Visual space can be distinguished from physical space. The first is found in visual experience, while the second is defined independently of perception. Theorists have wondered about the relation between the two. Some investigators have concluded that visual space is non-Euclidean, and that it does not have a single metric structure. Here it is argued that visual space exhibits contraction in all three dimensions with increasing distance from the observer, that experienced features of this contraction are not the same as (...) would be the experience of a perspective projection onto a fronto-parallel plane, and that such contraction is consistent with size constancy. These properties of visual space are different from those that would be predicted if spatial perception resulted from the successful solution of the inverse problem. They are consistent with the notion that optical constraints have been internalized. More generally, they are also consistent with the notion that visual spatial structures bear a resemblance relation to physical spatial structures. This notion supports a type of representational relation that is distinct from mere causal correspondence. The reticence of some philosophers and psychologists to discuss the structure of phenomenal space is diagnosed in terms of the simple materialism and the functionalism of the 1970s and 1980s. (shrink)

The relativistic optics of the nondispersive media endowed with the metric gij(x) [Eq. (1.6)] and with a nonlinear connection [Eq. (1.2)] is studied. The d-connection [Eqs. (3.3)– (3.4)] relates the conformal and projective properties of the space- time. A post-Newtonian estimation for the metric gij(x) is also given. It is shown that the solar system tests impose a constraint [Eq. (4.20)] on a combination of the post- Newtonian parameters describing the model.

The year 2009 marks the 400th anniversary of the publication of one of the most revolutionary scientific texts ever written. In this book, appropriately entitled, Astronomia nova, Johannes Kepler developed an astronomical theory which departs fundamentally from the systems of Ptolemy and Copernicus. One of the great innovations of this theory is its dependence on the science of optics. The declared goal of Kepler in his earlier publication, Paralipomena to Witelo whereby The Optical Part of Astronomy is Treated, was (...) to solve difficulties and expose illusions astronomers face when conducting astronomical observations with optical instruments. To avoid observational errors that had plagued the antiquated measuring techniques for calculating the apparent diameter and angular position of the luminaries, Kepler designed a novel device: the ecliptic instrument. In this paper we seek to shed light on the role optical instruments play in Kepler's scheme: they impose constraints on theory, but at the same time render astronomical knowledge secure. To get a comprehensive grasp of Kepler's astonishing achievements it is required to widen the approach to his writings and study Kepler not only as a mathematico-physical astronomer, but also as a designer of instruments and a practicing observer. (shrink)

The year 2009 marks the 400th anniversary of the publication of one of the most revolutionary scientific texts ever written. In this book, appropriately entitled, Astronomia nova, Johannes Kepler developed an astronomical theory which departs fundamentally from the systems of Ptolemy and Copernicus. One of the great innovations of this theory is its dependence on the science of optics. The declared goal of Kepler in his earlier publication, Paralipomena to Witelo whereby The Optical Part of Astronomy is Treated , (...) was to solve difficulties and expose illusions astronomers face when conducting astronomical observations with optical instruments. To avoid observational errors that had plagued the antiquated measuring techniques for calculating the apparent diameter and angular position of the luminaries, Kepler designed a novel device: the ecliptic instrument. In this paper we seek to shed light on the role optical instruments play in Kepler's scheme: they impose constraints on theory, but at the same time render astronomical knowledge secure. To get a comprehensive grasp of Kepler's astonishing achievements it is required to widen the approach to his writings and study Kepler not only as a mathematico-physical astronomer, but also as a designer of instruments and a practicing observer. (shrink)

One problem facing Hockney and Falco is the lack of evidence among optical sources to support their claim that artists used image-projection by the early 1400s. After all, if quattrocento artists knew about image-projection, they must have learned about it from experts in the field, and no one was more expert at the time than Perspectivist opticians. As I argue in this paper, however, Perspectivist reflection-analysis posed certain theoretical and conceptual constraints that would have prevented Perspectivist opticians from (...) recognizing, much less understanding, image-projection. Their silence on this matter is therefore not evidence against the Hockney-Falco thesis. (shrink)

One problem facing Hockney and Falco is the lack of evidence among optical sources to support their claim that artists used image-projection by the early 1400s. After all, if quattrocento artists knew about image-projection, they must have learned about it from experts in the field, and no one was more expert at the time than Perspectivist opticians. As I argue in this paper, however, Perspectivist reflection-analysis posed certain theoretical and conceptual constraints that would have prevented Perspectivist opticians from (...) recognizing, much less understanding, image-projection. Their silence on this matter is therefore not evidence against the Hockney-Falco thesis. (shrink)

This volume presents a collection of refereed papers reflecting the state of the art in the area of over-constrained systems. Besides 11 revised full papers, selected from the 24 submissions to the OCS workshop held in conjunction with the First International Conference on Principles and Practice of Constraint Programming, CP '95, held in Marseilles in September 1995, the book includes three comprehensive background papers of central importance for the workshop papers and the whole field. Also included is an introduction by (...) one of the volume editors together with a bibliography listing 243 entries. All in all this is a very useful reference book relevant for all researchers and practitioners interested in hierarchical, partial, and over-constrained systems. (shrink)

Although the study of visual perception has made more progress in the past 40 years than any other area of cognitive science, there remain major disagreements as to how closely vision is tied to general cognition. This paper sets out some of the arguments for both sides and defends the position that an important part of visual perception, which may be called early vision or just vision, is prohibited from accessing relevant expectations, knowledge and utilities - in other words it (...) is cognitively impenetrable. That part of vision is complex and articulated and provides a representation of the 3-D surfaces of objects sufficient to serve as an index into memory, with somewhat different outputs being made available to other systems such as those dealing with motor control. The paper also addresses certain conceptual and methodological issues, including the use of signal detection theory and event-related potentials to assess cognitive penetration of vision. A distinction is made among several stages in visual processing. These include, in addition to the inflexible early-vision stage, a pre-perceptual attention allocation stage and a post-perceptual evaluation, memory-accessing, and inference stage which provide several different highly constrained ways in which cognition can affect the outcome of visual perception. The paper discusses arguments that have been presented in both computer vision and psychology showing that vision is "intelligent" and involves elements of problem solving". It is suggested that these cases do not show cognitive penetration, but rather they show that certain natural constraints on interpretation, concerned primarily with optical and geometrical properties of the world, have been compiled into the visual system. The paper also examines a number of examples where instructions and "hints" are alleged to affect. (shrink)

The paper explores the fundamental physical principles of quantum mechanics (in fact, quantum field theory) that limit the bit rate for long distances and examines the assumption used in this exploration that losses can be ignored. Propagation of photons in optical fibers is modelled using methods of quantum electrodynamics. We define the “photon duration” as the standard deviation of the photon arrival time; we find its asymptotics for long distances and then obtain the main result of the paper: the (...) linear dependence of photon duration on the distance when losses can be ignored. This effect puts the limit to joint increasing of the photon flux and the distance from the source and it has consequences for quantum communication. Once quantum communication develops into a real technology (including essential decrease of losses in optical fibres), it would be appealing to engineers to increase both the photon flux and the distance. And here our “photon flux/distance effect” has to be taken into account. This effect also may set an additional constraint to the performance of a loophole free test of Bell’s type—to close jointly the detection and locality loopholes. (shrink)

A common approach to explaining the perception of form is through the use of static features. The weakness of this approach points naturally to dynamic definitions of form. Considering dynamical form, however, leads inevitably to the need to explain how events are perceived as time-extended—a problem with primacy over that even of qualia. Optic flow models, energy models, models reliant on a rigidity constraint are examined. The reliance of these models on the instantaneous specification of form at an instant, t, (...) or across a series of such instants forces the consideration of the primary memory supporting both the perception of time-extended events and the time-extension of consciousness. This cannot be reduced to an integration over space and time. The difficulty of defining the basis for this memory is highlighted in considerations of dynamic form in relation to scales of time. Ultimately, the possibility is raised that psychology must follow physics in a more profound approach to time and motion. (shrink)

The relationship between the photographic and optical images and time has been the subject of great deal of debate. Despite their differences, what many of these considerations have in common is their focus on the receiver, whether mechanical, biological, social or the memory and imagination of the observer. My aim here is to shift the emphasis from the receiver to the object or vista that is photographed or viewed and to explore how the constraints implied by our modern (...) understanding of the Universe, concerning space and time, impact on the way we perceive photographic and optical images. Viewed from this perspective, photographs can be treated as light projections of sections of the four-dimensional observable world onto two-dimensional spatial photographic or viewing surfaces. I shall show that despite the severe reduction that such projections imply, these modern considerations have the important consequence of bestowing a complex temporality upon optical images, including photographs. This realization dramatically changes the way we view photographs. I give examples of this rich temporality through considerations of terrestrial images – and more significantly images of the Sky, where these temporal effects are far more pronounced. (shrink)

Virtuosity in music performance is often associated with fast, precise, and efficient sound-producing movements. The generation of such highly skilled movements involves complex joint and muscle control by the central nervous system, and depends on the ability to anticipate, segment, and coarticulate motor elements, all within the biomechanical constraints of the human body. When successful, such motor skill should lead to what we characterize as fluency in musical performance. Detecting typical features of fluency could be very useful for technology-enhanced (...) learning systems, assisting and supporting students during their individual practice sessions by giving feedback and helping them to adopt sustainable movement patterns. In this study, we propose to assess fluency in musical performance as the ability to smoothly and efficiently coordinate while accurately performing slow, transitionary, and rapid movements. To this end, the movements of three cello players and three drummers at different levels of skill were recorded with an optical motion capture system, while a wireless electromyogrphy (EMG) system recorded the corresponding muscle activity from relevant landmarks. We analyze the kinematic and coarticulation characteristics of these recordings separately and then propose a combined model of fluency in musical performance predicting music sophistication. Results suggest movements from expert performers' are characterized by consistently smooth strokes and scaling of muscle phasic coactivation. The explored model of fluency as function of movement smoothness and coarticulation patterns was shown to be limited by the sample size but serves as a proof of concept. Results from this study show the potential of a technology-enhanced objective measure of fluency in musical performance, which could lead to improved practices for aspiring musicians, instructors, and researchers. (shrink)

The relationship between the photographic and optical images and time has been the subject of great deal of debate. Despite their differences, what many of these considerations have in common is their focus on the receiver, whether mechanical (the camera), biological (the eye–brain as the optical receiver), social or the memory and imagination of the observer. My aim here is to shift the emphasis from the receiver to the object or vista that is photographed or viewed and to (...) explore how the constraints implied by our modern understanding of the Universe, concerning space and time, impact on the way we perceive photographic and optical images. Viewed from this perspective, photographs can be treated as light projections of sections of the four-dimensional observable world onto two-dimensional spatial photographic or viewing surfaces. I shall show that despite the severe reduction that such projections imply, these modern considerations have the important consequence of bestowing a complex temporality upon optical images, including photographs. This realization dramatically changes the way we view photographs. I give examples of this rich temporality through considerations of terrestrial images – and more significantly images of the Sky, where these temporal effects are far more pronounced. (shrink)

Computational theories of vision typically rely on the analysis of two aspects of human visual function: (1) object and shape recognition (2) co-calibration of sensory measurements. Both these approaches are usually based on an inverse-optics model, where visual perception is viewed as a process of inference from a 2D retinal projection to a 3D percept within a Euclidean space schema. This paradigm has had great success in certain areas of vision science, but has been relatively less successful in understanding perceptual (...) representation, namely, the nature of the perceptual encoding. One of the drawbacks of inverse-optics approaches has been the difficulty in defining the constraints needed to make the inference computationally tractable (e.g. regularity assumptions, Bayesian priors, etc.). These constraints, thought to be learned assumptions about the nature of the physical and optical structures of the external world, have to be incorporated into any workable computational model in the inverse-optics paradigm. But inference models that employ an inverse optics plus structural assumptions approach inevitably result in a na. (shrink)

It is shown that below the threshold of pair creation, a consistent quantum mechanical interpretation of relativistic spin-0 and spin-1 particles (both massive and mussless) ispossible based an the Hamiltonian-Schrödinger form of the firstorder Kemmer equation together with a first-class constraint. The crucial element is the identification of a conserved four-vector current associated with the equation of motion, whose time component is proportional to the energy density which is constrainedto be positive definite for allsolutions. Consequently, the antiparticles must be interpreted (...) as positive-energy states traveling backward in time. This also makes it possible to define hermitian position operators with localized eigensolutions (δ-functions) as well as Bohmian trajectories for bosons. The exact theory is obtained by “second quantization” and is mathematically completely equivalent to conventional quantum field theory. The classical field emerges in the high mean number limit of coherent states of the exact theory. The formalism provides a new basis for computing tunneling times for photons and chaotic phenomena in optics. (shrink)

A major challenge for semantic video segmentation is how to exploit the spatiotemporal information and produce consistent results for a video sequence. Many previous works utilize the precomputed optical flow to warp the feature maps across adjacent frames. However, the imprecise optical flow and the warping operation without any learnable parameters may not achieve accurate feature warping and only bring a slight improvement. In this paper, we propose a novel framework named Dynamic Warping Network to adaptively warp the (...) interframe features for improving the accuracy of warping-based models. Firstly, we design a flow refinement module to optimize the precomputed optical flow. Then, we propose a flow-guided convolution to achieve the adaptive feature warping based on the refined optical flow. Furthermore, we introduce the temporal consistency loss including the feature consistency loss and prediction consistency loss to explicitly supervise the warped features instead of simple feature propagation and fusion, which guarantees the temporal consistency of video segmentation. Note that our DWNet adopts extra constraints to improve the temporal consistency in the training phase, while no additional calculation and postprocessing are required during inference. Extensive experiments show that our DWNet can achieve consistent improvement over various strong baselines and achieves state-of-the-art accuracy on the Cityscapes and CamVid benchmark datasets. (shrink)

Findings in dynamic unit formation suggest that completion processes reflect the optics of our world. Dynamic unit formation may depend on patterns of motion signals that are consistent with the causes of optical changes. In addition, dynamic completion conforms to a local curvature minimization constraint. Such relational aspects of vision are important to consider in linking perceptual experience and neural activity.

This paper exploits the modified simple equation and dynamical system schemes to integrate the Klein–Gordon model amid quadratic nonlinearity arising in nonlinear optics, quantum theories, and solid state physics. By implementing the modified simple equation technique, we develop some disguise adaptation of analytical solutions in terms of hyperbolic, exponential, and trigonometric functions with some special parameters. We apply the dynamical system to bifurcate the model and draw distinct phase portraits on unlike parametric constraints. Following each orbit of all phase (...) portraits, we originate bounded and unbounded solitary, periodic, and periodic rogue-type wave solutions of the KG model. These two schemes extract widespread classes of solitary, periodic, and periodic rogue-type wave solutions for the KG model jointly due to restrictions on parameters. We also analyze the effect of parameters on the obtained wave solutions and discuss why and when it changes its nature. We illustrate some dynamical features of the acquired solutions via the 3D, 2D, and contour graphics. (shrink)

"Rationality: Contexts and Constraints" is an interdisciplinary reappraisal of the nature of rationality. In method, it is pluralistic, drawing upon the analytic approaches of philosophy, linguistics, neuroscience, and more. These methods guide exploration of the intersection between traditional scholarship and cutting-edge philosophical or scientific research. In this way, the book contributes to development of a suitably revised, comprehensive understanding of rationality, one that befits the 21st century, one that is adequately informed by recent investigations of science, pathology, non-human thought, (...) emotion, and even enigmatic Chinese texts that might previously have seemed to be expressions of irrationalism. Addresses recent challenges and Identifies a direction for future research on rationalityInvestigates the relationship between rationality and mental disorders, such as delusion and depressionAssesses reasoning in artificial intelligence and nonhuman animalsReflects on ancient Chinese Philosophy and possible cultural differences in human psychology Employs philosophical reflection, along with linguistic, probabilistic, and logical techniques. (shrink)

It is widely accepted that pictures can only depict visible things. The paper criticises this ‘visibility constraint’ on the objects of depiction. The constraint is shown to imply that the range of visibilia is settled prior to an investigation of what can be seen in pictures. By contrast to this, I suggest that settling what can be seen in pictures is relevant to settling the range of visibilia. It is what we experience in pictures, and not the objects of depiction, (...) that is subject to a visibility constraint, I propose. After criticising the widely accepted visibility constraint in the first half of the paper, I outline an account of what we experience in pictures in the second half of the paper. (shrink)

We have compared two different laser-induced optical light traps for their utility in moving organelles within living animal cells and walled fungal cells. The first trap employed a continuous wave neodymium-yttrium aluminum garnet laser at a wavelength of 1.06 micron. A second trap was constructed using a titanium-sapphire laser tunable from 700 to 1000 nm. With the latter trap we were able to achieve much stronger traps with less laser power and without damage to either mitochondria or spindles. Chromosomes (...) and nuclei were easily displaced, nucleoli were separated and moved far away from interphase nuclei, and Woronin bodies were removed from septa. In comparison, these manipulations were not possible with the Nd-YAG laser-induced trap. The optical force trap induced by the tunable titanium-sapphire laser should find wide application in experimental cell biology because the wavelength can be selected for maximization of force production and minimization of energy absorption which leads to unwanted cell damage. (shrink)

Typically developing 3-day-old newborns take significantly more forward steps on a moving treadmill belt than on a static belt. The current experiment examined whether projecting optic flows that specified forward motion onto the moving treadmill surface would further enhance forward stepping. Twenty newborns were supported on a moving treadmill without optic flow, with optic flow matching the treadmill’s direction and speed, with optic flow in the same direction but at a faster speed, and in a control condition with an incoherent (...) optic flow moving at the same speed as in the Congruent condition but in random directions. The results revealed no significant differences in the number or coordination of forward treadmill steps taken in each condition. However, the Faster condition generated significantly fewer leg pumping movements than the Random control condition. When highly aroused, newborns made significantly fewer single steps and significantly more parallel steps and pumping movements. We speculate the null findings may be a function of the high friction material that covered the treadmill surface. (shrink)

Significantly, Berkeley, in his Essay Towards a New Theory of Vision, leveled a sustained attack on just this geometrical theory of distance perception. At first glance it may seem, as it did to Berkeley, that Descartes’ geometrical theory is produced by a simple error: namely, by the idea that a physiological optics provides an adequate description of the psychological processes of judging distances. In truth, this is the weakest of Berkeley’s objections to Descartes’ theory. Obviously we do not see the (...) angles and lines of convergence when we focus on a distant object, nor are we aware of having used any geometrical rules in judging distance. And Descartes never claimed this. (shrink)

Moral Constraints on War offers a principle-by-principle presentation of the transcultural roots of the ethics of war in an age defined by the increasingly international nature of military intervention.

_ Source: _Volume 29, Issue 1, pp 86 - 102 The aim of this paper is to give an overview of the place that Hobbes assigns to optics in the context of his classification of sciences and disciplinary boundaries. To do this, I will begin with an account of Hobbes’s conception of philosophy or science, and particularly his distinction between true and hypothetical knowledge. I will also show that in his demarcation between mathematics or geometry and natural philosophy Hobbes was (...) influenced by Galileo’s _Dialogue_. I then analyse the consequences of this distinction for optics, and conclude by clarifying its status among the scientific disciplines. (shrink)

Minkowski geometry is axiomatized in terms of the asymmetric binary relation of optical connectibility, using ten first-order axioms and the second-order continuity axiom. An axiom system in terms of the symmetric binary optical connection relation is also presented. The present development is much simpler than the corresponding work of Robb, upon which it is modeled.

Interpretation, Constraint, and the Prospects of Scientific Realism I explore the interaction between theory-based interpretations of scientific evidence and constraints on theories provided by that evidence. Interpretation is often viewed as a source of error and a reason for scepticism about scientific results. But, I argue, while interpretation does generate epistemic risk, it also points to new sources of evidence that can constrain our theories. This is especially clear in the development of instrumentation that increases the range of our (...) interactions with nature. While the design of such instruments and the interpretation of their outputs are deeply dependent on theory-based interpretations, these outputs can still challenge those very theories. At the same time, theory-guided instrumentation provides us access to aspects of nature that we cannot study with our unaided senses. This access allows us to extend the range of evidence that we collect, and thus increases the constraints on our theories. As a result, theory-guided evidence collection has a positive impact on the prospects of scientific realism since these increasing constraints on our theories provide our only reason for thinking that we may be approaching the development of true theories. (shrink)

The screen is not a pre established object: it becomes a screen—and that screen—when it interacts with a group of elements and relates to a set of practices that produce it as a screen. In this process of becoming screen, a crucial step is played by the space in which the screen is located and where spectators gather. The confluence of screen and space changes our perception of both: the screen displays the situatedness of its action, and the space its (...) nature of medium. The landscape becomes a screenscape, in which individuals access images through which they negotiate with reality and others. Eventually, the insistence on becoming screen highlights the role of contingency and conjuncture in the process of mediation: screenscapes emerge according opportunities, conflicts, and potentialities. Hence a media archeology that, far from being linear and teleological, follows unpredicted paths and creates surprising links—a rhizomatic media archeology. (shrink)

In recent work, Adlam (2022b), Chen & Goldstein (2022), and Meacham (2023) have defended accounts of laws that take laws to be primitive global constraints. A major advantage of these accounts is that they’re able to accommodate the many different kinds of laws that appear in physical theories. In this paper I’ll present these three accounts, highlight their distinguishing features, and note some key differences that might lead one to favor one of these accounts over the others. I’ll conclude (...) by briefly discussing a version of a “constraint” account that I think is especially attractive. (shrink)

Deontic constraints prohibit an agent performing acts of a certain type even when doing so will prevent more instances of that act being performed by others. In this article I show how deontic constraints can be interpreted as either maximizing or non-maximizing rules. I then argue that they should be interpreted as maximizing rules because interpreting them as non-maximizing rules results in a problem with moral advice. Given this conclusion, a strong case can be made that consequentialism provides (...) the best account of deontic constraints. (shrink)

Ever since Big Data became a mot du jour across social fields, optical metaphors such as the microscope began to surface in popular discourse to describe and qualify its epistemological impact. While the persistence of optics seems to be at odds with the datafication of vision, this article suggests that the optical metaphor offers an opportunity to reflect about the material consequences of the modes of seeing and knowing that currently shape datafied worlds. Drawing on feminist new materialism, (...) the article investigates the optical metaphor as a material-discursive practice that actively constitutes the world, as metaphors imply modes of thinking, knowing and doing that have material enactions. Expanding visual culture theories, the notion of ‘optical unconscious’ is taken up to discuss the tensions between displacement and persistence of optics within datafied worlds, that is, how optical vision is displaced but also mobilised and repurposed by data-driven knowledge. In dialogue with feminist science and technology studies and speculative ethics, I suggest that the datafication of vision offers a chance to reconceptualize the sense of sight towards a sensorial engagement with Big Data premised on responsibility, care, and an ethics of unknowability. Within this framework, vision may be conceived differently, perhaps not only as enhancement and control, but as generator of new possibilities. Ultimately, the article proposes that the visual theories after which Big Data is being imagined matter not only for our understanding of Big Data's epistemic potential, but also for the possibility of shaping emerging data worlds. (shrink)

Seventeenth-century optics naturalizes the eye while estranging the mind from objects. A mere screen, on which rests a blurry array of light stains, the eye no longer furnishes the observer with genuine re-presentations of visible objects. The intellect is thus compelled to decipher flat images of no inherent epistemic value, accidental effects of a purely causal process, as vague, reversed reflections of wholly independent objects. Reflecting on and trespassing the boundaries between natural and artificial, orderly and disorderly, this optical (...) paradox is a Baroque phenomenon; and it is the origin of Descartes’ celebrated doubt---whether we know anything at all. (shrink)

Constraints and dependencies among the elements of embodied cognition form patterns or microstrategies of interactive behavior. Hard constraints determine which microstrategies are possible. Soft constraints determine which of the possible microstrategies are most likely to be selected. When selection is non‐deliberate or automatic the least effort microstrategy is chosen. In calculating the effort required to execute a microstrategy each of the three types of operations, memory retrieval, perception, and action, are given equal weight; that is, perceptual‐motor activity (...) does not have a privileged status with respect to memory. Soft constraints can work contrary to the designer's intentions by making the access of perfect knowledge in‐the‐world more effortful than the access of imperfect knowledge in‐the‐head. These implications of soft constraints are tested in two experiments. In experiment 1 we varied the perceptual‐motor effort of accessing knowledge in‐the‐world as well as the effort of retrieving items from memory. In experiment 2 we replicated one of the experiment 1 conditions to collect eye movement data. The results suggest that milliseconds matter. Soft constraints lead to a reliance on knowledge in‐the‐head even when the absolute difference in perceptual‐motor versus memory retrieval effort is small, and even when relying on memory leads to a higher error rate and lower performance. We discuss the implications of soft constraints for routine interactive behavior, accounts of embodied cognition, and tool and interface design. (shrink)

A major intellectual shift between Copernicus and the mid-17th century was the rejection of Aristotelian assertions concerning the relationship of mathematics to physical nature. Aristotle asserted that “The minute accuracy of mathematics is not to be demanded in all cases, but only in the case of things which have no matter. Therefore its method is not that of natural science; for presumably all nature has matter.” Thus, he pulled out the rug from under the feet of the aspiration to a (...) mathematically based natural sciences, asserting that: “And at the same time not even this is true, that mensuration deals with perceptible and perishable magnitudes; for then it would have perished, when they perished. And astronomy also cannot be dealing with perceptible magnitudes nor with this heaven above us. For neither are perceptible lines such lines as the geometer speaks of, nor are the movement and complex orbits in the heaven like those which astronomy treats, nor have geometrical points the same nature as the actual stars.”. (shrink)

According to the Generality Constraint, mental states with conceptual content must be capable of recombining in certain systematic ways. Drawing on empirical evidence from cognitive science, I argue that so-called analogue magnitude states violate this recombinability condition and thus have nonconceptual content. I further argue that this result has two significant consequences: it demonstrates that nonconceptual content seeps beyond perception and infiltrates cognition; and it shows that whether mental states have nonconceptual content is largely an empirical matter determined by the (...) structure of the neural representations underlying them. (shrink)