There are two ways interpreters have tended to understand the nature of the laws of Kant’s pure general logic. On the first, these laws are unconditional norms for how we ought to think, and will govern anything that counts as thinking. On the second, these laws are formal criteria for being a thought, and violating them makes a putative thought not a thought. These traditions are in tension, in so far as the first depends on the possibility of thoughts that (...) violate these laws, and the second makes violation impossible. In this essay I develop an interpretation of Kant’s pure general logic that overcomes this tension. It accounts for the possibility of logical mistakes, as the first tradition does, while still establishing the absolute impossibility of logical aliens, as the second tradition does. I then argue that the formalist insight that illogical exercises of the understanding are not alternative ways coherent thoughts could have been, but are mere confusions, is fundamental for achieving a proper understanding of the absolute normativity of the laws of pure general logic. (shrink)

Do plants represent according to Kant? This is closely connected to the question of whether he held plants are alive, because he explains life in terms of the faculty to act on one’s own representations. He also explains life as having an immaterial principle of self-motion, and as a body’s interaction with a supersensible soul. I argue that because of the way plants move themselves, Kant is committed to their being alive, to their having a supersensible ground of their self-activity, (...) and to their having desires (although these are not conscious). This has important ramifications for Kant’s teleology and philosophy of mind. (shrink)

A recent issue of Topics in Cognitive Science featured 11 thoughtful commentaries responding to our article “What happened to cognitive science?” (Núñez et al., 2019). Here, we identify several themes that arose in those commentaries and respond to each. Crucial to understanding our original article is the fundamental distinction between multidisciplinary and interdisciplinary endeavors: Cognitive science began (and has stayed) as multidisciplinary but has failed to move on to form a cohesive interdisciplinary field. We clarify and elaborate our original argument (...) and reiterate the importance of a data‐driven evaluation of the current status of the field, which exhibits a marked disciplinary imbalance, a lack of a coherent conceptual core, and a striking absence of a consistent curriculum in the institutions that grant degrees in this domain. Half a century after the creation of cognitive science, it may now be a good time to revisit goals and visions for how to best approach the ever‐fascinating scientific study of the mind(s). (shrink)

A general conceptual framework for large-scale neocortical dynamics based on data from many laboratories is applied to a variety of experimental designs, spatial scales, and brain states. Partly distinct, but interacting local processes (e.g., neural networks) arise from functional segregation. Global processes arise from functional integration and can facilitate (top down) synchronous activity in remote cell groups that function simultaneously at several different spatial scales. Simultaneous local processes may help drive (bottom up) macroscopic global dynamics observed with electroencephalography (EEG) or (...) magnetoencephalography (MEG). A local/global dynamic theory that is consistent with EEG data and the proposed conceptual framework is outlined. This theory is neutral about properties of neural networks embedded in macroscopic fields, but its global component makes several qualitative and semiquantitative predictions about EEG measures of traveling and standing wave phenomena. A more general “metatheory” suggests what large-scale quantitative theories of neocortical dynamics may be like when more accurate treatment of local and nonlinear effects is achieved. The theory describes the dynamics of excitatory and inhibitory synaptic action fields. EEG and MEG provide large-scale estimates of modulation of these synaptic fields around background levels. Brain states are determined by neuromodulatory control parameters. Purely local states are dominated by local feedback gains and rise and decay times of postsynaptic potentials. Dominant local frequencies vary with brain region. Other states are purely global, with moderate to high coherence over large distances. Multiple global mode frequencies arise from a combination of delays in corticocortical axons and neocortical boundary conditions. Global frequencies are identical in all cortical regions, but most states involve dynamic interactions between local networks and the global system. EEG frequencies may involve a “matching” of local resonant frequencies with one or more of the many, closely spaced global frequencies. Key Words: binding problem; cell assemblies; coherence; EEG; limit cycles; neocortical dynamics; pacemakers; phase locking; spatial scale; standing waves; synchronization. Footnotes1 The relationship between the synaptic action fields proposed in the target article and cell assemblies is clarified with Figure R1 (p. 416) of the Response. (This figure was not available to Commentators. (shrink)

In this essay I examine Kant's analogy with life from §65 of the Critique of the power of Judgment. I argue that this analogy is central for understanding his notion of a natural end, for his account of the formative power of organisms in the third Critique, and for situating Kant's account of this power in relation to the Lebenskräfte of the vitalists.

Schools worldwide have started opening doors to welcome back students who, for almost two years, have been stuck studying at home. This study looks at the standpoint of Filipino students on going back to regular face-to-face schooling. There were 2,274 students of different tiers of education (high school, collegiate, graduate) from different major island groups of the Philippines (Luzon, Visayas, Mindanao) who participated in the study. The study used a mixed-method of descriptive statistics to present the quantitative data gathered and (...) thematic analysis of qualitative responses from the subjects. The majority of all the respondents favored going back to the physical classroom, and little only favored staying using the distance mode. In the qualitative analysis, the recurring reasons of the students varied from personal, economic, and fear of getting the virus. It was concluded that Filipino students want to go back to schooling. Moreover, a sizeable amount preferred hybrid while a small number preferred to stay in online or distance mode. Educational institutions should always observe the covid 19 protocol when students go back. (shrink)

Much work in the philosophy of action in the last few decades has focused on the elucidation and justification of a series of purported norms of practical rationality that concern the presence or absence of intention in light of belief, and that demand a kind of structural coherence in the psychology of an agent. Examples of such norms include: Intention Detachment, which proscribes intending to do something in case some condition obtains, believing that such condition obtains, and not intending to (...) do that thing; Intention-Belief Consistency, which proscribes intending to do what you believe you will not do; Intention Consistency, which proscribes intending each of two ends you believe to be inconsistent; and Means-End Coherence, which proscribes intending an end and not intending the means you believe to be implied by your end. In this paper, I present a series of examples that show that these requirements are not genuine requirements of rationality. The reason for this is simple: these requirements concern the presence or absence of intention in light of all-out belief. Rational agents like us, however, do not, and in fact should not, always form or revise their intentions in light of what they all-out believe. When such agents do not form or revise their intentions in light of what they all-out believe, they need not be irrational if they do not conform to these requirements. (shrink)

There is widespread agreement that an adequate understanding of the nature of science (NOS) is a critical component of scientific literacy and a major goal in science education. However, we still do not know many specific details regarding how students and teachers learn particular aspects of NOS and what are the most important feature traits of instruction. In this context, the main objective of this review is to analyze articles from nine main science education journals that consider the teaching of (...) NOS to K-12 students, pre-service, and in-service science teachers in search of patterns in teaching and learning NOS. After reviewing 52 studies in nine journals that included data regarding participants’ views of NOS before and after an intervention, the main findings were as follows: (1) some aspects of NOS (empirical basis, observation and inference, and creativity) are easier to learn than others (tentativeness, theory and law, and social and cultural embeddedness), and subjective aspects of NOS and “the scientific method” seemed to be difficult for participants to understand; (2) the interventions most frequently lasted 5 to 8 weeks for students, one semester for pre-service teachers, and 1 year for experienced teachers; and (3) most of the interventions incorporated both decontextualized and contextualized activities. Given the substantial diversity in the methods and intervention designs used and the variables studied, it was not possible to infer a pattern of more-effective NOS teaching strategies from the reviewed studies. Future investigation should focus on (a) disentangling whether a difference exists between the easy and difficult aspects of learning NOS and formulating a theoretical explanation for distinguishing the two types of aspects and (b) assessing the effectiveness of different kinds of courses (e.g., history of science, NOS or informal) and strategies (e.g., hands-on vs. drama activities; SSI vs. HOS). (shrink)

Expressivists claim that normative judgments (NJ) are non-cognitive states. But what kind of states are they, exactly? Expressivists need to provide us with an adequate account of their nature. Here, I argue that there are structural features that render this task rather daunting. The worry takes the form of a looming dilemma: NJ are either conative states (i.e. states with a world-to-mind direction of fit) or they are not. If they are, then they are either attitudes de se (i.e. attitudes (...) about oneself) or they are not. If they are, then they’re unable to account for disagreement. If they are not, then they're unable to account for agent-relative NJ. So NJ cannot be conative states (they cannot have a world-to-mind direction of fit). On the other hand, however, if NJ are not conative states (if they are states without a direction of fit, like affective or other sui generis non-cognitive, non-conative attitudes) then it remains a mystery how they support relations of disagreement. (shrink)

The Aymara of the Andes use absolute (cardinal) frames of reference for describing the relative position of ordinary objects. However, rather than encoding them in available absolute lexemes, they do it in lexemes that are intrinsic to the body: nayra (“front”) and qhipa (“back”), denoting east and west, respectively. Why? We use different but complementary ethnographic methods to investigate the nature of this encoding: (a) linguistic expressions and speech–gesture co-production, (b) linguistic patterns in the distinct regional Spanish-based variety Castellano Andino (...) (CA), (c) metaphorical extensions of CA’s spatial patterns to temporal ones, and (d) layouts of traditional houses. Findings indicate that, following fundamental principles of Aymara cosmology, people, objects, and land—as a whole—are conceived as having an implicit canonical orientation facing east, a primary landmark determined by the sunrise. The above bodily based lexicalizations are thus linguistic manifestations of a broader macro-cultural worldview and its psycho-cognitive reality. (shrink)

The canonical history of mathematics suggests that the late 19th-century “arithmetization” of calculus marked a shift away from spatial-dynamic intuitions, grounding concepts in static, rigorous definitions. Instead, we argue that mathematicians, both historically and currently, rely on dynamic conceptualizations of mathematical concepts like continuity, limits, and functions. In this article, we present two studies of the role of dynamic conceptual systems in expert proof. The first is an analysis of co-speech gesture produced by mathematics graduate students while proving a theorem, (...) which reveals a reliance on dynamic conceptual resources. The second is a cognitive-historical case study of an incident in 19th-century mathematics that suggests a functional role for such dynamism in the reasoning of the renowned mathematician Augustin Cauchy. Taken together, these two studies indicate that essential concepts in calculus that have been defined entirely in abstract, static terms are nevertheless conceptualized dynamically, in both contemporary and historical practice. (shrink)

The consensus view in the literature is that, according to Kant, definitions in philosophy are impossible. While this is true prior to the advent of transcendental philosophy, I argue that with Kant's Copernican Turn definitions of some philosophical concepts, the categories, become possible. Along the way I discuss issues like why Kant introduces the ‘Analytic of Concepts’ as an analysis of the understanding, how this faculty, as the faculty for judging, provides the principle for the complete exhibition of the categories, (...) how the pure categories relate to the schematized categories, and how the latter can be used on empirical objects. (shrink)

Despite recent research showing that children rapidly interpret human action in terms of intention, a long tradition of empirical research on moral development and recent conceptual analyses of the deontic domain suggest that children do not apply their understanding of intention to the deontic domain. However, two experiments are described showing that children do make that connection. Preschool children heard stories in which a protagonist was obliged to meet a particular condition if an action was to be taken (e.g. obliged (...) to wear a coat if playing outside). When shown four pictures depicting each possible combination of: (1) the protagonist either performing the action or not, and (2) deliberately or accidentally failing to meet the obligation, children appropriately identified the protagonist as naughty when he or she was depicted as deliberately not meeting the obligation while performing the action. The findings proved to be robust across two different cultural settings. Implications for research on children’s developing theory of mind and their understanding of deontic concepts are discussed. (shrink)

What is the nature of number systems and arithmetic that we use in science for quantification, analysis, and modeling? I argue that number concepts and arithmetic are neither hardwired in the brain, nor do they exist out there in the universe. Innate subitizing and early cognitive preconditions for number— which we share with many other species—cannot provide the foundations for the precision, richness, and range of number concepts and simple arithmetic, let alone that of more complex mathematical concepts. Numbers and (...) arithmetic, and mathematics in general, have unique features—precision, objectivity, rigor, generalizability, stability, symbolizability, and applicability to the real world—that must be accounted for. They are sophisticated concepts that developed culturally only in recent human history. I suggest that numbers and arithmetic are realized through precise combinations of non-mathematical everyday cognitive mechanisms that make human imagination and abstraction possible. One such mechanism, conceptual metaphor, is a neurally instantiated inference-preserving cross-domain mapping that allows the conceptualization of abstract entities in terms of grounded bodily experience. I analyze how the inferential organization of the properties and “laws” of arithmetic emerge metaphorically from everyday meaningful actions. Numbers and arithmetic are thus—outside of natural selection—the product of the biologically constrained interaction of individuals with the appropriate cultural and historical phenotypic variation supported by language, writing systems, and education. (shrink)

Thought: A Journal of Philosophy, EarlyView.

While we often talk about time using spatial terms, experimental investigation of space-time associations has focused primarily on the space in front of the participant. This has had two consequences: the disregard of the space behind the participant and the creation of potential task demands produced by spatialized manual button-presses. We introduce and test a new paradigm that uses auditory stimuli and vocal responses to address these issues. Participants made temporal judgments about deictic or sequential relationships presented auditorily along a (...) body-centered sagittal or transversal axis. Results involving the transversal axis replicated previous work while sagittal axis results were surprising. Deictic judgments did not use the sagittal axis but sequential judgments did, in a previously undocumented way. Participants associated earlier judgments with the space in front of them and later judgments with the space behind them. These findings, using a new approach, p.. (shrink)

One can intend the actions of others, even when one believes such actions are not under one’s control. Call the objects of intentions “ends”; the ends that consist of other people’s actions “social”; and the ends that consist of things one believes one cannot control “recalcitrant”. The thesis, then, is that one can intend recalcitrant social ends. I present a positive argument in favor of this idea, and then argue against some purported conditions on the possible content of intentions that (...) would rule out the possibility of intending such ends. The positive argument is the following: intentions are realized by a certain cluster of dispositions. One can come to be so disposed towards recalcitrant social ends. So one can come to be disposed toward such ends in the manner that realizes an intention. So one can intend recalcitrant social ends. The conditions against which I argue are known in the literature as the Own Action Condition, the Control Condition, and the Settle Condition. I present cases where, intuitively, agents genuinely intend ends that would be ruled out by these conditions. (shrink)

One can intend the actions of others, even when one believes such actions are not under one’s control. Call the objects of intentions “ends”; the ends that consist (partly or wholly) of other people’s actions “social”; and the ends that consist of things one believes one cannot control “recalcitrant”. The thesis, then, is that one can intend recalcitrant social ends. I present a positive argument in favor of this idea, and then argue against some purported conditions on the possible content (...) of intentions that would rule out the possibility of intending such ends. The positive argument is the following: intentions are realized by a certain cluster of dispositions. One can come to be so disposed towards recalcitrant social ends. So one can come to be disposed toward such ends in the manner that realizes an intention. So one can intend recalcitrant social ends. The conditions against which I argue are known in the literature as the Own Action Condition, the Control Condition, and the Settle Condition. I present cases where, intuitively, agents genuinely intend ends that would be ruled out by these conditions. (shrink)

This article examines the primacy of real-world bodily experience for understanding the human mind. I defend the idea that the peculiarities of the living human brain and body, and the bodily experiences they sustain, are essential ingredients of human sense-making and conceptual systems. Conceptual systems are created, brought forth, understood and sustained, through very specific cognitive mechanisms ultimately grounded in bodily experience. They don't have a transcendental abstract logic independent of the species-specific bodily features. To defend this position, I focus (...) on a case study: the fundamental concept of time flow. Using tools of cognitive linguistics, I analyse the foundations of this concept, as it is manifested naturally in everyday language. I show that there is a precise conceptual metaphor whose inferential structure gives an account of a huge variety of linguistic expressions, semantic contents, and unconscious spontaneous gestures: Time Events Are Things In Space. I discuss various special cases of this conceptual metaphor. This mapping grounds its source domain in specific spatial bodily experiences and projects its inferential structure onto a target domain making inferences in that domain possible. This mechanism allows us to unconsciously, effortlessly, and precisely understand expressions such as ‘the year 2000 is approaching’ or ‘the days ahead of us’. The general form of the mapping seems to be universal. The analysis raises important issues which demand a deeper and richer understanding of cognition and the mind: a view that sees the mind as fully embodied. In order to avoid misunderstandings with a general notion of ‘embodiment’ which has become fashionable in contemporary cognitive science, I describe what I mean by ‘full embodiment’: an embodied-oriented approach that has an explicit commitment to all of cognition, not just to low-level aspects of cognition such as sensory-motor activity or locomotion . I take embodiment to be a living phenomenon in which the primacy of bodily grounded experience is inherently part of the very subject matter of the study of the mind. (shrink)

Many faces of consciousness -- Ethics, religion, and the identity of self -- States of mind -- Why hearts don't love and brains don't pump -- EEG : a window on the mind -- Dynamic patterns as shadows of thought -- Networks, waves, and resonant binding -- The limits of science : What do we really know? -- Modern physics, cosmology, and consciousness -- The weird behavior of quantum systems -- Ontological interpretations of quantum mechanics -- Does the brain create (...) the mind? (shrink)

Traditional cognitive science is Cartesian in the sense that it takes as fundamental the distinction between the mental and the physical, the mind and the world. This leads to the claim that cognition is representational and best explained using models derived from AI and computational theory. The authors depart radically from this model.

Speakers of many languages around the world rely on body-based contrasts for spatial communication and cognition. Speakers of Yupno, a language of Papua New Guinea's mountainous interior, rely instead on an environment-based uphill/downhill contrast. Body-based contrasts are as easy to use indoors as outdoors, but environment-based contrasts may not be. Do Yupno speakers still use uphill/downhill contrasts indoors and, if so, how? We report three studies on spatial communication within the Yupno house. Even in this flat world, uphill/downhill contrasts are (...) pervasive. However, the terms are not used according to the slopes beyond the house's walls, as reported in other groups. Instead, the house is treated as a microworld, with a “conceptual topography” that is strikingly reminiscent of the physical topography of the Yupno valley. The phenomenon illustrates some of the distinctive properties of environment-based reference systems, as well as the universal power and plasticity of spatial contrasts. (shrink)

Speakers of many languages around the world rely on body‐based contrasts (e.g., left/right) for spatial communication and cognition. Speakers of Yupno, a language of Papua New Guinea's mountainous interior, rely instead on an environment‐based uphill/downhill contrast. Body‐based contrasts are as easy to use indoors as outdoors, but environment‐based contrasts may not be. Do Yupno speakers still use uphill/downhill contrasts indoors and, if so, how? We report three studies on spatial communication within the Yupno house. Even in this flat world, uphill/downhill (...) contrasts are pervasive. However, the terms are not used according to the slopes beyond the house's walls, as reported in other groups. Instead, the house is treated as a microworld, with a “conceptual topography” that is strikingly reminiscent of the physical topography of the Yupno valley. The phenomenon illustrates some of the distinctive properties of environment‐based reference systems, as well as the universal power and plasticity of spatial contrasts. (shrink)

Pointing is a cornerstone of human communication, but does it take the same form in all cultures? Manual pointing with the index finger appears to be used universally, and it is often assumed to be universally preferred over other forms. Non-manual pointing with the head and face has also been widely attested, but it is usually considered of marginal significance, both empirically and theoretically. Here, we challenge this assumed marginality. Using a novel communication task, we investigated pointing preferences in the (...) Yupno of Papua New Guinea and in U.S. undergraduates. Speakers in both groups pointed at similar rates, but form preferences differed starkly: The Yupno participants used non-manual pointing numerically more often than manual pointing, whereas the U.S. participants stuck unwaveringly to index-finger pointing. The findings raise questions about why groups differ in their pointing preferences and, more broadly, about why humans communicate in the ways they do. (shrink)

Resumen En el Leviatán Hobbes implementa la ley de naturaleza como la condición de posibilidad del desarrollo epistemológico que convierte al animal en humano, en el estado de naturaleza. De acuerdo con esta fórmula, la moral se desarrolla cuando los hombres empiezan a comportarse de acuerdo con el contenido no explícito de las leyes de naturaleza, comportamiento posibilitado por su sujeción a un hombre fuerte, quien tiene la función moral de administrar justicia. Esta doble función moral de las leyes de (...) naturaleza entre quien manda y quien obedece implica una experiencia de la justicia como comunicación de postulados racionales compartidos que condicionan el libre accionar de los hombres, manteniéndolos unidos en el tiempo.In the Leviathan, Hobbes employs the law of nature as the condition of possibility of the epistemological development that transforms the animal into a human in the state of nature. According to this formula, morality develops when men behave according to the non-explicit content of the laws of nature, behavior enabled by their subjection to a strong man who has the moral function of administrating justice. The moral function of the laws of nature is double, those who rule and those who obey, and implies an experience of justice as communication of shared rational postulates that conditions the free actions of men, keeping them united in time. (shrink)

Clarke and Beck's defense of the theoretical construct “approximate number system” is flawed in serious ways – from biological misconceptions to mathematical naïveté. The authors misunderstand behavioral/psychological technical concepts, such as numerosity and quantical cognition, which they disdain as “exotic.” Additionally, their characterization of rational numbers is blind to the essential role of symbolic reference in the emergence of number.

Should objects count as necessarily having certain properties, despite their not having those properties when they do not exist? For example, should a cat that passes out of existence, and so no longer is a cat, nonetheless count as necessarily being a cat? In this essay I examine different ways of adapting Aldo Bressan’s MLν so that it can accommodate an affirmative answer to these questions. Anil Gupta, in The Logic of Common Nouns, creates a number of languages that have (...) a kinship with Bressan’s MLν , three of which are also tailored to affirmatively answering these questions. After comparing their languages, I argue that metaphysicians and philosophers of language should prefer MLν to Gupta’s languages in most applications because it can accommodate essential properties, like being a cat, while being more uniform and less cumbersome. (shrink)

This article employs the basic tenets of critical realism to provide a philosophical foundation for understanding and resolving the dualisms of activity theory. Its argument follows in four parts. First I develop an immanent critique that shows the problems within activity theory; it reveals that several dualisms were present from the onset, and further that an implicit ontology allows activity theorists to presuppose critical realism in practice. I claim that the historical development of activity theory is marked by attempts to (...) resolve contradictions, which are signalling devices pointing to the need for theoretical expansion. To shed light on attempts to mend dualisms, I then introduce the notion of a ‘patch’ because it functions as a mechanism that sustains dualisms and gaps in practice. An omissive critique identifies the key omitted element that causes the dualisms; namely, the omission of a critique of Humean philosophy and classical empiricism. Finally,, after effectively isolating and explaining the source of dualisms, I prepare the ground for a protoexplanatory critique to rectify them. (shrink)

In daily academic life, students are exposed to a wide range of potentially stressful situations which could negatively affect their academic achievement and their health. Among the factors that could be weakened by academic stress, attention has been paid to expectations of self-efficacy, which are considered one of the most important determinants for student engagement, persistence, and academic success. From a proactive perspective, research on academic stress has emphasized the importance of coping strategies in preventing harmful consequences. In recent years, (...) there has been a growing interest in discovering the extent to which individuals are able to combine different coping strategies and the adaptive consequences this flexibility entails. However, studies using this person-centered approach are still scarce in the academic context. On that basis, this current study had two objectives: (a) to examine the existence of different profiles of university students based on how they combined different approach coping strategies (positive reappraisal, support seeking, and planning); and (b) to determine the existence of differences in general expectations of self-efficacy between those coping profiles. 1072 university students participated in the study. The coping profiles were determined by Latent Profile Analysis (LPA). The differences in the self-efficacy variable were determined using ANCOVA, with gender, university year, and degree type as covariates. Four approach coping profiles were identified: (a) low generalized use of approach coping strategies; (b) predominance of social approach coping approaches; (c) predominance of cognitive approach coping approaches; (d) high generalized use of approach coping strategies. The profile that showed that a greater combination of the three strategies was related to higher general self-efficacy expectations, and vice versa. These results suggest that encouraging flexibility in coping strategies would help to improve university students’ self-efficacy. (shrink)

Introduction to Special Issue on ‘Reclaiming Cognition: The Primacy of Action, Intention and Emotion’. Making sense of the mind is the human odyssey. Today, the cognitive sciences provide the vehicles and equipage. As do all culturally shaped activities, they manifest crystallized generalizations and ideological legacies, many of which go unquestioned for centuries. From time to time, these ideologies are successfully challenged, generating revisions and new forms of understanding. We believe that the cognitive sciences have reached a situation in which they (...) have been frozen into one narrow form by the machine metaphor. There is a need to thaw that form and move from a reductionist, atemporal, disembodied, static, rationalist, emotion- and culture-free view, to fundamentally richer understandings that include the primacy of action, intention, emotion, culture, real-time constraints, real-world opportunities, and the peculiarities of living bodies. These essays constitute an array of moves in that direction. (shrink)

Philosophers of mathematics often rely on the historical progress of mathematics in support of mathematical realism. These histories typically build on formal semantic tools to evaluate the changes in mathematics, and on these bases present later mathematical concepts as refined versions of earlier concepts which are taken to be vague. Claiming that this view does not apply to mathematical concepts in general, we present a case-study concerning projective geometry, for which we apply the tools of cognitive linguistics to analyse the (...) developmental trajectory of the domain. On the basis of this analysis, we argue for the existence of two conceptually incompatible inferential structures, occurring at distinct moments in history, both of which yield the same projective geometric theorems; the first invoked by the French mathematicians Girard Desargues (1591–1661) and Jean-Victor Poncelet (1788–1867), and the second characterising a specific modern mode. We demonstrate that neither of these inferential structures can be considered as a refinement of the other. This case of conceptual development presents an issue to the standard account of progress and its bearing on mathematical realism. Our analysis suggests that the features that distinguish the underlying conceptually incompatible inferential structures are invisible to the standard application of the tools of formal semantics. Thus this case-study stands as an example of the manner and necessity of linguistics—specifically cognitive linguistics—to inform the philosophy of mathematics. (shrink)

The interest of assigning homework is frequently discussed due to its alleged low impact on student achievement. One of the current lines of research is to emphasize the quality of student homework engagement rather than the amount of time spent on homework. The aim of this study was to determine (a) the extent to which students’ prior achievement affects their homework engagement (i.e., time spent, time management, and amount of teacher-assigned homework done), and (b) how students’ intrinsic motivation towards homework (...) may mediate or moderate the relationship between prior achievement and the homework engagement variables. A large sample of students from the first four years of Secondary Education (N = 1899) completed questionnaires. The results showed that intrinsic motivation partially mediates, but does not moderate, the effect of prior achievement on the three variables related to homework engagement (time spent, time management, and amount of teacher-assigned homework done). These results highlight the importance of considering both students’ current level of achievement and their motivation towards homework engagement when assigning homework. (shrink)