Abstract
The verification of a sentence against a visual display in experimental conditions reveals a procedure that is driven solely by the properties of the linguistic input and not by the properties of the context (the set-up of the visual display) or extra-linguistic cognition (operations executed to obtain the truth value). This procedure, according to the Interface Transparency Thesis (ITT) (Lidz et al. in Nat Lang Semant 19(3):227–256, 2011), represents the meaning of an expression at the interface with the ‘conceptual-intentional’ system (Chomsky in The minimalist program. MIT Press, Cambridge, 1995). My experiments provide support for the ITT by replicating in Polish and in Bulgarian the findings of Lidz et al. (Nat Lang Semant 19(3):227–256, 2011) for the English quantifier most. We also obtain new evidence that participants are prompted to switch between verification procedures by a change in the linguistic input (a different superlative quantifier entailed by most), but not by a change in the visual input. Thus, the motivation for the subconscious switch in procedures is not to maximize efficiency. Participants use the procedure associated with each quantifier, and in effect, the same display is verified differently depending on which information the visual system is instructed to use by the semantic representation of the sentence.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Actually, the procedure in (2) has not been ruled out. For consistency I follow the conclusion in Lidz et al. (2011), but their data as well as mine may be also compatible with (2).
Halberda et al. (2008) have shown that children who have not yet learned to count are perfectly able to understand most. Odić et al. (2013)show that among children who are full counters and are asked to count two sets before verifying a sentence containing most, some will use the obtained numbers to verify the sentence, while others ignore this information and rely on the ANS representation.
ANS operates across different modalities, not just vision. It is activated whenever humans perform symbolic number tasks, for example, estimate the result of an arithmetic operation, estimate a number of acoustic events or perform a number of actions (Feigenson et al. 2004).
The appendix in Lidz et al. (2011) contains a detailed explanation of how ordinal comparison, carried out by the ANS on numerosities represented by Gaussian curves, is an operation of subtraction that results in a Gaussian representation of the difference, whose variance adds the variances of the original Gaussian variables. Hence, the variance of the Gaussian variable resulting from subtraction is greater than that of the Gaussian variable obtained by Selection in Table 2.
Out of the 40 Bulgarian participants one had to be excluded for failing to respond on 41 out of 180 displays, everyone else missed no more than a few displays.
Partial Eta Squared expresses the variance that is explained by a given variable when the variance explained by other variables is excluded. Post hoc tests using the Bonferroni correction revealed significant differences (p \(<\) .001) between all levels of the ratio variable. There are no significant interactions in Polish. In Bulgarian there are significant interactions between Ratio and Distractor F(3.225, 122.56) \(=\) 5.333, p \(=\) .001, and between Distractor and Truth/Falsity F(1.553, 59.004) = 12.407, p \(<\) .001.
Because of the violations of sphericity (\(p = .019\)), we are reading the Greenhouse–Geisser corrected value. Whether or not we use this correction, there is still no significance: \(\mathrm F (2, 38) = 1.64\), \(p = .208\).
Using the ogive graph to combine the true and false screen data was suggested to me by Justin Halberda and Darko Odić.
Pair-wise comparisons for the main effect of ratio and the main in effect of distractor in Bulgarian (using a Bonferroni correction) revealed significant differences (\(p< .001\)) between all levels. For Polish the differences between all levels of the ratio variable were significant (\(p< .001\)). The differences between 1–3 and 2–3 distractors were significant (\(p< .001\) and \(p = .001\), respectively), while the difference between 1–2 distractors was not (\(p = .316\)).
In Bulgarian mean accuracy on false screens was 80 and 66 % on true screens. In Polish, it was 74 % on false screens and 72 % on true screens.
One might wonder if the three set limit predicts that enumeration on the 2- and 3-distractor conditions should be just impossible. It does not. The selection of the yellow set and one of the distractors is automatic. When there are two distractors, the pure chance of selecting the larger one at random could account for the success rate above chance (60–80 %) (Jeff Lidz, p.c.). To test this prediction my results could be compared with the performance of an ideal observer (in psychophysics it is a hypothetical observer whose responses reflect optimal efficiency) consistently enumerating the yellow set and one other set at random.
Effect size of Quantifier type is lower than the effect size of ratio. The effect of ratio in Bulgarian: true screens \(\mathrm F (2,76) = 70.9\), \(p<.001\), \(\eta _{p}^{2}=.651\), false screens F(2,76) = 88.495, \(p<.001\), \(\eta _{p}^{2}=.7\). Polish: true screens \(\mathrm F (2,38) = 17.69\), \(p<.001\), \(\eta _{p}^{2}= .482\), false screens \(\mathrm F (2,38) = 44.723\), \(p<.001\), \(\eta _{p}^{2}= .702\).
It could be the case that when the target subset is smaller than the competitor subset, the two are automatically selected by the visual system in accordance with (c) in Table 1. A ‘no’-judgment with Most2 might then be harder because the competitor set, being larger, attracts more attention (a bias for looking at the more numerous target has been observed in the visual world eye-tracking studies, e.g. Grodner et al. 2010). The Subtraction hypothesis for Most1 predicts that this should not happen with Most1 where the competitor subset, although selected by the visual system, is not attended to at all.
Twenty-eight participants were tested, but the data from one subject was excluded because the subject’s overall accuracy rate was 3 standard deviations lower than the average. No other participant in Exp. 3 scored lower than 2 standard deviations below the average. (No participant in Exp. 1 and 2 scored lower than 2.5 standard deviations.)
There is a significant interaction between ratio and distractor, \(\mathrm F (4,104)=6.156\), \(p<.001\).
To be precise, the output of the syntactic component is the Logical Form that receives the interpretation specified in the logical form, i.e. a semantic formula.
As one of the reviewers observes, my evidence for the different verification processes for Most1 and Most2 is based on the use of the ANS representation of magnitude for the comparisons required by the semantics. It would be interesting to see if we find evidence for different verification procedures also in experiments where counting is not precluded.
References
Bourdon, B. (1908). Sur le temps nécessaire pour nommer les nombres. Revue Philosophique de la France et de l’étranger, 65, 426–431.
Chierchia, G., & McConnell-Ginet, S. (1990). Meaning and grammar. Cambridge, MA: MIT Press.
Chomsky, N. (1986). Knowledge of language: Its nature, origin, and use. New York: Praeger Publishers.
Chomsky, N. (1995). The minimalist program. Cambridge, MA: MIT Press.
Clark, R., & Grossman, M. (2007). Number sense and quantifier interpretation. Topoi, 26, 51–62.
Dehaene, S. (1997). The number sense: How the mind creates mathematics. New York: Oxford University Press.
Dehaene, S. (2009). Origins of mathematical intuitions: The case of arithmetic. Annals of the New York Academy of Sciences, 1156, 232–259.
Dummett, M. (1978). Truth and other enigmas. London: Duckworth.
Green, D. M., & Swets, J. A. (1966). Signal detection theory and psychophysics. New York: Wiley.
Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8, 307–314.
Grodner, D. J., Klein, N. M., Carbary, K. M., & Tanenhaus, M. K. (2010). “Some”, and possibly all, scalar inferences are not delayed: Evidence for immediate pragmatic enrichment. Cognition, 116(1), 42–55.
Halberda, J., Sires, S. F., & Feigenson, L. (2006). Multiple spatially overlapping sets can be enumerated in parallel. Psychological Science, 17(7), 572–6.
Halberda, J., Taing, L., & Lidz, J. (2008). The development of “most” comprehension and its potential dependence on counting-ability in preschoolers. Language Learning and Development, 4(2), 99–121.
Heim, I., & Kratzer, A. (1998). Semantics in generative grammar. Oxford: Blackwell.
Larson, R. K., & Segal, G. (1995). Knowledge of meaning. Cambridge, MA: MIT Press.
Lewis, D. (1975). Languages and language. In Keith Gunderson (Ed.), Minnesota studies in the philosophy of science (Vol. VII, pp. 3–35). Minneapolis: University of Minnesota Press.
Lidz, J., Pietroski, P., Hunter, T., & Halberda, J. (2011). Interface transparency and the psychosemantics of most. Natural Language Semantics, 19(3), 227–256.
Moschovakis, Y. (1994). Sense and denotation as algorithm and value. In Logic Colloquium ’90 (Helsinki 1990). Volume 2 of Lecture Notes in Logic, (pp. 210–249). Berlin: Springer.
Muskens, R. (2005). Higher order modal logic. In P. Blackburn, J. van Benthem, & F. Wolter (Eds.), Handbook of modal logic, studies in logic and practical reasoning (pp. 621–653). Dordrecht: Elsevier.
Odić D., Pietroski, P., Lidz, J. & Halberda, J. (2013). The language-number interface: Evidence from the acquisition of ‘most’.
Pietroski, P., Lidz, J., Hunter, T., & Halberda, J. (2009). The meaning of most: Semantics, numerosity and psychology. Mind and Language, 24(5), 554–585.
Pietroski, P., Lidz, J., Hunter, T., Odic, D., & Halberda, J. (2011). Seeing what you mean, mostly. In J. Runner (Ed.), Experiments at the interfaces, syntax & semantics 37 (pp. 181–217). Bingley, UK: Emerald Publications.
Quine, W. V. (1972). Methodological reflections on current linguistic theory. In G. Harman & D. Davidson (Eds.), Semantics of natural language (pp. 442–454). New York: Humanities Press.
Schlotterbeck, F., & Bott, O. (2012). Easy solutions for a hard problem? The computational complexity of reciprocals with quantificational antecedents. In J. Szymanik & R. Verbrugge (Eds.), Journel of logic, Language and Information. Spriner.
Suppes, P. (1982). Variable-free semantics with remarks on procedural extensions. In T. Simons & R. Scholes (Eds.), Language, mind and brain (pp. 21–34). Hillsdale, NJ: Erlbaum.
Szymanik, J., & Zajenkowski, M. (2010). Comprehension of simple quantifiers. Empirical evaluation of a computational model. Cognitive Science, 34(3), 521–532.
Tichý, P. (1969). Intensions in terms of Turing machines. Studia Logica, 26, 7–25.
Tomaszewicz, B. M. (2011). Verification strategies for two majority quantifiers in Polish. In I. Reich, et al. (Eds.), Proceedings of Sinn & Bedeutung 15 (pp. 597–612). Saarbrücken, Germany: Saarland Unversity Press.
Tomaszewicz, B. M. (2012) Semantics and visual cognition: The processing of Bulgarian and Polish majority quantifiers. LSA Annual Meeting Extended Abstracts 2012. http://elanguage.net/journals/lsameeting/article/view/2884
Trick, L. M. (2008). More than superstition: Differential effects of featural heterogeneity and change on subitizing and counting. Perception and Psychophysics, 70(5), 743–60.
Troiani, V., Peelle, J., Clark, R., & Grossman, M. (2009). Is it logical to count on quantifiers? Dissociable neural networks underlying numerical and logical quantifiers. Neuropsychologia, 47(1), 104–111.
Wellwood, A., Odic, D., Halberda, J., Hunter, T., Pietroski, P., Lidz, J., (To appear) Meaning more or most: evidence from 3-and-a-half year-olds. Proceedings of the Chicago Linguistic Society (CLS) 48 annual meeting.
Wolfe, J. M. (1998). Visual search. In H. Pashler (Ed.), Attention (pp. 13–73). Hove, England: Psychology Press/Erlbaum, UK Taylor & Francis.
Acknowledgments
I would like to thank Roumi Pancheva as well as Jeff Lidz, Paul Pietroski, Justin Halberda and Elsi Kaiser for extensive discussion and encouragement. Special thanks are due to Darko Odić for help with the interpretation of the data. I am also grateful for the comments to the anonymous reviewers, the audience at ESSLLI 2012 Logic & Cognition Workshop, LSA 2012, SuB 9, CUSP 3, VSSoL 2010 as well as the help and advice of the following people: Petya Bambova, Hagit Borer, Mary Byram-Washburn, Tom Buscher, Robin Clark, Victor Ferreira, Jon Gajewski, Martin Hackl, Ed Holsinger, Patrycja Jabłońska, Grzegorz Jakubiszyn, Dorota Klimek-Jankowska, Halina Krystewa, Katy McKinney-Bock, Bilian Marinov, Marieta Maneva, Krzysztof Migdalski, Toby Mintz, Petya Osenova, Ewa Panewa, Barry Schein, Marcin Suszczyński, Ewa Tomaszewicz and the students of IFA at Wroclaw University, WSF Wroclaw, and the Polish Institute in Sofia. My work was partially supported by an Advancing Scholarship in the Humanities and Social Sciences Grant from USC awarded to R. Pancheva.
Author information
Authors and Affiliations
Corresponding author
Appendix
Rights and permissions
About this article
Cite this article
Tomaszewicz, B. Linguistic and Visual Cognition: Verifying Proportional and Superlative Most in Bulgarian and Polish. J of Log Lang and Inf 22, 335–356 (2013). https://doi.org/10.1007/s10849-013-9176-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10849-013-9176-6