When people make sense of situations, illustrations, instructions and problems they do more than just think with their heads. They gesture, talk, point, annotate, make notes and so on. What extra do they get from interacting with their environment in this way? To study this fundamental problem, I looked at how people project structure onto geometric drawings, visual proofs, and games like tic tac toe. Two experiments were run to learn more about projection. Projection is a special capacity, similar (...) to perception, but less tied to what is in the environment. Projection, unlike pure imagery, requires external structure to anchor it, but it adds ‘mental’ structure to the external scene much like an augmented reality system adds structure to an outside scene. A person projects when they look at a chessboard and can see where a knight may be moved. Because of the cognitive costs of sustaining and extending projection, humans make some of their projections real. They create structure externally. They move the piece, they talk, point, notate, represent. Much of our interactivity during sense making and problem solving involves a cycle of projecting then creating structure. (shrink)

When people make sense of situations, illustrations, instructions and problems they do more than just think with their heads. They gesture, talk, point, annotate, make notes and so on. What extra do they get from interacting with their environment in this way? To study this fundamental problem, I looked at how people project structure onto geometric drawings, visual proofs, and games like tic tac toe. Two experiments were run to learn more about projection. Projection is a special capacity, similar (...) to perception, but less tied to what is in the environment. Projection, unlike pure imagery, requires external structure to anchor it, but it adds ‘mental’ structure to the external scene much like an augmented reality system adds structure to an outside scene. A person projects when they look at a chessboard and can see where a knight may be moved. Because of the cognitive costs of sustaining and extending projection, humans make some of their projections real. They create structure externally. They move the piece, they talk, point, notate, represent. Much of our interactivity during sense making and problem solving involves a cycle of projecting then creating structure. (shrink)

It is proposed that there are important generalizations about problem solving in design activity that reach across specific disciplines. A framework for the study of design is presented that (a) characterizes design as a radial category and fleshes out the task environment of the prototypical cases; (b) takes the task environment seriously; (c) shows that this task environment occurs in design tasks, but does not occur in every nondesign task; (d) explicates the impact of this task environment on the (...) design problem space; and (e) demonstrates that, given the structure of the information-processing system, the features noted in the problem spaces of design tasks will not all occur in problem spaces where the task environment is vastly different. This analysis leads to the claim that there are a set of invariant features in the problem spaces of design situations that collectively constitute a design problem space. Protocol studies are reported in which the problem spaces of three design tasks in architecture, mechanical engineering, and instructional design are explored and compared with several protocols from nondesign problem-solving tasks. (shrink)

It is proposed that there are important generalizations about problem solving in design activity that reach across specific disciplines. A framework for the study of design is presented that (a) characterizes design as a radial category and fleshes out the task environment of the prototypical cases; (b) takes the task environment seriously; (c) shows that this task environment occurs in design tasks, but does not occur in every nondesign task; (d) explicates the impact of this task environment on the (...) design problem space; and (e) demonstrates that, given the structure of the information-processing system, the features noted in the problem spaces of design tasks will not all occur in problem spaces where the task environment is vastly different. This analysis leads to the claim that there are a set of invariant features in the problem spaces of design situations that collectively constitute a design problem space. Protocol studies are reported in which the problem spaces of three design tasks in architecture, mechanical engineering, and instructional design are explored and compared with several protocols from nondesign problem-solving tasks. (shrink)

A blue-ribbon panel convened by the National Council for Accreditation of Teacher Education (NCATE) concluded in 2010 that teacher education in the United States must be “turned upside down,” with practical experience at its center and academic content woven around the practical. It might seem that the new clinical model based on medical education, which has been adopted by eight states, would be well-aligned with a Deweyan inquiry-based pedagogy. Dewey himself recognized a paradox, however: preparation for the combination of rigor (...) and flexibility needed for inquiry-based pedagogical skills absolutely requires immersion in clinical settings, even as immersion in the teaching environment that prevails in U.S. public schools systematically socializes new teachers to a very different set of skills than those needed for this model of effective pedagogy. Recent scholarship by Kuhnian scholars provides practical guidance for an alternative understanding of how changes in practice occur and may be transmitted to future generations. (shrink)

This essay develops three key claims made in my 2018 book, Exceptional Technologies. Part one argues for ‘trivialising the transcendental’, to remove stigmas attached to the word ‘transcendental’ in philosophy in general and philosophy of technology in particular. Part two outlines the concept of ‘exceptional technologies’. These are artefacts and practices that show up as limit cases for our received pictures of what constitutes a ‘technology’ and that force us to reassess the conditions for the possibility of these pictures. I (...) focus on the case of autonomous vehicles here, arguing that Google Street View provides a relatively better picture for approaching philosophical issues at stake than the famous ‘Trolley Problem’. Part three then concludes with a focus on Heidegger’s ‘Question Concerning Technology’ essay. Heidegger asserts that philosophical questioning ‘builds a way’. I argue that philosophical approaches to technologies might better be considered in terms of a multidimensional problem space. (shrink)

Learning to solve a class of problems can be characterized as a search through a space of hypotheses about the rules for solving these problems. A series of four experiments studied how different learning conditions affected the search among hypotheses about the solution rule for a simple computational problem. Experiment 1 showed that a problem property such as computational difficulty of the rules biased the search process and so affected learning. Experiment 2 examined the impact of examples (...) as instructional tools and found that their effectiveness was determined by whether they uniquely pointed to the correct rule. Experiment 3 compared verbal directions with examples and found that both could guide search. The final experiment tried to improve learning by using more explicit verbal directions or by adding scaffolding to the example. While both manipulations improved learning, learning still took the form of a search through a hypothesis space of possible rules. We describe a model that embodies two assumptions: the instruction can bias the rules participants hypothesize rather than directly be encoded into a rule; participants do not have memory for past wrong hypotheses and are likely to retry them. These assumptions are realized in a Markov model that fits all the data by estimating two sets of probabilities. First, the learning condition induced one set of Start probabilities of trying various rules. Second, should this first hypothesis prove wrong, the learning condition induced a second set of Choice probabilities of considering various rules. These findings broaden our understanding of effective instruction and provide implications for instructional design. (shrink)

Laura Berchielli - Color, Space and Figure in Locke: An Interpretation of the Molyneux Problem - Journal of the History of Philosophy 40:1 Journal of the History of Philosophy 40.1 47-65 Color, Space, and Figure in Locke: An Interpretation of the Molyneux Problem Laura Berchielli THIS IS HOW LOCKE, in the second edition of his Essay Concerning Human Understanding , introduces a question that had been suggested to him in a letter from William Molyneux: . . (...) . I shall here insert a Problem of that very Ingenious and Studious promoter of Knowledge, the Learned and Worthy Mr. Molineux, which he was pleased to send me in a Letter some Months since; and it is this: Suppose a Man born blind, and now adult, and taught by his touch to distinguish between a Cube, and a Sphere of the same metal, and nighly of the same bigness, so as to tell, when he felt one and t'other, which is the Cube, which the Sphere. Suppose then the Cube and Sphere placed on a Table, and the Blind Man to be made to see. Quaere, Whether by his Sight, before he touch'd them, he could now distinguish, and tell, which is the Globe, which the Cube. In the standard interpretation of the Molyneux problem as presented in Locke, the question is always linked to the general issue of differences in the ideas of figure received by the various senses. This interpretation -- put forward by Berkeley --says that for Locke, the ideas of figure produced by sight are specifically different from.. (shrink)

When a proposition might be the case, for all an agent knows, we can say that the proposition is epistemically possible for the agent. In the standard possible worlds framework, we analyze modal claims using quantification over possible worlds. It is natural to expect that something similar can be done for modal claims involving epistemic possibility. The main aim of this paper is to investigate the prospects of constructing a space of worlds—epistemic space—that allows us to model what (...) is epistemically possible for ordinary, non-ideally rational agents like you and me. I will argue that the prospects look dim for successfully constructing such a space. In turn, this will make a case for the claim that we cannot use the standard possible worlds framework to model what is epistemically possible for ordinary agents. (shrink)

Wittgenstein’s atomist picture, as embodied in his Tractatus, is initially very appealing. However, it faces the famous colour-exclusion problem. In this paper, I shall explain when the atomist picture can be defended in the face of that problem; and, in the light of this, why the atomist picture should be rejected. I outline the atomist picture in Section 1. In Section 2, I present a very simple necessary and sufficient condition for the tenability of the atomist picture. The (...) condition is: logical space is a power of two. In Sections 3 and 4, I outline the colour-exclusion problem, and then show how the cardinality-condition supplies a response to exclusion problems. In Section 5, I explain how this amounts to a distillation of a proposal due to Moss, which goes back to Carruthers. And in Section 6, I show how all this vindicates Wittgenstein’s ultimate rejection of the atomist picture. The brief reason is that we have no guarantee that there are any solutions to a given exclusion problem but, if there are any, then there are far too many. (shrink)

L’objet de cet article n’est pas de répondre à une question de nature physique ou métaphysique : « qu’est-ce que l’espace? », mais de se concentrer sur un problème pragmatique : « quand interprétons-nous l’espace? ». Dans ses trois dimensions (le corps propre, la chose, le social), l’espace devient interprétable quand il a perdu ses repères habituels, quand nous sommes confrontés à des phénomènes de désorientation, quand nous sommes face à des espaces inconnus, étranges ou étrangers. À la différence d’une (...) herméneutique de l’espace qui se focalise sur les technologies savantes de déchiffrement de signes, l’article donne la priorité à une anthropologie interprétative de la spatialité qui met en lumière les technologiques ordinaires de dévoilement du sens. À une herméneutique de l’espace qui tire son modèle du texte, la contribution ajoute une analytique interprétative d’une spatialité mouvante, irréductible à toute inscription comme expression durablement fixée. (shrink)

I present a discussion of some open issues in the philosophy of space-time theories. Emphasis is put on the ontological nature of space and time, the relation between determinism and predictability, the origin of irreversible processes in an expanding Universe, and the compatibility of relativity and quantum mechanics. In particular, I argue for a Parmenidean view of time and change, I make clear the difference between ontological determinism and predictability, propose that the origin of the asymmetry observed in (...) physical processes is related to the existence of cosmological horizons, and present a non-local concept of causality that can accommodate both special relativity and quantum entanglement. (shrink)

In a surface-dwelling animal like the rat, experimental strategies for investigating the hippocampal correlates of three-dimensional space appear inevitably complicated by the interplay of global versus local reference frames. We discuss the impact of the resulting confounds on present and future empirical analysis of the hypothesis by Jeffery and colleagues.

From the comparative framework of writing on the meaning of ritual in the field of the history of religions, this essay argues that one of the major problems in Benjamin’s thinking is how to make certain forms of materiality stand out against other forms. In his early work, the way that Benjamin deals with this problem is to call degraded forms “symbolic”, and those forms of materiality with positive value, “allegorical”. The article shows how there is more than an (...) incidental connection with the recent approach to ritual in the field of history of religions, seeing that Benjamin too wants to set out the significance of certain material forms against those that are “ritualistic” and hence false. It is argued that he treats the latter in his essay on Elective Affinities and the former in his Trauerspiel. The key claim is that the way material forms stand out as meaningful is akin to the Kantian description of the aesthetic attitude, which identifies how certain formations warrant and attract reflective attention and underpin moral orientation. The point is significant since Kantian aesthetics is an object of polemical attention across Benjamin’s heterogeneous corpus. Moreover, the approach shows the main difficulty in Benjamin’s treatment of sensible forms: what are the criteria he uses to distinguish the “bad” way a sensible form has of being meaningful from the “good”? (shrink)

It is taken for granted that the explanation of the Universe’s space-time dimension belongs to the host of the arguments that exhibit the superiority of modern (inflationary) cosmology over the standard model. In the present paper some doubts are expressed . They are based upon the fact superstring theory is too formal to represent genuine unification of general relativity and quantum field theory. Neveretheless, the fact cannot exclude the opportunity that in future the superstring theory can become more physical. (...) Hence this paper does not aim to query neither string cosmology, nor superstring theory; it asks for “tolerance in the matters cosmological”. It advices the researchers not to dwell on the common way of unification and to take into consideration the other ways as well. (shrink)

There are many points of contact between Deleuze’s spatial concepts, in their variegated forms, and the prose work of Samuel Beckett. With particular emphasis on the concept of any-space-whatever, it is shown that Beckett’s interrogation of spatiality in the work immediately following the Second World War can be seen to anticipate the very qualities of his late work which would lead Deleuze to make such extensive use of the concept in ‘The Exhausted’. For the purposes of this chapter Beckett’s (...) novella ‘The Expelled’ is explored. In addition to the direct links between the any-space-whatever and Beckett in ‘The Exhausted’, reference is made to the two distinct but related formulations of the concept in the Cinema books. (shrink)

We propose a Lorentz-covariant deformed algebra describing a -dimensional quantized spacetime, which in the nonrelativistic limit leads to undeformed one. The deformed Poincaré transformations leaving the algebra invariant are identified. In the classical limit the Lorentz-covariant deformed algebra yields the deformed Lorentz-covariant Poisson brackets. Kepler problem with the deformed Lorentz-covariant Poisson brackets is studied. We obtain that the precession angle of an orbit of the relativistic particle in the gravitational field depends on the mass of the particle, i.e. equivalence (...) principle is violated. We propose a condition for the recovery of the equivalence principle in the space with the deformed Poisson brackets. Comparing our analytical result with the experimental data for the precession angle of Mercury’s orbit we provide an estimation of minimal length. (shrink)

My goal in this paper is to elucidate a problematic feature of Newton's metaphysics of absolute space. Specifically, I argue that Newton's theory has the untenable consequence that God depends on space for His existence and is therefore not an independent entity. I argue for this conclusion in stages. First, I show that Newton believed that space was an entity and that God and space were ontologically distinct entities. Part of this involves arguing that Newton denies (...) that space is a divine attribute. I then show that Newton endorsed a principle according to which the existence of space is a necessary condition for the existence of any other entity. Following this, I discuss the ways in which this makes God depend on space for His existence and the reasons why this is unacceptable for traditional conceptions of God. Specifically, I show that it is incompatible with the orthodox position that God be entirely independent and self-determining. Finally, I offer two considerations which, I hope, make the problem seem less serious than it first appears. The first consideration has to do with Newton's polemical context and the second has to do with the nature of his theological thought. (shrink)

In the wake of the recent global refugee and migration crisis, Hannah Arendt’s defense of the right to have political rights has become prominent again. Her work is read as an early reminder that the internationally promoted human rights regime may be merely a rhetorical reference, without the will or international authority for political action. I examine Arendt’s analysis in its historical context and then turn to consider Ricœur’s understanding of human rights. The capability to respond to and to be (...) held accountable by others marks Ricœur’s ethics of responsibility. He agrees with Arendt that legal authority must rest upon power and not domination, but he insists that the undercurrent of common power is the moral capability of an agent. The essay examines the ramifications of Ricœur’s ethics for the current crisis of refugees and migration, and it argues that he offers, at the same time, a correction useful for the ethical foundation of human rights. (shrink)

This article is concerned to formulate some open problems in the philosophy of space and time that require methods characteristic of mathematical traditions in the foundations of geometry for their solution. In formulating the problems an effort has been made to fuse the separate traditions of the foundations of physics on the one hand and the foundations of geometry on the other. The first part of the paper deals with two classical problems in the geometry of space, that (...) of giving operationalism an exact foundation in the case of the measurement of spatial relations, and that of providing an adequate theory of approximation and error in a geometrical setting. The second part is concerned with physical space and space-time and deals mainly with topics concerning the axiomatic theory of bodies, the operational foundations of special relativity and the conceptual foundations of elementary physics. (shrink)

We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.

One important role of belief systems is to allow us to represent information about a certain domain of inquiry. This paper presents a formal framework to accommodate such information representation. Three cognitive models to represent information are discussed: conceptual spaces, state-spaces, and the problem spaces familiar from artificial intelligence. After indicating their weakness to deal with partial information, it is argued that an alternative, formulated in terms of partial structures, can be provided which not only captures the positive features (...) of these models, but also accommodates the partiality of information ubiquitous in science and mathematics. (shrink)

This book investigates Hermann Weyl’s work on the problem of space from the early 1920s onwards. It presents new material and opens the philosophical problem of space anew, crossing the disciplines of mathematics, history of science and philosophy. With a Kantian starting point Weyl asks: among all the infinitely many conceivable metrical spaces, which one applies to the physical world? In agreement with general relativity, Weyl acknowledges that the metric can quantitatively vary with the physical situation. (...) Despite this freedom, Weyl “deduces”, with group-theoretical technicalities, that there is only one “kind” of legitimate metric. This construction was then decisive for the development of gauge theories. Nevertheless, the question of the foundations of the metric of physical theories is only a piece of a wider epistemological problem. Contributing authors mark out the double trajectory that goes through Weyl’s texts, from natural science to philosophy and conversely, always through the mediation of mathematics. Readers may trace the philosophical tradition to which Weyl refers and by which he is inspired, and explore the mathematical tradition that permitted Weyl to elaborate and solve his mathematical problem of space. Furthermore, this volume analyzes the role of the interlocutors with whom Weyl discussed the nature of physical space. This volume features the work of top specialists and will appeal to postgraduates and scholars in philosophy, the history of science, mathematics, or physics. (shrink)

This paper is to investigate the existence and uniqueness of solutions for an integral boundary value problem of new fractional differential equations with a sign-changed parameter in Banach spaces. The main used approach is a recent fixed point theorem of increasing Ψ − h, r -concave operators defined on ordered sets. In addition, we can present a monotone iterative scheme to approximate the unique solution. In the end, two simple examples are given to illustrate our main results.