How many words is a bilingual 2-year-old supposed to know or say in each of her languages? Speech and language therapists or researchers lack the tools to answer this question, because several factors have an impact on bilingual language skills: gender, amount of exposure, mode of acquisition, socio-economic status and the distance between L1 and L2. Unfortunately, these factors are usually studied separately, making it difficult to evaluate their weight on a unique measure of vocabulary. The present study measures the (...) contribution of the following factors to the vocabulary scores of bilingual toddlers: i) gender; ii) sibling ranking; iii) relative amount of exposure to each language; iv) mode of exposure; v) SES; vi) linguistic distance; vii) language spoken between parents. Close to the child’s second birthday, parents of 278 UK-based bilinguals completed successively: a 100-word version of the Oxford-CDI, the CDI in the child’s Additional Language, a family questionnaire, and the Language Exposure Questionnaire. Thirty-six British-English-AL pairs were considered, with languages contrasted on a second-language-learning scale : for example, Dutch and French are close to British-English, while Polish or Cantonese are more distant. Data from the corpus were included in two mixed-effect models, one with the English scores in comprehension as the dependent variable, and the other with production scores. The seven factors listed above were included as predictors. The amount of English exposure was the strongest predictor of comprehension scores = 9.35, p <.005, β = 0.02, t = 3.08, p <.005), followed by the language that parents speak between themselves = 14.94, p <.001, β = 1.37, t = 3.76, p <.0005), linguistic distance = 6.92, p <.01, β = -0.74, t = -2.66, p <.01) and age = 4.86, p <.05, β = 0.55, t = 2.17, p <.05). In production, gender = 13.57, p <.0005, β = -0.91, t = -03.72, p <.0005), amount of exposure to English = 13.57, p <.0005, β = -0.91, t = -03.72, p <.0005), the language that parents speak between themselves = 11.85, p <.005, β = 1.09, t = 3.41, p <.001), and the mother’s occupation = 4.51, p <.05, β = 0.63, t = 2.13, p <.05) were the significant predictors. The more English parents use to address one another, the more English words the child says and understands. This surprising result could be simply explained by the fact that parents who speak English together are also more likely to speak English to their child. The main results of this study is that linguistic distance is a powerful predictor of toddlers’ vocabulary in English, with children learning two close languages growing their vocabulary faster than those learning distant languages. (shrink)

We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. We show that although these sentences are known to have a diagrammatic expres- sion (in the form of the Gergonne circles) that constitutes a semantic representation, these concepts can also be expressed syntactically in the form of algebraic formulas. (...) We hypothesized that the quantified sen- tences have an abstract underlying representation common to the formulas and their associated sets of dia- grams (models). We derived 9 predictions (3 semantic, 2 pragmatic, and 4 mixed) regarding people’s as- sessment of how well each of the 5 diagrams expresses the meaning of each of the quantified sentences. We report the results from 3 experiments using Gergonne’s (1817) circles or an adaptation of Leibniz (1903/ 1988) lines as external representations and show them to support the predictions. (shrink)

William C. Dell teaches us to move our imaginations beyond the bounds of ordinary space time into the realm of eternal Zen consciousness, of the endless process of Zen deconstructing.

We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. It is shown that, although these sentences are known to have a diagrammatic expression (in the form of the Gergonne circles) which constitute a semantic representation, these concepts can also be expressed syntactically in the form of algebraic formulas. (...) It is hypothesized that the quantified sentences have an abstract underlying representation common to the formulas and their associated sets of diagrams (models). Nine predictions are derived (three semantic, two pragmatic, and four mixed) regarding people's assessment of how well each of the five diagrams expresses the meaning of each of the quantified sentences. The results from three experiments, using Gergonne's circles or an adaptation of Leibniz lines as external representations, are reported and shown to support the predictions. (shrink)

This note addresses the issue as to which ceers can be realized by word problems of computably enumerable (or, simply, c.e.) structures (such as c.e. semigroups, groups, and rings), where being realized means to fall in the same reducibility degree (under the notion of reducibility for equivalence relations usually called “computable reducibility”), or in the same isomorphism type (with the isomorphism induced by a computable function), or in the same strong isomorphism type (with the isomorphism induced by a computable permutation (...) of the natural numbers). We observe, e.g., that every ceer is isomorphic to the word problem of some c.e. semigroup, but (answering a question of Gao and Gerdes) not every ceer is in the same reducibility degree of the word problem of some finitely presented semigroup, nor is it in the same reducibility degree of some non‐periodic semigroup. We also show that the ceer provided by provable equivalence of Peano Arithmetic is in the same strong isomorphism type as the word problem of some non‐commutative and non‐Boolean c.e. ring. (shrink)