Re-establishing the distinction between numerosity, numerousness, and number in numerical cognition

Santos, César Frederico dos

doi:10.1080/09515089.2022.2029387

Cited by 9 publications

(7 citation statements)

References 48 publications

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“…Although “number,” “numerosity,” and “numerousness” are often used interchangeably (see Dos Santos, 2022, for a review), these terms were originally introduced and differentiated by Stevens (1939/2006) in the domain of psychophysics in an attempt at rigorous terminology. In most of the philosophy of mathematics, numbers are considered abstract concepts that denote physical ones and that can be used to measure any quantity, discrete or continuous (Frege, 1980).…”

Section: Discussionmentioning

confidence: 99%

Magnitudes for Nervous Systems: Theoretical Issues and Experimental Evidence

Vallortígara

Lorenzi

Messina

et al. 2022

Curr Dir Psychol Sci

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Animals’ negotiations with the environment frequently involve quantitative assessments. However, it is largely unknown how different nervous systems can deal with information about magnitude and perform operations on it. Here we review some of the literature on this topic and discuss a few issues worthy of debate that can guide future research directions. First, we present experimental evidence suggesting that, in addition to the cortical (pallial) brain regions that are widely acknowledged to play a role in magnitude estimation, subcortical (more generally, subpallial) brain regions also play an important role. Second, we discuss interactions between different domains of magnitude and put forward a hypothesis to account for the directionality of associations between discrete and continuous magnitude. Finally, we suggest how the distinction between the concepts of number and discrete quantity should foster more attention to the role of sensory areas and circuits in assessing discrete quantities.

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Section: Discussionmentioning

confidence: 99%

Magnitudes for Nervous Systems: Theoretical Issues and Experimental Evidence

Vallortígara

Lorenzi

Messina

et al. 2022

Curr Dir Psychol Sci

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“…Estimation is the ability to assess the size of larger collections approximately, with increasing error (the larger the collection, the larger the estimation error) (Dehaene, 2011; Gilmore et al, 2018; Knops, 2020). Although these abilities are often called ‘numerical’ in the literature, they are not really numerical, since they do not display the most distinguishing properties of numerical systems (dos Santos, 2022; 2023; Núñez, 2017). For example, subitising has a very low upper limit (whereas numbers constitute an infinite set), and estimation is imprecise and produces only fuzzy estimates (whereas numbers are exact).…”

Section: Interpreting Scientific Data On Arithmetic Learningmentioning

confidence: 99%

An empirically informed account of numbers as reifications

dos Santos

2023

Theoria

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The field of numerical cognition provides a fairly clear picture of the processes through which we learn basic arithmetical facts. This scientific picture, however, is rarely taken as providing a response to a much‐debated philosophical question, namely, the question of how we obtain number knowledge, since numbers are usually thought to be abstract entities located outside of space and time. In this paper, I take the scientific evidence on how we learn arithmetic as providing a response to the philosophical question of how we obtain number knowledge. I reject the view that numbers are abstract entities located outside of space and time and, alternatively, derive from the scientific evidence a novel account of the nature of numbers. In this account, numbers are reifications of the counting procedure and arithmetic statements are seen as describing the functioning of counting and calculation techniques.

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“…Some even phrased numerical cognition terminological problems as "terminological chaos" (Davis & Pérusse, 1988). The distinction between the terms of number, numerosity and quantity is not always clear (Dos Santos, 2022;Nelson & Bartley, 1961;Stevens et al, 1937). More consistency will help in bridging theoretical as well as methodological gaps preventing advances in studying numerical cognition.…”

Section: ✓ ✓mentioning

confidence: 99%

A Methodological Framework for Stimuli Control: Insights from Numerical Cognition (published)

Shilat¹,

Henik²,

Galili³

et al. 2023

Preprint

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Non-symbolic numerical stimuli play a crucial role in numerical cognition. Physical properties such as surface area, density, and item circumference are inherently correlated with quantity. The correlations between physical properties and quantity mask the mechanism underlying numerical perception. Non-symbolic stimuli are generated using different generation methods (GMs) aimed at controlling physical properties. The way a GM controls physical properties affects numerical judgments. Here, using a novel data-driven approach, we provide a methodological review of non-symbolic stimuli GMs developed since 2000. Annotators tagged the GMs’ control over physical properties. Next, GMs were qualitatively analyzed for different property controls, terminology, and definitions. The tagging and qualitative analysis provided data suitable for quantitative analysis of GMs. We found that the field thrives with a wide variety of GMs aimed at tackling new methodological and theoretical ideas. However, the field lacks a common language and a method to incorporate new ideas in the existing literature. Furthermore, these shortcomings impair the comparison, replication, and reanalysis of previous studies in light of new ideas. We present guidelines for GMs that will hopefully contribute to the field. First, researchers should define controlled properties explicitly and consistently. Second, researchers should provide the code package used to generate stimuli. Third, researchers should also provide the actual stimuli, coupled with the behavioral and neuronal responses. This last guideline would enable researchers to reanalyze previously obtained data, enabling incorporating new ideas in the context of prior research.

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Re-establishing the distinction between numerosity, numerousness, and number in numerical cognition

Cited by 9 publications

References 48 publications

Magnitudes for Nervous Systems: Theoretical Issues and Experimental Evidence

Magnitudes for Nervous Systems: Theoretical Issues and Experimental Evidence

An empirically informed account of numbers as reifications

A Methodological Framework for Stimuli Control: Insights from Numerical Cognition (published)

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