Can statistical learning bootstrap the integers?

Rips, Lance J.; Asmuth, Jennifer; Bloomfield, Amber N.

doi:10.1016/j.cognition.2013.04.001

“…It empirically motivates its claims of the exhaustive set of primitives with numerical content, (the three CS1s), and provides evidence for syntactic bootstrapping as an account for how the child breaks into the meanings of the first numerals. As Rips et al (2013) point out in their illuminating discussion of the Piantadosi model, this model does not provide an account for how the hypothesis space is conveniently limited to just the 15 numerically relevant primitives it randomly generates hypotheses from. The child has much other numerically relevant knowledge at the time of the CP induction.…”

Section: Quinian Bootstrappingmentioning

confidence: 99%

“…These critics deny the very possibility of conceptual discontinuities, as well as offering a positive view of conceptual development in terms of Premises 1 and 2 of Fodor's argument which they claim shows how conceptual development is possible without discontinuity. Rips and his colleagues suggest that claims for discontinuities are incompatible with claims that concepts are learned (Rips and Hespos 2011;Rips, Asmuth and Bloomfield 2013). Again, the key is understanding that, and how, new conceptual primitives can be learned.…”

Section: Introductionmentioning

confidence: 99%

Why Theories of Concepts Should Not Ignore the Problem of Acquisition

Carey

¹

2015

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A theory of conceptual development must provide an account of the innate representational repertoire, must characterize how these initial representations differ from the adult state, and must provide an account of the processes that transform the initial into mature representations. In The Origin of Concepts (Carey 2009), I defend three theses: (1) the initial state includes rich conceptual representations, (2) nonetheless, there are radical discontinuities between early and later developing conceptual systems, (3) Quinean bootstrapping is one learning mechanism that underlies the creation of new representational resources, enabling such discontinuity. Here I argue that the theory of conceptual development developed in The Origin of Concepts constrains our theories of concepts themselves, and addresses two of Fodor’s challenges to cognitive science; namely, to show how learning could possibly lead to an increase in expressive power and to defeat Mad Dog Nativism, the thesis that all concepts lexicalized as mono-morphemic words are innate. In response to Fodor, I show that, and how, new primitives in a language of thought can be learned, that there are easy routes and hard ones to doing so, and that characterizing the learning mechanisms in each illuminates how conceptual role partially determines conceptual content.

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“…Piantadosi et al () modeled how children may shift from understanding a few small set sizes to understanding the cardinality principle. In this computational model, as in the original bootstrapping theory, children start with a few cognitive primitives from which they can construct more advanced concepts (but note that according to Carey () and Rips, Asmuth, & Bloomfield () the model does not perform Quinian bootstrapping per se). These primitives include, among other things, the ability to understand the order of the words on the count list and an ability to understand the cardinal labels for a few small set sizes.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, children with two set size primitives will reach the capacity of their primitive system with less input than children with four set size primitives. Note that some researchers have already argued that the primitives model does not capture how children's learning occurs in the real world (e.g., Rips, Asmuth, & Bloomfield, ), but to date there has been no empirical test of the account's key prediction. This study fills this gap by trying to manipulate children's ability to identify and label set sizes without counting (i.e., increasing children's set‐size primitives) prior to exposing them to a counting intervention.…”

Section: Introductionmentioning

confidence: 99%

Improved set‐size labeling mediates the effect of a counting intervention on children's understanding of cardinality

O'Rear

¹

,

McNeil

²

2019

Developmental Science

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How does improving children's ability to label set sizes without counting affect the development of understanding of the cardinality principle? It may accelerate development by facilitating subsequent alignment and comparison of the cardinal label for a given set and the last word counted when counting that set (Mix et al., 2012).Alternatively, it may delay development by decreasing the need for a comprehensive abstract principle to understand and label exact numerosities (Piantadosi et al., 2012).In this study, preschoolers (N = 106, M age = 4;8) were randomly assigned to one of three conditions: (a) count-and-label, wherein children spent 6 weeks both counting and labeling sets arranged in canonical patterns like pips on a die; (b) label-first, wherein children spent the first 3 weeks learning to label the set sizes without counting before spending 3 weeks identical to the count-and-label condition; (c) print referencing control. Both counting conditions improved understanding of cardinality through increases in children's ability to label set sizes without counting. In addition to this indirect effect, there was a direct effect of the count-and-label condition on progress toward understanding of cardinality. Results highlight the roles of set labeling and equifinality in the development of children's understanding of number concepts. K E Y W O R D Scardinality, cognitive development, counting, early learning, preschool mathematics

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“…It empirically motivates its claims of the exhaustive set of primitives with numerical content, (the three CS1s), and provides evidence for syntactic bootstrapping as an account for how the child breaks into the meanings of the first numerals. As Rips et al , , point out in their illuminating discussion of the Piantadosi model, this model does not provide an account for how the hypothesis space is conveniently limited to just the 15 numerically relevant primitives it randomly generates hypotheses from. The child has much other numerically relevant knowledge at the time of the CP induction.…”

Section: Quinean Bootstrappingmentioning

confidence: 99%

On Learning New Primitives in the Language of Thought: Reply to Rey

Carey

¹

2014

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A theory of conceptual development must provide an account of the innate representational repertoire, must characterize how these initial representations differ from the adult state, and must provide an account of the processes that transform the initial into mature representations. In Carey, 2009 (The Origin of Concepts), I defend three theses: 1) the initial state includes rich conceptual representations, 2) nonetheless, there are radical discontinuities between early and later developing conceptual systems, 3) Quinean bootstrapping is one learning mechanism that underlies the creation of new representational resources, enabling such discontinuity. I also claim that the theory of conceptual development developed in The Origin of Concepts addresses two of Fodor's challenges to cognitive science; namely, to show how learning could possibly lead to an increase in expressive power and to defeat Mad Dog Nativism, the thesis that all concepts lexicalized as mono-morphemic words are innate. A recent article by Georges Rey (Mind & Language, 29.2, 2014) argues that my responses to Fodor's challenges fail, because, he says, I fail to distinguish concept possession from manifestation and I do not confront Goodman's new riddle of induction. My response is to show that, and how, new primitives in a language of thought can be learned, that there are easy routes and hard ones to doing so, and that characterizing the learning mechanisms involved is the key to understanding both concept possession and constraints on induction.Thanks to Georges Rey for many discussions of the points that articulate our debates, to Ned Block and Jake Beck for comments on earlier drafts of this reply to Rey, and to Samuel Guttenplan and a blind reviewer for helpful criticisms and suggestions. characterize the learning mechanisms that achieve the transformation of the initial into the final state. The Origin of Concepts (henceforth TOOC) defends three theses. With respect to the initial state, contrary to historically important thinkers such as the British empiricists, Quine, and Piaget, as well as many contemporary scientists, the innate stock of primitives is not limited to sensory, perceptual or sensorymotor representations; rather, there are also rich innate conceptual representations with contents such as object, agent, goal, cause, and approximate cardinal value of a set of individuals (part of what makes the human conceptual repertoire possible). With respect to developmental change, contrary to 'continuity theorists' such as Fodor, Pinker, Rey and others, conceptual development involves qualitative change, resulting in systems of representation that are more powerful than, and sometimes incommensurable with, those from which they are built (part of what makes attaining the human conceptual repertoire sometimes hard). With respect to a learning mechanism that achieves conceptual discontinuity, I offer Quinean bootstrapping (part of what makes attaining the human conceptual repertoire possible.)While the goal of TOOC was to explicate and def...

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Can statistical learning bootstrap the integers?

Cited by 12 publications

References 19 publications

Why Theories of Concepts Should Not Ignore the Problem of Acquisition

Why Theories of Concepts Should Not Ignore the Problem of Acquisition

Improved set‐size labeling mediates the effect of a counting intervention on children's understanding of cardinality

On Learning New Primitives in the Language of Thought: Reply to Rey

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