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.     

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.     

O regułach rachunku zdań

Streszczenie Zmienn istotn wyraenia rachunku zda nazywam zmienn, której warto przy pewnym ukadzie wartoci innych zmiennych wpywa na warto caego wyraenia.     

Kinematic gait parameters for older adults with Parkinson's disease during street crossing simulation

Safe street crossing is important for older adults' social inclusion. We assessed gait kinematic adaptation under different simulated street crossing conditions in older adults with Parkinson's disease (PD) and made comparisons with older adults without PD to understand how PD interferes in outdoor task performance, helping in the development of strategies to reduce road traffic accident risk. In 20 older adults without PD (control group – CG) and 20 with PD (GPD), we assessed usual gait (C1), gait during street crossing simulation (C2), and gait during reduced-time street crossing simulation (C3). Velocity, step length, and step, swing, stance, and double support time were analyzed. Spatiotemporal differences in gait between groups and conditions were analyzed. The GPD walked 16% slower in C1 and 12% slower in C2 and C3 than the CG. GPD also took 11% shorter steps in C1 and 9.5% shorter steps in C2. The double support time was 8.5% greater in C1. In intragroup comparisons, there were significant differences in all gait conditions. The CG showed increased velocity (C2 15% > C1; C3 13% > C2; C3 26% > C1), step length (C2 8% > C1; C3 5% > C2; C3 13% > C1), and swing time (C2 2% > C1; C3 3.7% > C2; C3 6% > C1), and decreased step time (C2 7.5% < C1; C3 8% < C2; C3 15% < C1), stance time (C2 1.3% < C1; C3 2.5% < C2; C3 3.6% < C1), and double support time (C2 6.3% < C1; C3 10.5% < C2; C3 16% < C1). GPD showed increased velocity (C2 19% > C1; C3 13.5% > C2; C3 29.7% > C1), step length, (C2 6% > C1; C3 7% > C2; C3 16% > C1), and swing time (C2 3% > C1; C3 3% > C2; C3 5.5% > C1) and decreased step time (C2 10.3% < C1; C3 7.7% < C2; C3 17% < C1), stance time (C2 1.7% < C1; C3 1.7% < C2; C3 3.4% < C1), and double support time (C2 7% < C1; C3 9.5% < C2; C3 16% < C1). Kinematic changes observed in the intergroup comparison show that participants with PD had lower velocity in all conditions. However, per the intragroup results, both participants with and without PD managed to significantly modify gait variables to attempt to cross the street in the given time. It is necessary to assess whether this increases fall risk by exposing them to road traffic accidents.     

The role of therapy productiveness on MFT clients’ intentions to persist in therapy

Many clients drop out of therapy before reaching their goals (Bohart &; Wade, 2013 Bohart, A. C., &; Wade, A. M. (2013). The client variables in psychotherapy. In M. Lambert (Ed.) Bergin &; Garfield’s Handbook of psychotherapy and behavior change. (p. 219–257). New York: Wiley. [Google Scholar]), though being in therapy produces more change than not being in therapy (Lambert, 1992 Lambert, M. J. (1992). Implications of outcome research for psychotherapy integration. In J. C. Norcross &; M. R. Goldfried (Eds.), Handbook of psychotherapy integration (pp. 94–129). New York: Basic Books. [Google Scholar]). To investigate the factors that affect clients’ decisions to persist in therapy, we surveyed a convenience sample of 72 clients of MFTs in individual, couple or family therapy currently in treatment in a community-based therapy center. We tested moderation using regression analysis to determine the extent to which productiveness moderates the relationship between therapeutic alliance and intended persistence. Results showed that productiveness moderated the relationship between therapeutic alliance and intended persistence. Specifically, higher levels of therapy productiveness strengthened the relationship between therapeutic alliance and therapy persistence. Implications for future research and practice are presented and discussed.     

Intermediate logics with the same disjunctionless fragment as intuitionistic logic

Given an intermediate prepositional logic L, denote by L ^–d its disjuctionless fragment. We introduce an infinite sequence {J _n}_n1 of propositional formulas, and prove:(1)For any L: L ^–d =I ^–d (I=intuitionistic logic) if and only if J _n L for every n 1.Since it turns out that L{J _{n} n}1 = Ø for any L having the disjunction property, we obtain as a corollary that L ^–d = I ^–d for every L with d.p. (cf. open problem 7.19 of [5]). Algebraic semantic is used in the proof of the if part of (1). In the last section of the paper we provide a characterization in Kripke's semantic for the logics J _n =I+ +J _n (n 1).     

Predictive model for early math skills based on structural equations

Early math skills are determined by higher cognitive processes that are particularly important for acquiring and developing skills during a child's early education. Such processes could be a critical target for identifying students at risk for math learning difficulties. Few studies have considered the use of a structural equation method to rationalize these relations. Participating in this study were 207 preschool students ages 59 to 72 months, 108 boys and 99 girls. Performance with respect to early math skills, early literacy, general intelligence, working memory, and short‐term memory was assessed. A structural equation model explaining 64.3% of the variance in early math skills was applied. Early literacy exhibited the highest statistical significance (β = 0.443, p < 0.05), followed by intelligence (β = 0.286, p < 0.05), working memory (β = 0.220, p < 0.05), and short‐term memory (β = 0.213, p < 0.05). Correlations between the independent variables were also significant (p < 0.05). According to the results, cognitive variables should be included in remedial intervention programs.     

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.     

REVIEWS

Book reviewed: Idolatry and Representation: The Philosophy of Franz Rosenzweig Reconsidered by Leora Batnitzky (Princeton: Princeton University Press, 2000) x + 281 pp.
Reviewed by Charles T. Mathewes
Department of Religious Studies
University of Virginia
Charlottesville, VA 22904‐4126
SA Violence, Hospitality, and the Cross: Reappropriating the Atonement Tradition by Hans Boersma (Grand Rapids, Michigan: Baker Academic, 2004) + 288 pp.
Reviewed by Gladstone H. Stevens, S.S.
St. Mary's Seminary and University
5400 Roland Ave.
Baltimore, MD 21210
USA The Creativity of God: World, Eucharist, Reason by Oliver Davies (Cambridge: Cambridge University Press, 2004) xi + 210 pp.
Reviewed by Matthew Levering
Ave Maria University
1025 Commons Circle
Naples, Florida 34119
USA Lord Jesus Christ: Devotion to Jesus in Earliest Christianity by Larry W. Hurtado (Grand Rapids, Michigan: Wm. B. Eerdmans Publishing Company, 2003) xxii + 745 pp.
Reviewed by Stephen Fowl
Department of Theology
Loyola College in Maryland
4501 N. Charles Street
Baltimore, MD 21210
USA Culture and the Thomist Tradition after Vatican II by Tracey Rowland (London and New York: Routledge, 2003) xiv + 226 pp.
Reviewed by Joseph Wawrykow
Department of Theology
University of Notre Dame
Notre Dame, Indiana
46556
USA Spinoza's Revelation: Religion, Democracy, and Reason by Nancy K. Levene (Cambridge: Cambridge University Press, 2004) xxii + 256pp.
Reviewed by Martin Kavka
Department of Religion
Florida State University
Tallahassee, FL 32306‐1520
USA Religion and the Domestication of Dissent: Or How to Live in a Less than Perfect Nation by Russell T. McCutcheon (London: Equinox, 2005) xi + 123 pp.
Reviewed by Stefan Skrimshire
75 Rockdove Avenue
Hulme
Manchester
M15 5EH
UK Furthering Humanity: A Theology of Culture by Timothy Gorringe (Burlington, Vermont: Ashgate, 2004) vi + 283 pp.
Reviewed by J. Matthew Ashley
Department of Theology
University of Notre Dame
Notre Dame, IN 46556
USA Flannery O’Connor and the Christ‐Haunted South by Ralph C. Wood (Grand Rapids, Michigan: Wm. B. Eerdmans Publishing Company, 2004) xii + 272 pp.
Reviewed by Frederick C. Bauerschmidt
Department of Theology
Loyola College
4501 N. Charles Street
Baltimore, MD 21210
USA     

Towards a New Epistemology of Mathematics

In this introduction we discuss the motivation behind the workshop “Towards a New Epistemology of Mathematics” of which this special issue constitutes the proceedings. We elaborate on historical and empirical aspects of the desired new epistemology, connect it to the public image of mathematics, and give a summary and an introduction to the contributions to this issue.

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The adequacy of the theories of deductive systems with respect to sentential calculi

Summary The sentential calculiR, under discussion, are axiomatizable and implication is among their primitive terms. The modus ponens and the rule of substitution are their primitive rules. ByS _r is denoted the set of sentences obtained from the formulae of the calculusR by substituting sentences of a given language for all variables. The variablesx, y, z ... represent the elements of the setS _r , the variablesX, Y, Z ... represent the subsets ofS _R . The formulacxy designates an implication withx as its antecedent andy as its consequent,cxy is always an element ofS _R δ(X) means, thatX is closed with respect to the modus ponens rule.A _R designates the class of allS _R -substitutions of the axioms of the sentential calculusR.     

The Effect of CS Administration or an R-Optimized Alternative on R–PAS Variables: A Meta-Analysis of Findings From Six Studies

Controlling the number of Rorschach responses (R) as a method to reduce variability in the length of records has stimulated controversy among researchers for many years. Recently, the Rorschach Performance Assessment System (R–PAS; Meyer, Viglione, Mihura, Erard, &; Erdberg, 2011 Meyer, G. J., Viglione, D. J., Mihura, J. L., Erard, R. E., &; Erdberg, P. (2011). Rorschach Performance Assessment System: Administration, coding, interpretation, and technical manual. Toledo, OH: Rorschach Performance Assessment System. [Google Scholar]) introduced an R-Optimized method to reduce variability in R. Using 4 published and 2 previously unpublished studies (N = 713), we examine the extent to which 51 Comprehensive System–based scores on the R–PAS profile pages are affected as a result of receiving Comprehensive System (CS; Exner, 2003 Exner, J. E. (2003). The Rorschach: A Comprehensive System. Vol. 1. Basic foundations (4th ed.). Hoboken, NJ: Wiley. [Google Scholar]) administration versus a version of R-Optimized administration. As hypothesized, R—the intended target of R-Optimized administration—showed reliable weighted average differences across each method of administration. As expected, its mean modestly increased and its standard deviation notably decreased. Also as hypothesized, the next largest effects were decreases in the variability (SD) of 2 variables directly related to R, R8910% and Complexity. No other reliable differences were observed. Therefore, because R-Optimized administration does not notably modify the existing CS-based normative values for other profiled R–PAS variables, the data do not support concerns that R-Optimized administration notably modifies the Rorschach task or that existing CS research data would not generalize to R–PAS. However, because R-Optimized administration reduces variability in R, it allows a single set of norms to apply readily to more people.     

Die Möglichkeit einer objektiven Messung der Stärke von Gefühlen

Zusammenfassung Es war das Ziel, ein Maß für die Stärke von Gefühlen aus einem ihrer physischen Korrelate, der sog. psychogalvanischen Reaktion, zu gewinnen. Zu diesem Zweck wurden Vergleichsurteile über die Gefühlsbetonung von Reizwortpaaren den durch die Darbietung der Wörter ausgelösten Hautreaktionen zugeordnet. Mit den Maßzahlen wurden eine logarithmische Transformation und eine Quadratwurzeltransformation vorgenommen. Die Auswertung erfolgte jeweils gemäß dem Skalierungsverfahren für Vergleichsurteile. Es zeigte sich, daß die auf Grund der Quadratwurzeltransformation erhaltenen Skalenwerte für die Gefühlsstärke in voll befriedigender Weise durch eine Gerade angenähert werden können, während dies mit der logarithmischen Transformation weniger gut gelingt.Um aus der gefundenen Intervallskala der Gefühlsstärke eine Verhältnisskala zu erhalten, wurde die Gefühlsschwelle der galvanischen Hautreaktion zu bestimmen versucht. Es ergab sich, daß der Schwellenwert der emotionalen Veränderung bei der Größe 0 der Hautwiderstandsänderung liegt. Es folgt daraus, daß die Stärke eines Gefühls als der Quadratwurzel der relativen Widerstandsänderung proportional anzunehmen ist.Dieses Ergebnis wird durch ein Anwendungsbeispiel veranschaulicht.     

Maximum likelihood estimation of the joint covariance matrix for sections of tests given to distinct samples with application to test equating

Consider an old testX consisting ofs sections and two new testsY andZ similar toX consisting ofp andq sections respectively. All subjects are given testX plus two variable sections from either testY orZ. Different pairings of variable sections are given to each subsample of subjects. We present a method of estimating the covariance matrix of the combined test (X ₁, ...,X _s ,Y ₁, ...,Y _p ,Z ₁, ...,Z _q ) and describe an application of these estimation techniques to linear, observed-score, test equating.The author is indebted to Paul W. Holland and Donald B. Rubin for their encouragement and many helpful comments and suggestions that contributed significantly to the development of this paper.This research was supported by the Program Statistics Research Project of the ETS Research Statistics Group.