Husserl on Geometry and Spatial Representation

Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of physical geometry (or idealized perceptual space), the space of the mathematical science of physical nature (in which science, not only raw perception has a word) and the abstract spaces of mathematics (free creations of the mathematical mind), each of them with its peculiar geometrical structure. Perceptual space is proto-Euclidean and the space of physical geometry Euclidean, but mathematical physics, Husserl allowed, may find it convenient to represent physical space with a non-Euclidean structure. Mathematical spaces, on their turn, can be endowed, he thinks, with any geometry mathematicians may find interesting. Many other related questions are addressed here, in particular those concerning the a priori or a posteriori character of the many geometric features of perceptual space (bearing in mind that there are at least two different notions of a priori in Husserl, which we may call the conceptual and the transcendental a priori). I conclude with an overview of Weyl’s ideas on the matter, since his philosophical conceptions are often traceable back to his former master, Husserl.     

Speculative foundations of phenomenology

This essay tries to account for a certain ??speculative turn?? in contemporary philosophy (Q. Meillassoux, G. Harman, M. Gabriel, etc.) from a phenomenological point of view. A first objective of it will consist in exposing the link between, on the one hand, the methodological sense of Husserl??s concrete phenomenological analyses (concerning, for example, time and intersubjective structure of transcendental subjectivity,) and on the other hand, the consequences that follow from the grounding of phenomenology as first philosophy. This will allow a largely underestimated research angle to be opened up, one that I call a ??constructive phenomenology,?? that constitutes an essential and original figure of transcendental philosophy in general. A second objective will then consist in the attempt to sketch the foundation of knowledge as knowledge, the core of a ??phenomenological metaphysics.?? Whereas the first part will remain within a Husserlian framework, the second will develop some elements of a ??speculative transcendentalism?? in a phenomenological perspective.     

Autopoietic Enactivism,Phenomenology, and the Problem of Naturalism: A Neutral Monist Proposal

In this paper, I compare the original version of the enactive view—autopoietic enactivism—with Husserl’s phenomenology, regarding the issue of the relationship between consciousness and nature. I refer to this issue as the “problem of naturalism.” I show how the idea of the co-determination of subject and object of cognition, which is at the heart of autopoietic enactivism, is close to the phenomenological form of correlationism. However, I argue that there is a tension between an epistemological reading of the subject-object correlation that renounces to search for its metaphysical ground, and the enactivist focus on the biological basis of cognition, which seems to imply a view of nature as the metaphysical ground of the conscious mind. A similar problem arises in Husserl’s phenomenology in the contrast between the idea of the fundamental subject-object correlation, the concept of nature as a correlate of transcendental constitution, and the investigation of the corporeal and material grounding of consciousness. I find a way out of this problem by drawing on the distinction between static and genetic phenomenology. I argue that the investigation of the temporality of experience in genetic phenomenology leads us to investigate the metaphysical ground of the subject-object correlation, understood dynamically as co-constitution and co-origination. Then I propose to complement phenomenology and enactivism with a form of neutral monism, which conceives of the co-constitution of subject and object as grounded in a flow of fundamental, pre-phenomenal qualities.

     

Husserl on symbolic technologies and meaning-constitution: A critical inquiry

This paper reconstructs and critically analyzes Husserl’s philosophical engagement with symbolic technologies—those material artifacts and cultural devices that serve to aid, structure and guide processes of thinking. Identifying and exploring a range of tensions in Husserl’s conception of symbolic technologies, I argue that this conception is limited in several ways, and particularly with regard to the task of accounting for the more constructive role these technologies play in processes of meaning-constitution. At the same time, this paper shows that a critical examination of Husserl’s account of symbolic technologies, particularly as developed in his mature, genetic phenomenology, can be enduringly fruitful—if some of the specific conceptual weakness of this account are identified and properly accounted for. My discussion will proceed as follows. In the first part I briefly analyze the early Husserl’s account of the role the ‘method of sensible signs’ plays in arithmetic cognition. In the second, main part I critically examine the bearing the genetic-phenomenological concepts of sedimentation and technization have on the conceptualization of symbolic technologies in Husserl’s work. In the final part I summarize the major strengths and weaknesses of Husserl’s account of symbolic technologies, and in the process make a case for the ongoing relevance of some of the crucial elements of this account.     

Making ontology sensitive

The characteristic feature of phenomenology is the phenomenological constraint it exerts on its concepts: they should be embodied in concrete cases. Now, one might take that that possible match between concepts and the given would require some ontological foundation: as if the general determination provided by the concept should correspond to a particular piece of given to be found in the object itself as an abstract ??moment??. Phenomenology would then call for an ontology of abstract particulars. Against such view, the author advocates that such ontological foundation is flawed in principle, and that phenomenology as such does not call for any particular ontology: phenomenology rather introduces some kind of phenomenological constraint on the very way of ontological analysis. In order to determine what one can say to be in particular circumstances, one has to consider what one usually says to be in that kind of circumstances: on this alternative view, ontology rests on examples, as paradigmatic applications of concepts. The phenomenological move consists in disclosing how the very content of concepts depends on the ways they are applied, rather than what would be supposed to ??correspond?? to them would depend on their alleged content??as if the latter was independent of any previous connection with the given.     

Kant on geometry and spatial intuition

I use recent work on Kant and diagrammatic reasoning to develop a reconsideration of central aspects of Kant??s philosophy of geometry and its relation to spatial intuition. In particular, I reconsider in this light the relations between geometrical concepts and their schemata, and the relationship between pure and empirical intuition. I argue that diagrammatic interpretations of Kant??s theory of geometrical intuition can, at best, capture only part of what Kant??s conception involves and that, for example, they cannot explain why Kant takes geometrical constructions in the style of Euclid to provide us with an a priori framework for physical space. I attempt, along the way, to shed new light on the relationship between Kant??s theory of space and the debate between Newton and Leibniz to which he was reacting, and also on the role of geometry and spatial intuition in the transcendental deduction of the categories.     

Mathematical symbols as epistemic actions

Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols are not only used to express mathematical concepts??they are constitutive of the mathematical concepts themselves. Mathematical symbols are epistemic actions, because they enable us to represent concepts that are literally unthinkable with our bare brains. Using case-studies from the history of mathematics and from educational psychology, we argue for an intimate relationship between mathematical symbols and mathematical cognition.     

Existential Phenomenology and the Conceptual Problem of Other Minds

We ordinarily think that self and other coexist as subjects with mutually exclusive mental lives. The conceptual problem of other minds challenges this common thought by raising doubts that coexistence and mutual exclusivity come together in a coherent idea of others. Existential phenomenology is usually taken to be exempt from skeptical worries of this sort because it conceives of subjects as situated or embodied, offering an inclusive account of coexistence. I submit that this well‐entrenched view faces a serious dilemma: either the ordinary distinction between self and other has to be given up, or accounts of situated and embodied coexistence presuppose a non‐phenomenological solution to (a close relative of) the conceptual problem of other minds. I then propose a way out for existential phenomenology by sketching a Sartre‐inspired phenomenological response to the problem.     

Rethinking the Body and Space in Alfred Schutz’s Phenomenology of Music

What is initially striking about Alfred Schutz’s phenomenological account of the musical experience, which encompasses both the performance and reception of music, is his apparent dismissal of the corporeal and spatial aspects of that experience. The paper argues that this is largely a product of his wider understanding of temporality wherein the mind and time are privileged over the body and space, respectively. While acknowledging that Schutz’s explicit or stated view is that the body and space are relatively insignificant to his account, the paper reveals how they actually feature significantly in the latter, but in ways that remain largely implicit. First, the analysis demonstrates that the mental and temporal aspects of Schutz’s phenomenology of the musical experience cannot be considered independently of their interrelations with the equally important, albeit under-examined, corporeal, and spatial aspects. Concepts from Nietzsche’s early aesthetics are recruited to fulfil this task. Second, the analysis challenges Schutz’s dismissal of space in his theory of music perception. Lastly, it reveals the crucial, yet implicit, role of the body and space in his key examination of the intersubjective phenomenon he terms “making music together”. By presenting the above arguments, the paper aims to draw out the implicit dimensions of Schutz’s phenomenology of music and thereby enrich his influential account.     

生成认知：理论基础与实践走向

生成认知是具身认知思潮中的一个新取向。它主张认知是通过身体活动“生成的” (enacted)。认知的起点不是一个怎样精确表征世界的信息加工问题, 而是行动者在情境中怎样利用知觉来指导自己的行动。认知不是通过精确的心理表征“恢复”世界, 而是通过知觉引导的行动“生成”或“造就”一个自己的世界。认知是具身的行动, 认知结构形成于经常和反复出现的感觉运动模式, 与身体构造和身体活动具有深刻连续性。梅洛·庞蒂的身体现象学对生成认知具有深刻影响。同时, 詹姆斯、杜威等人的实用主义哲学对于实践行动的强调也深刻影响了生成认知。这种认知观强调了“行动”对心智的意义, 引发许多争议, 也促进了心理学研究范式的转变。     

Beyond Establishment and Separation: Political Liberalism, Religion and Democracy

Does John Rawls??s political liberalism require the institutional separation between state and religion or does it allow space for moderate forms of religious establishment? In this paper I address this question by presenting and critically evaluating Cécile Laborde??s recent claim that political liberalism is ??inconclusive about the public place of religion?? and ??indeterminate about the symbolic dimensions of the public place of religion??. In response to Cécile Laborde, I argue that neither moderate separation nor moderate establishment, intended as regimes of religious governance that fix specific interpretations of principles of social and economic justice, are compatible with Rawls??s political liberalism. Furthermore, I claim that a state can ensure that both its religious and non-religious citizens enjoy a sense of self-respect and identification with their polity by leaving issues of symbolic establishment and separation open to democratic debate. I conclude that Rawls??s political liberalism transcends the standard distinction between moderate establishment and moderate separation and leaves the public place of religion open to the democratic contestation of ordinary legislative politics.     

The Relationship Between Visual Illusion and Aesthetic Preference – an Attempt to Unify Experimental Phenomenology and Empirical Aesthetics

Experimental phenomenology has demonstrated that perception is much richer than stimulus. As is seen in color perception, one and the same stimulus provides more than several modes of appearance or perceptual dimensions. Similarly, there are various perceptual dimensions in form perception. Even a simple geometrical figure inducing visual illusion gives not only perceptual impressions of size, shape, slant, depth, and orientation, but also affective or aesthetic impressions. The present study reviews our experimental phenomenological work on visual illusion and experimental aesthetics, and examines how aesthetic preference is influenced by stimulus factors determining visual illusions including anomalous surface and transparency as well as geometrical illusion. Along with line figures producing geometrical illusions, illusory surface figures inducing neon color spreading and transparency effects were used as test patterns. Participants made both of psychophysical judgments and of aesthetic judgments for the same test pattern. Both of geometrical illusions and aesthetic preferences were found to change similarly as a function of stimulus variables such as the number of filling lines and the size ratio of the inner and outer figural components. Also, following specific stimulus variables such as lightness contrast ratio and spatial interval between inducing figural elements (so called ``packmen''), strong effects of color spreading and transparency were accompanied with strong preferences. It seems that the paradigm to investigate aesthetic phenomena along with perceptual dimensions is useful to bridge the gap between experimental phenomenology and experimental aesthetics.     

TAKING STOCK OF PHENOMENOLOGY FUTURES

In this paper, I review recent contributions of phenomenology to a variety of disciplines, including the cognitive sciences and psychiatry, and explore (1) controversies about phenomenological methods and naturalization; (2) relations between phenomenology and the enactive and extended mind approaches; and (3) the promise of phenomenology for addressing a number of controversial philosophical issues.     

Fractions We Cannot Ignore: The Nonsymbolic Ratio Congruity Effect

Although many researchers theorize that primitive numerosity processing abilities may lay the foundation for whole number concepts, other classes of numbers, like fractions, are sometimes assumed to be inaccessible to primitive architectures. This research presents evidence that the automatic processing of nonsymbolic magnitudes affects processing of symbolic fractions. Participants completed modified Stroop tasks in which they selected the larger of two symbolic fractions while the ratios of the fonts in which the fractions were printed and the overall sizes of the compared fractions were manipulated as irrelevant dimensions. Participants were slower and less accurate when nonsymbolic dimensions of printed fractions were incongruent with the symbolic comparison decision. Results indicated a robust basic sensitivity to nonsymbolic ratios that exceeds prior conceptions about the accessibility of fraction values. Results also indicated a congruity effect for overall fraction size, contrary to findings of prior research. These findings have implications for extending theory about the nature of human number sense and mathematical cognition more generally.     

The mathematical form of measurement and the argument for Proposition I in Newton’s Principia

Newton characterizes the reasoning of Principia Mathematica as geometrical. He emulates classical geometry by displaying, in diagrams, the objects of his reasoning and comparisons between them. Examination of Newton??s unpublished texts (and the views of his mentor, Isaac Barrow) shows that Newton conceives geometry as the science of measurement. On this view, all measurement ultimately involves the literal juxtaposition??the putting-together in space??of the item to be measured with a measure, whose dimensions serve as the standard of reference, so that all quantity (which is what measurement makes known) is ultimately related to spatial extension. I use this conception of Newton??s project to explain the organization and proofs of the first theorems of mechanics to appear in the Principia (beginning in Sect. 2 of Book I). The placementof Kepler??s rule of areas as the first proposition, and the manner in which Newton proves it, appear natural on the supposition that Newton seeks a measure, in the sense of a moveable spatial quantity, of time. I argue that Newton proceeds in this way so that his reasoning can have the ostensive certainty of geometry.     

Phenomenological reduction in Merleau‐Ponty's The Structure of Behavior: An alternative approach to the naturalization of phenomenology

Approaches to the naturalization of phenomenology usually understand naturalization as a matter of rendering continuous the methods, epistemologies, and ontologies of phenomenological and natural scientific inquiry. Presupposed in this statement of the problematic, however, is that there is an original discontinuity, a rupture between phenomenology and the natural sciences that must be remedied. I propose that this way of thinking about the issue is rooted in a simplistic understanding of the phenomenological reduction that entails certain assumptions about the subject matter of phenomenology and its relationship to the natural sciences. By contrast, Merleau‐Ponty's first work, The Structure of Behavior, presents a radically different approach to the phenomenological reduction, one that traverses the natural sciences and integrates them into phenomenology from the outset. I outline the argument for this position in The Structure of Behavior and then discuss consequences for current methodological issues surrounding the naturalization of phenomenology, focusing on the relationship between empirical sciences of mind, phenomenological psychology, and transcendental phenomenology. This novel exegesis of Merleau‐Ponty's view on the reduction offers new insight into his oft‐quoted remark that the phenomenological reduction is impossible to complete.     

The Field of Consciousness and Extended Cognition

Extended cognition theorists claim that the definition of cognition can be extended to include not only the brain, but also the body and environment. In a series of works, Mark Rowlands has envisioned a new science of mind that explores the externalism of consciousness and cognition. This paper connects Rowlands’ work with the phenomenology of Aron Gurwitsch. It shows how Gurwitsch’s field of consciousness, in particular his conception of the marginal halo, can provide a distinct, organized way of thinking about extended cognition. A key question considered is from where do cognitive processes project and disclose meanings? By thinking of location as locus—a projecting pathway of points of intentional opportunity—organization in extended cognition becomes organization in a field of consciousness. The marginal halo in the field of consciousness is articulated as this locus of intentionality, what Rowlands (The new science of the mind: from extended mind to embodied phenomenology, MIT Press, Cambridge, 2010) calls “the noneliminable intentional core”. Problems of cognitive bloat and personal character are addressed in light of the findings. In addition to situating Gurwitsch’s work within the extended mind movement for the first time, this study highlights the importance of the marginal halo, largely neglected in previous Gurwitsch scholarship.