On What Ground Do Thin Objects Exist? In Search of the Cognitive Foundation of Number Concepts
Bibliographic Data
| ID | 20142309 |
|---|---|
| Authors | Markus Pantsar (0000-0001-8572-1453, Department of Philosophy, History, Culture and Art Studies Helsingin Yliopisto Humanistinen Tiedekunta, corresponding author) |
| Year | 2023 |
| Volume | 89 |
| Issue | 3 |
| Pages | 298-313 |
| Publication date | 2023-06-01 |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Theoria (JOURNAL) |
| Journal identifiers | ISSN: 0040-5825 • E-ISSN: 1755-2567 |
| Publisher | Wiley (PUBLISHER • GB) |
| DOI | 10.1111/theo.12366 |
| OpenAlex | W3215069753 |
| Language | EN |
| Citations received | 3 |
| References cited | 34 |
Linnebo in 2018 argues that abstract objects like numbers are “thin” because they are only required to be referents of singular terms in abstraction principles, such as Hume's principle. As the specification of existence claims made by analytic truths (the abstraction principles), their existence does not make any substantial demands of the world; however, as Linnebo notes, there is a potential counter‐argument concerning infinite regress against introducing objects this way. Against this, he argues that vicious regress is avoided in the account of arithmetic based on Hume's principle because we are specifying numbers in terms of the concept of equinumerosity, or its ordinal equivalent. But far from being only a matter for philosophy, this implies a distinct empirical prediction: in cognitive development, the principle of equinumerosity is primary to number concepts. However, by analysing and expanding on the bootstrapping theory of Carey in 2009, I argue in this paper that there are good reasons to think that the development could be the other way around: possessing numerosity concepts may precede grasping the principle of equinumerosity. I propose that this analysis of early numerical cognition can also help us understand what numbers as thin objects are like, moving away from Platonist interpretations
Abstraction · Argument (complex analysis) · Bootstrapping (finance) · Cognition · Development (topology) · Discrete mathematics · Epistemology · Foundation (evidence) · Mathematical economics · Modulo · Numerosity adaptation effect · Perception · Cognitive and developmental aspects of mathematical skills · Computer Science · History and Theory of Mathematics · Law · Mathematics · Mathematics Education and Teaching Techniques · Philosophy · Psychology
The Origin of Concepts
The Reason's Proper Study
Numerical Cognition Without Words
How counting represents number
Exact and Approximate Arithmetic in an Amazonian Indigene Group
The Child’s Understanding of Number
Growing a numeral system
Enculturation and the historical origins of number words and concepts
Bootstrapping of integer concepts
An empirically feasible approach to the epistemology of arithmetic
Radicalizing numerical cognition
What Numbers Could not Be
Numbers and the Making of Us
The Foundations of Arithmetic
The co-evolution of number concepts and counting words
| Citations per year | 1 |
|---|---|
| Citation span | 2023 - 2025 (3) |
| Highly cited | No |