This is a philosophical work that develops a general theory of ontological objects and object-relations. It does this by examining concepts as acquired dispositions, and then focuses on perhaps the most important of these: the concept of learning. This concept is important because everything that we know and do in the world is predicated on a prior act of learning. A concept can have many meanings and can be used in a number of different ways, and this creates difficulty when considering the nature of objects and the relationships between them. To enable this, David Scott answers a series of questions about concepts in general and the concept of learning in particular. Some of these questions are: What is learning? What different meanings can be given to the notion of learning? How does the concept of learning relate to other concepts, such as innatism, development and progression? The book offers a counter-argument to empiricist conceptions of learning, to the propagation of simple messages about learning, knowledge, curriculum and assessment, and to the denial that values are central to understanding how we live. It argues that values permeate everything: our descriptions of the world, the attempts we make at creating better futures and our relations with other people.

The first part of this book concerns the present state of the theory of chains (= total or linear orderings), in connection with some refinements of Ramsey's theorem, due to Galvin and Nash-Williams. This leads to the fundamental Laver's embeddability theorem for scattered chains, using Nash-Williams' better quasi-orderings, barriers and forerunning.The second part (chapters 9 to 12) extends to general relations the main notions and results from order-type theory. An important connection appears with permutation theory (Cameron, Pouzet, Livingstone and Wagner) and with logics (existence criterion of Pouzet-Vaught for saturated relations). The notion of bound of a relation (due to the author) leads to important calculus of thresholds by Frasnay, Hodges, Lachlan and Shelah. The redaction systematically goes back to set-theoretic axioms and precise definitions (such as Tarski's definition for finite sets), so that for each statement it is mentioned either that ZF axioms suffice, or what other axioms are needed (choice, continuum, dependent choice, ultrafilter axiom, etc.).

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1987.