The doctrine of distribution

Peter Geach describes the ‘doctrine of distribution’ as the view that a term is distributed if it refers to everything that it denotes, and undistributed if it refers to only some of the things that it denotes. He argues that the notion, so explained, is incoherent. He claims that the doctrine of distribution originates from a degenerate use of the notion of ‘distributive supposition’ in medieval supposition theory sometime in the 16th century. This paper proposes instead that the doctrine of distribution occurs at least as early as the 12th century, and that it originates from a study of Aristotle's notion of a term's being ‘taken universally’, and not from the much later theory of distributive supposition. A detailed version of the doctrine found in the Port Royal Logic is articulated, and compared with a slightly different modern version. Finally, Geach's arguments for the incoherence of the doctrine are discussed and rejected.     

The distribution of information within letters

To study the relative importance of various letter segments for letter recognition, we presented each letter of two alphabets, English and Hebrew, preceded by a brief presentation of an intact or a mutilated version of it. Mutilations were done by eliminating a specific segment. It was reasoned that the more critical the eliminated segment is, the less the mutilated version activates the letter code in memory and, thus, the longer it takes to name the subsequently presented target letter. This procedure was successful in detecting significant differences consistent with our expectations. In further analysis, it was shown that the latency data were highly correlated with the distinctiveness of the mutilated segment, its uniqueness over the alphabet, its impact on the letter global shape, and its topography within the letter and other variables. The dependency of latency on the various factors varied considerably between alphabets. Some correlational analyses were done to evaluate the roles of the various factors.     

The distribution of early childhood memories

The quantitative distribution of autobiographical memories for the first decade of life is described. The distribution, based on over 11,000 autobiographical memories from age 10 and younger from published studies, is nearly identical for males and females, for participants of different ages, and for different methods of collecting data, including using words to cue memories from anywhere in the lifespan or from just the childhood years, exhaustive listing of all early memories, and interviews.     

The asymptotic distribution of commonality components

Commonality components have been defined as a method of partitioning squared multiple correlations. In this paper, the asymptotic joint distribution of all 2 ^k – 1 squared multiple correlations is derived. The asymptotic joint distribution of linear combinations of squared multiple correlations is obtained as a corollary. In particular, the asymptotic joint distribution of commonality components are derived as a special case. Simultaneous and nonsimultaneous asymptotic confidence intervals for commonality components can be obtained from this distribution.This work was supported in part by the Spencer Foundation and the National Science Foundation.The authors are grateful to Bryna Siegel-Gorlick for her help in obtaining the data used in Example 4.3, and to the referees for their comments and suggestions.     

The distribution of early childhood memories

The quantitative distribution of autobiographical memories for the first decade of life is described. The distribution, based on over 11,000 autobiographical memories from age 10 and younger from published studies, is nearly identical for males and females, for participants of different ages, and for different methods of collecting data, including using words to cue memories from anywhere in the lifespan or from just the childhood years, exhaustive listing of all early memories, and interviews.     

The spatial distribution of inhibition of return

Inhibition of return (IOR) refers to the finding that response times (RTs) are typically slower for targets at previously attended (cued) locations than for targets at novel (uncued) locations. Although previous research has indicated that IOR may spread beyond a cued location, the present study is the first to examine the spatial distribution of IOR with high spatial resolution over a large portion of the central visual field. This was done by using a typical IOR procedure (cue, delay, target) with 4 cue locations and 441 target locations (each separated by 1° of visual angle). The results indicate that IOR spreads beyond the cued location to affect the cued hemifield. However, the cues also produced a gradient of RTs throughout the visual field, with inhibition in the cued hemifield gradually giving way to facilitation in the hemifield opposite the cue.     

Multiple schedules: effects of the distribution of reinforcements between components on the distribution of responses between components

Two pigeons were trained to peck a key under several multiple variable-interval variable-interval schedules of reinforcement; different numbers of reinforcements were scheduled in two components of equal duration which were correlated with red and green illumination of the response key respectively. The results showed: (1) that the total number of responses in a session was proportional to the one-sixth power of the total number of reinforcements delivered in that session; and (2) that the ratio of responses between the two components was equal to the one-third power of the ratio of reinforcements between them. This latter exponent may be regarded as reflecting the sensitivity of the distribution of responses between the components to the distribution of reinforcements. It was suggested that the effects of a number of complex schedules of reinforcement could be summarized by different values of this exponent.     

Attentional distribution in visual space

Summary The horizontal extent of the visual attentive field was measured by the use of a two-choice-RT task and compatible and incompatible distractors. The target was a line that inclined either to the left or to the right. Whether or not the subject performed the choice RT was made contingent upon whether two other stimuli presented in the visual display matched or mismatched. The match-mismatch stimuli varied in locations so as to manipulate the relevant visual area (the attended area). The locations of the distractors were also varied. The increase in RT associated with incompatible distractors was found to vary inversely with their distance from the edge of the area attended to and independently of their distance from the target lines. The results were interpreted in terms of an inhibitory field that surrounds the area attended to.