О двояком понимании дедуктивного обоснования

Резюме Термин “дедуктивное обоснование” понимается либо в относительном смысле, либо в абсолютном. В первом случае предложение дедуктивно обосновано только по отношению к некоторому классу посылок и является более или менее вероятным, в зависимости от степени обоснования посылок. Обоснование посылок не всегда является дедуктивным. Во втором случае обоснованное дедуктивно предложение в области языка, к которому оно принадлежит, достоверно и непременно истинно, всегда, когда постулированный семантической характеристикой способ понимания слов этого языка может быть реализован (Т. е. если существуют денотаты отвечающие этим словам по их семантической характе⌕истике). Следовательно в этом языке это предложение является аналитическим. Таким образом объяснение этого второго понятия дедуктивного обоснования сводится к объяснению понятия аналитического предложения данного языка.     

Decision policies minimizing risk in a multistage betting game

Considered in this paper is a decision task which has been employed to study multistage betting behavior. When the task commences, a decision maker (DM) is provided with some capital x (x > 0) which he is required to allocate over m (m > 1) mutually exclusive and collectively exhaustive alternatives, each of which occurs with probability p_i (p_i > 0, i = 1,…, m; Σ_i=1^mp_i = 1). If the amount y_i is allocated to alternative i (y_i ≥ 0, Σ_i=1^my_i = x) and alternative i obtains, DM's capital for the next stage of the game becomes y_ir_i, where r_i (r_i > 0) is the return per unit allocated to alternative i. The task consists of N stages.Defining risk in terms of the mean and variance of DM's bets, and assuming that the minimization of risk is DM's objective, decision policies satisfying this objective are derived in closed form and their testable properties are briefly discussed.     

Two years of physically active mathematics lessons enhance cognitive function and gross motor skills in primary school children

Physically active lessons have been shown to enhance academic achievement. However, the effects on cognitive function and gross motor skill development remain unknown. The present study examined how the incorporation of physical activity bouts within Mathematics lessons affects cognitive function and gross motor skill development across 2 years in primary school children. Eighty-two children (6.6 ± 0.3 y) were allocated to an intervention (n = 36; completing 8 h/wk of physically active lessons) or control (n = 46) group. A battery of cognitive function tests was completed, alongside the TGMD-3 to assess gross motor skills. Physically active Mathematics lessons led to greater improvements across all measures of cognition, when compared to the control group (digit span forwards, p < 0.001, d = 1.5; digit span backwards, p = 0.017, d = 1.0; free word recall: p < 0.001, d = 1.3; selective visual attention: p < 0.001, d = 0.3; verbal fluency: p < 0.001, d = 0.9; arithmetic: p < 0.001, d = 1.8). Furthermore, the intervention group demonstrated greater improvements in overall score on the TGMD-3 (p < 0.001, d = 1.7), as well as the locomotion (p < 0.001, d = 1.1) and object control (p < 0.001, d = 1.5) sub-scales. The physically active Mathematics lessons intervention appears to offer synergistic benefits in relation to cognitive and motor development, which are critical for optimal development in the early years.     

Теория нормативных предлозений

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Prior's puzzle generalized

Prior's puzzle is standardly taken to be the puzzle of why, given the assumption that that-clauses denote propositions, substitution of $⌜$the proposition that $P$$⌝$ for $⌜$that $P$$⌝$ within the complements of many propositional attitude verbs is invalid. I show that Prior's puzzle is much more general than is ordinarily supposed. There are two variants on the substitutional form of the puzzle—a quantificational variant and a pronominal variant—and all three forms of the puzzle arise in a wide range of verbal complements, rather than merely in the complements of propositional attitude verbs. The generalized puzzle shows that a range of proposed solutions to the original puzzle fail, or are radically incomplete, and also reveals the connections between Prior's puzzle and debates over the nature of semantic types and higher-order quantification. I go on to develop a novel, higher-order solution to the generalized form of the puzzle, and I argue that this higher-approach is superior to its first-order alternatives.