‘Number sense’ is a short‐hand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence suggesting that number sense constitutes a domain‐specific, biologically‐determined ability are reviewed: the presence of evolutionary precursors of arithmetic in animals; the early emergence of arithmetic competence in infants independently of other abilities, including language; the existence of a homology (...) between the animal, infant, and human adult abilities for number processing; and the existence of a dedicated cerebral substrate. In adults of all cultures, lesions to the inferior parietal region can specifically impair number sense while leaving the knowledge of other cognitive domains intact. Furthermore, this region is demonstrably activated during number processing. I postulate that higher–level cultural devel‐opments in arithmetic emerge through the establishment of linkages between this core analogical representation and other verbal and visual representations of number notations. The neural and cognitive organization of those representations can explain why some mathematical concepts are intuitive, while others are so difficult to grasp. Thus, the ultimate foundations of mathematics rests on core representations that have been internalized in our brains through evolution. (shrink)

‘Number sense’ is a short‐hand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence suggesting that number sense constitutes a domain‐specific, biologically‐determined ability are reviewed: the presence of evolutionary precursors of arithmetic in animals; the early emergence of arithmetic competence in infants independently of other abilities, including language; the existence of a homology (...) between the animal, infant, and human adult abilities for number processing; and the existence of a dedicated cerebral substrate. In adults of all cultures, lesions to the inferior parietal region can specifically impair number sense while leaving the knowledge of other cognitive domains intact. Furthermore, this region is demonstrably activated during number processing. I postulate that higher–level cultural devel‐opments in arithmetic emerge through the establishment of linkages between this core analogical representation (the ‘number line’ ) and other verbal and visual representations of number notations. The neural and cognitive organization of those representations can explain why some mathematical concepts are intuitive, while others are so difficult to grasp. Thus, the ultimate foundations of mathematics rests on core representations that have been internalized in our brains through evolution. (shrink)

Many recent cognitive studies reveal that human cognition is inherently perceptual, sharing systems with perception at both the conceptual and the neural levels. This paper introduces Barsalou's theory of perceptual symbols and explores its implications for philosophy of science. If perceptual symbols lie in the heart of conceptual processing, the process of attribute selection during concept representation, which is critical for defining similarity and thus for comparing taxonomies, can no longer be determined solely by background beliefs. The analogous nature of (...) perceptual symbols and the spatial nature of intraconceptual relations impose new constraints on attribute selection. These constraints help people with different background beliefs select compatible attributes, which constitute a common "platform" for taxonomy comparison. (shrink)

“Probably Peirce’s best-known works are the first two articles in a series of six that originally were collectively entitled Illustrations of the Logic of Science and published in Popular Science Monthly from November 1877 through August 1878. The first is entitled ‘The Fixation of Belief’ and the second is entitled ‘How to Make Our Ideas Clear.’ In the first of these papers Peirce defended, in a manner consistent with not accepting naive realism, the superiority of the scientific method over other (...) methods of overcoming doubt and ‘fixing belief.’” — Robert Burch, “Charles Sanders Peirce,” entry in the Stanford Encyclopedia of Philosophy (2021 revision) -/- “Pragmatist epistemologies often explore how we can carry out inquiries in a self-controlled and fruitful way. (Where much analytic epistemology centres around the concept of knowledge, considered as an idealised end-point of human thought, pragmatist epistemology centres around the concept of inquiry, considered as the process of knowledge-seeking and how we can improve it.) So pragmatists often provide rich accounts of the capacities or virtues that we must possess in order to inquire well, and the rules or guiding principles that we should adopt. A canonical account is Peirce’s classic early paper ‘The Fixation of Belief‘. Here Peirce states that inquiry is a struggle to replace doubt with “settled belief“, and that the only method of inquiry that can make sense of the fact that at least some of us are disturbed by inconsistent beliefs, and will subsequently reflect upon which methods of fixing belief are correct is the Method of Science, which draws on the Pragmatic Maxim described above. This contrasts with three other methods of fixing belief: i) refusing to consider evidence contrary to one’s favored beliefs (the Method of Tenacity), ii) accepting an institution’s dictates (the Method of Authority), iii) developing the most rationally coherent or elegant-seeming belief-set (the A Priori Method).“ — Catherine Legg, “Pragmatism,” entry in the Stanford Encyclopedia of Philosophy (2021 revision). (shrink)

The paper uses the tools of mereotopology (the theory of parts, wholes and boundaries) to work out the implications of certain analogies between the 'ecological psychology' of J. J Gibson and the phenomenology of Edmund Husserl. It presents an ontological theory of spatial boundaries and of spatially extended entities. By reference to examples from the geographical sphere it is shown that both boundaries and extended entities fall into two broad categories: those which exist independently of our cognitive acts (for example, (...) the planet Earth, its exterior surface); and those which exist only in virtue of such acts (for example: the equator, the North Sea). The visual field, too, can be conceived as an example of an extended entity that is dependent in the sense at issue. The paper suggests extending this analogy by postulating entities which would stand to true judgments as the visual field stands to acts of visual perception. The judgment field is defined more precisely as that complex extended entity which comprehends all entities which are relevant to the truth of a given (true) judgment. The work of cognitive linguists such as Talmy and Langacker, when properly interpreted, can be shown to yield a detailed account of the structures of the judgment fields corresponding to sentences of different sorts. A new sort of correspondence-theoretic definition of truth for sentences of natural language can then be formulated on this basis. (shrink)

Just before the Scientific Revolution, there was a "Mathematical Revolution", heavily based on geometrical and machine diagrams. The "faculty of imagination" (now called scientific visualization) was developed to allow 3D understanding of planetary motion, human anatomy and the workings of machines. 1543 saw the publication of the heavily geometrical work of Copernicus and Vesalius, as well as the first Italian translation of Euclid.

With mention of Ogden and Richards' The Meaning of Meaning, and drawing on Mailinowski, for an opening example, Dewey argues for the importance of the relationship of interpretation and meaning, to context and and situation of usage or utterance. In this article, Dewey expounds, among other themes, on the the prospect of interpretation of a radically alien language and what this prospect tells us about linguistic meaning.