Aristotle on Universal Quantification: A Study from the Point of View of Game Semantics

In this paper we provide an interpretation of Aristotle's rule for the universal quantifier in Topics Θ 157^a34–37 and 160^b1–6 in terms of Paul Lorenzen's dialogical logic. This is meant as a contribution to the rehabilitation of the role of dialectic within the Organon. After a review of earlier views of Aristotle on quantification, we argue that this rule is related to the dictum de omni in Prior Analytics A 24^b28–29. This would be an indication of the dictum’s origin in the context of dialectical games. One consequence of our approach is a novel explanation of the doctrine of the existential import of the quantifiers in dialectical terms. After a brief survey of Lorenzen's dialogical logic, we offer a set of rules for dialectical games based on previous work by Castelnérac and Marion, to which we add here the rule for the universal quantifier, as interpreted in terms of its counterpart in dialogical logic. We then give textual evidence of the use of that rule in Plato's dialogues, thus showing that Aristotle only made explicit a rule already implicit in practice, while providing a new interpretation of ‘epagogic’ arguments. Finally, we show how a proper understanding of that rule involves further rules concerning counterexamples and delaying tactics, stressing again the parallels with dialogical logic.     

The flow stress contribution of the dislocation 'forest' in bcc lattices

The athermal flow stress contribution by junction reactions of a glide dislocation with a 'forest' of density rho is usually written as tau = alpha mu b rho ^1/2. The strength coefficient alpha has been computed for the bcc lattice by virtual displacement of triple nodes following the method of Puschl et al. (1982, Physica status solidi (a), 74, 211). In the isotropic approximation, the values for glide dislocations with 0, 30, 60 and 90^o character are as alpha = 0.18, 0.21, 0.19 and 0.22 respectively. A comparison with values calculated previously by Frydman is made, and good agreement is found when differences in the cut-off radii of the linear elastic solution are accounted for.     

Assessing Approximate Fit in Categorical Data Analysis

A family of Root Mean Square Error of Approximation (RMSEA) statistics is proposed for assessing the goodness of approximation in discrete multivariate analysis with applications to item response theory (IRT) models. The family includes RMSEAs to assess the approximation up to any level of association of the discrete variables. Two members of this family are RMSEA₂, which uses up to bivariate moments, and the full information RMSEA_n. The RMSEA₂ is estimated using the M₂ statistic of Maydeu-Olivares and Joe (2005, 2006), whereas for maximum likelihood estimation, RMSEA_n is estimated using Pearson's X² statistic. Using IRT models, we provide cutoff criteria of adequate, good, and excellent fit using the RMSEA₂. When the data are ordinal, we find a strong linear relationship between the RMSEA₂ and the Standardized Root Mean Squared Residual goodness-of-fit index. We are unable to offer cutoff criteria for the RMSEA_n as its population values decrease as the number of variables and categories increase.     

Quantification Theory in *8 of Principia Mathematica and the Empty Domain

The second printing of Principia Mathematica in 1925 offered Russell an occasion to assess some criticisms of the Principia and make some suggestions for possible improvements. In Appendix A, Russell offered *8 as a new quantification theory to replace *9 of the original text. As Russell explained in the new introduction to the second edition, the system of *8 sets out quantification theory without free variables. Unfortunately, the system has not been well understood. This paper shows that Russell successfully antedates Quine's system of quantification theory without free variables. It is shown as well, that as with Quine's system, a slight modification yields a quantification theory inclusive of the empty domain.     

Generating interior search directions for multiobjective linear programming

A new multiobjective linear programming (MOLP) algorithm is presented. The algorithm uses a variant of Karmarkar's interior-point algorithm known as the affine-scaling primal algorithm. Using this single-objective algorithm, interior search directions are generated and used to provide an approximation to the gradient of the (implicitly known) utility function. The approximation is guided by assessing locally relevant preference information for the various interior directions through interaction with a decision maker (DM). The resulting algorithm is an interactive approach that makes its progress towards the solution through the interior of the constraints polytope.     

QUASI‐NATURALISM AND MORAL REALITY

In his recent book Moral Reality, Paul Bloomfield has put forward an original set of arguments for moral realism. Central to his treatment is an argument for the reality of moral properties, one which models them on the property of being healthy. The paper is a critical examination of Bloomfield's central line of argument. It is contended that his proposed method of grounding moral realism fails, inasmuch as his Distinction Test criterion for property reality – essentially the claim that a property exists if its existence is required for distinctions that we make and must make – is inadequate. An alternative approach toward properties is suggested, which has the result, inter alia, that Bloomfield's quasi‐naturalistic approach is unnecessary for the defense of moral realism.¹     

Locating the Extrema of Fungible Regression Weights

In a multiple regression analysis with three or more predictors, every set of alternate weights belongs to an infinite class of “fungible weights” (Waller, Psychometrica, in press) that yields identical SSE (sum of squared errors) and R ² values. When the R ² using the alternate weights is a fixed value, fungible weights (a _i ) that yield the maximum or minimum cosine with an OLS weight vector (b) are called “fungible extrema.” We describe two methods for locating fungible extrema and we report R code (R Development Core Team, 2007) for one of the methods. We then describe a new approach for populating a class of fungible weights that is derived from the geometry of alternate regression weights. Finally, we illustrate how fungible weights can be profitably used to gauge parameter sensitivity in linear models by locating the fungible extrema of a regression model of executive compensation (Horton & Guerard, Commun. Stat. Simul. Comput. 14:441–448, 1985).     

Least-squares theory based on general distributional assumptions with an application to the incomplete observations problem

The linear regression modely=x+ is reanalyzed. Taking the modest position that x is an approximation of the best predictor ofy we derive the asymptotic distribution ofb andR ², under mild assumptions.The method of derivation yields an easy answer to the estimation of from a data set which contains incomplete observations, where the incompleteness is random.     

Estimation of the hypothesis hierarchy in probabilistic inference tasks*

Is there a hierarchical order among the hypotheses about functional rules in probabilistic inference tasks, i.e. what is the construction and the procedure of the “hypothesis sampling mechanism” employed by the subjects in this kind of task? According to the hypothesis sampling model initially proposed by Brehmer (1974) there should be a hierarchical order among the hypotheses in the subject's hypothesis pools. The procedures of hypothesis sampling and testing ought to follow this strict data independent order (see e.g. Sniezek, 1986; Brehmer, 1987). Knez (1991a, b) showed, however, that this assumption may be incorrect. As a follow up to these results the question regarding the construction of the subject's hypothesis pools was reapproached in the present study. The results indicated a consistency with the hierarchical assumption (Brehmer, 1974) only regarding the relation between the linear and nonlinear rules but not within these types of rules.     

The relationship between non-symbolic multiplication and division in childhood

Children without formal education in addition and subtraction are able to perform multi-step operations over an approximate number of objects. Further, their performance improves when solving approximate (but not exact) addition and subtraction problems that allow for inversion as a shortcut (e.g., a?+?b???b?=?a). The current study examines children's ability to perform multi-step operations, and the potential for an inversion benefit, for the operations of approximate, non-symbolic multiplication and division. Children were trained to compute a multiplication and division scaling factor (*2 or /2, *4 or /4), and were then tested on problems that combined two of these factors in a way that either allowed for an inversion shortcut (e.g., 8*4/4) or did not (e.g., 8*4/2). Children's performance was significantly better than chance for all scaling factors during training, and they successfully computed the outcomes of the multi-step testing problems. They did not exhibit a performance benefit for problems with the a*b/b structure, suggesting that they did not draw upon inversion reasoning as a logical shortcut to help them solve the multi-step test problems.     

Police Suicides Revisited

ABSTRACT: Between January 1, 1934 and January 1, 1940, 91 New York City policemen committed suicide. Dr. Paul Friedman, in the only previously published account describing this special group, speculated that the high suicide rate for those years was due, in part, to the turbulence caused by changes in New York City's political administration attendant to Tammany Hall's fall from political hegemony as a result of the 1933 election of Fiorello H. La Guardia. The purpose of this paper is to reexamine the original police files and case histories, now residing in the Zilboorg-Friedman Archives, and to offer new comments and speculations concerning these police suicides. Involved in this examination will be (a) the use of the “psychological autopsy” in assessing several equivocal deaths; (b) the use of statistical techniques to analyze both previously unpublished archival material and recently acquired police suicide data from other cities in America and England; and (c) a discussion of the impact of Tammany Hall politics on the police department, including an assessment of the effects of the La Guardia election in 1933.     

Leaders as eponyms: Individual and situational determinants of ruler eminence

The eponymic theory of leadership maintains that the eminence of rulers depends on their utility as historical labels without regard for their personal attributes. The explanatory scope of this interpretation was tested, for methodological reasons, on a sample of 342 European hereditary monarchs. In support of eponymic theory: (a) About two-thirds of the variance in leader eminence can be ascribed to the number of significant events occurring during the leader's tenure in office; (b) events with positive and negative social valence carry approximately equal and positive weight; (c) events over which the leader exerts considerable control have about the same weight as those over which personal control is virtually nonexistent; and (d) the effects of epochcentric bias and reign span are mediated by the number of significant events. But qualifying eponymic theory: (a) Eminence is not determined solely by the event tabulations (e.g., leader frame is a J-curve function of intelligence and a U-curve function of morality); (b) the number of events is not exclusively accounted for by reign span; and (c) reign span is not solely a function of life span (e.g., reign span is a positive linear function of assessed leadership). The results endorse a form of the theory in which some provision is made for intellectual and personality factors.     

The Trapezoidal Illusion as a Function of Age,Intellectual Status,Size Constancy,and Form Discrimination

One hundred twenty-two, middle-class white boys and girls aged 3 through 12 years were interviewed to determine the nature and the development of their concepts of death and the impact of experience on those concepts.

Five conclusions were drawn from the results of this inquiry: (a) children's concepts of death were found to be constituted of components which were suggested prior to the study; (b) children's understanding of each of the components developed from absence to incomplete presence to complete presence; (c) children's concepts of death developed as a function of age maturity; (d) children's experiences with death accelerated death concept development only in 6-year-olds and below; and (e) children's concepts of death developed in three stages clearly related to the preoperational, concrete operations, and formal operations stages suggested by Piaget. In contrast with Nagy's results, children did not reify death; furthermore, children 8-years-old and above were consistent in showing adult ideas of death.     

Parental Apologies,Empathy, Shame,Guilt, and Attachment: A Path Analysis

The authors investigated the complex relationships of parental attitudes toward apologies, empathy, shame, guilt, and the parent's attachment orientation. Survey responses were obtained from 327 parents. A path analysis of the developed model demonstrated a close model fit (root‐mean‐square error of approximation = .07; comparative fit index = .93; incremental fit index = .94; χ² = 30.71, p < .001), supporting previous research on apologies as beneficial to relationships. A parent's proclivity toward apologies, positively influenced by empathy and guilt and negatively influenced by shame‐withdraw behaviors, produced a more secure parent–child attachment.     

A new goodness-of-fit measure for probit models: Surrogate R2

Probit models are used extensively for inferential purposes in the social sciences as discrete data are prevalent in a vast body of social studies. Among many accompanying model inference problems, a critical question remains unsettled: how to develop a goodness-of-fit measure that resembles the ordinary least square (OLS) R² used for linear models. Such a measure has long been sought to achieve ‘comparability’ of different empirical models across multiple samples addressing similar social questions. To this end, we propose a novel R² measure for probit models using the notion of surrogacy – simulating a continuous variable $S$ as a surrogate of the original discrete response (Liu & Zhang, Journal of the American Statistical Association, 113, 845 and 2018). The proposed R² is the proportion of the variance of the surrogate response explained by explanatory variables through a linear model, and we call it a surrogate R². This paper shows both theoretically and numerically that the surrogate R² approximates the OLS R² based on the latent continuous variable, preserves the interpretation of explained variation, and maintains monotonicity between nested models. As no other pseudo R², McKelvey and Zavoina's and McFadden's included, can meet all the three criteria simultaneously, our measure fills this crucial void in probit model inference.