The Meaning of ‘Most’: Semantics, Numerosity and Psychology

The meaning of 'most' can be described in many ways. We offer a framework for distinguishing semantic descriptions, interpreted as psychological hypotheses that go beyond claims about sentential truth conditions, and an experiment that tells against an attractive idea: 'most' is understood in terms of one-to-one correspondence. Adults evaluated 'Most of the dots are yellow', as true or false, on many trials in which yellow dots and blue dots were displayed for 200 ms. Displays manipulated the ease of using a 'one-to-one with remainder' strategy, and a strategy of using the Approximate Number System to compare of (approximations of) cardinalities. Interpreting such data requires care in thinking about how meaning is related to verification. But the results suggest that 'most' is understood in terms of cardinality comparison, even when counting is impossible. How is the word 'most' related to human capacities for detecting and comparing numerosities? One might think the answer is obvious, and explicit in standard semantic theories: 'most' is understood in terms of a capacity to compare cardinal numbers; e.g. 'Most of the dots are yellow' means that the number of yellow dots is greater than the number of nonyellow dots. But there are other possibilities for how competent speakers understand 'most', and we offer experimental evidence that tells against some initially attractive hypotheses. By discussing one lexical item in this way, we hope to illustrate how semantics and psychology can and should be pursued in tandem, especially with regard to the capacities that let humans become numerate. Following common practice in semantics, we begin by characterizing the contribution of 'most' to the truth conditions of sentences that have the following form: Most (of the)� sa re� . At this level of analysis, there are many equivalent characterizations, as discussed below. Our aim is to give some of these formal distinctions empirical bite, in a way that permits adjudication of distinct hypotheses about how speakers understand 'most' (cf. Hackl, 2009). In short, we want to know how speakers represent the truth conditions in question.

[1]  Gottlob Frege,et al.  The Foundations of Arithmetic , 2017 .

[2]  A. Church The calculi of lambda-conversion , 1941 .

[3]  O. Spies Die grundlagen der arithmetik: by G. Frege. English translation by J. L. Austin. 119 pages, 14 × 22 cm. Breslau, Verlag von Wilhelm Koebner, 1884, and New York, Philosophical Library, 1950. Price, $4.75 , 1950 .

[4]  Willard Van Orman Quine,et al.  Word and Object , 1960 .

[5]  J. Heijenoort From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931 , 1967 .

[6]  M. Dummett Frege: Philosophy of Language , 1973 .

[7]  Stanley Coren,et al.  Sensation and perception , 1979 .

[8]  Uriel Weinreich,et al.  On semantics , 1980 .

[9]  P. G. Vos,et al.  A probabilistic model for the discrimination of visual number , 1982, Perception & psychophysics.

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

[11]  R. Goodstein,et al.  The Basic Laws of Arithmetic , 1966, The Mathematical Gazette.

[12]  Peter Eggenberger,et al.  Knowledge of meaning , 1983 .

[13]  R. Church,et al.  A mode control model of counting and timing processes. , 1983, Journal of experimental psychology. Animal behavior processes.

[14]  H. Barlow Vision: A computational investigation into the human representation and processing of visual information: David Marr. San Francisco: W. H. Freeman, 1982. pp. xvi + 397 , 1983 .

[15]  J. E. Tiles,et al.  Frege's Conception of Numbers as Objects , 1984 .

[16]  Noam Chomsky Knowledge of Language , 1986 .

[17]  Christopher Peacocke,et al.  Explanation in Computational Psychology: Language, Perception and Level 1.5 , 1986 .

[18]  Martin Davies,et al.  Tacit Knowledge and Semantic Theory: Can a Five per cent Difference Matter? , 1987 .

[19]  Noam Chomsky Knowledge of language: its nature, origin, and use , 1988 .

[20]  K. Wynn Children's acquisition of the number words and the counting system , 1992, Cognitive Psychology.

[21]  C. Peacocke A Study of Concepts , 1994 .

[22]  Robert Kirk,et al.  A Study of Concepts , 1994 .

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

[24]  William Demopoulos,et al.  Frege’s Philosophy of Mathematics , 1997 .

[25]  J. Fodor,et al.  Concepts: Where Cognitive Science Went Wrong , 1998 .

[26]  George Boolos,et al.  Logic, Logic, and Logic , 2000 .

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

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

[29]  C. Gallistel,et al.  Non-verbal numerical cognition: from reals to integers , 2000, Trends in Cognitive Sciences.

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

[31]  E. Spelke,et al.  The construction of large number representations in adults , 2003, Cognition.

[32]  Andreas Nieder,et al.  A parieto-frontal network for visual numerical information in the monkey. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[33]  S. Dehaene,et al.  Exact and Approximate Arithmetic in an Amazonian Indigene Group , 2004, Science.

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

[35]  D. Davidson Belief and the basis of meaning , 1974, Synthese.

[36]  Lisa Feigenson,et al.  A double-dissociation in infants' representations of object arrays , 2005, Cognition.

[37]  Michael Beaney,et al.  Frege's philosophy of mathematics , 2005 .

[38]  L. Feigenson,et al.  Multiple Spatially Overlapping Sets Can Be Enumerated in Parallel , 2006, Psychological science.

[39]  Susan Carey,et al.  One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles , 2007, Cognition.

[40]  P. Pietroski Induction and Comparison , 2007 .

[41]  John F. Horty Frege on Definitions: A Case Study of Semantic Content , 2007 .

[42]  Tim Hunter,et al.  Beyond Truth Conditions: The Semantics of "most" , 2008 .

[43]  Justin Halberda,et al.  The Development of “Most” Comprehension and Its Potential Dependence on Counting Ability in Preschoolers , 2008 .

[44]  C. Gallistel,et al.  The generative basis of natural number concepts , 2008, Trends in Cognitive Sciences.

[45]  Justin Halberda,et al.  Developmental change in the acuity of the "Number Sense": The Approximate Number System in 3-, 4-, 5-, and 6-year-olds and adults. , 2008, Developmental psychology.

[46]  Pieter A. M. Seuren Meaning and Grammar , 2009 .

[47]  Martin Hackl,et al.  On the grammar and processing of proportional quantifiers: most versus more than half , 2009 .

[48]  G. Frege,et al.  Grundgesetze der Arithmetik : begriffsschriftlich abgeleitet , 2009 .

[49]  Justin Halberda,et al.  Infants' ability to enumerate multiple spatially-overlapping sets in parallel , 2010 .

[50]  Bernhard Thalheim,et al.  About Semantics , 2010, SDKB.