This paper examines Berkeley's attitude toward our perception of spatial relations on the two- dimensional visual field. This is a topic on which there has been some controversy. Historians of visual theory have tended to suppose that Berkeley took "all" spatial relations to be derived in the way our knowledge of depth is: from association of more primitive sensations which are themselves in no way spatial. But many philosophers commenting on Berkeley have supposed that he takes our awareness (...) of two- dimensional visual layout to be directly perceived. I argue that Berkeley's position on this issue is deeply ambivalent and that neither alternative sits well with the rest of his philosophy. (shrink)

In this study, 44 late elementary students’ visual behavior patterns when reading mind maps were investigated, more particularly, the intuitive processing nature of their visual characteristics, reading sequence and presentation mode. Eye-tracked data were investigated by means of static early attention and dynamic educational process mining analysis and combined with learning performance and retrospective interview data. All students seem to struggle with the map’s radial structure during initial reading. Also, the picture’s position in the map diverts students from (...) consecutively reading interconnected branches. EPM analyses revealed different reading patterns in proceeding reading behavior. Students receiving a text first, seem to grasp the radial structure slightly more and show higher information integration attempts. They also attained higher free recall and coherence scores. The study concludes with instructional design principles for urgently needed explicit visual literacy instruction in elementary grades. (shrink)

This paper provides a précis of Ernst Cassirer's concept of art as a symbolic form. It does so, though, in a specific respect. It points to the fact that Cassirer's concept of "symbolic form" is two-sided. On the one hand, the concept captures general cultural phenomena that are not only meaningful but also manifest the way man makes sense of the world; thus myth, religion, and art are considered general symbolic forms. On the other hand, it captures the formal structures (...) and semiotic tools thanks to which meaning is constructed within each general symbolic form (Cassirer called these structures "modes of objectivation"); thus, in art, perspective or the golden section are well-known examples of symbolic forms, now in a narrow sense, i.e. they are means to configure parts into an organized, meaningful whole. The paper will comment on art along both these two dimensions, but its main goal is to provide with concrete examples of aesthetic symbolic forms in the narrow sense in order to show how conceptual meaning can be inscribed in the space of aesthetic intuition. (shrink)

This paper provides a précis of Ernst Cassirer’s concept of art as a symbolic form. It does so, though, in a specific respect. It points to the fact that Cassirer’s concept of “symbolic form” is two-sided. On the one hand, the concept captures general cultural phenomena that are not only meaningful but also manifest the way man makes sense of the world; thus myth, religion, and art are considered general symbolic forms. On the other hand, it captures the formal structures (...) and semiotic tools thanks to which meaning is constructed within each general symbolic form ; thus, in art, perspective or the golden section are well-known examples of symbolic forms, now in a narrow sense, i.e. they are means to configure parts into an organized, meaningful whole. The paper will comment on art along both these two dimensions, but its main goal is to provide with concrete examples of aesthetic symbolic forms in the narrow sense in order to show how conceptual meaning can be inscribed in the space of aesthetic intuition. (shrink)

This book is about the relationship between necessary reasoning and visual experience in Charles S. Peirce’s mathematical philosophy. It presents mathematics as a science that presupposes a special imaginative connection between our responsiveness to reasons and our most fundamental perceptual intuitions about space and time. Central to this view on the nature of mathematics is Peirce’s idea of diagrammatic reasoning. In practicing this kind of reasoning, one treats diagrams not simply as external auxiliary tools, but rather as immediate visualizations (...) of the very process of the reasoning itself. Thus conceived, one's capacity to diagram their thought reveals a set of characteristics common to ordinary language, visual perception, and necessary mathematical reasoning. The book offers an original synthetic approach that allows tracing the roots of Peirce’s conception of a diagram in certain patterns of interrelation between his semiotics, his pragmaticist philosophy, his logical and mathematical ideas, bits and pieces of his biography, his personal intellectual predispositions, and his scientific practice as an applied mathematician. (shrink)

How should we characterize the functional role of conscious visual experience? In particular, how do the conscious contents of visual experience guide, bear upon, or otherwise inform our ongoing motor activities? According to an intuitive and (I shall argue) philosophically influential conception, the links are often quite direct. The contents of conscious visual experience, according to this conception, are typically active in the control and guidance of our fine-tuned, real-time engagements with the surrounding three-dimensional world. But this (...) idea (which I shall call the Assumption of Experience-Based Control) is hostage to empirical fortune. It is a hostage, moreover, whose safety is in serious doubt. Thus Milner and Goodale (1995) argue for a deep and abiding dissociation between the contents of conscious seeing, on the one hand, and the resources used for the on-line guidance of visuo-motor action, on the other. This ‘dual visual systems’ hypothesis, which finds many echoes in various other bodies of cognitive scientific research, poses a prima facie challenge to the Assumption of Experience-Based Control. More importantly, it provides (I shall argue) fuel for an alternative and philosophically suggestive account of the functional role of conscious visual experience. (shrink)

It is often assumed that when we see common opaque objects in standard light this is in virtue of seeing their facing surfaces. Here I argue that we should reject that claim. Either we don't see objects' facing surfaces, or—if we hold on to the claim that we do see such things—it is at least not in virtue of seeing them that we see common opaque objects. I end by showing how this conclusion squares both with our intuitions and with (...) the facts of vision science. (shrink)

"Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as (...) if it were the Third Eye, something only mathematical "mystics", like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or holistic, or incomplete, or perhaps even convincing in spite of lack of proof. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge. I shall argue that mathematical intuition is not any special or mysterious kind of faculty, and that it is possible to make progress in the philosophical analysis of this notion. This kind of undertaking has a precedent in the philosophy of Kant. While I shall be mostly developing ideas about intuition due to Edmund Husser! there will be a kind of Kantian argument underlying the entire book. (shrink)

The usual visual experiences possess a perspectival phenomenology as they seem to present objects from a certain perspective. Nevertheless, it is not obvious how to characterise experiential content determining such phenomenology. In particular, while there are many works investigating perspectival properties of experienced objects, a question regarding how subject is represented in visual perspectival experiences attracted less attention. In order to address this problem, I consider four popular phenomenal intuitions regarding perspectival experiences and argue that the major theories (...) of perspectival experiences do not account for all of them. Relying on these observations, I show how a theory which accommodates all these intuitions can be developed by (a) recognising that visual perspectival experiences are, in fact, multimodal visuo-bodily experiences and (b) distinguishing between egocentric and structural contents. (shrink)

How should we characterize the functional role of conscious visual experience? In particular, how do the conscious contents of visual experience guide, bear upon, or otherwise inform our ongoing motor activities? According to an intuitive and philosophically influential conception, the links are often quite direct. The contents of conscious visual experience, according to this conception, are typically active in the control and guidance of our fine-tuned, real-time engagements with the surrounding three-dimensional world. But this idea is hostage (...) to empirical fortune. It is a hostage, moreover, whose safety is in serious doubt. Thus Milner and Goodale argue for a deep and abiding dissociation between the contents of conscious seeing, on the one hand, and the resources used for the on-line guidance of visuo-motor action, on the other. This ‘dual visual systems’ hypothesis, which finds many echoes in various other bodies of cognitive scientific research, poses a prima facie challenge to the Assumption of Experience-Based Control. More importantly, it provides fuel for an alternative and philosophically suggestive account of the functional role of conscious visual experience. (shrink)

Susanna Siegel argues that visual contents are rich: visual experiences represent a variety of properties, over and above mere colors and shapes, including, notably, kind properties, e.g., the property of being a pine tree. To argue her case, she makes use of the method of phenomenal contrasts, which involves choosing among different explanatory hypotheses to account for phenomenal contrasts between relevant experiences. I will argue that there is reason to question whether the method of phenomenal contrasts is suitable (...) for establishing that kind properties are represented in visual experiences, insofar as the method draws upon first-person intuitions eclectically. (shrink)

Criteria of acceptability for mathematical proofs are field-dependent. In topology, though not in most other domains, it is sometimes acceptable to appeal to visual intuition to support inferential steps. In previous work :829–842, 2014; Lolli, Panza, Venturi From logic to practice, Springer, Berlin, 2015; Larvor Mathematical cultures, Springer, Berlin, 2016) my co-author and I aimed at spelling out how topological proofs work on their own terms, without appealing to formal proofs which might be associated with them. In this article, (...) I address two criticisms that have been raised in Tatton-Brown against our approach: that it leads to a form of relativism according to which validity is equated with social agreement and that it implies an antiformalizability thesis according to which it is not the case that all rigorous mathematical proofs can be formalized. I reject both criticisms and suggest that our previous case studies provide insight into the plausibility of two related but quite different theses. (shrink)

Much of the current imaging literature either denies the existence of wakeful non-mental imagers, views non-imagers motivationally as 'repressors' or 'neurotic', or acknowledges them but does not fully incorporate them into their models. Neurobiologists testing for imaging loss seem to assume that visual recognition, describing objects, and free-hand drawing require the forming of conscious images. The intuition that 'the psyche never thinks without an image.... the reasoning mind thinks its ideas in the form of images' (Aristotle) has a long (...) tradition in philosophical psychology, from Aristotle through the British empiricists to the British-empiricist-inspired introspection paradigm of Titchener. The massive shift in early experimental psychology to the introspective-antagonistic paradigm of Watson's behaviourism, may have sprung from the contrary intuition that no one thinks in mental images. In both cases, people seemed to assume that what is in one's own mind is in everybody's mind. A third, mediating, intuition - that some people do not think with conscious mental imagery -- seems to be confirmed by empirical studies on many levels. From the early imagery interviews of Francis Galton through many modern surveys, including my own, a consistent diversity of self-reports on ones own mental imagery abilities suggests that some 2-5% of people are very poor- or non-visual- imagers who, yet, maintain normal visual recognition abilities. Comparable estimates have been made in auditory and other imagery modalities. (shrink)

Geometry defines entities that can be physically realized in space, and our knowledge of abstract geometry may therefore stem from our representations of the physical world. Here, we focus on Euclidean geometry, the geometry historically regarded as “natural”. We examine whether humans possess representations describing visual forms in the same way as Euclidean geometry – i.e., in terms of their shape and size. One hundred and twelve participants from the U.S. (age 3–34 years), and 25 participants from the Amazon (...) (age 5–67 years) were asked to locate geometric deviants in panels of 6 forms of variable orientation. Participants of all ages and from both cultures detected deviant forms defined in terms of shape or size, while only U.S. adults drew distinctions between mirror images (i.e. forms differing in “sense”). Moreover, irrelevant variations of sense did not disrupt the detection of a shape or size deviant, while irrelevant variations of shape or size did. At all ages and in both cultures, participants thus retained the same properties as Euclidean geometry in their analysis of visual forms, even in the absence of formal instruction in geometry. These findings show that representations of planar visual forms provide core intuitions on which humans’ knowledge in Euclidean geometry could possibly be grounded. (shrink)

Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late 19th century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis received much attention in the 19th century. They helped to instigate what Hans Hahn called a ‘crisis of intuition’, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this ‘crisis’ as follows : " Mathematicians (...) had for a long time made use of supposedly geometric evidence as a means of proof in much too naive and much too uncritical a way, till the unclarities and mistakes that arose as a result forced a turnabout. Geometrical intuition was now declared to be inadmissible as a means of proof … "Avoiding geometrical evidence, Hahn continued, mathematicians aware of this crisis pursued what he called ‘logicization’, ‘when the discipline requires nothing but purely logical fundamental concepts and propositions for its development’. On this view, an epistemically ideal mathematics would minimize, or avoid altogether, appeals …. (shrink)

Embark on a visual journey of self-discovery. In Beaming, Marilyne Verschueren-the artist behind internet sensation @beamingdesign-presents 100 expansive visuals designed to stimulate your mind and awaken your intuition. Messages of hope, resilience, and joy are incorporated into radiant art, with each image offering the reader an opportunity for deep contemplation and introspection. Powerful imagery is paired with 25 guided exercises for mindfulness, journaling, and breathwork to deepen your interactive experience. Full of warmth and positive energy, Beaming is an exquisite (...) companion and a stirring call to follow your truth. (shrink)

In this paper we discuss visualizations in mathematics from a historical and didactical perspective. We consider historical debates from the 17th and 19th centuries regarding the role of intuition and visualizations in mathematics. We also consider the problem of what a visualization in mathematical learning can achieve. In an empirical study we investigate what mathematical conclusions university students made on the basis of a visualization. We emphasize that a visualization in mathematics should always be considered in its proper context.

Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late 19th century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis received much attention in the 19th century. They helped to instigate what Hans Hahn called a ‘crisis of intuition’, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this ‘crisis’ as follows : " Mathematicians (...) had for a long time made use of supposedly geometric evidence as a means of proof in much too naive and much too uncritical a way, till the unclarities and mistakes that arose as a result forced a turnabout. Geometrical intuition was now declared to be inadmissible as a means of proof … "Avoiding geometrical evidence, Hahn continued, mathematicians aware of this crisis pursued what he called ‘logicization’, ‘when the discipline requires nothing but purely logical fundamental concepts and propositions for its development’. On this view, an epistemically ideal mathematics would minimize, or avoid altogether, appeals …. (shrink)

‘Seeing is believing’ perhaps means that some visual experience provides good evidence for some claims that go beyond the content of the experience. Intuition—intellectual ‘seeming’—does not provide similarly good evidence, at least not for metaphysical claims, or so I shall argue. In §2, I sketch the conception of ‘metaphysics’ that is in use here, a conception that leads naturally to a problem about what counts as evidence in metaphysics. Some have suggested that intuition counts. In §3 I raise some (...) doubts (but not radical skeptical doubts) about intuition. These doubts are directed specifically at Bealer’s (1998) account of philosophical intuition. In §4 I will consider an argument in favor of the appeal to rational intuition as evidence in philosophy, and suggest that the argument is circular. I conclude §4 with some additional doubts about intuition, focused on whether intuitions could ever be ‘calibrated’. (shrink)

The image is the raw material of the twenty-first century. Images infiltrate all social and cultural spaces. Its digital-mediated realities drive communication, industry and knowledge. Images saturate life and adolescent learners are familiar with the participatory nature of image production and its social, educational and personal communicative realities. Vision and visibility, seeing and being now dominate how we inter-subjectively recognise ourselves and perform our world. We also find our aesthetic and embodied self increasingly constituted within imaging acts that are relational. (...) Visual culture may have colonised the self and learning, but imagination is without borders. The current pictorial turn opens possibilities to explore truth in flux through visual artistic acts. This article embeds Deleuzian method, which is one of intuitions, going beyond the actual, or our limited forms of representing life, to recognising that life has future imaginative potential forms and is always becoming. The article discusses an arts-based inquiry project for gifted artist visualiser/learners at an Australian regional university who are given broad topics on science phenomena and asked to give them expression. It suggests that pedagogies of the visual with their performative acts can prise open curriculum where an art-science interchange between two disciplines is made difficult by the current siloed nature of curriculum knowledge. Drawing on an analysis of Anika’s and Joel’s artworks and visual diaries it aims to reveal how their learning events dwell and are performed in aesthetic borderlands and how visual pedagogies forge new fluid visual borderlands and new learning. (shrink)

Neuroimaging studies on moral decision-making have thus far largely focused on differences between moral judgments with opposing utilitarian (well-being maximizing) and deontological (duty-based) content. However, these studies have investigated moral dilemmas involving extreme situations, and did not control for two distinct dimensions of moral judgment: whether or not it is intuitive (immediately compelling to most people) and whether it is utilitarian or deontological in content. By contrasting dilemmas where utilitarian judgments are counterintuitive with dilemmas in which they are intuitive, we (...) were able to use functional magnetic resonance imaging to identify the neural correlates of intuitive and counterintuitive judgments across a range of moral situations. Irrespective of content (utilitarian/deontological), counterintuitive moral judgments were associated with greater difficulty and with activation in the rostral anterior cingulate cortex, suggesting that such judgments may involve emotional conflict; intuitive judgments were linked to activation in the visual and premotor cortex. In addition, we obtained evidence that neural differences in moral judgment in such dilemmas are largely due to whether they are intuitive and not, as previously assumed, to differences between utilitarian and deontological judgments. Our findings therefore do not support theories that have generally associated utilitarian and deontological judgments with distinct neural systems. (shrink)

The paper builds on a methodological idea from experimental philosophy and on findings from psycholinguistics, to develop and defend ordinary language analysis (OLA) as practiced in J.L. Austin’s Sense and Sensibilia. That attack on sense-datum theories of perception focuses on the argument from illusion. Through a case-study on this paradoxical argument, the present paper argues for a form of OLA which is psychologically informed, seeks to expose epistemic, rather than semantic, defects in paradoxical arguments, and is immune to the main (...) objections to ordinary language philosophising, including those arising from the semantic/pragmatics distinction: A key project in current experimental philosophy is to develop psychological explanations of philosophically relevant intuitions that help us determine what warrant thinkers have for accepting them. Psycholinguistic work on the role of stereotypes in verb-comprehension has shown that intuitive judgments can be generated by automatic cognitive processes that duplicate both semantic and pragmatic inferences and are shaped by dominant uses of words. For systematic reasons, philosophers are prone to unwittingly deviate from such dominant uses. Where this happens, they are liable to automatically infer unwarranted conclusions that strike them as intuitively compelling. OLA helps us to determine those dominant uses, to identify unwitting deviations from them, and thus to expose unwarranted intuitions – e.g., in the premises of paradoxical arguments. Ordinary language does not determine the bounds of sense but shapes our leaps of thought. The paper shows how this enables its ‘Austinian’ analysis to contribute to a novel, epistemic, resolution of philosophical paradoxes and problems. (shrink)

Intuition. Originally an alleged direct relation, analogous to visual seeing, between the mind and something abstract and so not accessible to the senses. What are intuited (which can be derivatively called 'intuitions') may be abstract objects, like numbers or properties, or certain truths regarded as not accessible to investigation through the senses or calculation; the mere short circuiting of such processes in 'bank managers intuition' would not count as intuition for philosophy. Kant talks of our intuiting space and time, (...) in a way which is direct and entirely free from any mediation by the intellect - but this must be distinguished from an alleged pure reception of 'raw data' from the senses; the intuiting is presupposed by, and so cannot depend upon, sensory experience. (shrink)

In the present study, we addressed the problem of whether hand representations, derived from the control of hand gesture, are used in handedness recognition. Pictures of hands and fingers, assuming either common or uncommon postures, were presented to right-handed subjects, who were required to judge their handedness. In agreement with previous results (Parsons, 1987, 1994; Gentilucci, Daprati, & Gangitano, 1998), subjects recognized handedness through mental movement of their own hand in order to match the posture of the presented hand. This (...) was proved by a control experiment of physical matching. The new finding was that presentation of common finger postures affected responses differently from presentation of less common finger postures. These effects could be not attributed to mental matching movements nor related to richness in hand-finger cues useful for handedness recognition. The results of the present study are discussed in the context of the notion that implicit visual analysis of the presented hands is performed before mental movement of one's hand takes place (Parsons, 1987; Gentilucci et al., 1998). In this process, hand representation acquired by experience in the control and observation of one's and other people's hand gestures is used. We propose that such an immediate recognition mechanism belongs to the class of mental processes which are grouped under the name of intuition, that is, the processes by which situations or people's intentions are immediately understood, without conscious reasoning. (shrink)

Understanding of elementary topological equivalencies is impaired by preconceptions about the topological structure of ordinary objects, so that the equivalencies turn out to be counterintuitive. Here I will discuss some of these preconceptions, namely the dominance of gestalt properties of the visual display of the configuration, the neglect of holistic properties, the dominance of transformations the preserve metric properties over those that preserve topological properties only, the assumption that holes are objects of their own. These factors delineate an empirical (...) research field, intuitive topology. An explanatory hypothesis for the preconceptions suggests that they are hard-wired. (shrink)

In the epistemology of his middle period, Plato repeatedly describes the alleged ‘intellection of true reality’ in terms of sight, vision, illumination, or touch. Does this show more than Plato’s preference for optic and haptic metaphors? Should we assume that this goes back to a specific reason to be found in his underlying epistemological position? On the traditional reading, Plato actually wants to defend a sort of intuitionism. According to this still wide-spread reading, he claims that there is a very (...) particular way of grasping Forms: Philosophers manage to come into a sort of direct contact with intelligible objects. Intellection is thus conceived as a quasi-visual presence of intelligible Forms. In our contribution, we want to challenge this interpretation by raising several objections against it. Surprisingly, there exists a close parallel in Aristotelian scholarship: Although Aristotle’s epistemology is built on considerably different foundations, there is an interpretative tradition according to which one has to assume a strict discontinuity between the methodical procedure and the intellection of the highest epistemic objects. As for Plato, we want to refuse an interpretation of Aristotle based on a concept of intuition characterized by the following features: Intuition is a specific way of gaining knowledge. It is independent of empirical conditions and leads to apriori knowledge. It consists of some experience of evidence or is accompanied by it. Knowledge gained by this kind of intuition does not need any further argument or justification. (shrink)

The transparency of visual experience is a widely held and important thesis in the philosophy of perception. Critical discussion of transparency has focused on visual experiences, such as the experience of visual blur that are taken to be counter examples to transparency. Here, I consider a novel objection to transparency that does not depend on intuitions about examples. The objection is that if transparency is true then we cannot explain our ability to think about our visual (...) experiences as such. In response to this objection, I develop an account of how we are able to think about our own visual experiences as such that is compatible with transparency. (shrink)

Psychologists and philosophers are often tempted to make general claims about the importance of certain experimental results for our commonsense notions of intentional agency, moral responsibility, and free will. It is a strong intuition that if the agent does not intentionally control her own behavior, her behavior will not be an expression of agency, she will not be morally responsible for its consequences, and she will not be acting as a free agent. It therefore seems natural that the interest centers (...) on the notion of intentional control. If it can be experimentally shown that agents do as a matter of fact not control their own actions, even though they think they do, it will have far reaching consequences for our moral psychology. In this paper I look at recent eliminative arguments allegedly demonstrating that our commonsense notion of intentional control is incompatible with experimental data in support of the dual visual stream theory. (shrink)

The habit of separating the intuitive from the abstractive functions, as they were called in the Middle Ages, goes far back in our tradition. Descartes, in the sixth Meditation, defined man as "a thing that thinks," to which reasoning came naturally; whereas imagining, the activity of the senses, required a special effort and was in no way necessary to the human nature or essence. The passive ability to receive images of sensory things, said Descartes, would be useless if there did (...) not exist in the mind a further and higher active faculty capable of shaping these images and of correcting the errors that derive from sensory experience. A century later Leibnitz spoke of two levels of clear cognition.1 Reasoning was cognition of the higher degree: it was distinct, that is, it could analyze things into their components. Sensory experience, on the other hand, was cognition of the lower order: it also could be clear but it was confused, in the original Latin sense of the term; that is, all elements fused and mingled together in an indivisible whole. Thus artists, who rely on this inferior faculty, are good judges of works of art but when asked what is wrong with a particular piece that displeases them can only reply that it lacks nescio quid, a certain "I don't know what." · 1. Leibnitz, Nouveaux essais sur l'entendement humain , bk. 2, chap. 29. Rudolf Arnheim is the author of Art and Visual Perception: A Psychology of the Creative Eye, Toward a Psychology of Art, The Dynamics of Architectural Form, and Visual Thinking. His previous contributions to Critical Inquiry are "On the Nature of Photography" and "A Stricture on Space and Time". (shrink)

It seems obvious that signs in visual art and musical notation are static carriers of visual and acoustic information. Both types of sign, however, represent dynamic processes. In real space-time, there exists no static visible thing or static audible sound. The sources of visible or audible information are dynamic – i.e. complementary substantialenergetic-informational – entities extending in space-time. The same is true of an artificial or organic receiver and processor of visual or audible information. Reality and semiosis (...) – to be, to be perceived, and to be understood or to communicate – are dynamic processes. From a semiotic point of view, thus, pictures, photographic or artistic sign structures can’t be icons – in any case, if icons in a Peirceian manner are understood as signs representing objects for an interpretant by similarity . Similarity between icon and object is not a static precondition but a dynamic result of visual semiosis, i.e. of categorizing. Seeing something or hearing something is, as a consequence, not an “intuitive” or instantaneous Gestalt shift between representamen and object ongoing in an interpretant. And so, according to Fernande SaintMartin 1990: “visual semiotics … has to adopt an epistemology which is more in agreement with the dynamics of observed phenomena. It will recognize that matter is not inertness, but energy.” If the material carrier of semiosis, the representamen, already is to be understood as energy or dynamic process, all the more the whole complementary triadic sign-relation – object-representamen-interpretant – has to be understood as energetic information flow. This is being recognized in the transition from naturalistic, i.e. reproducing or mapping art, to modern, i.e. processing or interpreting/transducing art. Paul Klee 1990 for example says about the semiotic function of visual art: “Art doesn’t reproduce the visible but makes visible” . And he correlates the artistic activity of visualizing with the primordial, cosmogonic process of formation: “Reduced to the primordial process of formation, to creation, the process of cell division emerges” . Visual artistic semiosis is, thus, obviously to be understood as the process of emerging dynamic sign structures. It is the skill of the painter that makes the static results of dynamic semiosis “readable” for the viewer as signs – lines and surfaces - of the dynamic visual meaning of the picture. (shrink)

According to Kant, the axioms of intuition, i.e. space and time, must provide an organization of the sensory experience. However, this first orderliness of empirical sensations seems to depend on a kind of faculty pertaining to subjectivity, rather than to the encounter of these same intuitions with the real properties of phenomena. Starting from an analysis of some very significant developments in mathematical and theoretical physics in the last decades, in which intuition played an important role, we argue that nevertheless (...) intuition comes into play in a fundamentally different way to that which Kant had foreseen: in the form of a formal or “categorical” yet not sensible intuition. We show further that the statement that our space is mathematically three-dimensional and locally Euclidean by no means follows from a supposed a priori nature of the sensible or subjective space as Kant claimed. In fact, the three-dimensional space can bear many different geometrical and topological structures, as particularly the mathematical results of Milnor, Smale, Thurston and Donaldson demonstrated. On the other hand, it has been stressed that even the phenomenological or perceptual space, and especially the visual system, carries a very rich geometrical organization whose structure is essentially non-Euclidean. Finally, we argue that in order to grasp the meaning of abstract geometric objects, as n-dimensional spaces, connections on a manifold, fiber spaces, module spaces, knotted spaces and so forth, where sensible intuition is essentially lacking and where therefore another type of mathematical idealization intervenes, we need to develop a new form of intuition. (shrink)

Here are four examples of “seeing.” You see that something green is wriggling. You see that an iguana is in distress. You see that someone is wrongfully harming an iguana. You see that torturing animals is wrong. The first is an example of low-level perception. You visually represent color and motion. The second is an example of high-level perception. You visually represent kind properties and mental properties. The third is an example of moral perception. You have an impression of moral (...) properties. The fourth is an example of intuition. You intellectually grasp a general moral truth. Should moral perceptions be thought of as high-level perceptions or as intuitions? Most proponents of moral perception have thought of them as high-level perceptions. I give epistemological and methodological reasons for thinking that at least some are examples of what I call low-level intuitions—experiences in which we both apprehend abstract generalities and apply them to concrete particulars. (shrink)

In modern German ‘Anschauung’ is translated as intuition. But in Kant’s technical philosophical context, it means an intuition derived from previous visualizations of physical processes in the world of perceptions. The nineteenth century chemists’ predilection for Kantian Anschauung led them to develop an intuitive representation of what exists beyond the bounds of the senses. Molecular structure is one of the illuminating outcomes. (Ochiai 2021, pp. 1–51) This mental habit seems to be dominant among chemists even in the twentieth century, as (...) is illustrated by the electronic theory of organic chemistry and the frontier orbital theory as well. The former assumes that (1) bonds are paired electrons shared by bonded atoms—in fact, electrons in molecules are not localized in bonds; (2) the difference of electronegativities between bonded atoms causes electron drifts—expressed by the curly arrow—that result in bond formation or bond cleavage. The latter focuses on the orbitals that make the greatest contribution to the energy of a system undergoing electron delocalization, while the LCAO method says, as is suggested by the word Linear Combination of Atomic Orbitals, molecular orbitals should be constructed from all of the atomic orbitals that have the appropriate symmetry. In other words, every molecular orbital contributes to some extent to the electronic state of a molecule. The curly arrow in the electronic theory and the orbital lobe in the frontier orbital theory illustrate an intuitive character of these theories. Although both theories rely on such simple and qualitative models rather than mathematically rigid quantum mechanical calculations, they are successful in explaining, predicting, and designing chemical reactions. What makes these prima facie intuitive theories so successful? In this study we address this problem from a historical and philosophical as well as scientific point of view. The key to solve this problem is that they are concerned with only bond formation or bond cleavage, in which the localized-bond principle holds. (shrink)

This article gives an overview of the visual culture shared by a number of scientists studying human variation in the first half of the 20th century. This was a time when most scientists shared the conceptual and terminological framework of ‘racial classifications’ to capture the structure of human variation. Clearly, drawings – and later photographs – of people from all over the world constituted a crucial part of the well-established visual culture concerned with human variation. The article, however, (...) focuses on the representational tools for visualizing aspects of human variation that were not so obvious to the eye of the observer. It contextualizes researchers’ strategies of visualizing human diversity within the pictorial traditions of relevant fields, particularly physical anthropology and human genetics. Starting from 1900, the article demonstrates how scientists built up a rich visual repertoire for understanding human diversity, one that integrated maps, tables, photos, drawings, diagrams, family and phylogenetic trees. The representations included abstract and non-abstract elements, but increasingly rested on diagrammatic visualizations. Notably, although these diagrammatic visualizations grew in sophistication and methodological rigor, they were rarely used in academic textbooks. More often, mixed strategies of visualizations – diagrammatic elements integrated into non-diagrammatic images – were chosen as representations for human diversity. In the postwar period, most of those visualizations disappeared from scientific publications, but not from popular media. For the scientific publications, one can argue that a number of scientists paid specific attention to visualizations and their deterministic potential. Some argued that particularly maps and trees were altogether problematic in their visualization of human evolution and human diversity. Others sought out new and better ways of constructing trees and maps to visualize truth-claims about human diversity. Here, diagrammatic elements played a key role. Notably, researchers who employed typological approaches for physical anthropology, and who admitted that there was a moment of intuition in their practices, aspired to meet the demands of mechanical objectivity by establishing abstract inscriptions of their typological assessments. (shrink)

Often implicit in visual display design and development is a gold standard of photorealism. By approximating direct perception, photorealism appeals to users and designers by being both attractive and apparently effortless. The vexing result from numerous performance evaluations, though, is that increasing realism often impairs performance. Smallman and St. John (2005) labeled misplaced faith in realistic information display Naïve Realism and theorized it resulted from a triplet of folk fallacies about perception. Here, we illustrate issues associated with the wider (...) trend towards realism by focusing on a specific current trend for high-fidelity perspective view (3D) geospatial displays. In two experiments, we validated Naïve Realism for different terrain understanding tasks, explored whether certain individuals are particularly prone to Naïve Realism, and determined the ability of task feedback to mitigate Naïve Realism. Performance was measured for laying and judging a concealed route across realistic terrain shown in different display formats. Task feedback was either implicit, in Experiment 1, or explicit in Experiment 2. Prospective and retrospective intuitions about the best display formats for the tasks were recorded and then related to task performance and participant spatial ability. Participants generally intuited they would perform tasks better with more realism than they actually required. For example, counter to intuitions, lowering fidelity of the terrain display revealed the gross scene layout needed to lay a well-concealed route. Individuals of high spatial ability calibrated their intuitions with only implicit task feedback, whereas those of low spatial ability required salient, explicit feedback to calibrate their intuitions about display realism. Results are discussed in the wider context of applying perceptual science to display design, and combating folk fallacies. (shrink)

In this thesis, I investigate the nature of geometric knowledge and its relationship to spatial intuition. My goal is to rehabilitate the Kantian view that Euclid's geometry is a mathematical practice, which is grounded in spatial intuition, yet, nevertheless, yields a type of a priori knowledge about the structure of visual space. I argue for this by showing that Euclid's geometry allows us to derive knowledge from idealized visual objects, i.e., idealized diagrams by means of non-formal logical inferences. (...) By developing such an account of Euclid's geometry, I complete the "standard view" that geometry is either a formal system or an empirical science, which was developed mainly by the logical positivists and which is currently accepted by many mathematicians and philosophers. My thesis is divided into three parts. I use Hans Reichenbach's arguments against Kant and Edmund Husserl's genetic approach to the concept of space as a means of arguing that the "standard view" has to be supplemented by a concept of a geometry whose propositions have genuine spatial content. I then develop a coherent interpretation of Euclid's method by investigating both the subject matter of Euclid's geometry and the nature of geometric inferences. In the final part of this thesis, I modify Husserl's phenomenological analysis of the constitution of visual space in order to define a concept of spatial intuition that allows me not only to explain how Euclid's practice is grounded in visual space, but also to account for the apriority of its results. (shrink)

Geometrical intuitions spontaneously drive visuo-spatial reasoning in human adults, children and animals. Is their emergence intrinsically linked to visual experience, or does it reflect a core property of cognition shared across sensory modalities? To address this question, we tested the sensitivity of blind-from-birth adults to geometrical-invariants using a haptic deviant-figure detection task. Blind participants spontaneously used many geometric concepts such as parallelism, right angles and geometrical shapes to detect intruders in haptic displays, but experienced difficulties with symmetry and complex (...) spatial transformations. Across items, their performance was highly correlated with that of sighted adults performing the same task in touch (blindfolded) and in vision, as well as with the performances of uneducated preschoolers and Amazonian adults. Our results support the existence of an amodal core-system of geometry that arises independently of visual experience. However, performance at selecting geometric intruders was generally higher in the visual compared to the haptic modality, suggesting that sensory-specific spatial experience may play a role in refining the properties of this core-system of geometry. (shrink)

What influences people’s appreciation of works of art? In this paper, we provide a new cognitive approach to this big question, and the first empirical results in support of it. As a work of art typically does not activate intuitive cognition for functional artefacts, it is represented as an instance of non-verbal symbolic communication. By application of Sperber and Wilson’s Relevance Theory of communication, we hypothesize that understanding the artist’s intention plays a crucial role in intuitive art appreciation judgements. About (...) 60 works of fine art, representing a wide range of periods, genres and styles, were selected in the permanent exhibitions at Tate Britain in London, and rated by more than 500 visitors for goodness and understanding of the artist’s intention. Results suggest that works of art whose artist’s intention is easy to understand tend to be preferred over those with more obscure intentions, even when controlling for familiarity effects. (shrink)

Recently, a number of experiments have emphasized the degree to which subjects fail to detect large changes in visual scenes. This finding, referred to as “change blindness,” is often considered surprising because many people have the intuition that such changes should be easy to detect. Levin, Momen, Drivdahl, and Simons documented this intuition by showing that the majority of subjects believe they would notice changes that are actually very rarely detected. Thus subjects exhibit a metacognitive error we refer to (...) as “change blindness blindness.” Here, we test whether CBB is caused by a misestimation of the perceptual experience associated with visual changes and show that it persists even when the pre- and postchange views are separated by long delays. In addition, subjects overestimate their change detection ability both when the relevant changes are illustrated by still pictures, and when they are illustrated using videos showing the changes occurring in real time. We conclude that CBB is a robust phenomenon that cannot be accounted for by failure to understand the specific perceptual experience associated with a change. (shrink)

In the philosophy of perception, direct realism has come into vogue. Philosophical authors assert and assume that what their readers want, and what anyone should want, is some form of direct realism. There are disagreements over precisely what form this direct realism should take. The majority of positions in favor now offer a direct realism in which objects and their material or physical properties constitute the contents of perception, either because we have an immediate or intuitive acquaintance with those objects (...) and properties, or because our perceptual states have informational content that represents the properties of those objects (and which is not itself an object of perception and has no specifically subjective aspect). This paper considers various forms of perceptual realism, including, for purposes of comparison, the largely abandoned indirect or representative realism. After surveying the variety of perceptual realisms and considering their various commitments, I introduce some considerations concerning the phenomenology of visual space that cause trouble for most forms of direct realism. These considerations pertain to the perception of objects in the distance and, secondarily, to the perception of shapes at a slant. I argue that one of the lesser known varieties of perceptual realism, critical direct realism, can meet the challenges offered by the facts of spatial perception. (shrink)

The advent of experimental philosophy has recently expanded the domain of philosophical debates so as to include discussions about survey-based methodology and the validity of its employment in philosophical inquiry. One of the main criticisms of this approach questions the alleged response-intuition equation, by claiming that ‘pragmatic cues’ might prevent the subjects from reporting their genuine intuitions about the survey scenarios and questions. The pragmatic cues discussed by the literature include aspects of a quite different nature, ranging from thinking-styles to (...) semantic ambiguities. In order to distinguish between language-related pragmatic cues, and other features not strictly dependent on language, the distinction between the ‘response problem’ and the ‘interpretation problem’—potentially triggered by language-related pragmatic cues—is introduced. By employing an illustrated survey, this study aims at revealing the extent to which the use of ‘non-linguistic’ vignettes might constitute a valid aid to the traditional ‘linguistic’ vignette. A positive response would encourage the usage of illustrations and other non-linguistic or minimally-linguistic models in survey-based studies, which considerably restricts the liability of surveys for the interpretation problem. (shrink)

What is the relationship between complexity in the world and complexity in the mind? Intuitively, increasingly complex objects and events should give rise to increasingly complex mental representations (or perhaps a plateau in complexity after a certain point). However, a counterintuitive possibility with roots in information theory is an inverted U-shaped relationship between the “objective” complexity of some stimulus and the complexity of its mental representation, because excessively complex patterns might be characterized by surprisingly short computational descriptions (e.g., if they (...) are represented as having been generated “randomly”). Here, we demonstrate that this is the case, using a novel approach that takes the notion of “description” literally. Subjects saw static and dynamic visual stimuli whose objective complexity could be carefully manipulated, and they described these stimuli in their own words by giving freeform spoken descriptions of them. Across three experiments totaling over 10,000 speech clips, spoken descriptions of shapes (Experiment 1), dot-arrays (Experiment 2), and dynamic motion-paths (Experiment 3) revealed a striking quadratic relationship between the raw complexity of these stimuli and the length of their spoken descriptions. In other words, the simplest and most complex stimuli received the shortest descriptions, while those stimuli with a “medium” degree of complexity received the longest descriptions. Follow-up analyses explored the particular words used by subjects, allowing us to further explore how such stimuli were represented. We suggest that the mind engages in a kind of lossy compression for overly complex stimuli, and we discuss the utility of such freeform responses for exploring foundational questions about mental representation. (shrink)

This paper investigates the role of pictures in mathematics in the particular case of Cayley graphs—the graphic representations of groups. I shall argue that their principal function in that theory—to provide insight into the abstract structure of groups—is performed employing their visual aspect. I suggest that the application of a visual graph theory in the purely non-visual theory of groups resulted in a new effective approach in which pictures have an essential role. Cayley graphs were initially developed (...) as exact mathematical constructions. Therefore, they are legitimate components of the theory and the pictures of Cayley graphs are a part of practical mathematical procedures. (shrink)

The notion that a false positive (false conviction) is worse than a false negative (false acquittal) is a deep-seated commitment in the theory of criminal law. Its most illustrious formulation, the so-called Blackstone’s ratio, affirms that “it is better that ten guilty persons escape than that one innocent suffer”. Are people’s evaluations of criminal statutes consitent with this tenet of the Western legal tradition? To answer this question, we conducted three experiments (total _N_ = 2492) investigating how people reason about (...) a particular class of offenses—proxy crimes—known to vary in their specificity and sensitivity in predicting actual crime. By manipulating the extent to which proxy crimes convict the innocent and acquit those guilty of a target offense, we uncovered evidence that attitudes toward proxy criminalization depend primarily on its propensity toward false positives, with false negatives exerting a substantially weaker effect. This tendency arose across multiple experimental conditions—whether we matched the rates of false positives and false negatives or their frequencies, whether information was presented visually or numerically, and whether decisions were made under time pressure or after a forced delay—and was unrelated to participants’ probability literacy or their professed views on the purpose of criminal punishment. Despite the observed inattentiveness to false negatives, when asked to justify their decisions, participants retrospectively supported their judgments by highlighting the proxy crime’s efficacy (or inefficacy) in combating crime. These results reveal a striking inconsistency: people favor criminal policies that protect the rights of the innocent, but report comparable concern for their expediency in fighting crime. (shrink)

According to what I’ll call the ‘two visual systems account’ (TWO-SYSTEMS), the visual system is divided into two independent sub- systems, a ventral system implementing ‘vision for perception’ and a dorsal system implementing ‘vision for action’ (Milner and Goodale, 2006). TWO-SYSTEMS is widely discussed in philosophy due to the counter-intuitive role that it posits for conscious experience in the control of actions. However, recent evidence undermines the model’s core tenets: it no longer appears that the ventral and dorsal (...) streams constitute isolated processing systems, and there is now evidence for the involvement of both streams in conscious experience and online motor control. I articulate a new ‘direct dorsal control account’ (DORSAL-CONTROL), show that it is immune to three empirical challenges facing TWO-SYSTEMS, and show that it nonetheless has similarly significant implications for the perceiving mind. -/- Section 1 articulates TWO-SYSTEMS and its philosophical implications. Section 2 describes three empirical challenges to TWO-SYSTEMS. Section 3 articulates DORSAL-CONTROL and shows that it is immune to the three challenges. Section 4 articulates DORSAL-CONTROL’s philosophical implications. (shrink)

Great intuitions are fundamental to conjecture and discovery in mathematics. In this paper, we investigate the role that intuition plays in mathematical thinking. We review key events in the history of mathematics where paradoxes have emerged from mathematicians' most intuitive concepts and convictions, and where the resulting difficulties led to heated controversies and debates. Examples are drawn from Riemannian geometry, set theory and the analytic theory of the continuum, and include the Continuum Hypothesis, the Tarski-Banach Paradox, and several works by (...) Gödel, Cantor, Wittgenstein and Weierstrass. We examine several fallacies of intuition and determine how far our intuitive conjectures are limited by the nature of our sense-experience, and by our capacities for conceptualization. Finally, I suggest how we can use visual and formal heuristics to cultivate our mathematical intuitions and how the breadth of this new epistemic perspective can be useful in cases where intuition has traditionally been regarded as out of its depth. (shrink)