozar (2006, 2010, 2013), Sean Kelly (2002), Michael Kelly (2016b, c), and Paul Gyllenhammer (2011). There's also another group up here, specifcally Matthew Ratcliffe (2008, 2009, 2014, 2017) and Jan Slaby (2008, 2017); see also Slaby and Stephan (2008), Slaby et al. (2019), Schmitz et al. (2011), who take a different approach to the emotions. They exploit the Heideggerian discussions of *Befndlichkeit* (what John Haugeland called "sofndingness"), moods, and emotions and thereby expand the consideration to affectivity or affectedness or disposedness (depending on your translation of *Befndlichkeit*) in general. This captures the sense of how all these affective experiences are tied to what *matters* to us and how they encompass the evaluative dimension of our encounters of the world and entities therein.

Since actions express thoughts (perhaps more honestly than words!), Speakers' Corner also attracts phenomenologists who connect their phenomenological refections to ethics (and metaethics). Some of these thinkers are ones we've already seen in the park, ones who connect their (metaethical) discussions of feelings and emotions as evaluative to discussions of the actions undertaken to achieve the goods valued in our emotional experiences. Among those we've already mentioned in the discussion of emotions are Íngrid Vendrell Ferran, Sonja Rinofner-Kreidl, John Drummond, Anthony Steinbock, Paul Gyllenhammer, Sara Heinämaa, Anne Ozar, and Michael Kelly. Also contributing to these discussions are Ullrich Melle (1991, 2002, 2007) and Henning Peucker (2012), both of whom, in addition to editing Husserl's ethical writings, have offered careful commentary on those writings. Jack Reynolds (2013), Janet Donohoe (2004), and James Hart (1992, 2009) have developed ethical views in relation to Husserl's philosophy. Sophie Loidolt (2012, 2014, 2017, 2018, 2021) has developed ideas from both Husserl and Hannah Arendt, while Steven Crowell (2013, 2015), William Smith (2011b), and Irene McMullin (2018) have addressed the question of moral normativity from a Heideggerian perspective.

We're back to the east-coast pond. Let's complete the trip around the perimeter of the park. Wedged between the pond and Manchester Meadow lies a structure with a domed top and skylights that makes me think of a domed observatory with its opening for a telescope. I imagine that the skylights retract at night, and telescopes emerge to explore the night sky. Of course, that would never work in New York with all its ambient light. And alas, in any event the structure is less romantic than that; it just a meeting house, and a group interested in the purely formal side of Husserlian phenomenology meets in there now and then. (They should get out in the sunlight and fresh air!) Arguing the fner points of the interpretations of Husserl's philosophy of mathematics by Gian-Carlo Rota, Richard Tieszen, and Robert Tragesser are Burt Hopkins (2002, 2011), Stefania Centrone (2010, 2017), Claire Ortiz Hill (2002, 2009, 2016), Dieter Lohmar (2002, 2010, 2011), Mark van Atten (2007, 2010, 2015), and Mirja Hartimo (2006, 2010, 2017).

We've been skirting the edges of the park, but all the while I've noticed that many folks are heading toward the middle of the park and the well-known Great Lawn where many a concert has been performed. Let's follow the crowd. Ah, now I see why all those folks were earlier streaming into the park. There, on the Lawn, is an open-air, physically distanced conference whose program promises something to satisfy the interests of all the park-goers. In our covid-times, deprived of live music for so long, I confess I'd prefer an open-air concert.

#### **References**

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## **Constitution Through Noema and Horizon: Husserl's Theory of Intentionality**

**David Woodruff Smith**

#### **1 To the Things Themselves: Phenomenology Emergent**

What is phenomenology? Merleau-Ponty posed the question in 1945, pondering why the question needed to be asked nearly 50 years after Husserl had launched phenomenology. Today the question is well posed again, for philosophers have developed a variety of "phenomenologies", and we are gathered in this volume to refect on the horizons of our tradition of phenomenological refection.

Phenomenology is the study of experience as lived in familiar forms of perception, thought, imagination, emotion, and action. Husserl characterized phenomenology as the "science of consciousness", the disciplined study of *acts of consciousness*, as enacted or experienced from the frst-person perspective: for example, "I see …", "I think …", "I imagine …", "I feel angry about …", "I act with intention to do …".

In the science of phenomenology, Husserl proposed, we are to focus on the character or structure of our lived experiences. This study is not an empirical study like psychology, but rather a logic of the phenomena of pure consciousness. Thus, we study various *forms* of consciousness we fnd in our everyday experience: most fundamentally, what Husserl called "intentionality".

The leading principle of phenomenology, in Husserl's program, holds that consciousness is typically a consciousness *of* something: each act of consciousness is in that sense intentional, i.e. directed toward something in a certain way. Suppose, for example, I am gazing up at a tree in my backyard. This form of experience is more or less familiar to us all, and we may begin to refect on what this experience is like. This token experience shares a type or essence with other token experiences. In refection on this type of experience, we begin to analyze the form of visual consciousness itself. Thus, while watering plants around the patio, hearing a crow cawing high in the tree overhead, I raise my head and look upward into the tree. And

to Phenomenology 122, https://doi.org/10.1007/978-3-031-26074-2\_4

D. W. Smith (\*)

University of California, Irvine, CA, USA e-mail<EMAIL_ADDRESS>
© The Author(s) 2023

J. Yoshimi et al. (eds.), *Horizons of Phenomenology*, Contributions

now "I see"—I have a visual experience of "this towering Podocarpus tree overhead, its plentiful needle-shaped leaves obscuring the crow high in the tree".

Husserl introduced technical terms designed to articulate the structure of intentionality. On Husserl's account, my current act of consciousness in seeing the tree unfolds in a shifting fow of sensory visual impressions informed by a cognitive apprehension of this large Podocarpus tree. My visual experience consists, in Husserl's terms, in a fusion of sensory data informed by an interpretive "noesis" yielding my experience of seeing "this Podocarpus tree …". The noetic part of my experience realizes an ideal type that Husserl calls a "noematic content", or "noema", glossed as "the tree *as perceived*".

So, for Husserl, my act of consciousness is an occurrent process of consciousness, and the act's noema is the ideal form by virtue of which the act is directed in a certain way. Moreover, my visual experience in seeing the tree carries a horizon of further signifcance, a pattern of further expectations about the same tree, expectations drawing on my prior experience of this and other trees—as when I have observed crows circling trees in the neighborhood.

With Husserl writing in the wake of Brentano, phenomenology would analyze the structure of an act of consciousness, featuring intentionality. Thus, in the above case of visual perception (adapting Husserl's famous example), I see this huge tree in my backyard. In phenomenological refection on this experience, we distinguish: my conscious experience, the noematic content of my experience, and the object of my experience, the tree before me. Here we distinguish the tree itself, the botanic thing in nature, from the way the tree is given in my experience, viz. as a huge Podocarpus looming over my backyard patio. For Husserl, the noema carried in my act of consciousness embodies this way of being given in phenomenal consciousness. This noematic form of meaning (*Sinn*, in German) fans out to include a horizon (*Horizont*) of implicated meaning including something of the biology of the tree and something of its cultural signifcance, the latter featuring my patio and my city's designation of this particular tree as a "heritage tree".

While scholars have debated how to read Husserl's texts defning noema, I here leave aside the interpretation of Husserl's texts and focus on results of phenomenological analysis in a Husserlian style.1 We'll focus on the structure of intentionality, the form of consciousness central to phenomenology in Husserl's wake: including *inter alia* the ontology of noematic meaning and the cognate form of meaning called horizon.

Thus, we turn to "the things themselves": *phenomena*, in the original sense of things as we are given them in our experience of the world around us. The ways things are given in consciousness we call *noemata*, forms of experience carrying the

1Two competing models have developed, nicknamed the "West Coast" and "East Coast" approaches to the analysis of this phenomenological structure Husserl called "noema" (from the Greek for what is known or "minded"). Roughly, the "West Coast", or "California", model takes the noema to be a richly structured form of ideal *meaning* (*Sinn*), abstracting the *way* the object is *given*, whereas the "East Coast" model takes the noema to be the *object just as given*.

meaning that structures our consciousness of things in the world. The present aim is to lay out fundamentals and motivations of the California approach to phenomenology—a particular research program in the feld of phenomenology (Yoshimi et al., 2019).

On the story to follow, you might say, we bring the logic to the phenomena in phenomenology. Or, inversely, we bring the lived phenomena to the logic in phenomenology. For, as Husserl distinguished formal ontology from material ontology, the logic is the formal structure shaping the lived forms of experience we appraise in phenomenology.

#### **2 Phenomenological Description and Analysis**

Phenomenology begins in description: pure description of experience, just as it is lived and given from the frst-person perspective.

"Plain" phenomenology proceeds, to begin the enterprise, with formulating a description of an everyday form of experience. Husserl famously used an example of his seeing a tree in blossom, a similar example being my seeing a huge Popocarpus tree. I begin discussion now with an example bearing a rich horizon of meaning.

I am seated near a large window, glass from foor to ceiling. I am gazing thoughtfully out the window.  I am at the Horizons of Phenomenology conference (in April 2018), beginning to think about phenomenology itself just as our group is stirring into discussion.

We may form a phenomenological description of my experience, indicating a bit of structure, in everyday language:

I am attentively watching that elegant tall white egret, stepping stealthily through the waving grass, one long and slow step at a time, hunting something, perhaps a mouse.

More formally, simplifying for purposes of phenomenological analysis, we say:

I now here attentively see that tall white egret stepping through waving grass.

The point of this description of experience is to begin analysis of various features of the experience as lived: a conscious, phenomenal, intentional experience, a fairly simple act of consciousness. Indeed, as I watch the serene scene of the egret's movement, I am beginning to refect on this visual experience itself, because colleagues and I are gathered to consider varieties of forms of phenomenology more than a century after the discipline took shape.

In the California approach to phenomenology with Husserlian roots, we begin to analyze *forms of experience* by looking to *forms of our language* about our own experience which "intends" *forms of things* in our surrounding world. In this approach we model our consciousness of things in our language about our own experience as of those things. Adapting techniques of contemporary logic, specifcally semantic theory, we focus on attendant structures of meaning realized in our experience. With this emphasis, we approach the "semantic" model of phenomenal intentionality.

In this mode of phenomenological analysis, we spell out a semantic alignment of forms of language, forms of experience, and forms of things in the world. This model articulates the basic structure of intentionality.

That said, we must bear in mind that our phenomenological descriptions are designed to articulate a model of our lived, sensuous, meaningful experience such as that of my seeing the egret as I crane my neck to look out the window during our conference. In a meta-phenomenological perspective, we may even adapt model theory or possible-worlds semantics to model more precisely the rich phenomenal content of our lived experience. Still, the formal structures so modelled are precisely structures realized in phenomenal experience. Indeed, I rely on my reader's empathic sensibility for grasping the character and structure of the type of experience I am appraising and modelling.

#### **3 The Logical/Semantic Turn in Phenomenology**

Husserl brought a mathematician's eye to Brentano's conception of the descriptive analysis of the structure of consciousness. Husserl re-conceived phenomenology as a logical rather than an empirical, "psychologistic", account of mind. Phenomenology as we know it was thus introduced in Husserl's *Logical Investigations* (1900–01), which unfolded a complex structural analysis of world, language, consciousness, and knowledge: with intentionality central to the structure. In Husserl's conception of phenomenology, "pure" logic models the relations among mind, language, and world. Accordingly, pure phenomenology mirrors pure logic in articulating the logical structure of intentionality: where an act of consciousness is by virtue of its content or *Sinn* directed intentionally toward an appropriate object in the world. Husserl amplifed his logical account of phenomenology in subsequent works, including *Ideas* I (1913). Therein he introduced the transcendental technique of *epoché*: we are to "bracket" questions of the existence of things we experience, and thereby to focus on the way we experience things, thus the meaning things have for us in consciousness.

To appreciate Husserl's mathematical sense of structure, and its role in phenomenology, we should bear in mind that the notion of manifold, a structured whole, is featured in all of Husserl's writings, from early to late: echoing Riemann's axiomatic re-fashioning of geometry and Leibniz's ideal of a *mathesis universalis*.

Nineteenth century logicians had championed a notion of ideal meanings including propositions (aka *Satz an sich*), articulated by Bernard Bolzano, and also Hermann Lotze and others. However, contemporary mathematical logic was taking further shape right around Husserl, in the works of Cantor, Peano, Weyl, Hilbert, and Frege. In the 1930s Alfred Tarski and Kurt Gödel revolutionized logic with theorems about the powers of logical systems. Tarski's semantic theory of truth (for formalized languages) introduced the idiom of semantics as we know it today. A formal semantics would prescribe a structured pattern of relations—a mathematical model—between expressions in a language and the objects designated by the language: or a model, following Husserl's "pure logic", of the structured correlation between language and world, between structures of language and a model of structures of things in the world. This form of semantics can be seen as a mathematized model of intentionality expressed in language. And Tarski himself, though a pure mathematician, had studied with Polish philosophers trained by Brentano. Years later Gödel found in Husserl a philosophical vision supporting Gödel's own view of both truth and mathematical intuition.

The logical side of Husserl's thinking caught the eye of Dagfnn Føllesdal as he worked in mathematics and modal logic while reading Husserl, Frege, and Bolzano. Further, as model-theoretic semantics developed after Tarski, possible-worlds semantics emerged as a philosophical logic, specifcally in the work of Jaakko Hintikka. Reading Kant and Husserl and Descartes and Aristotle alongside modal logics, Hintikka devised formal systems of semantics for our language about knowledge, belief, perception, and ultimately intentionality: philosophically inspired "models for modalities" (Hintikka, 1969).

The California approach to Husserlian phenomenology evolved in the light of these developments in logic and semantics. And accordingly, following that approach, a "semantic" conception of intentionality features a conception of noematic content as a structured ideal meaning.

#### **4 The Fregean Perspective on Noema**

As phenomenology developed in the 1960s, Føllesdal proposed a way of understanding the Husserlian notion of noema by comparison with Gottlob Frege's notion of sense, or *Sinn*. Frege's logic (or semantics) of sense and reference, of *Sinn und Bedeutung*, was familiar to many analytic philosophers who were largely unfamiliar with Husserl and phenomenology. So Føllesdal—who worked in logic and philosophy of mathematics alongside phenomenology—defned a structural parallel between reference via sense (per Frege) and intentionality via noema (per Husserl). For Frege, a linguistic expression (say, 'the morning star') expresses a *sense* (an ideal meaning) in virtue of which the expression designates or refers to an *object* (the planet Venus); similarly, for Husserl, an act of consciousness (say, seeing the morning star) has a *noema* (a form of ideal meaning) in virtue of which the act is intentionally directed toward an object (the planet Venus).

Frege himself said very little about what a *Sinn* is, but what little he said is illuminating. A Sinn embodies a "way of being given" (*Art des Gegebenseins*): that can only mean, a way of being given in thought, viz. *in consciousness*. The sense of a declarative sentence (say, 'the morning star is a planet') Frege called a "thought" (*Gedanke*). This is unmistakably the terrain of Husserlian phenomenology, and in fact Husserl detailed his own schematic logic of sense and object, or *Sinn* and *Gegenstand*, technical details differing here and there from Frege's scheme.

From this semantic perspective on noema, and its role in intentionality, California phenomenology proceeds to study the rich formations of experience that Husserlian phenomenology explores: time-consciousness, space-consciousness, embodied perception, intersubjectivity, sociality, the life-world, and onward. Noematic analysis thus articulates the *structure* of the many ways in which we experience things. There are, however, several ways this idea is commonly misunderstood.

First, noematic meaning does not reside in some other-worldly Platonic heaven. Noematic meaning takes its ontological place *within* the concrete act of consciousness. An act's noema is drawn into the act as ideal correlate of the noesis in the act. In Husserl's idiom, the noesis is a dependent part (*Moment*) within the act, and the noema correlated with the noesis is thus an abstractable aspect of the temporal act in the stream of consciousness. Husserl said the act "harbors" or "carries" the noema in itself (*in sich zu bergen*). Ronald McIntyre and I said the act "entertains" the noema, or literally "holds" it "in" the act. Importantly, the noema is an *ideal* entity, as opposed to a spatiotemporal entity. A frst cut on noematic meaning is that the noema of an act is simply the *type* of a token act of that type, what Husserl called the act's intentional essence (*Wesen*). A more refned "director's cut" on the notion holds that meanings, including noemata, are a distinctive kind of ideal entity, distinguished by their role in consciousness. (On these distinctions, see Smith, 2013).

Second, an act's noema does not stand like a veil of appearance between consciousness and the object intended. The Kantian distinction between phenomena and noumena has sometimes been taken to imply that consciousness reaches only phenomena, things-as-they-appear, and never reaches *noumena*, things-inthemselves. Kant interpretation aside, the so-called Fregean model of noema does not entail that consciousness is *directed toward* the noema, behind which lies the object. Rather, the act is directed toward the object (if such exists) but only by virtue of the noematic content the act entertains.

Formally, on the "Fregean" view, the intentional relation of act to object is a composition of two relations: the act's entertaining a noema and that noema's prescribing a certain object (enjoining the terms McIntyre and I employed). A successful intentional relation obtains only if there exists an object that satisfes the noema. If no such object exists, the act is intentional, but merely as if veridically of an object.

The noema is not, then, an intermediate object of consciousness that serves as a Platonic "representative" of the real thing, say, the actual egret which I see in the waving grass. Rather, the act's noema is an abstraction of the way the act is directed toward its "intended" object. And a *bona fde* intentional relation is achieved only if the "intention" is successful. Only in phenomenological refection does the noema of my experience come into view as an object of my consciousness: that is the aim of the technique of "bracketing" the question of the existence of the egret as visually given in my experience.

An important extension of this semantic approach to intentionality invokes the *actual* context of an experience, especially in the case of perception. What I see, as I am visually presented "that tall white egret stepping through waving grass", is an

object in a situation within my spatiotemporal surroundings—my *Umwelt*. Accordingly, the indexical content "that … egret" semantically invokes the actual context of my experience: I am visually presented "that egret (actually now here before me and affecting my eyes)". Perceptual acquaintance thus requires a sharp distinction between the object in my *Umwelt* and the noematic content in my visual experience. As Husserl already emphasized, the "object as perceived" is distinguished from the object itself that is perceived. Indeed, the object has physical properties that the content does not—even if the content is indexical. Thus, the focal content in my visual experience of the egret already implicates features beyond, say, the purely sensory qualities of color and shape, and there we feel the pull of "horizon". For I experience the external object itself—white and egret-shaped and moving egretly—as drawing me to look it over from different perspectives in the space-time of my current experience.

#### **5 The Horizon of Meaning in an Intentional Experience**

A crucial part of the intentional content of an experience is what Husserl called "horizon". When I see the white egret stalking through the grass, I would be very surprised if on a closer look I saw the egret moving with three long legs rather than the expected two spindly legs. Accordingly, part of my seeing the egret moving is my expectation that it move as I expect birds to move—having seen many birds strut around, from pigeons to crows and even long-legged egrets. The egret's having three long legs is not a possibility motivated by how I experience the egret; however, its searching for a mouse in the grass is a motivated possibility regarding what I am seeing. Thus, Husserl held, the content of my experience "predelineates" a horizon of further motivated possibilities left open by the content.

In California phenomenology, the notion of horizon has been explicated, a bit more formally, in terms of noema. Føllesdal has sometimes characterized an act's noema as a "pattern of expectations", building horizon into the noema itself. McIntyre and I characterized an act's horizon as the structure of meaning *implicit* in the act's noema, a pattern of further noematic meanings indicating—predelineating—an open-ended array of further possibilities "left open" yet motivated by the explicit specifcations in the noema.

On this model, an act of consciousness entertains a noema which takes its place in a manifold of interrelated meanings that defne a horizon of meaning accruing to the act. Thus, the noematic Sinn entertained in my experience of seeing the egret implicates a system of further noematic meanings that characterize the same object in different ways compatible with and motivated by what the core noema prescribes of that object as so given. In the case of perception, as I regard "that egret stepping through waving grass", the *motivated* possibilities are circumscribed by my immediate *Lebenswelt*, as I turn my eyes toward the egret outside the window at UC Merced.

In this scheme, we may speak of a correlation among horizons of object, act, and meaning. Thus, we defne a correlation among *object-horizon*, *act-horizon*, and *meaning-horizon*. Accordingly, in an act of consciousness the object is given with a horizon of further possibilities regarding the object; the object is so given by virtue of a horizon of noematic meanings prescribing those possibilities; and the act takes its place within a horizon of further possible acts regarding the object so given.

Thus, we may say: the object of a particular experience is given within a horizon of possibilities, and so given via a horizon of meanings, a system of meanings entertained in a horizon of possible experiences presenting the object in various aspects. The system of noematic meanings entertained in appropriate experiences, actual and possible, then forms a model of the range of possibilities for the object as intended in the act and its associated further possible acts. This model structure correlates object-horizon, act-horizon, and meaning-horizon: for simplicity, however, we just speak intuitively of horizon, assuming the intentional relationship among act, meaning, and object.

Such formal models chart basic structures of lived experience, where phenomenology in practice delves into the concrete ways in which we experience time, space, perceived things, ourselves and others, our *Lebenswelt*. The rich notion of horizon keeps phenomenology grounded in our lived everyday experience. At the same time, the complex structure of horizon is aptly modelled by what has come to be called "possible-worlds" semantics, to which we turn briefy.

#### **6 The Possible-Worlds Structure of Intentionality**

The notion of horizon draws possibility—*modality*—into the very structure of consciousness. Thus, we defne the horizon of my experience in seeing the egret as my sense of the range of possibilities left open by the noematic content in my visual experience: motivated possibilities, possible situations compatible with what I see just as I see it ("that egret stepping through waving grass"). That the egret is hunting a mouse is such a possible situation; that it is hunting a lion is not. That the egret few in from marshlands to the west is such a possibility; that the egret is a clever robotic drone is not such a possibility, for my current visual experience.

The Leibnizian notion of possible worlds can be used to develop a formal model of the Husserlian notion of horizon. Leibniz was one of Husserl's heroes, the notion of possible worlds occasionally appears in Husserl, and Husserl speaks of "modalities" of belief. However, we turn to more recent logical theory to amplify the Husserlian notion of horizon. In the 1950s, in the wake of Rudolf Carnap's work in the 1940s, Jaakko Hintikka (with Stig Kanger) began a style of formal semantics for modalities, not only the logic of possibility/necessity, but also the logic of obligation. And in the 1960s Hintikka outlined a style of *possible-worlds semantics* for expressions of knowledge, belief, and perception. McIntyre and I subsequently deployed a variation on Hintikka's logic of perception, explicating thereby the Husserlian notion of horizon as part of the formal structure of intentionality.

Consider again the case of my seeing the egret, characterized thus:

I now here see that tall white egret stepping through waving grass.

Not only does this experience aim toward or intend a particular egret outside the window where I'm seated. The experience intends that object within a horizon of perceptually possible worlds compatible with what the noema in my experience prescribes: a horizon of further possibilities involving the egret at work in the grass before me—not merely logically possible states of affairs à la Leibniz, but perceptually possible situations, that is, intentionally possible situations, those "motivated" in line with the noema in my experience.

On this possible-worlds model, the structure of intentionality in the egret case is a complex structure comprising: me ("I"), my visual experience (the act wherein "I see …"), the noema in my experience (the meaning prescribing "that egret" before me), the horizon of associated noematic meanings (prescribing expected features of the egret's legs and habits), and the horizon of alternative intentionally-possible "worlds" compatible with the noema conditioned by its associated meanings. Accordingly, the possible-worlds structure of intentionality may be formally rendered—mathematized—as a style of model theory: where the experience, or its phenomenological description, is structurally aligned with an appropriate array of intentionally possible worlds, and thereby this "manifold" of possibilities is precisely a model of the intentional structure of the experience featuring what is "intended".

As Husserl would have insisted, this mathematized model-theoretic structure is an abstraction from our lived phenomenal experience in our Lebenswelt. We draw upon the logical form of semantics in order to clarify the rich structure we fnd in our own lived intentional experience of things in our surrounding world.

#### **7 The Constitution of Our World by Virtue of Noema and Horizon**

According to Husserl's phenomenology, the familiar things we encounter in everyday experience—trees, egrets, people around us—are "constituted" in our consciousness. This idiom invites misunderstanding.

Husserl's doctrine of "constitution" may seem to be saying that things around us are constructed in our consciousness. The favor of "is constituted" in English may encourage this view, but the German form is "*sich constitutiert*", a refexive form of grammar not retained in English. If we say the egret "is constituted" in my experience, one may want to ask: what does the constituting? Is it I *qua* subject, or is it the act *qua* intending? No, nothing like that. The literal rendering is "constitutes-itself", or "self-constitutes", but there is no entity that does the constituting.

Rather, in a typical act of consciousness, the object is given as "constituted" in a certain way, as having a particular constitution: viz., a structure of features prescribed by the act's noema *cum* horizon. Husserl's analysis of "constitution" follows his paradigm case of looking at an object from different sides. On Husserl's account, the object is "intended" with a pattern of adumbrations (*Abschattungen*), comprising aspects of the object as it might be seen from different perspectives. *Abschattungen*, literally, are shadings as in different perspectives in the shifting light. Thus, when I see a thing before me, I am *visually given* a thing with a back side, indeed, with many different sides, each potentially visible from a particular perspective, visible with a particular adumbration of shape, color, kind, and spatiotemporal perspective (being now there before me).

The constitution of an object in consciousness is defned by a complex structure of intentionality. On Husserl's analysis, an object is intended in an act of consciousness by virtue of the act's noema within its horizon of further possible meaning. The constitution of the object in consciousness arises within this structure: wherein the object is intended as having a variety of features surrounded, as it were, by a horizon of further possible features. The constitution of the object consists, accordingly, in the array of properties and relations prescribed for the object by virtue of noema cum horizon.

And that complex structure is precisely the form of phenomenal intentionality realized, for example, in my experience of seeing the egret stepping through the waving grass as I am seated at the Horizons conference at UC Merced.

Husserl's texts have been read by some as endorsing an absolute idealism where all the world is drawn into pure consciousness: as absolute consciousness constitutes itself and all things in the world as mere intentional artifacts (cf. *Ideas* I, §§ 49, 55). Here, by contrast, we follow a *constitutive realism* running through the results of California phenomenology. Husserl seemed to experiment with a form of idealism, a transcendental idealism, yet he regularly inveighed against a subjective or Berkeleyan idealism, and he ultimately abandoned talk of "idealism". In the spirit of refective equilibrium, then, we pursue a model of mind and world that preserves a basic realism in the structure of intentionality. And so the egret and I are acquainted in the very real world in which my consciousness of the egret takes shape, including its "constitution" in my experience.2

On Husserl's account, we should bear in mind, constitution is achieved in a dynamic process of consciousness. As I notice the egret moving stealthily in the grass, I turn my head and move to get a better look at the object. Is that an egret? Looking more closely, I see, more clearly, yes, "that egret …" (not a blue heron, certainly not an osprey or an eagle …). Were I not looking through the tall window, I might walk toward the egret for a closer look. What is it doing, hunting for a fsh? No, the grass I can see is not in standing water. So I take it the egret I see is stepping through the grass while tracking something moving in the grass, perhaps a mouse? I am reminded of once seeing an egret spearing something in tall grass, then tossing it in the air and catching and swallowing it. Here we see the process of my experience fowing along in time, as my anticipations regarding the egret are gradually

2See the concept of "Constituted Platonism" developed in (Tieszen, 2011) and "constitutive realism" in (Smith, 2020), which was originally suggested by Dagfnn Føllesdal in reference to Tieszen's work.

fulflled by what I am seeing as the egret moves slowly within my visual feld. Here the constitution of the object is a shifting pattern of signifcance, as I see "that white thing", then "that white bird", then a moment later "that egret", then "that egret moving step by step", then "that egret hunting a mouse in the waving grass". As my stream of experience unfolds, my visual noesis at one moment is followed by a sequence of evolving *noeses*, each carrying a distinctive noematic content. The evolving constitution of the egret I see consists in this structure of noemata—each bearing a horizon of meaning—*realized* in a temporal sequence of noetic phases in my process of observing the egret in motion.

What Husserl called "genetic" phenomenology begins with the temporal dynamics of intentional experience wherein different forms of noematic meaning are successively drawn into the subject's fowing stream of consciousness. Clearly, in the case of my evolving visual perception of the egret, rather sophisticated forms of meaning appear in the constitution of the egret in my experience. That is to say, the horizon of meaning accruing to my experience comprises ideas and concepts richer than pure sensory impressions. As I am sitting by the window, something "white" catches my attention, I see "a white bird" in the grass, I see "that white egret stepping through the grass", I see it "hunting a mouse". The concepts involved in this pattern of meaning depend on a background of not only my own experience (having seen egrets before), but also the experience and theorizing of biologists and birders who have formed the concepts I have acquired from their practices. Without those concepts, extant in my wider culture, I would not be able to see "that egret … stalking a mouse". Accordingly, genetic phenomenology places my particular experience, in seeing the egret beyond the window, within a *Lebenswelt* beyond my stream of consciousness.

#### **8 Ontology Amid the Transcendental Turn in Phenomenology**

Around 1907 Husserl took a transcendental turn, reconfguring his fundamental conception of phenomenology, incorporating something of a Kantian perspective into his philosophy. Thus, in *Ideas* I (1913), Husserl re-launched phenomenology with the transcendental methodology of *epoché*. It is said that phenomenology turns away from the world with *epoché*. For we are to bracket, or withhold judgment about, the actual existence of what we intend in our activities of consciousness. Metaphysics, or ontology, is then to be bracketed as we practice phenomenology, or so it is said.

However, as Husserl developed his transcendental form of phenomenology, he made full use of the ontology he outlined at the opening of *Ideas* I. For Husserl, formal ontology features categories including ideal species, part-whole relations, dependencies, states of affairs, and numbers, sets, manifolds. Material ontology features substantive regions including nature (spatiotemporal things), consciousness

(intentional experiences), and Geist (social formations). Material structures of mind, nature, and society are accordingly shaped by formal structures of parts/ wholes, dependence, states of affairs, groups, etc. This categorial scheme of formal and material structures weaves through the whole of *Ideas* I and *Ideas* II and onward into the late works of *Formal and Transcendental Logic* (1929) and the *Crisis* (1935–38). The transcendental in phenomenology should thus be seen through Husserl's own eyes, rather than in terms of the neo-Kantian program of avoiding both radical skepticism and all metaphysics.

Kantian transcendental philosophy seeks the "necessary conditions of the possibility of cognition": defning synthetic a priori knowledge of things in space and time as necessarily constrained by fundamental conceptual categories that shape the sensory manifold defning what is possible in the phenomenal world—setting aside the noumenal world that lies beyond our cognitive reach. Husserl's transcendental phenomenology follows a structure of *formal and material* ontological categories that fnd motivation not in the Kantian retreat from noumena to phenomena. Rather, the formal ontological categories envisioned by Husserl draw motivation from the developments of logic and mathematics in Husserl's day. Husserl's early conception of pure logic defned an alignment of forms among mind, language, and world, and this proto-model theory confgures Husserl's results even as he follows his transcendental turn.

When we deal with ideal *forms*, in the practice of pure mathematics, or pure logic, or pure phenomenology, however, Husserl holds that we posit such forms with "evidence" or "intuition". In this way ontology and phenomenology work together—interdependently—in Husserl's systematic philosophy.3

Thus, *epoché* in Husserl's methodology does not eschew all metaphysics, by "reducing" the world to mere phenomena. Rather, Husserl explicitly uses an intricate ontology of formal and material categories that structure the world: including our own consciousness in its relations to the surrounding world. The structure of our consciousness is defned in terms of the material features of intentionality, noema, and horizon framed by the formal features of kinds and properties and relations, parts and wholes, dependence and independence, as well as number, set, manifold, etc. That complex structure, realized in consciousness, comprises the "necessary conditions of the possibility" of phenomenal intentional experience. Whence Husserl's logical turn in phenomenology is not replaced but ramifed in his transcendental turn. This perspective is evident in Husserl's rather late work, *Formal and Transcendental Logic* (1929). Basically, transcendental logic is formal logic grounded in intentionality theory: in a more contemporary idiom, a semantic theory of intentionality.

The doctrine of "constitutive realism" at work here (cf. Smith, 2020) fts comfortably in a complex system of ontology along the lines of Roman Ingarden's

3Cf. *Ideas* I, §§10ff on formal and material ontology; §16 on synthetic a priori knowledge, prefguring the introduction of *epoché* in §§27ff; and §59, on *epoché* allowing "evident" use of "formal logic and the entire mathesis [universalis]", which includes a pure logic that embraces formal ontological categories.

monumental work, *The Controversy over the Existence of the World* (written in the mid-1940s). Ingarden studied with Husserl but argued against Husserl's transcendental idealism, which Ingarden took as a form of subjective idealism. In my view, Ingarden's ontology can be seen as a richly detailed extension of key ideas in Husserl's system of formal and material ontology, obviating any radical idealism. In particular, Ingarden's system details a variety of different "modes of being". Thus, cultural works (from art to law) are, for Ingarden, intentional artifacts, dependent in their existence on our intentional activities; by contrast, things in nature are not ontologically dependent on our intentional experiences of perception, judgment, and scientifc theorizing. Here is realism within a framework of intentionality and the "constitution" of egrets, mice, and felds of grass.4

Following Husserl, we may say both actual and possible situations are duly constituted in intentional activities but with different modes of being. Thus, the egret's movement is constituted in my perceptual experience as actual, whereas the egret's stalking a mouse is constituted in my perception merely as perceptually possible for my experience. Adapting Ingarden, we may specify the ontology more fully. Thus, the egret's walking in the grass is a situation whose mode of being is: actual, and intended in my perception, but ontologically independent of my perception. By contrast, the egret's stalking a mouse under foot is a situation whose mode of being is: not actual, but horizonally intended in my perception, and so perceptually possible for my perception, and ontologically dependent on my perception. That is, the horizonal situation (that of the egret stalking a mouse) is an intentional artifact of my visual experience, whereas the situation I see (that of the egret stepping through grass) is actual and not merely an artifact of my experience. To be clear, however, it is the same individual, that particular egret actually before me, which fgures in both situations, the actual and the perceptually possible.

As we look to ontology on the horizon of phenomenology, we note that our phenomenal intentional experiences occur in a world whose structure clearly outruns the limits of our forms of consciousness and our evolving *Lebenswelt*. In the *Crisis* (writings from 1935 to 1938), Husserl worried about the "mathematization" of nature. Husserl had in mind Einstein and relativity physics, considering the differences between Riemannian and Euclidian geometry, the former defning spacetime in a relativistic way that differs from the way we seem to experience spacetime as in accord with Euclidian principles. Moreover, quantum mechanics was already on the horizon in Husserl's day, as Einstein himself saw the challenge of how quantum physics could even conceivably relate to observable objects or events (cf. the Einstein, Podolsky, Rosen thought experiment circa 1935). In a kindred spirit of "crisis", we worry today about the reduction of the intentional structure of experience to the mathematical structures of computation, as in the ontology of Artifcial Intelligence. And if our lived conscious experience is ontologically grounded in neural processes in the human brain, which arguably run on quantum-mechanical

4 Ingarden's complex ontology is laid out in two volumes, recently translated into English as (Ingarden, 2013, 2016).

principles in our natural universe, then the mathematization of consciousness is all the more problematic. Constitutive realism entails that our consciousness and the objects we experience in our *Umwelt* are real and are constituted for us through our perception, thought, and action—including our best scientifc and mathematical theorizing about all the above. We await twenty-frst century developments!

#### **9 The Modal Model of Consciousness**

The horizon structure of intentionality, as outlined above, assumes a notion of *intentional modality*—such as perceivability as opposed to metaphysical possibility. This notion leads into a signifcant extension of Husserl's own theory of intentionality.5

Husserl distinguished two basic components in the noema of an act of consciousness. The noematic *Sinn*, the core of the noema, articulates the way the object is given in the experience. The Sinn is modifed by a component that articulates the "thetic" or "positing" character of the experience, as it were, the way the act is enacted by the subject, whether positing the object by seeing, by judging, by imagining, by willing, etc.

For example, the noematic content of my experience in seeing the egret we may characterize, simply, as follows—using angle brackets to specify noematic meaning:

The frst part of the description, , expresses the act's basic *thetic* content, by virtue of which the object is posited *perceptually*. The second part, < that tall white egret … >, expresses the act's *Sinn* content, by virtue of which the object is presented or intended *as such and such*.

Hintikka's logic of perception would cast the act's linguistic description in a propositional form, say:

David sees that (that egret is walking in grass)

schematically rendered as

S*d* ( *p* ),

5See Banick (2020), Hintikka (1969) and Smith and McIntyre (1982). A reviewer asked how modes of being given (as in perception) are being distinguished from modalities. A "modality" in the modal-logical sense is already a "mode" of a special sort: a modifcation in being that carries us into relevantly "alternative" situations in "worlds", thus the special trick of two-world indexing invented by Hintikka and Kanger. The terms are etymologically fused. What has been largely missed in the literature is that, beyond the model-theoretic moves in the semantics of modal-logics, and beyond Hintikka's assimilation of 'It is necessary that' with 'It is perceived/believed [by a] that', we should see a genuine ontological assimilation: a modifcation of the status of being from actual to relevantly/motivationally alternative to the actual. This in turn has links to the method of *epoché*.

where the perceptual modifer "S*d*" is treated as a modal operator governing the sentence "*p*", which specifes the perceived situation. Semantically, per Hintikka, the perception description is interpreted as asserting: in every perceptually possible world compatible with what the subject *d* sees in the actual world, it is the case that *p*. Following this possible-worlds style of semantics, then, the possible-worlds model of intentionality assumes an ontological framework of intentional modalities alongside the familiar ontic modalities of possibility/necessity. (Similarly, probability theory divides between subjective probability, as a measure of belief, and objective probability, as a measure of physical propensity.)

Assuming these perspectives drawn from Husserl and Hintikka, I've proposed a *modal model* of the structure of self-consciousness (cf. Smith, 2004). The aim is to articulate, and to distinguish, several formal elements in the overall noematic structure of an act of consciousness. For the case of my seeing the egret, we may expand on a basic phenomenological description of the experience in the following form again using angle quotes to specify noematic meaning:

\* < Phenomenally in this very experience I now here see attentively and intuitively that tall white egret now there stepping slowly through waving grass >

Within this complex expression (\*), we indicate different formal elements of noematic content, each articulating a distinctive phenomenological trait in the experience. The separated underlinings mark out these distinguished traits: familiar aspects of experience, each a target of phenomenological study over many years, beginning not least with Descartes' "cogito", or "I think …" .

The leading idea, in this modal model, is the distinction between the mode of presentation of the object, and the modality of presentation in the experience. Thus, the object of consciousness is presented in a certain way by virtue of the content,

< that tall white egret … >

Here lies the mode of presentation of the object in the experience. By contrast, the *act* of consciousness is executed in ways experienced by virtue of the *modal content*,

< phenomenally in this very experience I now here see attentively and intuitively >

There lies the modality of presentation in the experience.

On this modal model, we detail an integrated structure of specifc phenomenological traits as follows:

< Phenomenally>: the phenomenal character per se of the experience.

< in this very experience>: the character of inner awareness of the experience.

: the subjective or egocentric character where "I" enact the experience.

< now >: the temporal character of the experience fowing off in "inner time".

< here >: the spatial character of my experience as oriented around "my lived body".

< see >: the principal thetic character of my experience.

< attentively >: the qualifying character of focus in my experience.

< intuitively >: the evidential character informing my experience.

< that tall white egret now there stepping slowly through waving grass >: the form of presentation of the intended object, including the sense of "outer time" as the egret moves.

In particular, we note three vital aspects of consciousness given a formal twist in the modal model. Phenomenality is treated as a primitive and ubiquitous modal form, often indicated by the theater metaphor of a spotlight, within which things appear in consciousness. Inner awareness is treated as a modal qualifcation of the act, rather than, say, a peripheral higher-order presentation of the act alongside the object, both presented by virtue of the *Sinn* component. Self-awareness—i.e. awareness of the subject "I" in action, in seeing, or in thinking, or in willing, etc.—is treated also as a qualifcation of the act, not as a presentation of the subject along with the intended object, placing myself and the egret within the purview of *Sinn*, making an object of both. Awareness of temporality and spatiality appears also within the modal content, as distinguished from the presentation of the object; the egret is indeed given "now" "there" before "me", but these presented features do not "make an object" of act, subject, time, or place.

Paradigmatically, these modal features in an act of consciousness are mutually interdependent. In the case of my seeing the egret, for example, consciousness does not consist simply in the appearance of "that tall white egret …". Rather, consciousness takes the form of "see[ing] that tall white egret …", and moreover the frstpersonal form of "I see that tall white egret …". Of course, consciousness takes the form of "phenomenally I see that tall white egret …"; that goes without saying in phenomenology. Further, consciousness typically includes a certain awareness-ofawareness, and so takes the form of "phenomenally in this very experience I see that tall white egret …". In Husserlian ontology, the features of phenomenality, inner awareness, and subject-awareness thus form a whole wherein these features are mutually dependent parts (or "moments"): thus comprising a basic "modal" character typical of everyday consciousness. As we turn to everyday visual perception, moreover, we fnd an intrinsic sense of spatiotemporal embodiment, as consciousness takes the form of "phenomenally in this very experience I now here see that tall white egret …"—and where "I …" typically move around, bodily, turning my eyes and head toward the object. In the normal course of everyday experience, these distinguishable characters do not come apart, but are mutually constitutive of consciousness. For a detailed study of interdependencies of noematic content, as assumed in the modal model, see the reconstruction of Husserl's system in (Smith, 2013).

The modal model thus adds complexity to the basic form of intentionality. For intentionality consists not simply in a direction of consciousness toward an object, but in a directedness duly *modifed* by a complex modal character comprising phenomenality, inner awareness, self-awareness, and even awareness of embodiment.

#### **10 Conclusion**

Our refections have moved through horizons of phenomenological analysis, formal and material, reconfguring the "transcendental" conditions of phenomenal intentionality. Husserl's writings constantly demonstrate an interplay between formal and material aspects of lived experience. Consider: our consciousness of the fow of time, our perceptual awareness of the space around us, our lived as opposed to physical bodies, our experience in bodily action, our empathy with the experience of others, our collective or intersubjective experience, our normative sense of what's happening in our *Lebenswelt*, the historical and social genesis of so many of our concepts or noematic meanings, the constitution of social reality, and so on. Of particular signifcance today is social ontology. What count as social relations, social groups, social and legal norms, and the basic forms of social reality turn on the structure of intersubjectivity grounded in empathy and informing our evolving communal *Lebenswelt*. Accordingly, the foundations of social phenomena are interwoven with the phenomenology of empathy and intersubjectivity, explored initially in Husserl's *Ideas* II (1912/1989) and sharply articulated in Edith Stein's *On the Problem of Empathy* (1916).

The formal side of phenomenology is not a rigid and absolute constraint on what we can see in refection on experience. We abstract from phenomena. We refect on the phenomena and the forms we recognize therein. We revise our sense of the phenomena. And on we go, seeking a refective equilibrium between what we experience just as we experience it and what we make of the forms of experience, the noematic and horizonal meanings that inform our everyday experience.

#### **References**

Banick, K. (2020). Husserl, model theory, and formal essences. *Husserl Studies*, 1–23.

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## **The Problem of the Unity of a Manifold in the Development of Husserl's Philosophy**

**Burt C. Hopkins**

#### **1 Introduction**

Husserl's most systematic phenomenological work, *Ideas for a Pure Phenomenology and Phenomenological Philosophy. First Book: General Introduction to Pure Phenomenology* (*Ideas I*) (Husserl, 2014), differentiates pure transcendental phenomenology, as an eidetic science, from the eidetic science of mathematics.1 In line with the tradition of transcendental philosophy arguably—*ante rem—*stretching back to Plato, Husserl contrasts transcendental phenomenology with mathematics and argues that its conceptuality cannot be appropriately articulated and conceived in analogy with mathematics. While both mathematics and transcendental phenomenology are eidetic sciences, phenomenology "belongs to a basic class of eidetic sciences … [that is] totally different from that to which the mathematical sciences belong" (Husserl, 2014, 136). The key differential between these two sciences on Husserl's view concerns the nature of the essences that are the subject matter of each discipline. Mathematics deals with exact essences, which he characterizes as ideas in the Kantian sense. Phenomenology deals with inexact essences, which Husserl characterizes as morphological.

Signifcantly, Husserl formulates the precise issue of the difference between the two kinds of essences at issue here in terms of the answer to the question: "Is the stream of consciousness a genuine mathematical manifold (*Mannigfaltigkeit*)?"2

1Husserl defnes an "eidetic" science as "a science of essences" in contrast with a "science of matters of fact", such as empirical psychology (See Husserl, 2014, 5).

2The term 'manifold' (*Mannigfaltigkeit*) as employed by Husserl has a range of meanings, all of which are related to the basic phenomenon of, on the one hand, a multitude (*Menge*) of items, and, on the other, their unity (*Einheit*). Multiplicity (*Vielheit*), collection (*Kollektivum*), totality (*Inbegriff*), are closely related terms and generally used by Husserl with the same intended mean-

B. C. Hopkins (\*)

Université de Lille | UMR-CNRS 8163 STL, Lille, FRANCE

J. Yoshimi et al. (eds.), *Horizons of Phenomenology*, Contributions

to Phenomenology 122, https://doi.org/10.1007/978-3-031-26074-2\_5

(Husserl, 2014, 132). His answer is "no." The discussion to follow will focus on Husserl's distinction between a mathematical and a phenomenological manifold in light of the development of his thought, together with an invariant problematic running through most of it, which is behind that distinction. For the purposes of this discussion, Husserl's development will be divided into three phases: (1) the early descriptive psychological account of mathematical manifolds, (2) the pure transcendental phenomenological account of mathematical and phenomenological manifolds, and (3) the transcendental phenomenological account of the historicity of the different meanings determinative of both kinds of manifolds. The invariant problematic running through the second and third phases of the development of Husserl's thought, the phenomenological account of the unity and multiplicity proper to the manifold of internal time consciousness, will also be discussed.

My discussion will endeavor to show that Husserl's phenomenological account of the formal structure of a mathematical manifold does not adequately distinguish the formality of meanings that are ideal from that of those that are formalized. Symptomatic of this is Husserl's use of the term "formal," which refers to both ideal and formalized meanings in a manner suggesting that they share a common essential structure of "formality." That they do not will be shown to be an important implication of Husserl's phenomenological analysis of the constitution of ideal—in the sense of "ideas in the Kantian sense"—and formalized—in the sense of symbolic mathematics—meanings. Two phenomenologically signifcant consequences will be drawn from this.3 On the one hand, Husserl's account of a mathematical

ing, which is, again, the presentation of a phenomenon that is essentially characterized by more than one item that is nevertheless somehow unifed as a whole or a totality. The technical, formalized mathematical meaning of 'manifold', discussed below, of course also fgures in Husserl's use of the term, and is clearly what is meant in this quote.

3Husserl consistently distinguishes formalized universality from generalized universality and the processes of formalization and generalization constitutive of them (Husserl, 2014, 27). On the one hand, generalized universality manifests the hierarchical structure of meanings constitutive of the material regions of being, from a given region's highest genus down to the infma species determinative of the meaning of the manifold of individuals that instantiate the material region. Husserl characterizes the process of generalization that constitutes generalized meanings in terms of the variation that begins with examples drawn from factical (*faktisch*) experience and culminates in the imaginative variation that yields the essence of the various levels of generic universality (Husserl, 1973, 339–364, 1977, 53–63). On the other hand, Husserl characterizes formalized universality in terms of the non-hierarchical universality of the formal region "any object whatever" (*Etwas überhaupt*), which encompasses—without being reducible to—the generalized universalities constitutive of the meaning structure of the material regions of being. Husserl mostly characterizes the process of formalization in terms of the "emptying" of material meaning from generalized universal meaning structures, a process that is then sharply distinguished from the variation operative in the generalization that yields generalized universality (Husserl, 1973, 357). But he sometimes also characterizes formalization in terms of variation (Husserl, 1969, 249, 306). While Husserl is quite clear that the essential forms of meaning that characterize generalized and formalized universality do not share a common genus (Husserl, 2014, 27), in the case of the essential forms of meaning characteristic of ideas in the Kantian sense and formalized universality, Husserl often speaks as if both shared the essential commonality "ideal." That they cannot do so on grounds intrinsic to Husserl's own phenomenological analysis, will be shown in Sect. 8 below.

manifold will be shown to be problematical, insofar as that account has a dimension that is determined by a logical norm rather than a descriptively constituted *eidos*. This is, of course, problematical, because phenomenology as a descriptive eidetic science cannot legitimately base its cognition, without more ado, on the appeal to norms, logical or otherwise. In the case at hand, its cognition must rather provide an account of a mathematical manifold that is based in the cognition of its descriptively constituted eidos. On the other hand, Husserl's account of the constitution of the temporal foundation of the manifold that composes the stream of consciousness will be shown to be crucially determined by the appeal to eidetic structures whose formal conceptuality is mathematical rather than phenomenological. That is, Husserl's account of the formal unity and multiplicity constitutive of any given phenomenological manifold does not adhere to the distinction between a mathematical and phenomenological manifold presented in *Ideas I.* Hence, the formal character of the concepts Husserl employs to account for the unity of a phenomenological manifold—that is to say, their formal "conceptuality"—are mathematical, not phenomenological.4 This is, of course, therefore inconsistent with the *eidetic* distinction Husserl himself draws between mathematical and phenomenological manifolds.

Once this is established, a detailed account of the phenomenological shortcomings of Husserl's employment of exact mathematical concepts to characterize the constitution of a phenomenological manifold will be provided. Its focus will be on the inability of the mathematical concept of a continuum5 to account for the phenomenal *discontinuity* of the past from consciousness of present, both in the case of the manifold streams of consciousness that begin and end and the foundation of those manifolds in the living present. This discontinuity will be shown to be manifest in the phenomenon of *forgetting*, which Husserl's appeal to the "law of modifcation" to account for the retentional and protentional fow of consciousness as a continuum is unable to account for. The connection between sedimentation and

4Mark van Atten (in an email exchange) pointed out to me that "Husserl realizes (at least sometimes) that in his account [of the manifold of time] the mathematical is an idealization—see the *Bernauer Manuskripte*, *Hua* XXXIII, p. 66 line 16, p. 307 lines 16–18." In the frst instance, the idealization in question concerns the ideal givenness of the limit of the modifcation responsible for the generation of the temporal manifold, insofar as its retentive fow fades into the infnite "in [a] mathematical idealization (my translation)." In the second, Husserl characterizes the duration of time—as the summation of concreta*—*in terms of "a performance that is ordered formally and systematically" and thus the "matter of a mathematical technique (my translations)." While these appeals of Husserl to mathematical idealization and mathematical technique are doubtlessly related generally to the question of the role of the mathematical in his account of the manifold of time consciousness, it is important to note that what I wish to call attention to here is *not* Husserl's idealized mathematical characterization of the extension of the concrete manifold of consciousness qua its fowing or streaming. Rather, what I want to point out is that Husserl's account of the very genesis of this streaming—which according to his presentation of the phenomenological method must have *constitutive* priority over its putative formal structure—already employs the (exact) formal conceptuality of mathematics. See below, Sects. 14, 15, and 16.

5 "The running-off continuity of an enduring object is therefore a continuum whose phases are the continua of the running-off modes belonging to the different time-points of the duration of the object" (Husserl, 1991, 30).

forgetfulness made by Husserl in a late manuscript will provide the occasion to articulate the horizons of four future tasks for phenomenology: (1) investigate the role of the phenomenon of forgetfulness in the constitution of both internal and historical time consciousness; (2) reassess Husserl's account of recollection in making present transcendent objects in the living present, in light of the discontinuity of the horizon of the past from that of the present; (3) investigate the role of sedimentation, forgetfulness, and recollection in the constitution of the unity and multiplicity of the manifolds of consciousness that begin and end; and (4), investigate the intentional-historical meaning that is sedimented in the origins of the universal formalization that is the *sine qua non* for a mathematical manifold in contemporary mathematics.

#### **2 The Collective Unity of a Manifold and the Formalized Unity of Its Units in Husserl's Early Work**

The unity of a manifold emerges as a problem in Husserl's thought within a specifcally mathematical context (*Philosophy of Arithmetic*, *PA*) (Husserl, 2003). The manifold in question is a multitude of discrete units whose unity is irreducible to either any property (or properties) of the individual units or to their simple aggregation. Because of this, the unity in question is termed "collective," in the precise sense of its capacity to unify the discrete units that compose a multitude into a whole while being neither a property of any one of the individual units nor of their aggregate; *and* to do so without the collective unity itself being predicable of any individual unit. The specifc problem here is that of accounting for the peculiar *collectivity* of the unity in question. This is a problem given the inability of the wholepart structure of individual objects and their aggregation to account for it. This is to say that neither an account of the whole-part unity of each *individual* object, nor the unity of anything that can be predicated of such objects, can address, let alone account for, the collective unity that composes the collection of such objects.

The nature of this problem has a mathematical context, because the most basic objects of mathematics—natural numbers beginning with two—are characterized by their collective unity, which determines exactly how many units each specifc number is composed of. Each number unifes collectively an exact amount of units, no individual unit of which is intelligible as a numerical entity, because only as a collection do the units belong to the number that determines their amount. For instance, the frst number, "two," is composed of a unit *and* a unit, each of which is one, not two. Their exact amount—"two"—is therefore not predicable of either unit taken in isolation but only when both units together are part of the collection whose amount is "two." Despite the mathematical context of this problem, however, addressing it is not a mathematical but a philosophical one. This is the case not only because mathematical knowledge and the cognition behind it are perfectly capable of realizing themselves without philosophical refection upon their basic objects and concepts, but also because at issue in the foundation of collective unity is the intelligibility of the most universal and most fundamental phenomenon available to human understanding. "Every complex phenomenon which presupposes parts that are separately and specifcally noticed, every higher mental and emotional activity, requires, in order to be able to arise at all, collective combination of partial phenomena" (Husserl, 2003, 75). Moreover, "simple relations (e.g., identity, similarity, etc.)" (ibid.) could not be presented "if a unitary interest and simultaneously with it, an act of noticing did not pick out the terms and hold them together as unifed" (ibid.).

Another foundational issue arises here: the formal categorial structure of the concept of a unit is such that any arbitrary object from any domain of being whatever—perceptual, conceptual, imaginary—can fall under it. But again, the problem is one whose scope is not limited to a multitude composed of the arbitrary objects unifed by number and therefore to mathematics. In this case, the problem is that of foundation of the intelligibility of the most basic concept of logic, that of the materially empty and therefore formalized category of "anything" (*Etwas*).

#### **3 The Failure of Husserl's Descriptive Psychological Account of the Objectivity of the Collective Unity of a Manifold and Its Formalized Units**

Husserl's attempt to account for the philosophical foundation of the intelligibility of natural numbers addressed both the objectivity of the collective unity and the formalized unity of the individual units that compose the collectively unifed multitude determinative of number. That is, for Husserl accounting for the intelligibility of number involves the answer to two questions. One, what is responsible for the peculiar unity of the units it unifes, given their materially empty and therefore formal universality? Two, how is it possible that a multitude of such units are unifed as a *multiplicity* whose unity is neither derived nor derivable from the unity of each of the units belonging to their multitude, but that, as such, is nevertheless able to encompass them all? Husserl's early work, however, attempted to account for this within the context of the method of descriptive psychology, which focused on the psychological acts in which each kind of objectivity is given. In the former case, the act in question was that of collective combination, wherein the items in a multitude are successively combined into a unity, with the acts in question being indicated by the word "and." In the latter case, the act in question was that of the presentation (*Vorstellung*) in which any object of perception is given. In both cases, the descriptive psychological account of the inner perception (or, equivalently, refexion6 ) of

6 "Refexion" is preferable to "refection" for translating the German word "Refexion" within the context of Husserl's early work under discussion here. That work was informed by the Empirical account of the opposition between inner and outer perception, neither of which involved or other-

the acts in question was supposed to be capable of abstracting from the contents of the acts the objective meanings in question. In the acts of collective combination, the objectivity of the 'collective unity' is at issue and in the acts of perceptual presentation, that of the formal category of 'anything' is at stake. But as Husserl himself soon came to realize, from the inner perception of or refexion on the psychological acts all that can be abstracted is the concept of the act in question and not the objective unity given in it.7 The method of descriptive psychology therefore was rejected by Husserl, because it is incapable of providing the philosophical foundation for the collective and formalized unities that make intelligible the whole-part structure of the exact meaning of the natural numbers.

The fallacy of "psychologism" at issue in Husserl's initial foray into the foundational problems connected with the most basic objects of mathematics, it is important to note, however, was not the logical variety that claimed that the exact meanings in question are in truth really psychological realities. That is, it wasn't the kind of psychologism that Husserl criticized in the *Prolegomena to the Logical Investigations* (Husserl, 1970a). Rather, despite being fully aware of the non-psychological basis of the objectivity of the collective unity and the formal category of 'anything' (*Etwas*), Husserl's initial approach to accounting for their foundations nevertheless sought to ground the *origin* of that objectivity in the description of its psychological genesis.

It's important to note here, because it is often not recognized, that the philosophical problem of accounting for the foundation of the collective unity of a multitude and the formalized category determinative of its units remained a problem for Husserl's thought subsequent to his rejection of the psychological method he had initially employed to address it. Thus, after Husserl's rejection of the act of collective combination as the source of the objectivity of the collective unity of a manifold, accounting for that unity's foundation remained a problem for his thought.8 Likewise, the problem of accounting for the philosophical foundation of the formalized category of 'anything' also remained after his rejection of the descriptive psychological account of that category's origin.

wise presupposed what Husserl would later characterize as the "thematic" mode of conscious awareness that is intrinsic to, for instance, the meaning of the English term "refection."

7 In 1913 Husserl concluded, "from the refexion on acts" of collecting "the concept of collecting … is all that can result" (Husserl, 1975, 127) and therefore not the concept of the unity of the collection.

8See (van Atten, 2013) for a recent phenomenological attempt to account for this unity on the basis of the objectivation of the temporal form of the pre-given absolute fow of consciousness.

#### 87

#### **4 Husserl's Self-Critique of the Descriptive Psychological Account of the Logical Foundation of Symbolic Mathematics**

What's behind the lack of recognition noted is Husserl's response to the second foundational problem in mathematics he sought to address in his early work. Namely, the foundation of the logic that allows both the blind manipulations of meaningful symbols and the use of meaningless symbols as if they had a meaning to achieve mathematical cognition. Husserl sought to establish the foundation of this logic by appealing to an understanding of "symbol" that took it to be a surrogate for the presentation of genuine mathematical objects. The genesis of symbolic surrogation on this view involved three crucial steps. One, the idealizing extension of the mind's fnite powers of apprehending large and indeed infnite mathematical objects. Two, the substitution of sense perceptible signs for the idealized concepts generated by this idealization. And three, the manipulation of those signs according to other signs that express algorithmic rules for their combination and separation in the complete absence of any reference to the following: both the idealized concepts the signs that are the substitutes for and the original mathematical objects of which those concepts are the idealized extensions.

Husserl's account of the third step in his frst book, *Philosophy of Arithmetic* (Husserl, 2003), led him to realize that the descriptive psychological thesis of the surrogative function of symbols in relation to the concepts of mathematics that had guided that book's account of the foundation of the logic of symbolic mathematics was wrong.9 As Husserl related it in his famous letter to Karl Stumpf (Husserl, 1994, 12–19) (written after the book's completion), symbolic mathematics "is not a matter of the 'possibility' or 'impossibility' of concepts" (Husserl, 1994, 16), but "an accomplishment of the signs and their rules" (ibid.). Husserl concluded that symbolic mathematics, therefore, is "no science, but a part of *formal* logic" (ibid., 17), albeit a part that doesn't yet exist, as he knew "of no logic that would even do justice to the possibility of ordinary arithmetic" (ibid.).

#### **5 Husserl's Account of Categorial Unity of Numbers Does**  *Not* **Account for the Objectivity of Their Collective Unity**

Husserl's next book, *Logical Investigations* (*LI*) (Husserl, 1970a), sought to lay the groundwork for formal logic, one that would include the capacity to account for the foundation of both the objectivity of natural numbers and the logic of symbolic mathematics. However, readers searching for non-psychologistic solutions to either of the two foundational issues raised in Husserl's earliest work will search in vain.

9See (Willard, 1980) and (Hopkins, 2011a, b, Ch. 13).

Regarding the foundation of the objectivity of the natural numbers (beginning, as noted above, with the number two), Husserl included the species of those numbers among the categorial objects whose objectivity the breakthrough discovery to pure phenomenology—categorial intuition—was tasked with providing nonpsychological perceptual access. Thus, for instance, in the case of the number fve, the multitude of objects that compose that exact number were said to be "instances" of the categorial species "fve," whose objective unity is given as an ideal object that is irreducible to the psychological experience in which it is given. However, the question of the source of the ideal givenness of the collective unity of the multitude that composes any instance of the objective species "fve" is nowhere addressed in that work nor anywhere else in Husserl's account of categorial intuition in general. Husserl, in fact, notes explicitly in the *LI* that its investigations do not explore the foundation of the categorial unity of "*collectiva*."10

#### **6 Husserl's Phenomenological Account of a Defnite Mathematical Manifold**

With regard to the foundation of the logic of symbolic mathematics, what Husserl presented in the *LI* (Husserl, 1970a, §§ 69–70) proved to be the basis of his defnitive account of that logic, namely, his defnition of a mathematical manifold.11 Termed a "defnite manifold" or "mathematical manifold in the precise sense" in *Ideas I* (Husserl, 2014, 130), this account of the logic of symbolic mathematics remained the basis of his account of that logic in his later published works, *Ideas I* and *Formal and Transcendental Logic* (*FTL*). The logic in question has its basis in a fnite system of axiomatic propositions and axioms that completely and univocally encompass the essence of a given mathematical domain (e.g., that of Euclidean geometry). As a result, *every* proposition formed from this fnite set of propositions and axioms—no matter what its logical form—is either a formal logical consequence of them or their formal logical contradiction. In addition, this account of a defnite or precise mathematical manifold also characterizes for Husserl the manifold that ensues when the material particularization of all the special domains of mathematical objects is subject to formalizing universalization. What then results is

10 In § 51 of the LI, "Collectiva and Disjunctiva," Husserl calls attention to the lack of sensible perception of the collectivum and the "unitary object which corresponds" to the "act of collection." However, signifcantly, he does not provide a foundational account the objective unity of that object, but instead refers to the investigations in his *Philosophy of Arithmetic* of the signitive reference to a multitude that "does not therefore as yet possess the character of a genuine intuition of the collection as such" (Husserl, 1970a, 799).

11 In *FTL* (Husserl, 1969), 29 years after the publication of *LI*, Husserl quotes extensively from § 70 of *LI*, noting that "I shall repeat here the strict characterization of the idea of a formal theory of theory forms—correlatively, a formal theory of manifolds. I cannot improve on it" (Husserl, 1969, 91).

the *pure* defnition of a mathematical manifold, which accounts for the specialized logical form of any symbolic mathematical manifold whatever.

#### **7 Fundamental Phenomenological and Logical Problems with Husserl's Account of Defnite Mathematical Manifolds**

There are two fundamental problems with Husserl's account of both specialized and pure mathematical manifolds, one that is based in his account of the difference between mathematical and phenomenological manifolds and the other in the development of the logic of mathematics in the early twentieth century.

The frst problem is that Husserl's defnition presupposes the possibility of a system of formalized axioms encompassing both the essence of the *objects* of the various specialized mathematical domains as well as the *forms* of the axioms of any such specialized domain. This possibility, however, is not established *phenomenologically* by Husserl. That is, Husserl nowhere provides concrete *descriptive* analysis of the morphological (*inexact*) essence or essences of the *genesis*12 of formalized mathematical axioms and the propositions formed on their basis that refer adequately to (or otherwise denote): (1) the essence of either a given specialized domain of mathematical objects, or; (2) the essence of the forms of the axioms of any specialized domain of mathematical objects whatever. On the one hand, (1) would require a foundational phenomenological account of *both* the essence of a given

12The paradox of a phenomenological account of the descriptive "essence" of mathematical—and therefore exact—cognition that would employ inexact essences, per Husserl's *Ideas I* account of phenomenology as a descriptive eidetic science, disappears when it is considered that Husserl's original foundational engagement with mathematics in *PA* was concerned with the genesis of symbolic mathematical cognition. The radicality of that concern and the problem of the foundation that characterizes what Husserl would later (in *FTL*, with explicit reference to *PA*) term the "constitution" (Husserl, 1969, 87) of the intelligibility proper to formalized mathematics, prevents accounting for the "essence" of the genesis of exact mathematical structures on the basis of essences that are themselves already exact. The paradox, then, is that the phenomenological essence of the genesis of the exactness of formalized cognition cannot itself be exact, because precisely what is at stake in that essence is an account of the origin of the peculiar exactness of formalized cognition. In other words, if—per impossible—the origin of exactness was already exact, it wouldn't properly be an origin. In this connection, it is interesting to note that Husserl's pure phenomenological distinction between "static" and "genetic" phenomenological approaches to the problem of phenomenological constitution reintroduced his original concern with the problem of genesis in *PA* into his transcendental phenomenology. It is also interesting to note that his concrete genetic analyses (both published and unpublished) did not return to the original problem of the genesis of symbolic mathematical cognition. Only in his fnal texts, so-called *Crisis* texts, did he return to this problem, albeit signifcantly in those texts the transcendental phenomenological problem of genesis was connected, on essential grounds, with the problem of the historicity inseparable from the genesis of the essence of the exact meanings constitutive of symbolic mathematics, and the mathematical concept of a manifold determinative of that mathematics.

specialized domain of mathematical objects *and* of its *specialized* axiomatic formalization. On the other hand, (2) would require a foundational phenomenological account of the *universal* formalization of the formalized axioms of the various specialized domains of mathematical objects.

As Dieter Lohmar (1989, 191ff) and most recently Thomas Seebohm (2015, 207) have shown, the context for Husserl's defnition of a defnite manifold was not only Hilbert's mathematical notion of axiomatic completeness, but the fact that Husserl accepted that notion as both mathematically and logically sound. Soon after Husserl published *FTL* Gödel proved that not all formalized axiom systems in mathematics are complete ("defnite" or "precise" in Husserl's terminology), from which it follows that the universal scope of Hilbert's logical norm of axiomatic completeness is not well-founded mathematically. This development in logic renders Husserl's phenomenological account of a mathematical manifold problematic.13

#### **8 Equivocation of Ideal and Formalized Meanings in Husserl's Account of the Mathematization of Nature**

Husserl's pre-*Crisis* account of the formalized objectivity constitutive of mathematics is both sparse and inconsistent. He sharply distinguishes formalized universality from generalized universality and the processes of formalization and generalization constitutive of them (Husserl, 2014, 27). On the one hand, generalized universality manifests the hierarchical structure of meanings constitutive of the material regions of being, from a given region's highest genus down to the infma species determinative of the meaning of the manifold of *individuals* that instantiate the material region. Husserl characterizes the process of generalization that constitutes generalized meanings in terms of the variation that begins with examples drawn from factical (*faktisch*) experience and culminates in the imaginative variation that yields the essence of the various levels of generic universality (Husserl, 1973, 339–364, 1977, 53–63). On the other hand, Husserl characterizes formalized universality in terms of the non-hierarchical universality of the formal region "any object whatever" (*Etwas überhaupt*), which encompasses—without being reducible to—the generalized universalities constitutive of the meaning structure of the material regions of being. Husserl mostly characterizes the process of formalization in terms of the "emptying" of material meaning from generalized universal meaning structures, a process that is then sharply distinguished from the variation operative in the generalization

13For comprehensive discussions of the implications of Gödel's incompleteness theorems for the concept of *mathematics* that guides Husserl's account of a defnite manifold, see (Okada, 2002) and (van Atten, 2022).

that yields generalized universality.14 But he sometimes also characterizes formalization in terms of variation.15

In the *Crisis* Husserl tends to equate the mathematization of nature with its idealization (Husserl, 1970a, b, 23, 35, 66, 301). Husserl's traces this tendency to Galileo's employment of the exact essences of Euclidean geometry to *idealize* both the primary and secondary qualities of the cognition of sensible bodies (Husserl, 1970b, 35). Hence, in Husserl's account the process of mathematization *per se* is not always distinguished from its idealizing origins. This is the case despite the fact that Husserl himself recognized that the mathematization initiated by Galileo did *not* employ the formalized symbolic mathematics invented by François Vieta's analytic method (pure algebra) (Husserl, 1970b, 44). Moreover, Husserl recognized that the implicit "arithmetization of geometry" (ibid.) and mathematics generally made possible by Vieta's analytic innovation—led to the formalization of mathematical manifolds (Husserl, 1970b, 45). The latter formalization, then, is what leads for Husserl to the radical "emptying" (Husserl, 1970a, b, 44, 46)—by mathematization—of the intuitive meaning inseparable from the ontology of the life-world.

That said, however, Husserl's account in the *Crisis* of the constitution of the objective meaning operative in the mathematical sciences employed in the service of modern physics' mathematization of nature goes beyond his pre-*Crisis* accounts in two crucial regards. One, the condition of possibility for the constitution of the objectivity proper to the *exact* meaning operative in mathematical physics is tied to history, insofar as the handing down by tradition of such meaning is explicitly recognized by Husserl as a *sine qua non* for its *objective* constitution (Husserl, 1970b, 369). Two, Husserl's recognition of the *historicity* of the foundational meaning of the exact sciences (and its transmission by tradition) has as its condition of possibility the phenomenon of *sedimentation* (Husserl, 1970b, 362).16 Thus, the constitution of the meaning of the exact sciences cannot be reduced or otherwise be traced back to the intentional modifcations of perception, as Husserl had thought prior to the *Crisis* (Husserl, 1969, 158). And, indeed, it cannot be so reduced even if such modifcations are understood to extend beyond that of merely subjective to the

14 "But formalization is something essentially different from variation. It does not consist in imagining that the determinations of the variants are changed into others; rather, it is a disregarding, an emptying of all objective, material determinations" (Husserl, 1973, 359).

15See *Formal and Transcendental Logic*, where Husserl explicitly connects the constitution of "analytico-formal universalities" (Husserl, 1969, 249) to "phantasy variation" (ibid.). See also (ibid., 306).

16Husserl's last writings introduce the radical claim that "history is from the start nothing other than the vital movement of the coexistence and interweaving of original formations and sedimentations of meaning" (Husserl, 1970b, 372). By "sedimentation" Husserl means "the constant presuppositions" of the scientist "of his constructions, concepts, propositions, theories," such that these "mental products" take on "the form of persisting linguistic acquisitions, which can be taken up again at frst merely passively and be taken over [merely passively] by anyone else" (Husserl, 1970b, 52). Husserl speaks in this context "about the possibility of complete and genuine reactivation [of the sedimented meanings] in full originality, through going back to the primal selfevidences, in the case of geometry and the so-called 'deductive' sciences" (Husserl, 1970b, 365).

intersubjective constitution of perception (Seebohm, 2015, 187). Thus, as the original editor of Husserl's core *Crisis* texts, Eugen Fink, refected in the subtitle he added to Husserl's "Origin of Geometry," the function of sedimentation in the constitution of the objective meaning of geometry, and, by extension, of the exact sciences in general, exhibits an "intentional-historical" (Husserl, 1970b, 353) dimension.

Husserl thus saw in the *Crisis* that the formalization of meaning presupposed by modern mathematics is inseparable from its institution in an intentional-historical process. This formalization cannot be accessed by the empirical methodology employed by the positive science of history (Husserl, 1970b, 371). The conceptual suppositions behind the method and facts established by empirical history on Husserl's view make it blind to the region of the formal concepts that compose the mathematical objects of modern algebra and the analytic conceptuality generally that is constitutive of modern mathematics. And empirical history's explanatory methodology, rooted in the notion of effcient causality as the engine that drives historical change, is incapable of accounting for the kind of change that occurs in the historically dated conceptual transformations at issue in the history of ideas. It is precisely the latter kind of change, operative in the mathematization of nature initiated by Galileo, that Husserl sought to account for in the *Crisis* by aligning transcendental phenomenology's epistemologically foundational concerns with historical refections whose quarry is not historical *facts* but the historically dated origins of the exact meanings that are both presupposed by and that drive the exact sciences (Husserl, 1970b, 72, 370).

As already mentioned, despite recognizing the distinction between the idealized conceptuality of Euclidean geometry and the formalized conceptuality of algebra and symbolic mathematics generally, Husserl was wont to use the terms "mathematization" and "idealization" interchangeably. Moreover, notwithstanding, as already mentioned, his attentiveness to the arithmetization of geometry responsible for the primal institution of formalization and the intuitive emptying of the life-world inseparable from the conceptuality of formalized mathematics, Husserl himself never analyzed the epistemological-historical origins of formalized mathematics.

#### **9 Phenomenological Manifolds in Husserl's Pure Transcendental Phenomenology**

Husserl's phenomenological account of the manifold of the stream of consciousness has its basis in the refective thematization of the subjective experience in which the objective identity of the things in the world and the world itself as their horizon appears. Prior to the methodological intervention requisite for the phenomenological description of the stream of consciousness, the objective identity of things and the world horizon appear directly, without any explicit awareness of the subjective experience that is disclosed by phenomenological refection to be a condition for the

appearing of objectivity as such to consciousness. This phenomenological refection thematizes the subjective experience in which the objective identity in question appears. As thematized, the experience in question itself *appears*, and does so as the *manifold* of perspectives that are conscious of the objective identity of both the things in the world and their worldly horizon. These latter, in turn, *appear* as *unities* that stand out from the multiple perspectives directed to the unity of each that composes the manifold stream of consciousness.

The manifold of perspectives thematized by phenomenological refection pertains to what Husserl terms the "eidetic singular" (Husserl, 2014, 26), which is an essence's lowest specifc difference. What is singular here is precisely the fowing perspectives that compose the manifold as a *concretum*, that is, the essence of that dimension of subjective experience that is "absolutely independent" (ibid., 30) of any other essential determination. The descriptive articulation of the essence of the concretum brings to the fore the objective unity of the thing that appears in the fowing perspectival appearances. The latter *fowing* of experience cannot be "conceptually and terminologically" (ibid.) secured. Rather, only "the essential content in the fullness of its concreteness" can be so secured and thus cognized eidetically. Hence, while there can be "no talk of a univocal determination of *eidetic singularities*" (ibid., 135), in this case, of all that belongs to the fowing manifold of consciousness that composes the essence of the subjective stream of experiences in which objective identities appear, the content of that essence *itself* can be taken as something univocal. Namely, "as an ideally identical essence that, like any essence, could be instantiated, not only *hic et nunc* but in countless exemplars" (ibid., 134). In the case at hand, it can be instantiated in any arbitrarily given refectively thematized subjective experience in which the unity of objective identity appears.

Presumably, the "essence" at issue in the phrase "like any essence" here refers to the non-exact, descriptive essences that are the concern of the eidetic science of phenomenology. Thus, for instance, the account of the manifold perspectives of the subjective experience in which the unity of the identical object appears through its fowing is descriptive, since fowing does not appear as the specifcation of an essence with the characteristic of an Idea in the Kantian sense. The essential status of 'fowing', therefore, is not—*per impossible*—that of a moment in the extension of experience inseparable from the passage to an exact (and therefore) mathematical limit. Rather, 'fowing' is an instance of the ideally identical descriptive essence of *any* arbitrarily given subjective experience in which the appearance of the unity of the objective identity of things and the world horizon appears.17 As the instance of

17The question whether Husserl's account of the ideally identical character of the descriptive essence, whose status is *inexact* according to Husserl's *eidetic* distinction between the exact status of mathematical essences and the morphological status of phenomenological essences, tacitly presupposes the *idealization* in some sense of the descriptive essence, cannot be addressed here in detail. What can be remarked here, however, is that the status of the *ideality* of the descriptive essence for Husserl is radically different from that of the mathematical essence. It is so, above all, because the *ideality* of the latter but *not* the former requires for its constitution the passage to a limit that according to Husserl is essentially characteristic of mathematical exactness. To the extent that Husserl's phenomenological account of the descriptive essence is not just terminologically but

an essence, 'fowing' therefore does not refer to anything individual according to Husserl, that is, to something whose unity is empirically determined and therefore contingent, because as contingent it can always appear otherwise.

#### **10 The Constitution of Internal Time Consciousness**

The fowing manifold of the stream of subjective experience exhibits a phenomenological unity, which according to Husserl is constituted in "internal time consciousness." The meaning of 'internal' here is initially developed in contradistinction to the time of the clock, so-called "external" or "objective" time. However, the subjectivity of Husserl's account of time consciousness and the temporality constituted therein is in no way opposed to the time of the object. Rather, it is tasked with presenting the constitution of the unity of the object's presentation *as objectively present* in subjective experience from *within the temporality of that experience's fowing manifold*. This is the case, because subsequent to the *epoché*, the ontological opposition between the perception of "inner" and "outer" objects is transformed into the transcendental distinction between the constitution of "immanent" and "transcendent" meanings (*Sinne*). The constitution of the unity of the latter meanings, therefore, cannot be accounted for in an opposition between the manifold of the stream of consciousness and the unity of an object external to it, but rather, it must be sought precisely in the phenomenon of the fowing manifold itself. This is to say, the phenomenological unity of the immanent and transcendent meanings must be sought within the manifold that composes the stream of consciousness.

Husserl's phenomenological account of the temporal unity of the manifold of consciousness tracked the development of his phenomenology from "static" to "genetic." On the one hand, the static account employed the perceptual presentation of the transcendent object and the unity of its meaning as the "guiding" clue to account for the constitution of the temporal unity of the manifold of consciousness. On the other hand, the genetic account sought to account for the constitution of the immanent unity of the temporal manifold of consciousness itself on the basis of syntheses of consciousness that are both passively given *and* pre-objective. Both accounts apply the same correlation between the three phases of time consciousness—retention, primal impression, and protention—to the temporality of objective presentation, i.e., past, present, future. In the static account, this correlation is presented by Husserl as the essence of the temporal unity of the fnite streams of consciousness that come and go (Husserl, 2014, 157). In the genetic account, the correlation is presented as the essence of the absolute, pre-objective and

also substantially related to both the status and controversy over the true being of the *eidê* in Plato and Aristotle—and that extent on my view is considerable—the defnitive answer to this question requires the disambiguation of that status and controversy which is sedimented in Husserl's selfinterpretation of phenomenology as an *eidetic* science. (For a detailed discussion of this, see Hopkins, 2011a, b, especially 21–82 and 254–272.)

unobjectifable, standing-streaming origin of the living-present wherein appear and disappear the manifold fnite streams of consciousness.

#### **11 Husserl's Static and Genetic Accounts of the Constitution of the Temporal Unity of the Ego**

The methodological commitment of transcendental phenomenology to account for the unity of the phenomenological manifold without appeal to objects or objective meanings that do not have their source in the *transcendental* immanence of that manifold, as has been remarked often enough, is broken by Husserl's Cartesian selfinterpretation of the phenomenological manifold's subjectivity. For my purpose, only the implications of this for his account of the unity of the phenomenological manifold will be taken up. These implications concern Husserl's account of the static and genetic constitution of the unity of the transcendental Ego as an object immanent to the phenomenological manifold.

In the case of Husserl's static account of the Ego's unity, that unity is accounted for as a *pole* that underlies the manifold fowing perspectives of the stream of consciousness, which are intentionally directed to the unity of the meaning of the transcendent object. As such, the Ego's unity, as a pole, is constituted in opposition to the objectivity of the meaning of the transcendent object, which is itself characterized by Husserl as a *pole* whose unity underlies—in the technical sense of transcending—the manifold perspectives in which it appears to consciousness. Husserl's static account of the constitution of the Ego's unity is therefore dependent on it being posited in opposition to the unity of the object's meaning as transcendent. One consequence of this is that the constitutive account of its unity as an object immanent to the phenomenological manifold is derivative. It is derivative in the precise sense that the account of its unity as a pole presupposes that of the objective pole to which it is opposed in Husserl's descriptive account of its unity.18

Husserl's genetic account of the Ego's unity recognizes that because the Ego's static unity as a pole belongs to the stream of consciousness, its unity as an enduring identity in the *temporality* of the fowing of that stream is something whose constitution must be accounted for in terms of its genesis in that temporality. The static account of the Ego's unity is limited in this regard, as its status as a pole underlying the temporal fowing of the manifold of consciousness places its unity as somehow being constituted outside of that fow. Husserl attempts to get around the temporal limits of this static account by providing an account of the temporality of the Ego's mode of givenness as a unity. This account attends specifcally to the Ego's mode of appearance as an object immanent to the fow consciousness, wherein its identity as

18See Klaus Held's (Held, in Drummond, 2019, 212–213) defnitive analysis of the correlation between the Ego as pole and the object pole and the dependence of the former on the latter in Husserl's account of the static constitution of the Ego.

the "subject" of that fow presents itself as a unity not only in that fow's present moment but also in the moments of that fow that are no longer present and therefore past. As such, the unity of the Ego's identity must encompass two temporal dimensions, those of the present and the past. The genesis of its unity therefore requires an account of *how* the two different temporal moments that compose its identity are unifed.

Husserl's account of the 'how' in question appeals to the *act* of refection in which the Ego is given as a refected phenomenon that manifests itself in terms of the radically different dimensions of time that characterize the *how* of its phenomenal manifestation. The refective act in question is charged by Husserl with the task of synthesizing the Ego's givenness as a unity *having been* present and therefore as no longer present but past, with its givenness as enduring in the present. Such a synthesis is supposed to take place on the basis of the recognition that both the present and past temporal dimensions of the Ego are essential components of its identity as Ego, such that its unity as the *same* Ego is constituted. The Ego's unity is therefore constituted as a *unity in temporal difference* or, equivalently, as a *difference in temporal unity*. 19 Husserl's term for the peculiar temporality of this unity is the "living present."

#### **12 Problems with Husserl's Genetic Account of the Ego's Temporal Identity**

There are two interrelated and fundamental problems with this genetic account of the Ego's temporal identity. The frst concerns the phenomenological status of its unity. The second concerns that of the phenomenological origin of the manifold its unity putatively unifes.

Regarding the account of the constitution of the Ego's unity as an identity that encompasses its past and present temporality, it is evident that Husserl's account of the form of this unity does not originate in the manifold that composes that temporality. But rather, it is imposed on it from without, by an act of refection that does not belong to that manifold. The resulting 'unity' of the Ego, as the putative *living present* wherein the past and present phases of the Ego are supposed to be united in the genesis of the Ego's identity despite the difference between these temporal phases, therefore has its basis in the unity of another temporal manifold: namely, the act that generates the refection on these phases. The genesis of the unity of this second manifold cannot be accounted for by the unity of the Ego's identity since it is supposed to be responsible for that unity. It is therefore apparent that this account

19For a particularly nuanced account of the lack of priority of 'unity' and 'difference' in the temporality of the Ego at issue here, see (Mickunas, 2001, 164–165).

of the genesis of the identity of the Ego, as that which encompasses the living present, does not have its basis in a unity generated from a phenomenological manifold. Instead, it has its basis in a *form-conten*t schema that is, in effect, a reconstruction of that which it is supposed to provide a *phenomenological* account of: namely, the Ego's unity as an identity constitutively generated by the phenomenological manifold to which it belongs. The 'form' in question is the living present that is supposed to be synthetically generated from the refective act of recognition that the temporally discrete past and present phases of the Ego's temporality belong to the same Ego. The 'content' in question is the temporally determinate manifold composed of the discrete temporal phases whose unity *as* temporal the form of the living present is supposed to unify.

Regarding this content, that is, the manifold phases of temporality that the refective act is supposed to synthesize into the unity of the living present, a closer look at Husserl's account of its genesis will disclose that this account, too, has its basis in the form-content schema. As such, this account reconstructs rather than evidentially discloses the *descriptive* essence of the fowing stream of consciousness that composes a phenomenological manifold. Moreover, Husserl's account of this content itself, on closer inspection, will be disclosed as having its basis in the conceptuality of exact mathematical essences. As mentioned, Husserl's account of the subjective phenomenon of time articulates it in terms of the essential correlation between the phases of time consciousness and those of temporality. Hence, essentially correlated to the temporal phase of the past is the consciousness of the past consciousness retention—while to the temporal phase of the future is correlated the consciousness of the future—protention—and to the temporal phase of the present is correlated the consciousness of the originary now—primal impression. These three phases of time and the consciousness of them are meant both to capture the essence of three of the four phenomenal dimensions of the unitary phenomenon of time and to prepare the way for capturing the essence of time's fourth dimension, that of its succession.

Husserl's account of succession employs the descriptive terms "fowing" or "streaming" to characterize the morphologically eidetic singular *movement* of time consciousness. Husserl traces this movement in terms of an account of the relation of retentions and protentions to the originary now. Retentional consciousness is described as the awareness of the past that at once is a succession of just passed (elapsed) nows *and* an enduring awareness of the passing of the elapsed nows *that takes place in* the primal impression of the originary now. Protentional consciousness is described as the awareness of the future that is at once the arrival into the originary now of a succession of anticipated nows and the enduring awareness of their anticipation in the original now's primal impression.

#### **13 Three Salient Aspects of Husserl's Account of the Essence of Temporal Succession**

Three things stand out in this account of the essence of the successive movement characteristic of the phenomenon of time. One, although it characterizes the essence of a succession, the essence in itself is not successive. That is, both the elapsing and arriving nows are characterized in terms of their relation to the original now's impressional awareness, which, unlike the nows that elapse and arrive, is characterized as unmoving. It is so characterized, since as the reference point for *elapsing* and *arriving* units of meaning, it itself does not move. Two, despite its non-motion, the primal impression is nevertheless the origin of the movement of time by virtue of its status as the *source* of the multitude of nows that compose the temporal manifold of consciousness. This is the case because Husserl's descriptive account of that manifold maintains that each just passed elapsing now retains a relation to the impressional now, which, among other things, can only be possible if each elapsing now is replenished by a *fresh* now that is fully present just insofar as it hasn't elapsed yet. And three, nowhere so far in this account of the content of the manifold of the phases of temporality and the consciousness of those phases has the eidetic singularity of the peculiar differentia of the units of meaning that compose these temporal and conscious phases been accounted for. Insofar as the differentia in question here concern the constitution of each of the phases *and* the consciousness of them as an instance of something that is multiple, this is to say that Husserl's account of the temporal manifold of consciousness discussed so far does *not* address the phenomenological conditions of the possibility of its givenness precisely as a phenomenological *manifold*.

#### **14 Husserl's Account of the Constitution of Time Consciousness Does** *Not* **Refect His Late Criticism of the Immediacy of the Givenness of Impressions**

Husserl's early investigations of inner time consciousness account for the differentia in question on the basis of a characterization of the material (*sachlich*) content of the primal impression, namely its phenomenal status as a *sensation*. In contrast with the characterization of sensation in empirical theories of perception, namely, as ununifed bundles, Husserl initially maintained that the *phenomenon* of sensation appears as a "datum." As such, its "apprehension makes us conscious of something objective as given, 'in person', which is then said to be objectively perceived" (Husserl, 1991, 7). Sensory or "hyletic data" composed half of Husserl's initial account of the most fundamental and primitive distinction in the composition of a phenomenological manifold, the other half being "intentional form." While Husserl's mature investigations in the *Crisis* rejected the fundamentality of this hylo-morphic schema and with that, of hyletic data as being "immediately given"

(Husserl, 1970b, 125), he nevertheless did not abandon the crucial role of the *primal impression* in his late manuscripts' account of time. Indeed, the primal impression remained absolutely essential in Husserl's account of the source of the most basic units of the meanings proper to the temporality of the phenomenological manifold. Specifcally, it is essential to his account of the original now given in it as something *punctual*, namely, as a "now point."

Husserl's account of the now as a *point*, as an *ideal limit*, as something *abstract*, as a *form*, gives rise to two crucial questions. On the one hand, in what sense, if any, are these terms descriptive, in the precise sense of the criteria Husserl presented in *Ideas I* for distinguishing essences that are phenomenological from those that are mathematical? On the other hand, what methodological perspective is responsible for discerning this as well as the other essential characteristics of the fowing manifold of time consciousness?

Mindful of Husserl's criteria for distinguishing mathematical, which is to say, *exact* essences from phenomenological, i.e., *morphological* essences, the frst question can be reformulated as follows: is it possible to understand the terms in question—point, ideal limit, abstract, form—morphologically? On the surface, the obvious answer would seem to be "no." 'Point' and 'ideal limit' signify something *exact*. And while 'form' and 'abstract' need not signify something exact, nevertheless, if the form and abstraction in question referred to a point and ideal limit, both would appear to mean something that is exact. But these terms are meant to describe *not* this or that *individual* phenomenological manifold but the *essence* of any arbitrarily given manifold, and therefore, to describe the essence in the sense of an *eidetic singular*. So, the question may be refned, such that what is under interrogation is whether the phenomenologically peculiar ideal status of the essence *itself* that is characteristic of the fowing dimension of the phenomenological manifold is appropriately characterized—in reference to the *phenomenon* of fowing—by terms that have exact conceptual meanings, even though that which instantiates this essence is something that is *inexact*. Point and ideal limit, then, would characterize *that which makes possible* the appearance of something like a fowing that, in its concreteness, is neither punctual nor limited in the exact sense.

The answer to this refned version of the question is no doubt connected with the answer to the question regarding the methodological perspective from which the basic units of the temporal phases of time are differentiated and time consciousness' relationship to them discerned. In general, of course, the perspective in question is governed by the methodological protocol of the *epoché*. More particularly, the refection in question is directed to the mode of givenness of the phenomenon of time, which is to say, its appearance. As mentioned already, Husserl's account of its appearance tracks the static and genetic phases of the development of his thought, and for both the crucial aspect characteristic of the appearance in question is the primal impression. Husserl's methodical access to the phenomenon of time clearly presupposes the attempt to *grasp* the primal impression, whether in terms of its static correlation with the appearance of the object or its pre-objective and passive genesis. Crucial to either methodical approach is the resolution into a unity of that component of the primal impression that is designated as 'fowing', together with an account of the origin of the movement associated with that fowing.

#### **15 Ambiguity in Husserl's Account of the Origin of the 'Now'**

Leaving aside for the moment the implications of Husserl's own late recognition that impressions are *not* immediately given for his account of the origin of the movement in question, his account of the relation of the primal impression to the now can be seen to be problematic on its own terms. On the one hand, new impressions or sensations are characterized by him as already informed by the now, in which case the now is not presented as the content of the impression but as its form. "[T]he primordial temporal form of sensation, or, as I can also put it, the temporal form of primordial sensation, here of the sensation belonging to the current nowpoint and only to this … must, in strictness, be defned through primordial sensation, so that the proposition asserted has to be taken only as an indication of what is supposed to be meant" (Husserl, 1991, 69). On the other hand, the primal impression is characterized by Husserl as the phase of time consciousness that "has as its content that which the word 'now' signifes… Each new now is the content of a new primal impression" (Husserl, 1991, 70).