Beyond natural geometry: on the nature of proto-geometry

Ferreirós, José; García-Pérez, Manuel J.

doi:10.1080/09515089.2019.1683726

Cited by 14 publications

(14 citation statements)

References 31 publications

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“…Similarly, geometry emerged from the processes of "thinging" (Gallagher, 2015), for objects with specific layouts, which were built with assorted materials and with pragmatic goals in mind (counting crops, keeping track of debts, etc. ), probably served as bases for the abstract ideas of geometrical figures and their properties (Ferreirós & García-Pérez, 2020).…”

Section: Numerosity and Metmentioning

confidence: 99%

Ecological-enactive scientific cognition: modeling and material engagement

Rolla

Novaes

2020

Phenom Cogn Sci

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Ecological-enactive approaches to cognition aim to explain cognition in terms of the dynamic coupling between agent and environment. Accordingly, cognition of one's immediate environment (which is sometimes labeled "basic" cognition) depends on enaction and the picking up of affordances. However, ecological-enactive views supposedly fail to account for what is sometimes called "higher" cognition, i.e., cognition about potentially absent targets, which therefore can only be explained by postulating representational content. This challenge levelled against ecological-enactive approaches highlights a putative explanatory gap between basic and higher cognition. In this paper, we examine scientific cognition-a paradigmatic case of higher cognition-and argue that it shares fundamental features with basic cognition, for enaction and affordance selection are central to the scientific enterprise. Our argument focuses on modeling, and on how models promote scientific understanding. We base our argument on a non-representational account of scientific understanding and on the material engagement theory, for models are hereby conceived as material objects designed for scientific engagements. Having done so, we conclude that the explanatory gap is significantly less threatening to the ecological-enactive approach than it might appear.

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Section: Numerosity and Metmentioning

confidence: 99%

Ecological-enactive scientific cognition: modeling and material engagement

Rolla

Novaes

2020

Phenom Cogn Sci

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“…2 For other works on somewhat related issues, see, e.g., Hohol & Miłkowski (2019), Hohol (2020), Ferreirós &García-Pérez (2020), andPantsar (2022).…”

Section: Introductionmentioning

confidence: 99%

“…Another motivation is that having models of the neural representation of geometric concepts gives us a new venue to address the issue of the relationship between geometric figures and geometric objects. That has already been addressed from a historical perspective (see, e.g., Valente, 2020), and also cognitive considerations have been taken into account in somewhat related issues (see, e.g., Giaquinto, 2007;Dal Magro & García-Pérez, 2019;and Ferreirós & García-Pérez, 2020). But here, we present specific models developed in the context of a theoretical framework (the hub-and-spoke theory), which provides a more 'tangible' way to address this issue (since we have models of the neural representation of geometric figures and objects).…”

Section: Introductionmentioning

confidence: 99%

A hub-and-spoke model of geometric concepts

Valente¹

2023

THEORIA

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The cognitive basis of geometry is still poorly understood, even the ‘simpler’ issue of what kind of representation of geometric objects we have. In this work, we set forward a tentative model of the neural representation of geometric objects for the case of the pure geometry of Euclid. To arrive at a coherent model, we found it necessary to consider earlier forms of geometry. We start by developing models of the neural representation of the geometric figures of ancient Greek practical geometry. Then, we propose a related model for the earliest form of pure geometry – that of Hippocrates of Chios. Finally, we develop the model of the neural representation of the geometric objects of Euclidean geometry. The models are based on the hub-and-spoke theory. In our view, the existence of specific models opens the possibility of addressing the relationship between geometric figures and geometric objects, in a novel way, in terms of their neural representation.

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“…Some researchers have argued for a "core cognitivist", nativist, view according to which geometric cognition is in an important way shaped by "evolutionarily ancient" abilities for shape recognition and orientation (e.g., Spelke & Dehaene & Brannon, 2011;Spelke & Lee, 2012;Spelke et al, 2010). This approach has been contested by researchers arguing for a "culturalist" view according to which geometric cognition is fundamentally a culturally developed phenomenon (Ferreirós & García-Pérez, 2020).…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, I aim to show that these two views, understood in a proper way, are not necessarily in conflict with each other. In particular, I will focus on the version of the nativist view proposed by Spelke and colleagues (Spelke et al, 2010) and the recent criticism of it by Ferreirós and García-Pérez (2020). The latter present Spelke et al as implying that geometric cognition is in a strong way shaped by genetically stored information, and thus fails to include the way geometry is the product of a long line of cultural development.…”

Section: Introductionmentioning

confidence: 99%

On the development of geometric cognition: Beyond nature vs. nurture

Pantsar

2021

Philosophical Psychology

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How is knowledge of geometry developed and acquired? This central question in the philosophy of mathematics has received very different answers. Spelke and colleagues argue for a "core cognitivist", nativist, view according to which geometric cognition is in an important way shaped by genetically determined abilities for shape recognition and orientation. Against the nativist position, Ferreirós and García-Pérez have argued for a "culturalist" account that takes geometric cognition to be fundamentally a culturally developed phenomenon. In this paper, I argue that when understood as moderate versions supported by the state-ofthe-art research, the nativist and culturalist views are in fact possible to reconcile. While Ferreirós and García-Pérez present the work of Spelke and colleagues as implying that geometric cognition is genetically determined, I argue that they fail to appreciate the role that Spelke and colleagues see for cultural factors. On this basis, I provide theoretical and terminological clarifications and show that moderate versions of the nativist and culturalist view are in fact consistent with each other. I then propose a unifying theoretical framework for future study that can integrate the two accounts in ontogeny by moving beyond the crude nature (nativism) vs. nurture (culturalism) dichotomy.

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Beyond natural geometry: on the nature of proto-geometry

Cited by 14 publications

References 31 publications

Ecological-enactive scientific cognition: modeling and material engagement

Ecological-enactive scientific cognition: modeling and material engagement

A hub-and-spoke model of geometric concepts

On the development of geometric cognition: Beyond nature vs. nurture

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