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Infrastructure and Transition in Developmental Analysis

Van den Daele, Leland D.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Mathematical Logic, Set Theory, Statistical Analysis


The logic of set theory is applied to the problem of infrastructure and transition in developmental analysis. The analysis necessitates the decomposition of stages into components. The decomposition generates sets within sets and, from a sequential perspective, progressions within progressions. The relation of lower to higher and precursor to successor items varies from the trivial to the rigorous. In a trivial analysis, a precursor is neither necessary nor sufficient for a successor; in a rigorous analysis, a precursor is necessary and sufficient. Infrastructure and transition are interdependent. When components are common to successive stages, stages are transformed or correlatively transformed; where components are discrete, stages are substituted, added or deleted, and when some components are common and some discrete, stages are hybrid. Any transformation or correlative transformation implies a correspondence, integration, or differentiation with parallelism, subordination, or emergence. Any substitution, adoption, or deletion implies a coincidence, augmentation, or reduction with coplanarity, expansion, or contraction. The implications of this analysis are discussed in relation to developmental theory and theory evaluation. (Author) (43pp.)

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