Adams, R. (1972). Watership Down. London: Rex Collings Ltd.
Almoammer, A., Sullivan, J., Donlan, C., Marušič, F., O'Donnell, T. & Barner, D. (2013). Grammatical morphology as a source of early number word meanings. Proceedings of the National Academy of Sciences
Bale, A. & Barner, D. (2009). The interpretation of functional heads: using comparatives to explore the mass/count distinction. Journal of Semantics
Barner, D. (2012). Bootstrapping numeral meanings and the origin of exactness. Language Learning and Development
Barner, D. & Bachrach, A. (2010). Inference and exact numerical representation in early language development. Cognitive Psychology
Barner, D., Brooks, N. & Bale, A. (2011). Accessing the unsaid: the role of scalar alternatives in children's pragmatic inference. Cognition
Barner, D., Chow, K. & Yang, S. J. (2009). Finding one's meaning: a test of the relation between quantifiers and integers in language development. Cognitive Psychology
Barner, D., Li, P. & Snedeker, J. (2010). Words as windows to thought: the case of object representation. Current Directions in Psychological Science
Barner, D., Libenson, A., Cheung, P. & Takasaki, M. (2009). Cross-linguistic relations between quantifiers and numerals in language acquisition: evidence from Japanese. Journal of Experimental Child Psychology
Barner, D. & Snedeker, J. (2005). Quantity judgments and individuation: evidence that mass nouns count. Cognition
Barner, D., Thalwitz, D., Wood, J., Yang, S. J. & Carey, S. (2007). On the relation between the acquisition of singular–plural morpho-syntax and the conceptual distinction between one and more than one. Developmental Science
Barth, H., Kanwisher, N. & Spelke, E. S. (2003). The construction of large number representations in adults. Cognition
Bloom, P. (1996). Possible individuals in language and cognition. Current Directions in Psychological Science
Bloom, P. & Wynn, K. (1997). Linguistic cues in the acquisition of number words. Journal of Child Language
Brannon, E. M. & Terrace, H. S. (2000). Representation of the numerosities 1–9 by rhesus macaques (Macaca mulatta). Journal of Experimental Psychology: Animal Behavior Processes
Briars, D. & Siegler, R. S. (1984). A featural analysis of preschoolers’ counting knowledge. Developmental Psychology
Brown, R. (1958). Words and things. Glencoe, IL: Free Press.
Brown, R. (1973). A first language: the early stages. London: George Allen & Unwin.
Butterworth, B., Reeve, R., Reynolds, F. & Lloyd, D. (2008). Numerical thought with and without words: evidence from indigenous Australian children. Proceedings of the National Academy of Sciences
Cantlon, J. F., Platt, M. L. & Brannon, E. M. (2009). Beyond the number domain. Trends in Cognitive Sciences
Cantrell, L. & Smith, L. B. (2013). Open questions and a proposal: a critical review of the evidence on infant numerical abilities. Cognition
Carey, S. (2004). Bootstrapping & the origin of concepts. Daedalus
Carey, S. (2009). Where our number concepts come from. Journal of Philosophy
Cazden, C. B. (1968). The acquisition of noun and verb inflections. Child Development
Cheung, P., Rubenson, M. & Barner, D. (2017). To infinity and beyond: children generalize the successor function to all possible numbers years after learning to count. Cognitive Psychology
Chierchia, G. (2010). Mass nouns, vagueness and semantic variation. Synthese
Condry, K. F. & Spelke, E. S. (2008). The development of language and abstract concepts: the case of natural number. Journal of Experimental Psychology: General
Coppola, M., Spaepen, E. & Goldin-Meadow, S. (2013). Communicating about number without a language model: innovation and integration of number devices into homesign grammar. Cognitive Psychology
Corbett, G. G. (2000). Number. Cambridge: Cambridge University Press.
Dale, P. S. & Fenson, L. (1996). Lexical development norms for young children. Behavior Research Methods, Instruments and Computers
Davidson, K., Eng, K. & Barner, D. (2012). Does learning to count involve a semantic induction?
Dehaene, S. (1997). The number sense: how the mind creates mathematics. New York: Oxford University Press.
Dixon, R. M. W. (2004). The Jarawara language of southern Amazonia. Oxford: Oxford University Press.
Donohue, M. (2008). Complexities with restricted numeral systems. Linguistic Typology
Epps, P. (2006). Growing a numeral system: the historical development of numerals in an Amazonian language family. Diachronica
Evans, D. W. (1983). Understanding zero and infinity in the early school years. Unpublished doctoral dissertation, University of Pennsylvania.
Evans, D. & Gelman, R. (1982). Understanding infinity: a beginning inquiry. Unpublished manuscript, University of Pennsylvania.
Feigenson, L. & Carey, S. (2005). On the limits of infants’ quantification of small object arrays. Cognition
Feigenson, L., Carey, S. & Hauser, M. (2002). The representations underlying infants’ choice of more: object files versus analog magnitudes. Psychological Science
Feigenson, L., Dehaene, S. & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences
Feiman, R. (2015). The structure and development of logical representations in thought and language. Unpublished doctoral dissertation, Harvard University, Cambridge, MA.
Fodor, J. (1980). On the impossibility of acquiring more powerful logical structures. In Piattelli-Palmarini, Massimo (ed.), Language and learning: the debate between Jean Piaget and Noam Chomsky, 142–9. Cambridge, MA: Harvard University Press.
Frank, M. C., Everett, D. L., Fedorenko, E. & Gibson, E. (2008). Number as a cognitive technology: evidence from Pirahã language and cognition. Cognition
Frege, G. (1974 ). Die Grundlagen der Arithmetik: Eine logisch-mathematische Untersuchung über den Begriff der Zahl. Breslau: W. Koebner. Translated as The foundations of arithmetic: a logico-mathematical enquiry into the concept of number, by Austin, J. L.. Oxford: Blackwell, second revised edition.
Frye, D., Braisby, N., Lowe, J., Maroudas, C. & Nicholls, J. (1989). Young children's understanding of counting and cardinality. Child Development
Fuson, K. C. (1982). An analysis of the counting-on solution procedure in addition. In Carpenter, T. P., Moser, J. M. & Romsberg, T. A. (eds), Addition and subtraction: a cognitive perspective, 67–81. Hillsdale, NJ: Erlbaum.
Fuson, K. C. (1988). Children's counting and concepts of number. New York: Springer-Verlag.
Fuson, K. C. (1992). Relationships between counting and cardinality from age 2 to age 8. In Bideaud, J., Meljac, C. & Fischer, J. (eds), Pathways to number: children's developing numerical abilities, 127–49. Hillsdale, NJ: Lawrence Erlbaum.
Fuson, K. C. & Hall, J. W. (1982). The acquisition of early number word meanings: a conceptual analysis and review. In Ginsburg, H. P. (ed.), Children's mathematical thinking, 50–108. New York: Academic Press.
Fuson, K. C. & Hall, J. W (1983). The acquisition of early number word meanings: a conceptual analysis and review. In Ginsburg, H. (ed.), The development of children's mathematical thinking, 49–107. New York: Academic Press.
Gallistel, C. R. (2016). The approximate number system. Paper presented at ‘Tightening the Articulation Between Language and Number’, Lorenz Center, Leiden, Holland.
Gallistel, C. R. & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition
Gallistel, C. R. & Gelman, R. (2000). Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences
Gelman, R. (1972). Logical capacity of very young children: number invariance rules. Child Development
Gelman, R. (1993). A rational-constructivist account of early learning about numbers and objects. Learning and Motivation
Gelman, R. & Gallistel, C. R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.
Giralt, N. & Bloom, P. (2000). How special are objects? Children's reasoning about objects, parts, and holes. Psychological Science
Gleitman, L. (1990). The structural sources of verb meanings. Language Acquisition
Gordon, P. (2004). Numerical cognition without words: evidence from Amazonia. Science
Greeno, J. G., Riley, M. S. & Gelman, R. (1984). Conceptual competence and children's counting. Cognitive Psychology
Grice, P. (1989) Studies in the way of words. Cambridge, MA: Harvard University Press.
Grimshaw, J. (1981). Form, function and the language acquisition device. In Baker, C. L. & McCarthy, J. J. (eds), The logical problem of language acquisition, 165–82. Cambridge, MA: MIT Press.
Groen, G. & Resnick, L. B. (1977). Can preschool children invent addition algorithms?
Journal of Educational Psychology
Gunderson, E. A., Spaepen, E. & Levine, S. (2015). Approximate number word knowledge before the cardinal principle. Journal of Experimental Child Psychology
Haddon, A. C. (1890). The ethnography of the western tribe of Torres Straits. Journal of the Anthropological Institute of Great Britain and Ireland
Halberda, J. (2016). Epistemic limitations and precise estimates in analog magnitude representation. In Barner, David & Baron, Andrew Scott (eds), Core knowledge and conceptual change, 171–90. New York: Oxford University Press.
Halberda, J. & Feigenson, L. (2008). Developmental change in the acuity of the ‘Number Sense’: the approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology
Halberda, J., Mazzocco, M. M. & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature
Hale, K. L. (1975). Gaps in grammar and culture. Lisse: Peter de Ridder Press.
Hammarström, H. (2010). Rarities in numeral systems. In Wohlgemuth, Jan & Cysouw, Michael (eds), Rethinking universals: how rarities affect linguistic theory, 11–60. Berlin: De Gruyter Mouton.
Hartnett, P. & Gelman, R. (1998). Early understandings of numbers: Paths or barriers to the construction of new understandings?
Learning and Instruction
Hochstein, L., Bale, A., Fox, D. & Barner, D. (2016). Ignorance and inference: Do problems with Gricean epistemic reasoning explain children's difficulty with scalar implicature?
Journal of Semantics
Ifrah, G. (2000). The universal history of numbers: from prehistory to the invention of the computer. Translated by Vellos, David, Harding, E. F., Wood, Sophie & Monk, Ian. New York: John Wiley & Sons, Inc.
Izard, V. & Dehaene, S. (2008). Calibrating the mental number line. Cognition
Izard, V., Streri, A. & Spelke, E. S. (2014). Toward exact number: young children use one-to-one correspondence to measure set identity but not numerical equality. Cognitive Psychology
Kahneman, D., Treisman, A. & Gibbs, B. J. (1992). The reviewing of object files: object-specific integration of information. Cognitive Psychology
Kennedy, C. (2013). A scalar semantics for scalar readings of number words. In Caponigro, Ivano & Cecchetto, Carlo (eds), From grammar to meaning: the spontaneous logicality of language, 172–200. Cambridge: Cambridge University Press.
Kouider, S., Halberda, J., Wood, J. & Carey, S. (2006). Acquisition of English number marking: the singular-plural distinction. Language Learning and Development
Krifka, M. (1999). At least some determiners aren't determiners. In Turner, Ken (ed.) The semantics/pragmatics interface from different points of view, vol. 1, 257–91. Oxford: Elsevier.
Landman, F. (2004). Indefinites and the type of sets. Oxford: Oxford University Press.
Laurence, S. & Margolis, E. (2005). Number and natural language. In Carruthers, P., Laurence, S. & Stich, S. (eds), The innate mind, vol. 1: structure and contents, 216–35. Oxford: Oxford University Press.
Le Corre, M. & Carey, S. (2007). One, two, three, four, nothing more: an investigation of the conceptual sources of the verbal counting principles. Cognition
Le Corre, M., Van de Walle, G., Brannon, E. M. & Carey, S. (2006). Re-visiting the competence/performance debate in the acquisition of the counting principles. Cognitive Psychology
Leibniz, G. W. (1886). Nouveaux essais sur l'entendement humain. Paris: Hachette.
Leslie, A. M., Gelman, R. & Gallistel, C. R. (2008). The generative basis of natural number concepts. Trends in Cognitive Sciences
Li, P., Ogura, T., Barner, D., Yang, S. J. & Carey, S. (2009). Does the conceptual distinction between singular and plural sets depend on language?
Link, G. (2002). The logical analysis of plurals and mass terms: a lattice-theoretical approach. In Portner, Paul & Partee, Barbara (eds), Formal semantics: the essential readings, 127–46. Oxford: Blackwell.
Lipton, J. S. & Spelke, E. S. (2005). Preschool children's mapping of number words to nonsymbolic numerosities. Child Development
Lourenco, S. F. & Longo, M. R. (2011). Origins and development of generalized magnitude representation. In Dehaene, Stanislas & Brannon, Elizabeth (eds), Space, time, and number in the brain: searching for the foundations of mathematical thought, 225–44. London: Elsevier.
Loukotka, C. (1955). Les Indiens Botocudo et leur langue. Pa'nstwowe Wydawnictwo Naukowe.
Lyons, I. M., Nuerk, H. C. & Ansari, D. (2015) Rethinking the implications of numerical ratio effects for understanding the development of representational precision and numerical processing across formats. Journal of Experimental Psychology: General
Macnamara, J. (1982). Names for things: a study of human learning. Cambridge, MA: MIT Press.
Markman, E. M. (1979). Realizing that you don't understand: elementary school children's awareness of inconsistencies. Child Development
Marušič, F., Plesničar, V., Razboršek, T., Sullivan, J. & Barner, D. (2016). Does grammatical structure accelerate number word learning? Evidence from learners of dual and non-dual dialects of Slovenian. PloS one
Menninger, K. (1969). Number words and number symbols: a cultural history of numbers. Cambridge, MA: MIT Press.
Mervis, C. B. & Johnson, K. E. (1991). Acquisition of the plural morpheme: a case study. Developmental Psychology
Mill, J. S. (1884). A system of logic, ratiocinative and inductive: being a connected view of the principles of evidence and the methods of scientific investigation. London: Longmans, Green, and Company.
Negen, J. & Sarnecka, B. W. (2012). Number-concept acquisition and general vocabulary development. Child Development
Noveck, I. A. (2001). When children are more logical than adults: experimental investigations of scalar implicature. Cognition
Odic, D., Le Corre, M. & Halberda, J. (2015). Children's mapping between number words and the approximate number system. Cognition
Odic, D., Lisboa, J. V., Eisinger, R., Olivera, M. G., Maiche, A. & Halberda, J. (2016). Approximate number and approximate time discrimination each correlate with school math abilities in young children. Acta Psychologica
Papafragou, A. & Musolino, J. (2003). Scalar implicatures: experiments at the semantics–pragmatics interface. Cognition
Partee, B. B., ter Meulen, A. G. & Wall, R. (2012). Mathematical methods in linguistics (Vol. 30). Dordrecht: Springer Science & Business Media.
Piantadosi, S. T., Tenenbaum, J. B. & Goodman, N. D. (2012). Bootstrapping in a language of thought: a formal model of numerical concept learning. Cognition
Pica, P., Lemer, C., Izard, V. & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science
Pinel, P., Piazza, M., Le Bihan, D. & Dehaene, S. (2004). Distributed and overlapping cerebral representations of number, size, and luminance during comparative judgments. Neuron
Pinker, S. (1984). Visual cognition: an introduction. Cognition
Pylyshyn, Z. (1989). The role of location indexes in spatial perception: a sketch of the FINST spatial-index model. Cognition
Rips, L. J., Asmuth, J. & Bloomfield, A. (2006). Giving the boot to the bootstrap: how not to learn the natural numbers. Cognition
Rips, L. J., Bloomfield, A. & Asmuth, J. (2008). From numerical concepts to concepts of number. Behavioral and Brain Sciences
Rittle-Johnson, B. & Siegler, R. S. (1998). The relation between conceptual and procedural knowledge in learning mathematics: a review. In Donlan, C. (ed.), The development of mathematical skill, 75–110. Hove: Psychology Press.
Sarnecka, B. W. & Carey, S. (2008). How counting represents number: what children must learn and when they learn it. Cognition
Sarnecka, B. W., Kamenskaya, V. G., Yamana, Y., Ogura, T. & Yudovina, Y. B. (2007). From grammatical number to exact numbers: early meanings of ‘one’, ‘two’, and ‘three’ in English, Russian, and Japanese. Cognitive Psychology
Schaeffer, B., Eggleston, V. H. & Scott, J. L. (1974). Number development in young children. Cognitive Psychology
Schlesinger, I. (1971). Production of utterances and language acquisition. In Slobin, D. (ed.), The ontogenesis of grammar (pp. 63–101). New York: Academic Press.
Schlesinger, I. (1988). The origin of relational categories. In Levy, Y., Schlesinger, I. M. & Braine, M. D. S. (eds), Categories and processes in language acquisition theory, 121–78. Hillsdale, NJ: Erlbaum.
Scholl, B. J. (2001). Objects and attention: the state of the art. Cognition
Secada, W. G., Fuson, K. C. & Hall, J. W. (1983). The transition from counting-all to counting-on in addition. Journal for Research in Mathematics Education
Smith, C. L. (1980). Quantifiers and question answering in young children. Journal of Experimental Child Psychology
Sommerfelt, A. (1938). La Langue et la Société. Oslo: Sommerfelt.
Spaepen, E., Coppola, M., Spelke, E. S., Carey, S. E. & Goldin-Meadow, S. (2011). Number without a language model. Proceedings of the National Academy of Sciences
Spaepen, E., Flaherty, M., Coppola, M., Spelke, E. S. & Goldin-Meadow, S. (2013). Generating a lexicon without a language model: Do words for number count?
Journal of Memory & Language
Spelke, E. & Tsivkin, S. (2001). Initial knowledge and conceptual change: space and number. In Bowerman, M. & Levinson, S. (eds), Language acquisition and conceptual development, 70–100. Cambridge: Cambridge University Press.
Starkey, P., Spelke, E. S. & Gelman, R. (1983). Detection of intermodal numerical correspondences by human infants. Science
Starkey, P., Spelke, E. S. & Gelman, R. (1990). Numerical abstraction by human infants. Cognition
Sullivan, J. & Barner, D. (2013). How are number words mapped to approximate magnitudes?
Quarterly Journal of Experimental Psychology
Sullivan, J. & Barner, D. (2014). Inference and association in children's early numerical estimation. Child Development
Tylor, E. B. (1871). Primitive culture: researches into the development of mythology, philosophy, religion, art, and custom. London: Murray.
Wagner, J. B. & Johnson, S. C. (2011). An association between understanding cardinality and analog magnitude representations in preschoolers. Cognition
Wagner, K., Kimura, K., Cheung, P. & Barner, D. (2015). Why is number word learning hard? Evidence from bilingual learners. Cognitive Psychology
Whalen, J., Gallistel, C. R. & Gelman, R. (1999). Nonverbal counting in humans: the psychophysics of number representation. Psychological Science
Wood, J. N., Kouider, S. & Carey, S. (2009). Acquisition of singular-plural morphology. Developmental Psychology
Wood, J. N. & Spelke, E. S. (2005). Infants’ enumeration of actions: numerical discrimination and its signature limits. Developmental Science
Wynn, K. (1990). Children's understanding of counting. Cognition
Wynn, K. (1992). Children's acquisition of the number words and the counting system. Cognitive Psychology
Wynn, K. (1992a). Addition and subtraction by human infants. Nature
Wynn, K. (1996). Infants’ individuation and enumeration of actions. Psychological Science
Wynn, K., Bloom, P. & Chiang, W. C. (2002). Enumeration of collective entities by 5-month-old infants. Cognition
Xu, F. & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition
Yang, C. (2016). The price of linguistic productivity. Cambridge, MA: MIT Press.