Number sense and quantifier interpretation

We consider connections between number sense—the ability to judge number—and the interpretation of natural language quantifiers. In particular, we present empirical evidence concerning the neuroanatomical underpinnings of number sense and quantifier interpretation. We show, further, that impairment of number sense in patients can result in the impairment of the ability to interpret sentences containing quantifiers. This result demonstrates that number sense supports some aspects of the language faculty.

[1]  S. Carey,et al.  The Representations Underlying Infants' Choice of More: Object Files Versus Analog Magnitudes , 2002, Psychological science.

[2]  C. Gallistel,et al.  Preverbal and verbal counting and computation , 1992, Cognition.

[3]  Brian Butterworth,et al.  What Counts: How Every Brain is Hardwired for Math , 1999 .

[4]  Robert S. Boyer,et al.  Automated Reasoning: Essays in Honor of Woody Bledsoe , 1991, Automated Reasoning.

[5]  E. Spelke,et al.  Sources of mathematical thinking: behavioral and brain-imaging evidence. , 1999, Science.

[6]  E. Spelke,et al.  Language and Conceptual Development series Core systems of number , 2004 .

[7]  Robin Clark,et al.  Neural basis for generalized quantifier comprehension , 2005, Neuropsychologia.

[8]  Johan van Benthem,et al.  Handbook of Logic and Language , 1996 .

[9]  Dag Westerståhl,et al.  Generalized Quantifiers in Linguistics and Logic , 1997, Handbook of Logic and Language.

[10]  G. Mandler,et al.  Subitizing: an analysis of its component processes. , 1982, Journal of experimental psychology. General.

[11]  S. Dehaene,et al.  THREE PARIETAL CIRCUITS FOR NUMBER PROCESSING , 2003, Cognitive neuropsychology.

[12]  Robin Clark,et al.  Quantifier comprehension in corticobasal degeneration , 2006, Brain and Cognition.

[13]  J. Benthem.  Essays in Logical Semantics , 1986 .

[14]  Rochel Gelman,et al.  Variability signatures distinguish verbal from nonverbal counting for both large and small numbers , 2001, Psychonomic bulletin & review.

[15]  J. Barwise,et al.  Generalized quantifiers and natural language , 1981 .

[16]  E. Spelke,et al.  Large number discrimination in 6-month-old infants , 2000, Cognition.

[17]  Murray Grossman,et al.  Calculation impairment in neurodegenerative diseases , 2003, Journal of the Neurological Sciences.

[18]  John R. Platt,et al.  Localization of position within a homogeneous behavior chain: Effects of error contingencies , 1971 .

[19]  Robert S. Boyer,et al.  MJRTY: A Fast Majority Vote Algorithm , 1991, Automated Reasoning: Essays in Honor of Woody Bledsoe.

[20]  A. Mostowski.  On a generalization of quantifiers , 1957 .

[21]  S. Dehaene,et al.  The Number Sense: How the Mind Creates Mathematics. , 1998 .

[22]  C. Gallistel,et al.  Nonverbal Counting in Humans: The Psychophysics of Number Representation , 1999 .

[23]  M. Grossman,et al.  Verbal mediation of number knowledge: Evidence from semantic dementia and corticobasal degeneration , 2004, Brain and Cognition.

[24]  Z. Pylyshyn,et al.  Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision. , 1994, Psychological review.

[25]  C. Gallistel,et al.  The Child's Understanding of Number , 1979 .

[26]  Edward L. Keenan,et al.  A semantic characterization of natural language determiners , 1986 .