Informative Aboutness

Pretheoretically, (B) ‘all believers are immortal’ is about all believers, but (1) B is not about any unbeliever. Similarly, (M) ‘all mortals are unbelievers’ is not about any immortal, but (2) M is about all mortals. But B and M are logically equivalent universal generalizations, so arguably they are about exactly the same objects; by (2), they are about those mortals who are unbelievers, contradicting (1). If one responds by giving up (1), is there still a sense in which B treats unbelievers differently from believers? I argue that there is. B is uninformative about unbelievers but informative about believers, in the following sense: for any object o, the information that B provides only about o—namely, ‘o is a believer only if o is immortal’—is entailed (and thus rendered redundant) by ‘o is an unbeliever’ but not by ‘o is a believer’.     

Equating test scores—A maximum likelihood solution

Certain problems of equating are discussed. The maximum likelihood solution is presented for the following special equating problem: Two tests,U andV, are to be equated, making use of a third anchor test,W. The examinees are divided into two random halves. TestsU andW are administered to one half; testsV andW are administered to the other half. It is assumed that any practice effect or other effect, exerted byU andV onW, is the same forU and forV.     

Improved Fisher z estimators for univariate random‐effects meta‐analysis of correlations

Several authors have studied or used the following estimation strategy for meta‐analysing correlations: obtain a point estimate or confidence interval for the mean Fisher z correlation, and transform this estimate to the Pearson r metric. Using the relationship between Fisher z and Pearson r random variables, I demonstrate the potential discrepancy induced by directly z‐to‐r transforming a mean correlation parameter. Point and interval estimators based on an alternative integral z‐to‐r transformation are proposed. Analytic expressions for the expectation and variance of certain meta‐analytic point estimators are also provided, as are selected moments of correlation parameters; numerical examples are included. In an application of these analytic results, the proposed point estimator outperformed its usual direct z‐to‐r counterpart and compared favourably with an estimator based on Pearson r correlations. Practical implications, extensions of the proposed estimators, and uses for the analytic results are discussed.     

Restricted ranking

This paper is a study of certain aspects of restricted ranking, a method intended for use by a panel ofm judges evaluating the relative merits ofN subjects, candidates for scholarships, awards, etc. Each judge divides theN subjects intoR classes so thatn _i individuals receive a gradei (i = 1, 2, ...,R; Σn _i =N) where theR numbersn _i are close toN/R (n _i =N/R whenN is divisible byR) and are preassigned and the same for all judges. This method is superior in several respects to other likely alternatives. Under the null hypothesis that allnR =N subjects are of equal merit, four tests of significance are developed. The effectiveness of the method is investigated both theoretically by means of the asymptotic relative efficiency and more generally by simulation studies. When the numbersn _i are not restricted to values close to or equal toN/R but instead are given values conforming to a normally distributed pattern, the resulting method is known as theQ-sort, so designated by certain investigators in psychotherapy. The simulation studies reveal that restricted ranking is only slightly inferior to complete ranking and generally superior in the cases considered to theQ-sort, although there are likely to be other situations when the latter is superior. The authors are indebted to Dr. Clyde Kramer of Virginia Polytechnic Institute for bringing theQ-sort ranking technique of psychotherapy to their attention.     

Estimation ofJ scales for unidimensional unfolding

In Coombs' unidimensional unfolding theory each individual ranks all stimuli, often in terms of preference judgments. These ranks, calledI scales, are used to infer the latent continuum called aJ scale which is presumed to have generated theI scale rankings. A major problem concerns the inference of theJ scale given a set ofI scales because anI scale is not unique to any oneJ scale. This paper presents a procedure for estimatingJ scale probabilities given a set ofI scales. Models for three and four or more stimuli are presented. Results of computer tests are reported.     

Categorical Abstract Algebraic Logic: Prealgebraicity and Protoalgebraicity

Two classes of π are studied whose properties are similar to those of the protoalgebraic deductive systems of Blok and Pigozzi. The first is the class of N-protoalgebraic π-institutions and the second is the wider class of N-prealgebraic π-institutions. Several characterizations are provided. For instance, N-prealgebraic π-institutions are exactly those π-institutions that satisfy monotonicity of the N-Leibniz operator on theory systems and N-protoalgebraic π-institutions those that satisfy monotonicity of the N-Leibniz operator on theory families. Analogs of the correspondence property of Blok and Pigozzi for π-institutions are also introduced and their connections with preand protoalgebraicity are explored. Finally, relations of these two classes with the (, N)-algebraic systems, introduced previously by the author as an analog of the -algebras of Font and Jansana, and with an analog of the Suszko operator of Czelakowski for π-institutions are also investigated. Presented by Josep Maria Font     

There are Intentionalia of Which it is True that Such Objects Do Not Exist

Abstract

According to Crane’s schematicity thesis (ST) about intentional objects, intentionalia have no particular metaphysical nature qua thought-of entities; moreover, the real metaphysical nature of intentionalia is various, insofar as it is settled independently of the fact that intentionalia are targets of one’s thought. As I will point out, ST has the ontological consequence that the intentionalia that really belong to the general inventory of what there is, the overall domain, are those that fall under a good metaphysical kind, i.e., a kind such that its members figure (for independent reasons) in such an inventory. Negatively put, if there are no things of a certain metaphysical kind, thoughts about things of that kind are not really committed to such things. Pace Crane, however, this does not mean that the intentionalia that are really there are only those that exist. For existence, qua first-order property, is no metaphysical kind. Thus, there may really be intentionalia that do not exist, provided that they belong to good metaphysical kinds.     

A model and algorithm for multidimensional scaling with external constraints on the distances

A method for externally constraining certain distances in multidimensional scaling configurations is introduced and illustrated. The approach defines an objective function which is a linear composite of the loss function of the point configurationX relative to the proximity dataP and the loss ofX relative to a pseudo-data matrixR. The matrixR is set up such that the side constraints to be imposed onX's distances are expressed by the relations amongR's numerical elements. One then uses a double-phase procedure with relative penalties on the loss components to generate a constrained solutionX. Various possibilities for constructing actual MDS algorithms are conceivable: the major classes are defined by the specification of metric or nonmetric loss for data and/or constraints, and by the various possibilities for partitioning the matricesP andR. Further generalizations are introduced by substitutingR by a set ofR matrices,R _i ,i=1, ...r, which opens the way for formulating overlapping constraints as, e.g., in patterns that are both row- and column-conditional at the same time.     

No Future

The difficulties with formalizing the intensional notions necessity, knowability and omniscience, and rational belief are well-known. If these notions are formalized as predicates applying to (codes of) sentences, then from apparently weak and uncontroversial logical principles governing these notions, outright contradictions can be derived. Tense logic is one of the best understood and most extensively developed branches of intensional logic. In tense logic, the temporal notions future and past are formalized as sentential operators rather than as predicates. The question therefore arises whether the notions that are investigated in tense logic can be consistently formalized as predicates. In this paper it is shown that the answer to this question is negative. The logical treatment of the notions of future and past as predicates gives rise to paradoxes due the specific interplay between both notions. For this reason, the tense paradoxes that will be presented are not identical to the paradoxes referred to above.     

What is Epistemological Violence in the Empirical Social Sciences?

This article discusses the meaning of epistemological violence in the empirical social sciences. It is argued that the concept is closer to personal than to structural violence in that it has a subject, an object, and an action, even if the violence is indirect and nonphysical: the subject of violence is the researcher, the object is the Other, and the action is the interpretation of data that is presented as knowledge. Using a hypothetical example, the problem of interpretation in empirical research on the Other is discussed. Epistemological violence refers to the interpretation of social-scientific data on the Other and is produced when empirical data are interpreted as showing the inferiority of or problematizes the Other, even when data allow for equally viable alternative interpretations. Interpretations of inferiority or problematizations are understood as actions that have a negative impact on the Other. Because the interpretations of data emerge from an academic context and thus are presented as knowledge, they are defined as epistemologically violent actions. Problems, consequences, and practices surrounding this concept are discussed.     

Transitions of Athletes: Developmental and Preventive Perspectives

Common anticipated and unanticipated transitions faced by athletes are examined from the perspectives of developmental psychology and a model of adult transitions developed by Nancy Schlossberg. Factors contributing to dysfunctional response to transitions associated with athletic careers are identified and discussed. Preventive strategies, targeting athletes at risk of experiencing dysfunctionality in such transitions, are examined, and illustrative programs described.     

The mental representation of causal conditional reasoning: mental models or causal models

In this paper, two experiments are reported investigating the nature of the cognitive representations underlying causal conditional reasoning performance. The predictions of causal and logical interpretations of the conditional diverge sharply when inferences involving pairs of conditionals—such as if P₁then Q and if P₂then Q—are considered. From a causal perspective, the causal direction of these conditionals is critical: are the P_icauses of Q; or symptoms caused byQ. The rich variety of inference patterns can naturally be modelled by Bayesian networks. A pair of causal conditionals where Q is an effect corresponds to a “collider” structure where the two causes (P_i) converge on a common effect. In contrast, a pair of causal conditionals where Q is a cause corresponds to a network where two effects (P_i) diverge from a common cause. Very different predictions are made by fully explicit or initial mental models interpretations. These predictions were tested in two experiments, each of which yielded data most consistent with causal model theory, rather than with mental models.     

Some necessary conditions for common-factor analysis

LetR be any correlation matrix of ordern, with unity as each main diagonal element. Common-factor analysis, in the Spearman-Thurstone sense, seeks a diagonal matrixU ² such thatG = R – U ² is Gramian and of minimum rankr. Lets ₁ be the number of latent roots ofR which are greater than or equal to unity. Then it is proved here thatr s ₁. Two further lower bounds tor are also established that are better thans ₁. Simple computing procedures are shown for all three lower bounds that avoid any calculations of latent roots. It is proved further that there are many cases where the rank of all diagonal-free submatrices inR is small, but the minimum rankr for a GramianG is nevertheless very large compared withn. Heuristic criteria are given for testing the hypothesis that a finiter exists for the infinite universe of content from which the sample ofn observed variables is selected; in many cases, the Spearman-Thurstone type of multiple common-factor structure cannot hold.This research was made possible in part by an uncommitted grant-in-aid from the Behavioral Sciences Division of the Ford Foundation.     

A maximum likelihood approach to test validation with missing and censored dependent variables

A maximum likelihood approach is described for estimating the validity of a test (x) as a predictor of a criterion variable (y) when there are both missing and censoredy scores present in the data set. The missing data are due to selection on a latent variable (y _s ) which may be conditionally related toy givenx. Thus, the missing data may not be missing random. The censoring process in due to the presence of a floor or ceiling effect. The maximum likelihood estimates are constructed using the EM algorithm. The entire analysis is demonstrated in terms of hypothetical data sets.     

Omniscience and worthiness of worship

At first glance, the properties being omniscient and being worthy of worship might appear to be perfectly co-instantiable. (To say that some properties are co-instantiable is just to say that it is possible that some object instantiate all of them simultaneously. Being entirely red and being a ball are co-instantiable; being entirely red and being entirely blue are not). But there are reasons to be worried about this co-instantiability, as it turns out that, depending on our commitments with respect to certain kinds of knowledge and notions of personhood, it might be the case that no being—God included—could instantiate both. In this paper, I lay out and motivate this claim before going on to consider a variety of responses—some more plausible than others—that may be offered by the theist.     

A geometrical analysis of the unfolding model: General solutions

Given the complete setR of rank orders obtained from any configuration ofn stimulus points inr dimensions in accordance with the unfolding model, a configuration from which just these orders may be derived will be described as a solution forR. The space is assumed to be Euclidean. Necessary and sufficient conditions are derived for a configuration to be a solution forR. The geometrical constraints which are necessary and sufficient to determine the subset of pairs of orders and opposites contained inR are also identified and constitute the constraint system for the ordinal vector model. The relationship between the two models is discussed.     

Estimation of other coefficients of correlation from the phi coefficient

Formulas are developed for estimating a point-biserialr or a tetrachoricr from an obtained phi coefficient. The estimate of a tetrachoricr, which is calledr _φ, is shown to be equivalent to that obtained from first-order use of the tetrachoricr series. A tabulation is made of corrections needed to maker _φ equivalent numerically to the tetrachoricr. In spite of its greater generality than estimates of tetrachoricr by previous methods, there are limitations, which are pointed out.     

K‐means clustering: A half‐century synthesis

This paper synthesizes the results, methodology, and research conducted concerning the K‐means clustering method over the last fifty years. The K‐means method is first introduced, various formulations of the minimum variance loss function and alternative loss functions within the same class are outlined, and different methods of choosing the number of clusters and initialization, variable preprocessing, and data reduction schemes are discussed. Theoretic statistical results are provided and various extensions of K‐means using different metrics or modifications of the original algorithm are given, leading to a unifying treatment of K‐means and some of its extensions. Finally, several future studies are outlined that could enhance the understanding of numerous subtleties affecting the performance of the K‐means method.     

Magnetic properties of Mn-doped armchair ZnO nanotubes: a Monte Carlo study

The magnetic properties of a Mn-doped armchair ZnO nanotube have been studied using Monte Carlo simulation. The variation of zero-field-cooled and field-cooled magnetisation with reduced temperatures for different values of the dilution x (where x is the Mn concentration: Zn_1?xMn_xO) are given. The freezing temperatures and magnetisation vs. crystal field are calculated for different dilutions x. Finally, the hysteresis loops for different dilutions and temperatures are given for a fixed reduced temperature and crystal field. Superparamagnetic behaviour is observed for small values of x and low temperatures.     

A perceptual account of definitions

The traditional definition per genus et differentiam is argued to be cognitively grounded in perception and in order to avoid needless argument, definitions are stipulated to assert boundaries. An analysis of the notion of perspective shows that a boundary is a composite of two distinctions: similarity that includes and difference that excludes. The concept is applied to the type-token distinction and percepts are shown to be the result of a comparison between a token as representing some phenomenon and a type as representing the kind of object the phenomenon might be. The Principle of Connection is proposed as the mental architecture that gives rise to percepts. The value of a percept is shown to be one of Identical, Similar, Different or Contrary and its perceptual aspects represent the cognitive schema of Essence, Quality, Quantity and Relation. The two notions of similarity and difference are claimed to constitute the necessary and sufficient conditions for definitions. Accordingly, the qualitative elements of a definition signify the genus as representing the similarity of the defined entity in terms of others of its kind and the quantitative elements signify the differentia as representing the difference it has from everything else. Paying proper attention to both qualitative and quantitative aspects will enable formulation of definitions that are ‘good’. This paper is based on my master’s thesis at Monash University (2003). I thank Keith Allan for commenting on an earlier draft—any remaining infelicities are mine only.