Des branches entières des mathématiques sont fondées sur des liens posés entre les nombres et l’espace : mesure de longueurs, définition de repères et de coordonnées, projection des nombres complexes sur le plan… Si les nombres complexes, comme l’utilisation de repères, sont apparus relativement récemment (vers le XVIIe siècle), la mesure des longueurs est en revanche un procédé très ancien, qui remonte au moins au 3e ou 4e millénaire av. J-C. Loin d’être fortuits, ces liens entre les nombres et l’espace (...) reflèteraient une intuition fondamentale, universelle, façonnée au cours des millénaires par la sélection naturelle, et qui aurait servi de guide et d’inspiration aux mathématiciens au fil des siècles. (shrink)

The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with (...) small or symbolic numbers and logarithmic mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education. (shrink)

On June 26, 2000, President Clinton, together with Francis Collins and Craig Venter, solemnly announced, from the East Room of the White House, that the grand effort to sequence the human genome, the Human Genome Project (HGP), was rapidly nearing its completion. Symbolism abounded. The event was framed as a crucial marker in the history of both humanity and knowledge by explicitly connecting the completion of the HGP with a number of already acknowledged and established scientific highlights. Tensions abounded (...) as well, however, notably between competing metaphors. In the course of the HGP, metaphors had become crucially important in framing and conveying what the HGP was really about. They had proved themselves to be of key importance when it came to defining and explaining the project’s significance for both science and society. Powerful images and metaphors had been deployed in order to secure unprecedented amounts of funding, on the one hand by comparing the HGP to other big technoscientific projects such as space travel, high energy physics, the atomic bomb and a territorial mapping exercise, and on the other hand through the suggestion that, once we have our “blueprint”, “code of codes”, “parts list”, etc. available, cancer genes will no longer have a place to hide. This article sets out to analyze this clash of metaphors, firmly embedded within the HGP but culminating at the press conference, arguing that the June 2000 event is even reminiscent of a somewhat similar event, depicted by a famous altarpiece, ‘The adoration of the Lamb’, on display in Ghent Cathedral and finished more than five centuries before. (shrink)

Description In this paper, we propose an advanced mathematical framework centered around the Energy Number Field (E), which fundamentally avoids the conventional concept of zero by introducing a neutral ele- ment, νE. Through this approach, we redefine core mathematical constructs, including limits, continuity, differentiation, integration, and series summation, ensuring they operate seamlessly within a zero-less paradigm. We address and redefine matrix operations, topology, metric spaces, and complex analysis, aligning them with the principles of E. Additionally, we explore non-mappable properties (...) of energy numbers in the context of symmetry groups, non-standard fields, fractional calculus, and non-Euclidean geometries. By employing νE as the central element, our framework resolves conventional zero-related sin- gularities and computational anomalies, offering a novel perspective that bridges advanced mathematical theories with practical applications in physics, computational algorithms, and topological transforma- tions. This work paves the way for future research to experimentally validate these formulations and explore potential applications in advanced physics, quantum mechanics, and beyond. (shrink)

In this paper, we highlight some problems for accounts of disability and enhancement that have not been sufficiently addressed in the literature. The reason, we contend, is that contemporary debates that seek to define, characterise or explain the normative valence of disability and enhancement do not pay sufficient attention to a wide range of cases, and the transition between one state and another. In section one, we provide seven cases that might count as disability or enhancement. We explain why each (...) case might count, and on what basis, and why it is been neglected. Each case is explained as a transition in what we call capacity space. We then argue that no definition of disability or enhancement addresses all of these cases, except for strict welfarist accounts of disability that do not rely on a depiction of any particular capacity. We argue further, however, that this is a serious deficiency of welfarist conceptions of disability. We then address objections to our account. (shrink)

Throughout history, education has always been essential for humanity's justice and fundamental for the creation of a free and satisfying society with the dissemination of knowledge. Hence, in addition to the life occurrences educating people, traditional higher education methods have played an important role for a long period. However, the age of technology has changed the educational system along with the people's lifestyles to meet the continuously changing conditions. During the past twenty years, the Information and Communication Technologies (ICTs) led (...) to the emergence of e-learning non-traditional educational methods bringing about an innovative dimension of virtual learning. With its beneficial features provided by the Internet and various technologies, this method passes the control of time and location from the tutors to the students during the learning process. Despite the entrance of online education into the students' life many years ago, the Covid-19 outbreak initiated in 2020 turned this method into the only possible way of education for almost two years. Afterward, plenty of studies investigated its effects on students' social and academic life, mostly considering its negative impacts on their mental health and motivation due to interaction issues. They also pointed out the specific problems of tactile learner students in the lack of face-to-face design courses. As an innovative solution able to be adopted, game technologies, increasing immersion of the learner in a real-world skill, and triggering motivation are one of the best methods integrated into educational systems. Known as serious games, these games, adopted by almost any domain, convey educational content along with entertainment, increasing interaction. They train or enhance a certain skill or topic to the player by immersing them. While serious games are more expanded nowadays, they are still not being played by the mass public due to people's immersiveness expectations of a game. Hence, the Head-Mounted Displays (HMDs), with their emergence, increased the players' engagement and immersion with all types of virtual environments in digital games. This technology, however, evolved serious games area most, among others, by enabling the opportunity to provide a riskless and low-cost learning environment for real-world skills. In the process of suggesting serious games as a replacement for the traditional educational methods, the most important factor is being aware of their effectiveness for education. Generally, digital games, one of the world's biggest and fastest-growing industries, rely heavily on the virtual landscape, a major part of its development process. Its design demands remarkable effort, and it directly affects the whole game's characteristics. Hence, serious games, as a type of digital game, carry the same attributes. With the appearance of virtual reality technology, gaming started to gain more immersiveness and engagement with artificial elements and environments. Although virtual landscapes were always being developed since the emergence of digital games, the studies taking virtual landscapes into account are mostly using them as a tool for enhancing real spaces, not as a domain for the sake of its development. While other design domains are applying various design methodologies, it is challenging to find a standard design methodology for the design and production of virtual landscapes in the gaming industry, leading to inconsistent and low-quality results. Hence, it comes to the question of what is the virtual landscapes' role in serious games and their effect on the data comprehension rate. Since the literature lacks regarding the gradual change of the virtual landscape in serious games and the content they transmit, this thesis aims to figure out the gradual chronological evolution of the virtual landscapes in serious games. It also aims to seek how this change and the virtual reality technology invention have affected the contents transmitted by digital games and its influence on the player interaction and learning rate. To do so, in the process of this thesis, we developed, tested, and evaluated various serious games, both text-based and with 360° photos. The steps taken revealed the reluctance of the players to follow the providing educational content and their inadequacy of interaction. Hence, the thesis seeks the reasons ending to this result and the ways of increasing this learning rate. Afterward, the thesis uses a currently available but not massively used digital game classification methodology. This methodology, which is based on the principles of architecture, landscape architecture, and urban planning, classifies the games based on their constituting virtual landscapes. Hence, the thesis considers all Steam games, one of the biggest video game digital distribution services, filtered with the 'education' tag, ending in 2531 digital games. Afterward, adding the 'game' tag the result reduced to 1102 games. Finally, with some manual filterings ignoring the irrelevant content, the final number decreased to 702. Sorting chronologically, we made an Excel database including the games' introductory information, the content they transmit, their release date, if they support HMD or not, and whether they are simulation games or not. Due to Steam's dating spectrum, our database includes games dating back from 1992 to 2020. Afterward, we classified all of these games using the virtual landscape classification methodology and generated their related codes based on their player scale, story, dimension, space shape, and interaction level. Investigating the results, they revealed some growth patterns relating to the content educated in the game, the VR technology, and the virtual landscape evolution. Adding the user reviews of Steam, we reverse engineered five of the best serious games on the database due to the digital game design methodology. This methodology divides the games' virtual environment into five layers, namely, player activity map (PAM), story layer, natural environment layer, virtual environment layer, and media layer. Reverse engineering the five best digital games ever, based on the IGN database, enabled us to compare the outcomes. Due to released data, we understand how the games' assets are distributed within the various layers of the virtual environment in the most successful games. Finally, the thesis aims to provide a framework based on these results for developing serious games to increase player interaction and enhance the learning rate. However, these results can be expanded to any virtual landscape other than only serious games' for their interaction enhancement. Currently, the landscape architecture domain only adopts the virtual landscape area as a tool for enhancing design in the real world. However, in the near future, landscape architects will perform in the virtual landscape area as a domain to be enhanced. Hence, that day, the results of this study will play an important role and will be a roadmap for generating highly interactive virtual landscapes. (shrink)

The paper discusses Hilbert mathematics, a kind of Pythagorean mathematics, to which the physical world is a particular case. The parameter of the “distance between finiteness and infinity” is crucial. Any nonzero finite value of it features the particular case in the frameworks of Hilbert mathematics where the physical world appears “ex nihilo” by virtue of an only mathematical necessity or quantum information conservation physically. One does not need the mythical Big Bang which serves to concentrate all the violations of (...) energy conservation in a “safe”, maximally remote point in the alleged “beginning of the universe”. On the contrary, an omnipresent and omnitemporal medium obeying quantum information conservation rather than energy conservation permanently generates action and thus the physical world. The utilization of that creation “ex nihilo” is accessible to humankind, at least theoretically, as long as one observes the physical laws, which admit it in their new and wider generalization. One can oppose Hilbert mathematics to Gödel mathematics, which can be identified as all the standard mathematics until now featureable by the Gödel dichotomy of arithmetic to set theory: and then, “dialectic”, “intuitionistic”, and “Gödelian” mathematics within the former, according to a negative, positive, or zero value of the distance between finiteness and infinity. A mapping of Hilbert mathematics into pseudo-Riemannian space corresponds, therefore allowing for gravitation to be interpreted purely mathematically and ontologically in a Pythagorean sense. Information and quantum information can be involved in the foundations of mathematics and linked to the axiom of choice or alternatively, to the field of all rational numbers, from which the pair of both dual and anti-isometric Peano arithmetics featuring Hilbert arithmetic are immediately inferable. Noether’s theorems (1918) imply quantum information conservation as the maximally possible generalization of the pair of the conservation of a physical quantity and the corresponding Lie group of its conjugate. Hilbert mathematics can be interpreted from their viewpoint also after an algebraic generalization of them. Following the ideas of Noether’s theorem (1918), locality and nonlocality can be realized both physically and mathematically. The “light phase of the universe” can be linked to the gap of mathematics and physics in the Cartesian organization of cognition in Modernity and then opposed to its “dark phase”, in which physics and mathematics are merged. All physical quantities can be deduced from only mathematical premises by the mediation of the most fundamental physical constants such as the speed of light in a vacuum, the Planck and gravitational constants once they have been interpreted by the relation of locality and nonlocality. (shrink)

In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case we ask the (...) question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (shrink)

Industrial heritage has become a very matter of debate among experts as the most significant reminder of the industrial era, it also is of great examples of 20th-century heritage. Nowadays, industrial heritage sites are suffering from intense physical conditions and are being intruded by massive economic projects since they are located in favorable places of towns and possess vast spaces. Conservation methods have mostly been limited to the surroundings of industrial heritage sites and have not considered the extended areas connected (...) to the site. The resolutions should be sought throughout these questions: How do outstanding values of an industrial heritage site affect its buffer zone mapping? Or what should a buffer zone map encompass to protect specific values of an industrial heritage site? During this research ample of evidence is seen which firstly depicts the appreciation of industrial heritage and the tendency to conserve them among the host countries. The main result concluded is a guideline based on the similarities and differences between various types of industrial heritage and their impacts on determining boundaries and zones. In case of increasing the number of case studies, the results of this paper can aid in charge organizations to take more effective measure in developing plans to determine boundaries and zones for different types of industrial heritage sites. The data gathered for this paper was collected through library resources about industrial heritage and basically from academic and universal management manuals of buffer zones. The information chiefly is adopted from registration files received by the world heritage committee of UNESCO. The method of this research is case study research and the method for analysis is descriptive-analytical. (shrink)

Francesca Biagioli’s Space, Number, and Geometry from Helmholtz to Cassirer is a substantial and pathbreaking contribution to the energetic and growing field of researchers delving into the physics, physiology, psychology, and mathematics of the nineteenth and twentieth centuries. The book provides a bracing and painstakingly researched re-appreciation of the work of Hermann von Helmholtz and Ernst Cassirer, and of their place in the tradition, and is worth study for that alone. The contributions of the book go far beyond (...) that, however. It is a clear, accurate, and deep account of fascinating and philosophically momentous implications of the move to relativity theory. (shrink)

This chapter develops a semantic theory for maps and situates it within the broader geography of meaning and semiotic significance. The discussion focuses on three central aspects of map semantics: the use of space, line marking, and linguistic tags. It is argued that the treatment of space in maps must be based on geometrical projection from a viewpoint rather than the traditional analysis in terms of spatial isomorphism. The chapter then shows how to integrate the projection-based semantics of (...) maps and the symbolic semantics of markers and tags, within the framework of possible-world semantics. The resulting account addresses issues of accuracy, viewpoint, orientation, and exhaustivity. (shrink)

In recent years, academics and educators have begun to use software mapping tools for a number of education-related purposes. Typically, the tools are used to help impart critical and analytical skills to students, to enable students to see relationships between concepts, and also as a method of assessment. The common feature of all these tools is the use of diagrammatic relationships of various kinds in preference to written or verbal descriptions. Pictures and structured diagrams are thought to be (...) more comprehensible than just words, and a clearer way to illustrate understanding of complex topics. Variants of these tools are available under different names: “concept mapping”, “mind mapping” and “argument mapping”. Sometimes these terms are used synonymously. However, as this paper will demonstrate, there are clear differences in each of these mapping tools. This paper offers an outline of the various types of tool available and their advantages and disadvantages. It argues that the choice of mapping tool largely depends on the purpose or aim for which the tool is used and that the tools may well be converging to offer educators as yet unrealised and potentially complementary functions. (shrink)

Shepard’s (1987) universal law of generalisation (ULG) illustrates that an invariant gradient of generalisation across species and across stimuli conditions can be obtained by mapping the probability of a generalisation response onto the representations of similarity between individual stimuli. Tenenbaum and Griffiths (2001) Bayesian account of generalisation expands ULG towards generalisation from multiple examples. Though the Bayesian model starts from Shepard’s account it refrains from any commitment to the notion of psychological similarity to explain categorisation. This chapter presents the (...) conceptual spaces theory (Gärdenfors 2000, 2014) as a mediator between Shepard’s and Tenenbaum & Griffiths’ conflicting views on the role of psychological similarity for a successful model of categorisation. It suggests that the conceptual spaces theory can help to improve the Bayesian model while finding an explanatory role for psychological similarity. (shrink)

Geographic Information Science (GIS) is an interdisciplinary science aiming to detect and visually represent patterns in spatial data. GIS is used by businesses to determine where to open new stores and by conservation biologists to identify field study locations with relatively little anthropogenic influence. Products of GIS include topographic and thematic maps of the Earth’s surface, climate maps, and spatially referenced demographic graphs and charts. In addition to its social, political, and economic importance, GIS is of intrinsic philosophical interest due (...) to its methodological richness and because it is an instructive analogue to other sciences. This chapter works towards a philosophy of GIS and cartography, or PGISC. In particular, it examines practices of classifying geographic space, objects, and relations. By focusing on the use of natural kinds in data modeling and map generalization practices, I show how the making and using of kinds is contextual, fallible, plural, and purposive. (shrink)

Value Sensitive Design (VSD) is an established method for integrating values into technical design. It has been applied to different technologies and, more recently, to artificial intelligence (AI). We argue that AI poses a number of challenges specific to VSD that require a somewhat modified VSD approach. Machine learning (ML), in particular, poses two challenges. First, humans may not understand how an AI system learns certain things. This requires paying attention to values such as transparency, explicability, and accountability. Second, (...) ML may lead to AI systems adapting in ways that ‘disembody’ the values embedded in them. To address this, we propose a threefold modified VSD approach: 1) integrating a known set of VSD principles (AI4SG) as design norms from which more specific design requirements can be derived; 2) distinguishing between values that are promoted and respected by the design to ensure outcomes that not only do no harm but also contribute to good; and 3) extending the VSD process to encompass the whole life cycle of an AI technology in order to monitor unintended value consequences and redesign as needed. We illustrate our VSD for AI approach with an example use case of a SARS-CoV-2 contact tracing app. (shrink)

Albert Einstein once made the following remark about "the world of our sense experiences": "the fact that it is comprehensible is a miracle." (1936, p. 351) A few decades later, another physicist, Eugene Wigner, wondered about the unreasonable effectiveness of mathematics in the natural sciences, concluding his classic article thus: "the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve" (1960, p. 14). (...) At least three factors are involved in Einstein's and Wigner's miracles: the physical world, mathematics, and human cognition. One way to relate these factors is to ask how the universe could possibly be structured in such a way that mathematics would be applicable to it, and we would be able to understand that application. This is roughly Wigner's question. Alternatively, the way of the mathematical naturalist is to argue that we abstract certain properties from the world, perhaps using our bodies and physical tools, thereby articulating basic mathematical concepts, which we continue building into the complex formal structures of mathematics. John Stuart Mill, Penelope Maddy, and Rafael Nuñez teach this strategy of cognitive abstraction, in very different manners. But what if the very concepts and basic principles of mathematics were built into our cognitive structure itself? Given such a cognitive a priori mathematical endowment, would the miracles of the link between world and cognition (Einstein) and mathematics and world (Wigner) not vanish, or at least significantly diminish? This is the stance of Stanislas Deheane and Elizabeth Brannon's 2011 anthology, following a venerable rationalist tradition including Plato and Immanuel Kant. (shrink)

In this paper I lay the foundations for the construction of an affective quality space. I begin by outlining what quality spaces are, and how they have been constructed for sensory qualities across different perceptual modalities. I then turn to tackle four obstacles that an affective quality space might face that would make an affective quality space unfeasible. After showing these obstacles to be surmountable, I propose a number of conditions and methodological constraints that should be (...) satisfied in attempts to construct an affective quality space. Before concluding, I detail the high explanatory pay-off such a project promises. (shrink)

One potentially extremely fruitful use of the tools of corpus analysis in the philosophy of science is to help us understand disputed terrains within the sciences that we study. For philosophers of biology, for instance, few controversies are as heated as those over the concepts we use in taxonomy to classify the living world, with the definition of ‘species’ perhaps most fundamental among them. As many understandings of biodiversity, in turn, involve counting the number of species present in a (...) given area, these taxonomic concepts thus become crucially implicated in our efforts in conservation biology and our response to climate change. In this chapter, we present a corpus of taxonomic journal papers, and illustrate how it might be used to make progress in the history and philosophy of taxonomy. What parts of the biological world do taxonomists most often study? Are these areas of focus related to other methodological commitments, or perhaps to their underlying conceptual disagreement? Are species that are more important to conservation, or economic concerns, or more important to local cultures, more or less likely to be the target of biological study? Corpus-based methods, we argue, are uniquely powerful for approaching questions such as these, and we hope that the case we present can serve as a fruitful example for others considering their implementation. (shrink)

In a now classic paper published in 1991, Alberch introduced the concept of genotype–phenotype (G!P) mapping to provide a framework for a more sophisticated discussion of the integration between genetics and developmental biology that was then available. The advent of evo-devo first and of the genomic era later would seem to have superseded talk of transitions in phenotypic space and the like, central to Alberch’s approach. On the contrary, this paper shows that recent empirical and theoretical advances have (...) only sharpened the need for a different conceptual treat- ment of how phenotypes are produced. Old-fashioned metaphors like genetic blueprint and genetic programme are not only woefully inadequate but positively misleading about the nature of G!P, and are being replaced by an algorithmic approach emerging from the study of a variety of actual G!P maps. These include RNA folding, protein function and the study of evolvable soft- ware. Some generalities are emerging from these disparate fields of analysis, and I suggest that the concept of ‘developmental encoding’ (as opposed to the classical one of genetic encoding) provides a promising computational–theoretical underpinning to coherently integrate ideas on evolvability, modularity and robustness and foster a fruitful framing of the G!P mapping problem. (shrink)

This paper is in two parts. Part I outlines three traditional approaches to the teaching of critical thinking: the normative, cognitive psychology, and educational approaches. Each of these approaches is discussed in relation to the influences of various methods of critical thinking instruction. The paper contrasts these approaches with what I call the “visualisation” approach. This approach is explained with reference to computer-aided argument mapping (CAAM) which uses dedicated computer software to represent inferences between premise and conclusions. The paper (...) presents a detailed account of the CAAM methodology, and theoretical justification for its use, illustrating this with the argument mapping software Rationale™. A number of Rationale™ design conventions and logical principles are outlined including the principle of abstraction, the MECE principle, and the “Holding Hands” and “Rabbit Rule” heuristics. Part II of this paper outlines the growing empirical evidence for the effectiveness of CAAM as a method of teaching critical thinking. (shrink)

It's possible to understand an infinite number of novel maps. I argue that Roberto Casati and Achille Varzi's compositional semantics of maps cannot explain this possibility, because it requires an infinite number of semantic primitives. So the semantics of maps is puzzlingly different from the semantics of language.

Space is one of the most fundamental concepts over which scientific knowledge has been constructed. But it is also true that space concepts extrapolate by far the scientific domain, and permeate many other branches of human knowledge. Those are fascinating aspects that could di per se justify the compilation of a long bibliography. Another one is the passion for books. My interest in some physical, historical and philosophical problems concerning the concept of space in Physics, and its (...) properties, can be traced back to the early 1980. Since that time, I have being studying, with several collaborators, the influence of space dimensionality in different physical phenomena, like the Casimir Effect, neutron diffraction, Cosmic Microwave Background Radiation and the stability of Schrödinger’s and Dirac’s hydrogen atom in arbitrary number of dimensions, as well as epistemological aspects of the works of Kant, Ehrenfest an others on this particular subject. Meanwhile, I gave lectures about the History of the Concepts of Space in Physics at the Centro Brasileiro de Pesquisas Físicas (CBPF), at the Program of History of Sciences, Technics and Epistemology of the Federal University of Rio the Janeiro (UFRJ) and also at the Physics Institute of the State University of Rio de Janeiro (UERJ). As a consequence of both this interest and my love for books, I continuously bought books on space for my personal library which contains now quite one half of all the books quoted here. In 1996, Roberto Moreira and I published the Sources for the History of Space concepts in Physics: From 1845 to 1995 in the series Notas de Física of the CBPF (NF # 084/96), which is still available online. This was a first initiative to share our bibliography on space. At that time, it contained 1075 references, including 414 books entirely devoted to space, 380 articles in periodical journals and proceedings and 281 miscellaneous citations. After fifteen years, I decided to focus my attention here to collect what in my opinion are the 601 essential books which could be useful for anyone interested on learning about space. An important restriction is imposed here by language: only texts written in English, French, German, Italian, Spanish, Portuguese and Latin were considered. References are given in chronological order covering the period between 1739 and 2010. For each year, the books are listed in alphabetical order of authors’ name. An onomastic index is included at the end of the book. -/- Francisco Caruso Rio de Janeiro, October 2011 . (shrink)

This paper outlines an Husserlian, phenomenological account of the first stages of the acquisition of empirical knowledge in light of some aspects of Wilfrid Sellars’ critique of the myth of the given. The account offered accords with Sellars’ in the view that epistemic status is attributed to empirical episodes holistically and within a broader normative context, but disagrees that such holism and normativity are accomplished only within the linguistic and conceptual confines of the space of reasons, and rejects the (...) limitation of the relevant normativity to the cognitive domain. Attention to the phenomenological notion of motivations in our mapping of the structure and acquisition of empirical knowledge reveals a form of weak categoriality given in experience, one outside exclusive mediation by language and concepts but also not merely causal. Section 1 outlines some basic aspects of Sellars’ account of empirical knowledge in Empiricism and the Philosophy of Mind, including a regress objection that arises due to his claim that empirical knowledge presupposes knowledge of general facts about perception. Section 2 examines Sellars’ later revisiting of the objection, via his critique of Roderick Firth, in “The Lever of Archimedes,” focusing on his analysis of the “Myth of the Categorial Given” and his use of the notion of ur-concepts. Section 3 looks at Sellars’ psychological nominalism and his rejection of the explanatory primacy of experience in light of the strict dichotomy between the space of causes and the space of reasons, and shows how Firth’s account aligns with phenomenology in its advocating for an irreducible and non-inferential role for experience. It also raises an important objection to Sellars’ account concerning the categorial givenness of causality. Section 4 turns to Husserl, arguing that his conception of motivation in the Logical Investigations and Ideas II reveals a third explanatory or logical space “between” that of causes and that of reasons. Section 5 further develops this account with regard to the explanatory role of lived experience. Section 6 revisits the regress objection to Sellars from the phenomenological standpoint developed earlier in the paper, and argues that an Husserlian account of empirical knowledge offers a viable alternative to Sellars’ that overcomes the regress objection and gives proper explanatory weight to the evidence of lived experience vis-à-vis scientific presuppositions about causality. (shrink)

This paper discusses the logical space of alternative conceptual engineering projects, with a specific focus on (1) the processes, (2) the targets and goals, and (3) the methods of such projects. We present an overview of how these three aspects interact in the contemporary literature and discuss those alternative projects that have yet to be explored based on our suggested typology. We show how choices about each element in a conceptual engineering project constrain the possibilities for the others, thereby (...) giving rise to distinct groupings of possible projects under the banner of conceptual engineering. We conclude with a critical reflection on the potential ethical issues that arise as a result of effectively putting conceptual engineering into practice. (shrink)

This paper examines connections between concepts of space and extension on the one hand and immaterial spirits on the other, specifically the immanentist concept of spirits as present in rerum natura. Those holding an immanentist concept, such as Thomas Aquinas, typically understood spirits non-dimensionally as present by essence and power; and that concept was historically linked to holenmerism, the doctrine that the spirit is whole in every part. Yet as Aristotelian ideas about extension were challenged and an actual, infinite, (...) dimensional space readmitted, a dimensionalist concept of spirit became possible—that asserted by the mature Henry More, as he repudiated holenmerism. Despite More’s intentions, his dimensionalist concept opens the door to materialism, for supposing that spirits have parts outside parts implies that those parts could in principle be mapped onto the parts of divisible bodies. The specter of materialism broadens our interest in More’s unconventional ideas, for the question of whether other early modern thinkers, including Isaac Newton, followed More becomes a question of whether they too unwittingly helped usher in materialism. This paper shows that More’s attack upon holenmerism fails. He illegitimately injects his dimensionalist concept of spirit into the doctrine, failing to recognize it as a consequence of the non-dimensionalist concept of spirit, which in itself secures indivisibility. The interpretive consequence for Newton is that there is no prima facie reason to suppose that the charitable interpretation takes him to deny holenmerism. (shrink)

Ikigai is a Japanese concept, which, in brief, refers to the “reason or purpose to live”. I-risks have been identified as a category of risks complementing x- risks, i.e., existential risks, and s-risks, i.e., suffering risks, which describes undesirable future scenarios in which humans are deprived of the pursuit of their individual ikigai. While some developments in AI increase i-risks, there are also AI-driven virtual opportunities, which reduce i-risks by increasing the space of potential ikigais, largely due to developments (...) in generative AI, virtual worlds as well as AI-driven hyper-personalization. The purpose of this paper is to present a first attempt to map the potential AI-driven virtual hyper-personalised ikigai universe. Moreover, challenges and further ideas are presented. (shrink)

This article provides a conceptual map of the debate on ideal and non‐ideal theory. It argues that this debate encompasses a number of different questions, which have not been kept sufficiently separate in the literature. In particular, the article distinguishes between the following three interpretations of the ‘ideal vs. non‐ideal theory’ contrast: (i) full compliance vs. partial compliance theory; (ii) utopian vs. realistic theory; (iii) end‐state vs. transitional theory. The article advances critical reflections on each of these sub‐debates, and (...) highlights areas for future research in the field. (shrink)

We argue that a cognitive semantics has to take into account the possibly partial information that a cognitive agent has of the world. After discussing Gärdenfors's view of objects in conceptual spaces, we offer a number of viable treatments of partiality of information and we formalize them by means of alternative predicative logics. Our analysis shows that understanding the nature of simple predicative sentences is crucial for a cognitive semantics.

Social space is superimposed on the civilization map of the world whereas the social time is correlated with the duration of civilization existence. Within own civilization the concept space is non-homogeneous, there are “singled out points” — “concept factories”. As social structures, cities may exist rather long, sometimes during several millennia, but as concept centres they are limited by the duration of civilization existence. If civilization is a “concept universe”, nobody and nothing may cross the boundaries, which include (...) cities as well. Death of civilization leads to reboot cultural and historical space-time. On the other hand, reformatted olds concepts are not preserved, but there may be reception of old concepts and their new interpretation. However, even in case of genetic links presence, they are the other concepts and not modified old ones. Under certain circumstances may take place “rebranding” when attractive name is connected to the concept of absolutely different order to attach to it authority of the past. (shrink)

Can we design a perfect democratic decision procedure? Condorcet famously observed that majority rule, our paradigmatic democratic procedure, has some desirable properties, but sometimes produces inconsistent outcomes. Revisiting Condorcet’s insights in light of recent work on the aggregation of judgments, I show that there is a conflict between three initially plausible requirements of democracy: “robustness to pluralism”, “basic majoritarianism”, and “collective rationality”. For all but the simplest collective decision problems, no decision procedure meets these three requirements at once; at most (...) two can be met together. This “democratic trilemma” raises the question of which requirement to give up. Since different answers correspond to different views about what matters most in a democracy, the trilemma suggests a map of the “logical space” in which different conceptions of democracy are located. It also sharpens our thinking about other impossibility problems of social choice and how to avoid them, by capturing a core structure many of these problems have in common. More broadly, it raises the idea of “cartography of logical space” in relation to contested political concepts. (shrink)

A classic analytic approach to biological phenomena seeks to refine definitions until classes are sufficiently homogenous to support prediction and explanation, but this approach founders on cases where a single process produces objects with similar forms but heterogeneous behaviors. I introduce object spaces as a tool to tackle this challenging diversity of biological objects in terms of causal processes with well-defined formal properties. Object spaces have three primary components: (1) a combinatorial biological process such as protein synthesis that generates objects (...) with parts that are modular, independent, and organized according to an invariant syntax; (2) a notion of “distance” that relates the objects according to rules of change over time as found in nature or useful for algorithms; (3) mapping functions defined on the space that map its objects to other spaces or apply an evaluative criterion to measure an important quality, such as parsimony or biochemical function. Once defined, an object space can be used to represent and simulate the dynamics of phenomena on multiple scales; it can also be used as a tool for predicting higher-order properties of the objects, including stitching together series of causal processes. Object spaces are the basis for a strategy of theorizing, discovery, and analysis in biology: as heuristic idealizations of biology, they help us transform inchoate, intractable problems into articulated, well-structured ones. Developing an object space is a research strategy with a long, successful history under many other names, and it offers a unifying but not overreaching approach to biological theory. (shrink)

This paper explores the integration of Michael Strevens' concept of idealizations with my previous framework of similarity spaces and context-dependence to develop a comprehensive account of ideal explanations in scientific practice. Idealizations, which involve deliberate falsifications, play a crucial role in distinguishing between causally relevant and irrelevant factors in scientific models. Context-dependent mapping provides a structured approach to handling complementarities and context-dependent phenomena by mapping different observational contexts to distinct sets of physical laws. By combining these two ideas, (...) I will construct an idealized context-dependent mapping structure and discuss how ideal similarity spaces within the framework of context-dependent mapping can enhance our understanding of complex scientific phenomena, especially those involving wave-particle duality and black hole complementarity. I also aim to discuss the types of idealizations that may exist within explanation and examine their relations to the mapping. (shrink)

Mental health research faces a suite of unresolved challenges that have contributed to a stagnation of research efforts and treatment innovation. One such challenge is how to reliably and validly account for the subjective side of patient symptomatology, that is, the patient’s inner experiences or patient phenomenology. Providing a structured, standardised semantics for patient phenomenology would enable future research in novel directions. In this contribution, we aim at initiating a standardized approach to patient phenomenology by sketching a tentative formalisation within (...) the framework of an applied ontology, in the broader context of existing open-source Open Biomedical Ontologies resources such as the Mental Functioning Ontology. We further discuss a number of prevailing challenges and observations bearing on this task. (shrink)

I am interested in the use Kant makes of the pure intuition of space, and of properties and principles of space and spaces (i.e. figures, like spheres and lines), in the special metaphysical project of MAN. This is a large topic, so I will focus here on an aspect of it: the role of these things in his treatment of some of the laws of matter treated in the Dynamics and Mechanics Chapters. In MAN and other texts, Kant (...) speaks of space as the “ground,” “condition,” and “basis” of various laws, including the inverse-square and inverse-cube laws of attractive and repulsive force, and the Third Law of Mechanics. Moreover, in his proofs of all the laws just mentioned, the language of “construction” figures prominently, which suggests that Kant’s proofs (somehow) rest on or involve mathematical construction in his technical sense. Such claims give rise to a number of questions. How do properties and principles of space and spaces serve to ground this particular set of laws? Which spatial properties and principles is Kant appealing to? What, if anything, does the spatial grounding of the inverse-square and inverse-cube laws of diffusion (treated in the Dynamics Chapter) have in common with that of the Third treated in the Mechanics Chapter)? What role—if any—does mathematical construction play in Kant’s proofs of these laws? Finally, how if at all, are Kant’s grounding claims consistent with his other commitments—for example, how are they consistent with his notorious denial in Prolegomena §38 that there are any laws that “lie in space” (Prol 4:321)? I offer answers to these questions. (shrink)

A Commonplace of recent philosophy of mind is that intentional states are relations between thinkers and propositions. This thesis-call it the 'Relational Thesis'-does not depend on any specific theory of propositions. One can hold it whether one believes that propositions are Fregean Thoughts, ordered n-tuples of objects and properties or sets of possible worlds. An assumption that all these theories of propositions share is that propositions are abstract objects, without location in space or time...

This essay brings Emmanuel Levinas and Watsuji Tetsurō into constructive philosophical engagement. Rather than focusing primarily on interpretation — admittedly an important dimension of comparative philosophical inquiry — my intention is to put their respective views to work, in tandem, and address the problem of the embodied social self.1 Both Watsuji and Levinas share important commonalities with respect to the embodied nature of intersubjectivity —commonalities that, moreover, put both thinkers in step with some of the concerns driving current treatments of (...) social cognition in philosophy and cognitive science. They can make a fruitful contribution to this discussion by lending a phenomenologically informed critical perspective. Each in their own way challenges the internalist and cognitivist presuppositions informing the currently dominant “Theory of Mind” paradigm driving much social cognition research. Moreover, their respective views receive empirical support from a number of different sources. (shrink)

Determinism is, roughly, the thesis that facts about the past and the laws of nature entail all truths. A venerable, age-old dilemma concerning responsibility distils to this: if either determinism is true or it is not true, we lack "responsibility-grounding" control. Either determinism is true or it is not true. So, we lack responsibility-grounding control. Deprived of such control, no one is ever morally responsible for anything. A number of the freshly-minted essays in this collection address aspects of this (...) dilemma. Responding to the horn that determinism undermines the freedom that responsibility (or moral obligation) requires, the freedom to do otherwise, some papers in this collection debate the merits of Frankfurt-style examples that purport to show that one can be responsible despite lacking alternatives. Responding to the horn that indeterminism implies luck or randomness, other papers discuss the strengths or shortcomings of libertarian free will or control. Also included in this collection are essays on the freedom requirements of moral obligation, forgiveness and free will, a "desert-free" conception of free will, and vicarious legal and moral responsibility. This chapter points to the importance of the topics discussed in the volume and interesting arguments worth noting. (shrink)

Part I of this paper outlined the three standard approaches to the teaching of critical thinking: the normative (or philosophical), cognitive psychology, and educational taxonomy approaches. The paper contrasted these with the visualisation approach; in particular, computer-aided argument mapping (CAAM), and presented a detailed account of the CAAM methodology and a theoretical justification for its use. This part develops further support for CAAM. A case is made that CAAM improves critical thinking because it minimises the cognitive burden of prose (...) and the demands that arguments in prose typically place on memory. CAAM also has greater usability, complements the imperfect human cognitive system, and adopts a logic of semi-formality which is both natural and intuitive. The paper claims that CAAM is an important advance given that traditional stand-alone critical thinking courses do not teach critical thinking as well as they as they are assumed to do. It is also important given that tertiary education fails to deliver improvements in critical thinking gains for too many students. The paper outlines results from a number of empirical studies that demonstrate that CAAM yields robust gains in critical thinking as measured by independent tests. Students themselves also believe CAAM to be beneficial as noted in coded responses to surveys. I conclude the paper by comparing the traditional approaches to the teaching of critical thinking to the visualisation approach. I argue that CAAM should taken seriously in the context of contemporary educational practices. (shrink)

A common way to understand memory structures in the cognitive sciences is as a cognitive map​. Cognitive maps are representational systems organized by dimensions shared with physical space. The appeal to these maps begins literally: as an account of how spatial information is represented and used to inform spatial navigation. Invocations of cognitive maps, however, are often more ambitious; cognitive maps are meant to scale up and provide the basis for our more sophisticated memory capacities. The extension is not (...) meant to be metaphorical, but the way in which these richer mental structures are supposed to remain map-like is rarely made explicit. Here we investigate this missing link, asking: how do cognitive maps represent non-spatial information?​ We begin with a survey of foundational work on spatial cognitive maps and then provide a comparative review of alternative, non-spatial representational structures. We then turn to several cutting-edge projects that are engaged in the task of scaling up cognitive maps so as to accommodate non-spatial information: first, on the spatial-isometric approach​ , encoding content that is non-spatial but in some sense isomorphic to spatial content; second, on the ​ abstraction approach​ , encoding content that is an abstraction over first-order spatial information; and third, on the ​ embedding approach​ , embedding non-spatial information within a spatial context, a prominent example being the Method-of-Loci. Putting these cases alongside one another reveals the variety of options available for building cognitive maps, and the distinctive limitations of each. We conclude by reflecting on where these results take us in terms of understanding the place of cognitive maps in memory. (shrink)

Some recently popular accounts of perception account for the phenomenal character of perceptual experience in terms of the qualities of objects. My concern in this paper is with naturalistic versions of such a phenomenal externalist view. Focusing on visual spatial perception, I argue that naturalistic phenomenal externalism conflicts with a number of scientific facts about the geometrical characteristics of visual spatial experience.

The widely accepted two-dimensional circumplex model of emotions posits that most instances of human emotional experience can be understood within the two general dimensions of valence and activation. Currently, this model is facing some criticism, because complex emotions in particular are hard to define within only these two general dimensions. The present theory-driven study introduces an innovative analytical approach working in a way other than the conventional, two-dimensional paradigm. The main goal was to map and project semantic emotion space (...) in terms of mutual positions of various emotion prototypical categories. Participants (N = 187; 54.5% females) judged 16 discrete emotions in terms of valence, intensity, controllability and utility. The results revealed that these four dimensional input measures were uncorrelated. This implies that valence, intensity, controllability and utility represented clearly different qualities of discrete emotions in the judgments of the participants. Based on this data, we constructed a 3D hypercube-projection and compared it with various two-dimensional projections. This contrasting enabled us to detect several sources of bias when working with the traditional, two-dimensional analytical approach. Contrasting two-dimensional and three-dimensional projections revealed that the 2D models provided biased insights about how emotions are conceptually related to one another along multiple dimensions. The results of the present study point out the reductionist nature of the two-dimensional paradigm in the psychological theory of emotions and challenge the widely accepted circumplex model. (shrink)

Reading, even when silent and individual, is a social phenomenon and has often been studied as such. Complementary to this view, research has begun to explore how reading is embodied beyond simply being ‘wired’ in the brain. This article brings the social and embodied perspectives together in a very literal sense. Reporting a qualitative study of reading practices across student focus groups from six European countries, it identifies an underexplored factor in reading behaviour and experience. This factor is the sheer (...) physical presence, and concurrent activity, of other people in the environment where one engages in individual silent reading. The primary goal of the study was to explore the role and possible associations of a number of variables (text type, purpose, device) in selecting generic (e.g. indoors vs outdoors) as well as specific (e.g. home vs library) reading environments. Across all six samples included in the study, participants spontaneously attested to varied, and partly surprising, forms of sensitivity to company and social space in their daily efforts to align body with mind for reading. The article reports these emergent trends and discusses their potential implications for research and practice. (shrink)

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which (...) is empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

The relationship between abstract formal procedures and the activities of actual physical systems has proved to be surprisingly subtle and controversial, and there are a number of competing accounts of when a physical system can be properly said to implement a mathematical formalism and hence perform a computation. I defend an account wherein computational descriptions of physical systems are high-level normative interpretations motivated by our pragmatic concerns. Furthermore, the criteria of utility and success vary according to our diverse purposes (...) and pragmatic goals. Hence there is no independent or uniform fact to the matter, and I advance the ‘anti-realist’ conclusion that computational descriptions of physical systems are not founded upon deep ontological distinctions, but rather upon interest-relative human conventions. Hence physical computation is a ‘conventional’ rather than a ‘natural’ kind. (shrink)

This paper introduces a conceptual framework, denoted as ‘Line Theory,’ which is predicated on the procedural anatomy inherent in ordinary plans. A plan, recognized as a set of instructions for execution, undergoes in-depth scrutiny to analyze its constituent elements. The concise examination delves into the formation of line and effect within real space stemming from procedures. Line theory serves the purpose of elucidating the absolute optimization of plans. It is formulated to inaugurate an exploration into the veracity of procedures (...) and their elemental changes, examining their correlation with space and motion at the most fundamental level. The scientific community has extensively delved into the examination of the behavior and structure of objects at the microscopic level. This paper endeavors to stimulate interest in the analogous analysis of procedures. The fundamental objective within this theoretical framework is to offer a distinct philosophical perspective on changes and effects. (shrink)

In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent’s personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the usual probability rules as required by Dutch-book coherence, but quantum mechanics imposes additional constraints upon them. In this paper, we explore the question of deriving the structure of quantum-state space from a set of assumptions in the spirit of quantum Bayesianism. The starting point is the (...) representation of quantum states induced by a symmetric informationally complete measurement or SIC. In this representation, the Born rule takes the form of a particularly simple modification of the law of total probability. We show how to derive key features of quantum-state space from (i) the requirement that the Born rule arises as a simple modification of the law of total probability and (ii) a limited number of additional assumptions of a strong Bayesian flavor. (shrink)

Can genealogical explanations affect the space of reasons? Those who think so commonly face two objections. The first objection maintains that attempts to derive reasons from claims about the genesis of something commit the genetic fallacy—they conflate genesis and justification. One way for genealogies to side-step this objection is to focus on the functional origins of practices—to show that, given certain facts about us and our environment, certain conceptual practices are rational because apt responses. But this invites a second (...) objection, which maintains that attempts to derive current from original function suffer from continuity failure—the conditions in response to which something originated no longer obtain. This paper shows how normatively ambitious genealogies can steer clear of both problems. It first maps out various ways in which genealogies can involve non-fallacious genetic arguments before arguing that some genealogies do not invite the charge of the genetic fallacy if they are interpreted as revealing the original functions of conceptual practices. However, they then incur the burden of showing that the conditions relative to which practices function continuously obtain. Taking its cue from the genealogies of E. J. Craig, Bernard Williams, and Miranda Fricker, the paper shows how model-based genealogies can avoid continuity failures by identifying bases of continuity in the demands we face. (shrink)

Previous work has shown that the Complex Conceptual Spaces − Single Observation Mathematical framework is a useful tool for event characterization. This mathematical framework is developed on the basis of Conceptual Spaces and uses integer linear programming to find the needed similarity values. The work of this paper is focused primarily on space event characterization. In particular, the focus is on the ranking of threats for malicious space events such as a kinetic kill. To make the Conceptual Spaces (...) framework work, the similarity values between the contents of observations on the one hand and the properties of the entities observed on the other needs to be found. This paper shows how to exploit Dempster-Shafer theory to implement a statistical approach for finding these similarities values. This approach will allow a user to identify the uncertainty involved in similarity value data, which can later be propagated through the developed mathematical model in order for the user to know the overall uncertainty in the observation-to-concept mappings needed for space event characterization. (shrink)

Although the Four Colour Theorem is passe, we give an elementary pre-formal proof that transparently illustrates why four colours suffice to chromatically differentiate any set of contiguous, simply connected and bounded, planar spaces; by showing that there is no minimal 4-coloured planar map M. We note that such a pre-formal proof of the Four Colour Theorem highlights the significance of differentiating between: (a) Plato's knowledge as justified true belief, which seeks a formal proof in a first-order mathematical language in order (...) to justify a belief as true; and (b) Piccinini's knowledge as factually grounded belief, which seeks a pre-formal proof, in Pantsar's sense, in order to justify the axioms and rules of inference of a first-order mathematical language which can, then, formally prove the belief as justifiably true under a well-defined interpretation of the language. (shrink)

We notice a number of interesting overlaps between the views on personhood of Ifeanyi Menkiti and Marya Schechtman. Both philosophers distance their views from the individualistic ones standard in western thought and foreground the importance of extrinsic or relational features to personhood. For Menkiti, it is ‘the community which defines the person as person’; for Schechtman, being a person is to have a place in person-space, which involves being seen as a person by others. But there are also (...) striking differences. Schechtman sees this aspect as expanding the scope of personhood to infants and those who are severely mentally disabled. Menkiti thinks that there is a line to be drawn at some point between those humans that are persons and those who are not. We consider the cases offered in questioning how the dispute between the two views should be resolved. (shrink)