For many centuries, philosophers and scientists have pondered the origins and nature of human intuitions about the properties of points, lines, and figures on the Euclidean plane, with most hypothesizing that a system of Euclidean concepts either is innate or is assembled by general learning processes. Recent research from cognitive and developmental psychology, cognitive anthropology, animal cognition, and cognitive neuroscience suggests a different view. Knowledge of geometry may be founded on at least two distinct, evolutionarily ancient, core (...) cognitive systems for representing the shapes of large-scale, navigable surface layouts and of small-scale, movable forms and objects. Each of these systems applies to some but not all perceptible arrays and captures some but not all of the three fundamental Euclidean relationships of distance (or length), angle, and direction (or sense). Like natural number (Carey, 2009), Euclidean geometry may be constructed through the productive combination of representations from these core systems, through the use of uniquely human symbolic systems. (shrink)

This review discusses the content of Mateusz Hohol’s new book Foundations of Geometric Cognition. Mathematical cognition has until now focused mainly on human numerical abilities. Hohol’s work tackles geometric cognition, an issue that has not been described in previous investigations into mathematical cognition. The main strength of the book lies in its critical analysis of a huge amount of results from empirical experiments. The author formulates his theoretical proposals very carefully, avoiding radical and one-sided solutions. He claims that human geometric (...) cognition is based mainly on two core systems, both being phylogenetically hardwired, namely the system of layout geometry and the system of object geometry. The interaction of these systems becomes amplified in the individual development of the mind, which, in turn, is supported by the use of language. The second part of the review contains the reviewer’s remarks concerning the history of geometry, experiments related to spatial representations, and the role of geometry in mathematical education. (shrink)

This review discusses the content of Mateusz Hohol’s new book Foundations of Geometric Cognition. Mathematical cognition has until now focused mainly on human numerical abilities. Hohol’s work tackles geometric cognition, an issue that has not been described in previous investigations into mathematical cognition. The main strength of the book lies in its critical analysis of a huge amount of results from empirical experiments. The author formulates his theoretical proposals very carefully, avoiding radical and one-sided solutions. He claims that human geometric (...) cognition is based mainly on two core systems, both being phylogenetically hardwired, namely the system of layout geometry and the system of object geometry. The interaction of these systems becomes amplified in the individual development of the mind, which, in turn, is supported by the use of language. The second part of the review contains the reviewer’s remarks concerning the history of geometry, experiments related to spatial representations, and the role of geometry in mathematical education. (shrink)

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

Does geometry constitues a core set of intuitions present in all humans, regarless of their language or schooling ? We used two non verbal tests to probe the conceptual primitives of geometry in the Munduruku, an isolated Amazonian indigene group. Our results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms.

Geometry, etymologically the “science of measuring the Earth”, is a mathematical formalization of space. Just as formal concepts of number may be rooted in an evolutionary ancient system for perceiving numerical quantity, the fathers of geometry may have been inspired by their perception of space. Is the spatial content of formal Euclidean geometry universally present in the way humans perceive space, or is Euclidean geometry a mental construction, specific to those who have received appropriate instruction? (...) The spatial content of the formal theories of geometry may depart from spatial perception for two reasons: first, because in geometry, only some of the features of spatial figures are theoretically relevant; and second, because some geometric concepts go beyond any possible perceptual experience. Focusing in turn on these two aspects of geometry, we will present several lines of research on US adults and children from the age of three years, and participants from an Amazonian culture, the Mundurucu. Almost all the aspects of geometry tested proved to be shared between these two cultures. Nevertheless, some aspects involve a process of mental construction where explicit instruction seem to play a role in the US, but that can still take place in the absence of instruction in geometry. (shrink)

This paper is an edited form of a letter written by the two authors (in the name of Tarski) to Wolfram Schwabhäuser around 1978. It contains extended remarks about Tarski's system of foundations for Euclidean geometry, in particular its distinctive features, its historical evolution, the history of specific axioms, the questions of independence of axioms and primitive notions, and versions of the system suitable for the development of 1-dimensional geometry.

Disoriented animals from ants to humans reorient in accord with the shape of the surrounding surface layout: a behavioral pattern long taken as evidence for sensitivity to layout geometry. Recent computational models suggest, however, that the reorientation process may not depend on geometrical analyses but instead on the matching of brightness contours in 2D images of the environment. Here we test this suggestion by investigating young children's reorientation in enclosed environments. Children reoriented by extremely subtle geometric properties (...) of the 3D layout: bumps and ridges that protruded only slightly off the floor, producing edges with low contrast. Moreover, children failed to reorient by prominent brightness contours in continuous layouts with no distinctive 3D structure. The findings provide evidence that geometric layout representations support children's reorientation. (shrink)

In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us, all directions are the same to us and all units of length we use to create geometric figures are the same to us. On the other hand, through the process of algebraic simplification, this system of axioms (...) directly provides the Weyl’s system of axioms for Euclidean geometry. The system of axioms, together with its a priori interpretation, offers new views to philosophy and pedagogy of mathematics: it supports the thesis that Euclidean geometry is a priori, it supports the thesis that in modern mathematics the Weyl’s system of axioms is dominant to the Euclid’s system because it reflects the a priori underlying symmetries, it gives a new and promising approach to learn geometry which, through the Weyl’s system of axioms, leads from the essential geometric symmetry principles of the mathematical nature directly to modern mathematics. (shrink)

Modern observations based on general relativity indicate that the spatial geometry of the expanding, large-scale Universe is very nearly Euclidean. This basic empirical fact is at the core of the so-called “flatness problem”, which is widely perceived to be a major outstanding problem of modern cosmology and as such forms one of the prime motivations behind inflationary models. An inspection of the literature and some further critical reflection however quickly reveals that the typical formulation of this putative problem (...) is fraught with questionable arguments and misconceptions and that it is moreover imperative to distinguish between different varieties of problem. It is shown that the observational fact that the large-scale Universe is so nearly flat is ultimately no more puzzling than similar “anthropic coincidences”, such as the specific values of the gravitational and electromagnetic coupling constants. In particular, there is no fine-tuning problem in connection to flatness of the kind usually argued for. The arguments regarding flatness and particle horizons typically found in cosmological discourses in fact address a mere single issue underlying the standard FLRW cosmologies, namely the extreme improbability of these models with respect to any “reasonable measure” on the “space of all spacetimes”. This issue may be expressed in different ways and a phase space formulation, due to Penrose, is presented here. A horizon problem only arises when additional assumptions—which are usually kept implicit and at any rate seem rather speculative—are made. (shrink)

Research on human infants, adult nonhuman primates, and children and adults in diverse cultures provides converging evidence for four systems at the foundations of human knowledge. These systems are domain specific and serve to represent both entities in the perceptible world (inanimate manipulable objects and animate agents) and entities that are more abstract (numbers and geometrical forms). Human cognition may be based, as well, on a fifth system for representing social partners and for categorizing the social world into groups. (...) Research on infants and children may contribute both to understanding of these systems and to attempts to overcome misconceptions that they may foster. (shrink)

This is an in-depth study of J.G. Fichte’s philosophy of mathematics and theory of geometry. It investigates both the external formal and internal cognitive parallels between the axioms, intuitions and constructions of geometry and the scientific methodology of the Fichtean system of philosophy. In contrast to “ordinary” Euclidean geometry, in his Erlanger Logik of 1805 Fichte posits a model of an “ursprüngliche” or original geometry – that is to say, a synthetic and constructivistic conception grounded (...) in ideal archetypal elements that are grasped through geometrical or intelligible intuition. -/- Accordingly, this study classifies Fichte’s philosophy of mathematics as a whole as a species of mathematical Platonism or neo-Platonism, and concludes that the Wissenschaftslehre itself may be read as an attempt at a new philosophical mathesis, or “mathesis of the mind.” -/- “This work testifies to the author's exact and extensive knowledge of the Fichtean texts, as well as of the philosophical, scientific and historical contexts. Wood has opened up completely new paths for Fichte research, and examines with clarity and precision a domain that up to now has hardly been researched.” Professor Dr. Marco Ivaldo -/- “This study, written in a language distinguished by its limpidity and precision, and constantly supported by a close reading of the Fichtean texts and secondary literature, furnishes highly detailed and convincing demonstrations. In directly confronting the difficult historical relationship between the Wissenschaftslehre and mathematics, the author has broken new ground that is at once stimulating, decidedly innovative, and elegantly audacious.” Professor Dr. Emmanuel Cattin. (shrink)

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

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished]. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of [Tarski 1959]: a predicate of betwenness (...) and a four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane - which obeys the Euclidean axioms in [Tarski and Givant, 1999] - and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagora’s theorem. We conclude with a Representation Theorem relating models of our system that satisfy second order continuity to the mathematical structure called ‘Minkowski spacetime’ in physics textbooks. (shrink)

Context: In this paper I expand aspects of the generalized bottom-up explanatory approach devised in Part I to expound the natural emergence of composite self-organized dynamic systems endowed with self-produced embodied boundaries and with observed degrees of autonomous behavior. In Part I, the focus was on the rules defined by Varela, Maturana & Uribe (VM&U rules), viewed as a validation test to assess if an observed system is autopoietic. This was accomplished by referring to Maturana’s ontological-epistemological frame and by (...) defining distinctions, concepts, and abstractions necessary to describe dynamic systems in any observational domain. This approach concentrates on pure causation flow rather than on domain-specific interaction mechanisms. Problem: It is essential to analyze the requirements imposed by the VM&U rules on the “intra-boundaries” phenomenology for compliance with the self-production capabilities expected from an autopoietic system. Beyond what is merely implied by the compact wording of the VM&U rules, a key point needs to be addressed explicitly: how to describe some “peculiar” capabilities that the components should be endowed with to participate in new component production (as macro-molecules do in the biological domain) so that system’s self-production can be assessed. Method: Using this approach, I first describe the process of constituting self-organized dynamic structures provided with embodied boundaries. Then I explain how a capability of self-organization emerges and how this results in ephemeral configurations that may evolve into self-regulated long-lasting dynamic system stability within a continuous causation flow inside the boundaries, up to the emergence of some “specialized” subsets of components. This explication allows us to distinguish the medium, the boundaries, and the core of a self-organized dynamic system and to focus attention on the “intra-boundaries” phenomenology that should be at the heart of self-production capabilities, as prescribed by the 5th and 6th VM&U rules. Results: I propose an abstract, domain-free description of the “peculiar” composition and decomposition transformation capabilities that components should possess while subject to state transitions triggered within the “intra-boundaries” causation flow. This is combined with a discussion concerning the “intra-boundaries” causation structure’s possible topological layouts that could be compliant with the 6th rule. Implications: The above-mentioned results allow us to improve our analytic criteria when observing dynamic systems existing in non-biological domains in order to assess their autopoietic nature. They also reveal that the task of consistently identifying possible non-biological autopoietic systems is harder than merely identifying self-organized dynamic systems provided with boundaries and some observable autonomous behavioral capabilities in a given observational domain. More implications will be discussed further in Part III. (shrink)

The target article carefully describes the memory system, centered on the temporal lobe that builds specific memory traces. It does not, however, mention the laterality effects that exist within this system. This commentary briefly surveys evidence showing that clear asymmetries exist within the temporal lobe structures subserving the core system and that the right temporal structures mainly underpin face familiarity feelings.

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in Maudlin and Malament. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of Tarski : a predicate of betwenness and a (...) four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane—which obeys the Euclidean axioms in Tarski and Givant, 175–214 1999)—and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagoras’ theorem. We conclude with a Representation Theorem relating models \ of our system \ that satisfy second order continuity to the mathematical structure \, called ‘Minkowski spacetime’ in physics textbooks. (shrink)

The Ministry of Education of China put forward the concept of “core literacy system” for the first time in the “Opinions on Comprehensively Deepening Curriculum Reform and Implementing the Fundamental Tasks of Moral Education” issued in 2014. This is a new educational reform policy put forward by China based on fully combining China’s national conditions and the new requirements for human development in the 21st century, which has important guiding significance for China’s educational reform. After discussing the background, (...) content, and meaning of core literacy, this study points out the current situation and development trend of core literacy in primary and secondary schools in China and then puts forward guiding opinions on the development of core literacy in rural primary and secondary schools. With the widening gap between urban and rural education, rural people are in urgent need of high-quality educational resources. To narrow the gap between urban and rural education and promote the democratization of education in China, we must unswervingly implement the education reform with the core element system as the key field and main link. This is also the significance of this study. (shrink)

The System of Ethics was published at the height of Fichte's academic career and marks the culmination of his philosophical development in Jena. Much more than a treatise on ethics narrowly construed, the System of Ethics presents a unified synthesis of Fichte's core philosophical ideas, including the principle I-hood, self-activity and self-consciousness, and also contains his most detailed treatment of action and agency. This volume brings together an international group of leading scholars on Fichte, and is the (...) first of its kind in English to offer critical and interpretive perspectives on this work, covering topics such as normativity, belief, justification, desire, duty, and the ethical life. It will be an essential guide for scholars wanting to deepen their understanding of Fichte's ethical thought, as well as for those interested in the history of ethics more broadly. (shrink)

What are the brain and cognitive systems that allow humans to play baseball, compute square roots, cook soufflés, or navigate the Tokyo subways? It may seem that studies of human infants and of non-human animals will tell us little about these abilities, because only educated, enculturated human adults engage in organized games, formal mathematics, gourmet cooking, or map-reading. In this chapter, we argue against this seemingly sensible conclusion. When human adults exhibit complex, uniquely human, culture-specific skills, they draw on a (...) set of psychological and neural mechanisms with two distinctive properties: they evolved before humanity and thus are shared with other animals, and they emerge early in human development and thus are common to infants, children, and adults. These core knowledge systems form the building blocks for uniquely human skills. Without them we wouldn’t be able to learn about different kinds of games, mathematics, cooking, or maps. To understand what is special about human intelligence, therefore, we must study both the core knowledge systems on which it rests and the mechanisms by which these systems are orchestrated to permit new kinds of concepts and cognitive processes. What is core knowledge? A wealth of research on non-human primates and on human infants suggests that a system of core knowledge is characterized by four properties (Hauser, 2000; Spelke, 2000). First, it is domain-specific: each system functions to represent particular kinds of entities such as conspecific agents, manipulable objects, places in the environmental layout, and numerosities. Second, it is task-specific: each system uses its representations to address specific questions about the world, such as “who is this?” [face recognition], “what does this do?” [categorization of artifacts], “where am I?” [spatial orientation], and “how many are here?” [enumeration]. Third, it is relatively encapsulated: each uses only a subset of the information delivered by an animal’s input systems and sends information only to a subset of the animal’s output systems. (shrink)

Hyperbolic geometry can be axiomatized using the notions of order andcongruence (as in Euclidean geometry) or using the notion of incidencealone (as in projective geometry). Although the incidence-based axiomatizationmay be considered simpler because it uses the single binary point-linerelation of incidence as a primitive notion, we show that it issyntactically more complex. The incidence-based formulation requires some axioms of the quantifier-type forallexistsforall, while the axiom system based on congruence and order can beformulated using only forallexists-axioms.

Hyperbolic geometry can be axiomatized using the notions of order andcongruence (as in Euclidean geometry) or using the notion of incidencealone (as in projective geometry). Although the incidence-based axiomatizationmay be considered simpler because it uses the single binary point-linerelation of incidence as a primitive notion, we show that it issyntactically more complex. The incidence-based formulation requires some axioms of the quantifier-type \forall\exists\forall, while the axiom system based on congruence and order can beformulated using only \forall\exists-axioms.

Many have taken Sellars’s critique of empiricism in “Empiricism and the Philosophy of Mind” (EPM) to be aimed at his teacher C. I. Lewis. But if so, why do the famous arguments of its opening sections carry so little force against Lewis’s views? Understandably, some respond by denying that Lewis’s epistemology is among the positions targeted by Sellars. But this is incorrect. Indeed, Sellars had earlier offered more trenchant (if already familiar) critiques of Lewis’s epistemology. What is original about EPM (...) is that it criticizes empiricist positions like Lewis’s not because of their foundationalism, but because of their psychologism about meaning. Since psychologism turns out to be unacceptable by Lewis’s own lights, EPM has a compelling (if implicit) critique of Lewis to offer after all, one that strikes at the heart of his philosophical system. (shrink)

Features of consciousness difficult to understand in terms of conventional neuroscience have evoked application of quantum theory, which describes the fundamental behavior of matter and energy. In this paper we propose that aspects of quantum theory (e.g. quantum coherence) and of a newly proposed physical phenomenon of quantum wave function "self-collapse"(objective reduction: OR -Penrose, 1994) are essential for consciousness, and occur in cytoskeletal microtubules and other structures within each of the brain's neurons. The particular characteristics of microtubules suitable for quantum (...) effects include their crystal-like lattice structure, hollow inner core, organization of cell function and capacity for information processing. We envisage that conformational states of microtubule subunits (tubulins) are coupled to internal quantum events, and cooperatively interact (compute) with other tubulins. We further assume that macroscopic coherent superposition of quantum-coupled tubulin conformational states occurs throughout significant brain volumes and provides the global binding essential to consciousness. We equate the emergence of the microtubule quantum coherence with pre-conscious processing which grows (for up to 500 milliseconds) until the mass-energy difference among the separated states of tubulins reaches a threshold related to quantum gravity. According to the arguments for OR put forth in Penrose (1994), superpositioned states each have their own space-time geometries. When the degree of coherent mass-energy difference leads to sufficient separation of space-time geometry, the system must choose and decay (reduce, collapse) to a single universe state. In this way, a transient superposition of slightly differing space-time geometries persists until an abrupt quantum classical reduction occurs. Unlike the random, "subjective reduction"( SR, or R) of standard quantum theory caused by observation or environmental entanglement, the OR we propose in microtubules is a self-collapse and it results in particular patterns of microtubule-tubulin conformational states that regulate neuronal activities including synaptic functions. (shrink)

In this article, I revisit Landau and Jackendoff's () paper, “What and where in spatial language and spatial cognition,” proposing a friendly amendment and reformulation. The original paper emphasized the distinct geometries that are engaged when objects are represented as members of object kinds, versus when they are represented as figure and ground in spatial expressions. We provided empirical and theoretical arguments for the link between these distinct representations in spatial language and their accompanying nonlinguistic neural representations, emphasizing the “what” (...) and “where” systems of the visual system. In the present paper, I propose a second division of labor between two classes of spatial prepositions in English that appear to be quite distinct. One class includes prepositions such as in and on, whose core meanings engage force-dynamic, functional relationships between objects, with geometry only a marginal player. The second class includes prepositions such as above/below and right/left, whose core meanings engage geometry, with force-dynamic relationships a passing or irrelevant variable. The insight that objects’ force-dynamic relationships matter to spatial terms’ uses is not new; but thinking of these terms as a distinct set within spatial language has theoretical and empirical consequences that are new. I propose three such consequences, rooted in the fact that geometric knowledge is highly constrained and early-emerging in life, while force-dynamic knowledge of objects and their interactions is relatively unconstrained and needs to be learned piecemeal over a lengthy timeline. First, the two classes will engage different learning problems, with different developmental trajectories for both first and second language learners; second, the classes will naturally lead to different degrees of cross-linguistic variation; and third, they may be rooted in different neural representations. (shrink)

In the era of the knowledge economy, the improvement of national innovation systems is playing a significant role in the global entrepreneurship ecosystem. Entrepreneurs are accelerating international intellectual property applications to be competitive. What remains to be explored is the evolution of international intellectual property network in the globe. With the application of social network analysis and intellectual property application database, the global innovation network structure from 2000 to 2019 is explored. Results showed that in the period 2000–2019, the global (...) innovation network has been expanding rapidly from a sparse network to a dense and complex one. Patent application is unevenly distributed in the globe. Countries such as the US, China, and Canada have been the top countries flowing in, while Japan, Korea, EU, and Switzerland have been the main countries flowing out. Global innovation network shows an obvious “core-periphery” pattern. The distribution pattern presents a quadrilateral structure with the four core regions of “US, Japan, EU, and China” as the apex. This analysis contributes to the visualization of the global layout of intellectual property and the evolution trend by analyzing intellectual property application networks. This can provide important experience reference for enterprises to study the global entrepreneurship ecosystem. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.4 (2003) 558-559 [Access article in PDF] Stephen Gaukroger. Descartes' System of Natural Philosophy. New York: Cambridge University Press, 2002. Pp. viii + 258. Cloth, $60.00. Paper, $22.00. Stephen Gaukroger, author of a definitive biography of Descartes, has now written an excellent account of Descartes's natural philosophy as presented in his Principia philosophiae. Gaukroger claims that the roots of modernity lay in (...) the philosophies of Francis Bacon and René Descartes, both of whom regarded natural philosophy, rather than either moral philosophy or metaphysics, as the core of the philosophical enterprise. Whereas Bacon developed his ideas from a background steeped in the writings of the Renaissance humanists who emphasized moral philosophy, Descartes developed his ideas in the context of Scholastic philosophy, particularly the textbooks of the Jesuits that he had encountered at La Flèche and that located the foundations of philosophy in metaphysics.Regarding the unpublished early works, Le monde and L'homme, as suppressed parts of Descartes's mature project and taking seriously Descartes's stated intention of dealing with living things and humans along with the physical world in his natural philosophy, Gaukroger presents a detailed account of this "complete" version of the Principia philosophiae. In a series of six chapters, he explicates Descartes's views on the principles of knowledge, the principles of material objects, the visible universe, the Earth, living things, and man. In addition to Le monde and L'homme, Gaukroger draws on Les Passions de l'âme as an important source for Descartes's views on human nature.Gaukroger situates Descartes's natural philosophy in the context of the Scholastic textbook tradition in a chapter preceding his account of the Principa philosophiae. He delves into the history of medieval universities, the place of natural philosophy in the medieval curriculum, and the changing relationship between metaphysics and natural philosophy, particularly after the Condemnations of 1277. Difficulties in reconciling Aristotelian natural philosophy and Christian theology, which had been formulated in terms of Aristotelian metaphysics, continued into the sixteenth century and provided the immediate background to the Jesuit commentaries and textbooks to which Descartes was exposed as a student. In these works, Jesuit philosophers attempted to derive a coherently unified Christian Aristotelianism from first principles. Gaukroger reminds us that Descartes's Principia philosophiae was a deliberate attempt to replace these Jesuit textbooks with one based on mechanistic principles.Despite the strength of Gaukroger's book as a contextualized study of a major philosophical figure who is frequently treated in an entirely ahistorical way, the book is not without its problems. The main problem is one that plagues many studies of Descartes (and other canonical figures in the history of philosophy), to wit, the presumption that he is somehow unique. For example, Gaukroger writes at length about Descartes's views about the differences between animals and humans with regard to cognition, arguing that Descartes did not consider animals to be automata because they lack rational souls but rather that they actually experience some but not all of the more abstract or reflexive forms of cognition usually ascribed to humans. Gaukroger does not mention the fact that many other early modern philosophers held a view like this. For example, Descartes's contemporary and fellow mechanical philosopher Pierre Gassendi claimed that animals could know universals, as when a dog recognizes that it is a human that is approaching, but differ from humans in not being capable of contemplating the nature of universality per se. Descartes was part of a community of thinkers concerned with similar problems, and his natural philosophy can be illuminated by viewing him in that context as well as against the backdrop of Scholasticism.Gaukroger underplays the significance of theology for Descartes's philosophy. Although he discusses how God's attributes, especially immutability, provide the basis for Descartes's laws of motion, he does not explore the specific aspects of Descartes's theological presuppositions and the way they influenced his entire natural philosophical project. Gaukroger repeats the received view that "One of the principal tasks of a mechanistic natural philosophy... (shrink)

The core principles of 7th century Korean Buddhist thinker and practitioner Wŏnhyo’s harmonization in non-obstruction thought and Wilberian Integral Theory may help us to understand ourselves and the world better and thus act and live well together accordingly in this contemporary world facing global crises. Whatare particularly noteworthy in Wŏnhyo’s thought and life is that as much as reality is unobstructed (無礙) in its profound calm so can our mode of being and relationships be awakened to its natural harmony (...) free of conflicts (和諍會通). This ideal can be optimally pursued by coming back to the source of One Mind (一心) while extensively benefiting sentient beings. Wŏnhyo consistently pursued and realized this soteriological project through his practice, works, and expediently dedicated life. The most recent version of Wilber’ Integral Theory consists of Integral Approach, Integral Methodological Pluralism, and Integral Post-Metaphysics. Their core principles consist of the AQAL (all quadrants, all levels, all lines, all states, and all types) and holons with their twenty tenets (holonic laws). Extensively utilizing scientific achievements Wilber attempted to map the whole developmental territory of occasions ranging from matter to Spirit or Emptiness and to formulate the Theory of Everything and then apply it to various fields including business, spirituality, and ecology. Within this framework, however, MarkEdwards tried to add an integral epistemology with its interpretive part and to complement Wilber’s more evolutionary ranking ascent with involutionary egalitarian descent. By also critiquing representational—and thus somewhat reifying—tendency of the AQAL framework and proposing to read it as an interpretive lens hesaves Integral Theory from internal conflicts and rendered it more consistent. Being based on experience and vast scholarship both Wŏnhyo’s and Wilberian visions have an integral nature. Whereas Wŏnhyo’s Enlightenment-anchored high vision-logic enabled him to actualize harmonization unobstructedly, backed by scientific achievements as well as his practice Wilber pioneered the AQAL Integral Theory, and then by adding an interpretive dimension Wilber has made it more balanced and consistent system. Now facing the human-caused threats of various global crises as well as the usual complexities of our ordinary life, we need to draw on mankind’s cultural resources including these two spectacular achievements. We may then further develop these soteriological visions in such a way as to satisfy hopefully all justifiable needs of men as well as the world in a futuristic perspective. (shrink)

The automatic integration of rapidly expanding information resources in the life sciences is one of the most challenging goals facing biomedical research today. Controlled vocabularies, terminologies, and coding systems play an important role in realizing this goal, by making it possible to draw together information from heterogeneous sources – for example pertaining to genes and proteins, drugs and diseases – secure in the knowledge that the same terms will also represent the same entities on all occasions of use. In the (...) naming of genes, proteins, and other molecular structures, considerable efforts are under way to reduce the effects of the different naming conventions which have been spawned by different groups of researchers. Electronic patient records, too, increasingly involve the use of standardized terminologies, and tremendous efforts are currently being devoted to the creation of terminology resources that can meet the needs of a future era of personalized medicine, in which genomic and clinical data can be aligned in such a way that the corresponding information systems become interoperable. (shrink)

It is commonplace to view the rigor of the mathematics in Euclid's Elements in the way an experienced teacher views the work of an earnest beginner: respectable relative to an early stage of development, but ultimately flawed. Given the close connection in content between Euclid's Elements and high-school geometry classes, this is understandable. Euclid, it seems, never realized what everyone who moves beyond elementary geometry into more advanced mathematics is now customarily taught: a fully rigorous proof cannot rely (...) on geometric intuition. In his arguments he seems to call illicitly upon our understanding of how objects like triangles and circles behave rather than grounding everything rigorously in axioms.Though widespread, the attitude is in a historical sense puzzling. For over two millenia, mathematicians of all levels studied the arguments in Elements and found nothing substantial missing. The book, on the contrary, represented the limit of mathematical explicitness. It served as the paradigm for careful and exact reasoning. How it could enjoy this reputation for so long is mysterious if careful and exact reasoning demands that all inferences be grounded in a modern axiomatic theory in the way Hilbert did in his famous Foundations of Geometry. By these standards, Euclid's work is deeply flawed. The holes in his arguments are not minor and excusable, but massive and cryptic.With his book Euclid and His Twentieth Century Rivals, Nathaniel Miller makes substantial progress in clearing this mystery up. The book is an explication of FG , a formal system of proof developed by Miller which reconstructs Euclid's deductions as essentially diagrammatic. The holes in Euclid's arguments are taken to appear precisely at those steps which are unintelligible without an accompanying geometric diagram. Interpreting the reasoning in the Elements in terms of a modern axiomatization , …. (shrink)

��Disoriented 4-year-old children use a distinctive container to locate a hidden object, but do they reorient by this information? We addressed this question by testing children’s search for objects in a circular room containing one distinctive and two identical containers. Children’s search patterns provided evidence that the distinctive container served as a direct cue to a hidden object’s location, but not as a directional signal guiding reorientation. The findings suggest that disoriented children’s search behavior depends on two distinct processes: a (...) modular reorientation process attuned to the geometry of the surface layout and an associative process linking landmarks to specific locations. (shrink)

The present system of politics is based on the centrality of economics. This system is not capable of coming to grips with the problems confronting humanity. A culture-based system of politics is required to do this and prevent ecological disaster. This system would make it possible to reduce the demands human beings are making on the natural environment and situate human welfare, environmental well-being, and the public interest at the core of the political process. The (...) risks of such a system could be reduced through cultural education and improved cultural understanding. (shrink)

In this paper, we discuss a proposal for reform in the teaching of Euclidean geometry that reveals the symbiotic relationship between axiomatics and pedagogy. We examine the role of intuition in this kind of reform, as expressed by Mario Pieri, a prominent member of the Schools of Peano and Segre at the University of Turin. We are well aware of the centuries of attention paid to the notion of intuition by mathematicians, mathematics educators, philosophers, psychologists, historians, and others. To (...) set a context for Pieri’s proposal, we only seek to open a small window on views of the pedagogical role of intuition, from primary education to university study that may have informed early 20th century efforts to improve the teaching of geometry at the secondary school level. Pieri addressed the topic of intuition in many of his axiomatizations, including those in projective geometry which was his main area of concentration in foundations. We focus here primarily on his axiom systems for elementary geometry, which embraced the transformational approach of Felix Klein’s vision for the subject. Our goal is to convey Pieri’s thoughts on how to integrate two types of intuition, denoted as sensible and rational, in his endeavors to improve the teaching of the geometry of Euclid. We show how Pieri’s views on geometric intuition and pedagogical reform were either ignored or misrepresented in several notable publications at the turn of the 20th century. In particular, we give Pieri a voice in response to specific comments made in the early 1900s by Federigo Enriques, Ugo Amaldi, and Florian Cajori in widely circulated publications inspired by Klein. (shrink)

Graphical AbstractOrganelles are reaction vessels containing metabolic pathways. As in a chemical factory, the size of the reaction vessels limits the rate of product formation. Organelle size is tuned to metabolic needs, hence reprogramming organelle size could be a novel therapeutic strategy as well as a new tool for metabolic engineering.

Twentieth-century developments in logic and mathematics have led many people to view Euclid’s proofs as inherently informal, especially due to the use of diagrams in proofs. In _Euclid and His Twentieth-Century Rivals_, Nathaniel Miller discusses the history of diagrams in Euclidean Geometry, develops a formal system for working with them, and concludes that they can indeed be used rigorously. Miller also introduces a diagrammatic computer proof system, based on this formal system. This volume will be of (...) interest to mathematicians, computer scientists, and anyone interested in the use of diagrams in geometry. (shrink)

The paper [Tarski: Les fondements de la géométrie des corps, Annales de la Société Polonaise de Mathématiques, pp. 29—34, 1929] is in many ways remarkable. We address three historico-philosophical issues that force themselves upon the reader. First we argue that in this paper Tarski did not live up to his own methodological ideals, but displayed instead a much more pragmatic approach. Second we show that Leśniewski's philosophy and systems do not play the significant role that one may be tempted to (...) assign to them at first glance. Especially the role of background logic must be at least partially allocated to Russell's systems of Principia mathematica. This analysis leads us, third, to a threefold distinction of the technical ways in which the domain of discourse comes to be embodied in a theory. Having all of this in place, we discuss why we have to reject the argument in [Gruszczyński and Pietruszczak: Full development of Tarski's Geometry of Solids, The Bulletin of Symbolic Logic, vol. 4, no. 4, pp. 481—540] according to which Tarski has made a certain mistake. (shrink)

This book features more than 20 papers that celebrate the work of Hajnal Andréka and István Németi. It illustrates an interaction between developing and applying mathematical logic. The papers offer new results as well as surveys in areas influenced by these two outstanding researchers. They also provide details on the after-life of some of their initiatives. Computer science connects the papers in the first part of the book. The second part concentrates on algebraic logic. It features a range of papers (...) that hint at the intricate many-way connections between logic, algebra, and geometry. The third part explores novel applications of logic in relativity theory, philosophy of logic, philosophy of physics and spacetime, and methodology of science. They include such exciting subjects as time travelling in emergent spacetime. The short autobiographies of Hajnal Andréka and István Németi at the end of the book describe an adventurous journey from electric engineering and Maxwell’s equations to a complex system of computer programs for designing Hungary’s electric power system, to exploring and contributing deep results to Tarskian algebraic logic as the deepest core theory of such questions, then on to applications of the results in such exciting new areas as relativity theory in order to rejuvenate logic itself. (shrink)

The characteristics of green intelligent engineering ethics emphasize the necessity of GI engineering ethics education. The ethics education of GI engineering is in the development stage, and it is urgent to fully understand the significance of evaluating the development of GI EEE. Only based on the GI manufacturing situation system to understand the implementation status of the core education of EEE can we objectively grasp the improvement space of GI EEE. In this study, the corresponding indicators were selected (...) from three dimensions of cultivation education, collaborative education, and situational education to form the element community of evaluation indicators. The fuzzy analytic hierarchy process and the fuzzy comprehensive evaluation method were used to empirically evaluate the implementation of the key mechanism of GI EEE. The results are as follows. The key education of GI EEE includes cultivation education of micro dimension, collaborative education of medium dimension, and situational education of macro dimension. The most important education is to strengthen the ethics education of GI engineering in the training process of college students. The coordination of GI EEE is becoming more and more important, and the integration and construction are the important pursuit of GI EEE. The cultivation education, collaborative education, and situational education of GI EEE are all at a general level. There is not only a gap between theory and practice in GI EEE but also insufficient attention to localization and coordination issues. The willingness of the government to participate in the ethical education of GI engineering is very insufficient. The optimized space of training education includes teaching cases and full-cycle ethical education. (shrink)

Recent decades have witnessed a sea change in thinking about emotion, which has gone from being seen as a disruptive force in human thought and action to being seen as an important source of situation- and goal-relevant information and evaluation, continuous with perception and cognition. Here I argue on philosophical and empirical grounds that the role of emotion in contributing to our ability to respond to reasons for action runs deeper still: The affective system is at the core (...) of the process of evaluatively modeling situations, actions, and outcomes, which is the foundation upon which rational deliberation and action can be built. Taking up this perspective affords new approaches to long-standing problems in the theory of reason-based action. (shrink)

This article intends to show that ideology is always organized systemically by undertaking the opposition between conformity and diversity as its fundamental criterion. In order to underpin this hypothesis, the present article examines the inner structure of five classic ideologies, that can be understood as ideal ideological types. The analysis reveals that ideologies do not form a system because at the core of any ideology there is a key-concept not determined nor influenced by the key concepts of other (...) ideologies. (shrink)

I concur with Merker and colleague's critiques, suggesting that hypotheses about the evolutionary function of consciousness can help address them. Brains are parallel systems that function to compute possible actions and predict outcomes. I hypothesize that a core function of consciousness per se is the global feedback of information about those actions actually executed, supporting local learning via neuronal updating.

I would like to know who of mycontemporaries should be more competent inKantian philosophy than me.(Schopenhauer in a letter to Rosenkranz and Schubert, 18371)In this paper the attempt is made to show how Schopenhauer's critique of Kant leads from initial disagreements to a fundamental modification, even a new formation, of the Kantian concepts of understanding, reason, imagination, perception, idea and thing-in-itself. The starting point and the core of his critique is the demand for the appreciation of intuitive knowledge which (...) is apart from and independent of reason. The intuitive knowledge goes back to images and its highest form is aesthetic contemplation. Without a participation of concepts it is sufficient to explain objective reality. Particularly on the basis of Schopenhauer's critical examination of Kant's schematism it can be shown that his alternative conception of an image-based objectivity of experience is to be taken seriously, even if the way he presents it sometimes gives the impression of a mere misunderstanding of Kant's theory of cognition. (shrink)