A simple proof of a personnel classification theorem

A simple algebraic proof of a theorem defining the optimal solution to the personnel classification problem is given. If a set of constants, one for each job, are known, the theorem indicates that each individual should be classified by adding the constants to the estimates of the individual's productivity in the several jobs and selecting the job for which the resulting sum is highest. The opinions expressed are those of the author and are not to be construed as reflecting official Department of the Army policy.     

On the proof of Solovay's theorem

Solovay's 1976 completeness result for modal provability logic employs the recursion theorem in its proof. It is shown that the uses of the recursion theorem can in this proof be replaced by the diagonalization lemma for arithmetic and that, in effect, the proof neatly fits the framework of another, enriched, system of modal logic (the so-called Rosser logic of Gauspari-Solovay, 1979) so that any arithmetical system for which this logic is sound is strong enough to carry out the proof, in particular I₀+EXP. The method is adapted to obtain a similar completeness result for the Rosser logic.     

A short proof of a theorem of Falmagne

Falmagne (J. Math. Psychol. 18 (1978) 52) proved the sufficiency of the Block-Marschak inequalities (in: I. Olkin, S. Ghurye, W. Hoefding, W. Madow, H. Mann (Eds.), Contributions to Probability and Statistics, Stanford University Press, Stanford, CA, 1960, pp. 97-132) and normalization equalities for a complete system of choice probabilities to be induced by rankings. Here, we give a considerably shorter proof of this result. Our approach combines Möbius inversion and network flows.     

The role of the head in configural body processing: Behavioural and electrophysiological evidence from the inversion and scrambling effect

The present study aimed to further explore the role of the head for configural body processing by comparing complete bodies with headless bodies and faceless heads (Experiment 1). A second aim was to further explore the role of the eye region in configural face processing (Experiment 2). Due to that, we conducted a second experiment with complete faces, eyeless faces, and eyes. In addition, we used two effects to manipulate configural processing: the effect of stimulus inversion and scrambling. The current data clearly show an inversion effect for intact bodies presented with head and faces including the eye region. Thus, the head and the eye region seem to be central for configural processes that are manipulated by the effect of stimulus inversion. Furthermore, the behavioural and electrophysiological body inversion effect depends on the intact configuration of bodies and is associated with the N170 as the face inversion effect depends on the intact face configuration. Hence, configural body processing depends not only on the presence of the head but rather on a complete representation of human bodies that includes the body and the head. Furthermore, configural face processing relies on intact and complete face representations that include faces and eyes.     

Color adaptation in a yellow-blue system: proof of a simple numerical relationship]

Three axes in color space are specified: a (unique) yellow - (unique) blue axis, a (unique) green - magenta axis and brightness. Based on the two chromatic axes two linear opponent colors systems are defined: a red/green-system and a yellowish/bluish-system. A numerical relation is presented to describe color adaptation for the yellowish/bluish-system under adaptation to (unique) yellow and (unique) blue: two pairs of color stimuli are equivalent with regard to the yellowish/bluish-system - consisting of a test stimulus and an adaptation stimulus, respectively - if the ratios from the yellowish/bluish-coordinates of test stimulus and adaptation stimulus are identical. A control of brightness and the red/green-system is presupposed. For several (unique) yellow and (unique) blue adaptation stimuli it is examined how a test stimulus that appears neither yellowish nor bluish changes its location on the (unique) yellow - (unique) blue axis within color space. Three observers take part in the experiment. For each observer a plane of constant brightness and the opponent colors axes are estimated experimentally. The data show that the ratios from the yellowish/bluish coordinates of test stimulus and adaptation stimulus are essentially constant. The results are compared with analogous data for the red/green-system. The findings provide evidence for the specification of the three phenomenal axes. The specification is discussed with regard to Hering's opponent colors theory and Krauskopf's three "cardinal" axes [1982, Vision Research, 22, 1123-1131].     

The threat of logical inversion and our need for philosophical attention: from thought-expression to discourse and discussion

Thought-expressions are not simply good; instead, they become good for us when they make sense, empower action, and support health. From time to time, we may need to (re)consider the difference between thought-expression and discourse, or thought-expression that really makes sense, and the difference between discourse and discussion, or a discourse-situation that makes genuine agreement or disagreement possible for us. In this essay, I explore a problem that D. Z. Phillips and Randy Ramal have termed “logical inversion,” and I argue that wherever logical inversions have gained a foothold in our thought-expressions, they threaten to render us incapable of authentic discourse and discussion by ensuring that we misunderstand the understandings of others such that we deceive ourselves and others by picturing the knowledge and truth of our perspective against an unreal background of conceivable falsehoods which we have falsely attributed to the perspectives of others. Where this has taken place, practices of philosophical attention and conceptual clarification are needed to help us move from a situation of endless thought expression toward authentic discourse and discussion.     

A note on an alternative proof of the representation theorem for bi-semiorder

In a paper written by J. C. Falmagne and the author a representation theorem for what was called a bi-semiorder was given. A quite different proof of this theorem is given here based on Scott's linear technique. This new proof is somewhat simpler than the first one and has the advantage to be an application of a general method well known in measurement theory.     

The analyst's narrative function: Inventing a possibility

This article describes a psychic function common to analysts that was gradually revealed through clinical work with children. It is a psychic quality derived from function α, which involves analysts’ capacity for reverie – their narrative function. The author presents two clinical situations where this function developed in the analytic field in relation to patients’ difficulty in symbolizing. In the first case there was an early traumatic experience unavailable for representation. The analyst lent the patient her ability to represent and produced a narrative that made it possible to create a world of phantasies and transform nightmares into ‘dreamable’ dreams. In other words, she removed the quality of unbearable, irrepresentable reality that characterized those raw experiences encrypted in the psyche. In the second case the analyst's narrative function sought to connect with the isolation, the shell that housed a child suffering from an autistic disorder whose ability to represent had not been established. The analyst provided meaning for the patient's repetitive, stereotyped play, thus weaving the child's subjectivity and gradually introducing a notion of alterity. The author seeks to show how this function, in the thematic construction of the session, facilitated both the working‐through of a traumatic situation (with the ability to share representations) and the constitution of the psychic fabric.     

A simple proof of the spearman-brown formula for continuous test lengths

A direct proof is given for the generalized Spearman-Brown formula for any real multiple of test length.