Abstract
This paper proposes an Interface Transparency Thesis concerning how linguistic meanings are related to the cognitive systems that are used to evaluate sentences for truth/falsity: a declarative sentence S is semantically associated with a canonical procedure for determining whether S is true; while this procedure need not be used as a verification strategy, competent speakers are biased towards strategies that directly reflect canonical specifications of truth conditions. Evidence in favor of this hypothesis comes from a psycholinguistic experiment examining adult judgments concerning ‘Most of the dots are blue’. This sentence is true if and only if the number of blue dots exceeds the number of nonblue dots. But this leaves unsettled, e.g., how the second cardinality is specified for purposes of understanding and/or verification: via the nonblue things, given a restriction to the dots, as in ‘|{x: Dot(x) & ~Blue(x)}|’; via the blue things, given the same restriction, and subtraction from the number of dots, as in ‘|{x: Dot(x)}| – |{x: Dot(x) & Blue(x)}|’; or in some other way. Psycholinguistic evidence and psychophysical modeling support the second hypothesis.
Similar content being viewed by others
References
Barwise J., Cooper R. (1981) Generalized quantifiers in natural language. Linguistics and Philosophy 4: 159–219
Boolos G. (1998) Logic, logic and logic. Harvard University Press, Cambridge, MA
Brannon E.M., Lutz D., Cordes S. (2006) The development of area discrimination and its implications for number representation in infancy. Developmental Science 9(6): F59–F64
Chomsky N. (1986) Knowledge of language: Its nature, origins and use. Praeger, New York
Church A. (1941) The calculi of lambda conversion. Princeton University Press, Princeton
Cordes S., Gallistel C., Gelman R., Lathan P. (2007) Nonverbal arithmetic in humans: light from noise. Perception & Psychophysics 69: 1185–1203
Cresswell M. (1985) Structured meanings. MIT Press, Cambridge, Mass.
Davidson, D. 1967. The logical form of action sentences. In Essays on actions and events, 105–148. Oxford: Clarendon Press.
Davies M. (1987) Tacit knowledge and semantic theory: Can a five per cent difference matter?. Mind 96: 441–462
Dehaene S. (1997) The number sense: How the mind creates mathematics. Oxford University Press, New York
Dummett M. (1973) Frege: Philosophy of Language. Harvard University Press, Cambridge, Mass.
Evans, G. 1981. Semantic theory and tacit knowledge. In Wittgenstein: To Follow a Rule, ed. S. Holtzman and C. Leich, 118–137. London: Routledge and Kegan Paul.
Feigenson L., Dehaene S., Spelke E.S. (2004) Core systems of number. Trends in Cognitive Science 8: 307–314
Fodor J. (2003) Hume variations. Oxford University Press, Oxford
Frege, G. 1884. Die Grundlagen der Arithmetik. Breslau: Wilhelm Koebner. J.L. Austin, English trans., The foundations of arithmetic (Oxford: Basil Blackwell, 1974).
Frege, G. 1892. Über Funktion und Begriff [English translation as ‘Function and concept’]. P. Geach and M. Black, trans., Translations from the philosophical writings of Gottlob Frege, 30–32 (Oxford: Blackwell, 1980).
Gallistel C., Gelman R. (2000) Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences 4(2): 59–65
Hackl M. (2009) On the grammar and processing of proportional quantifiers: most versus more than half. Natural Language Semantics 17: 63–98
Halberda, J. in prep. What is a Weber fraction? Ms., Johns Hopkins University.
Halberda J., Feigenson L. (2008) Developmental change in the acuity of the “Number Sense”: The approximate number system in 3-, 4-, 5-, 6-year-olds and adults. Developmental Psychology 44(5): 1457–1465
Halberda J., Mazzocco M.M.M., Feigenson L. (2008) Differences in primitive math intuitions predict math achievement. Nature 455: 665–668
Halberda J., Sires S.F., Feigenson L. (2006) Multiple spatially overlapping sets can be enumerated in parallel. Psychological Science 17: 572–576
Halle M. (2002) From memory to speech and back. Mouton de Gruyter, The Hague
Higginbotham J., May R. (1981) Questions, quantifiers, and crossing. The Linguistic Review 1: 41–80
Horty J. (2007) Frege on definitions. Oxford University Press, Oxford
Izard V., Dehaene S. (2008) Calibrating the mental number line. Cognition 106: 1221–1247
Jacobson, R., G. Fant, and M. Halle 1952. Preliminaries to speech analysis: the distinctive features and their correlates. Technical Report 13. Acoustics Laboratory, MIT.
Jackendoff R. (1983) Semantics and cognition. MIT Press, Cambridge, Mass.
Jackendoff R. (1990) Semantic structures. MIT Press, Cambridge, Mass.
Jackendoff R. (2002) Foundations of language. Oxford University Press, Oxford
Jusczyk P. (1997) The discovery of spoken language. MIT Press, Cambridge, Mass.
Kahneman D., Tversky A. (1973) On the psychology of prediction. Psychological Review 80: 237–251
Katz J.J., Fodor J.A. (1963) The structure of a semantic theory. Language 39: 170–210
Kuhl P. (1993) Early linguistic experience and phonetic perception: Implications for theories of developmental speech perception. Journal of Phonetics 21: 125–139
Landau B., Jackendoff R. (1993) “What” and “where” in spatial language and spatial cognition. Behavioral and Brain Sciences 16(2): 217–238
Liberman A.M., Cooper F.S., Shankweiler D.P., Studdert-Kennedy M. (1967) Perception of the speech code. Psychological Review 74: 431–461
Liberman A.M., Mattingly I.G. (1985) The motor theory of speech perception revised. Cognition 21: 1–36
Marr D. (1982) Vision. MIT Press, Cambridge, Mass.
Montague R. (1970) Universal grammar. Theoria 36: 373–398
Mostkowski A. (1957) On a generalization of quantifiers. Fundamenta Mathematicae 44: 12–36
Peacocke C. (1986) Explanation in computational psychology: Language, perception and level 1.5. Mind and Language 1: 101–123
Pica P., Lemer C., Izard V., Dehaene S. (2004) Exact and approximate arithmetic in an Amazonian indigene group. Science 306: 499–503
Pietroski P. (2010) Concepts, meaning and truth: First nature, second nature and hard work. Mind & Language 25(3): 247–278
Pietroski P., Lidz J., Hunter T., Halberda J. (2009) The meaning of most: Semantics, numerosity and psychology. Mind & Language 24(5): 554–585
Poeppel D., Idsardi W., van Wassenhove V. (2008) Speech perception at the interface of neurobiology and linguistics. Philosophical Transactions of the Royal Society of London B 363: 1071–1086
Rescher, N. 1962. Plurality quantification. Journal of Symolic Logic, 27: 373–347.
Ross J., Burr D. (2010) Vision senses number directly. Journal of Vision 10(2): 1–8
Stevens, K. 1972. The quantal nature of speech: Evidence from articulatory-acoustic data. In Human communication: A unified view, ed. E.E. David Jr. and P.B. Denes, 51–56. New York: McGraw-Hill.
Tarski A. (1944) The semantical concept of truth and the foundations of semantics. Philosophy and Phenomenological Research 4: 341–375
Treisman A., Gormican S. (1988) Feature analysis in early vision: Evidence from search asymmetries. Psychological Review 95(1): 15–48
Treisman A., Souther J. (1985) Search asymmetry: A diagnostic for preattentive processing of separable features. Journal of Experimental Psychology: Human Perception & Performance 16(3): 459–478
Werker, J.F. 1995. Exploring developmental changes in cross-language speech perception. In An invitation to cognitive science, Part I: Language, ed. D. Osherson (series), L. Gleitman and M. Liberman (vol. eds), 87–106. Cambridge, Mass.: MIT Press.
Whalen J., Gallistel C.R., Gelman R. (1999) Non-verbal counting in humans: The psychophysics of number representation. Psychological Science 10: 130–137
Wolfe, J.M. 1998. Visual search. In Attention, ed. H. Pashler, 13–73. London: University College London Press.
Zosh, J.M., L. Feigenson, and J.P. Halberda (submitted). Working memory capacity for multiple collections in infancy.
Author information
Authors and Affiliations
Corresponding author
Additional information
Guidelines for testing human research subjects were followed as certified by the Johns Hopkins University and the University of Maryland Institutional Review Boards. Subjects’ rights were protected throughout.
Rights and permissions
About this article
Cite this article
Lidz, J., Pietroski, P., Halberda, J. et al. Interface transparency and the psychosemantics of most . Nat Lang Semantics 19, 227–256 (2011). https://doi.org/10.1007/s11050-010-9062-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11050-010-9062-6