This chapter provides basic production theoretical underpinnings used in modeling and measuring performance in the healthcare realm, which covers a host of institutions, practitioners, regulators, insurers, and patients, among others. This is a difficult task given the complexity of the healthcare sector. In general, the authors seek some meaningful benchmarks to use in assessing performance that are rich enough to model these complex entities. They begin with introducing technology or sets, which include as elements the many inputs used to treat patients in clinics or hospitals, which are in turn employed to improve patient outcomes (outputs), which may be multidimensional as well. They introduce key axioms that are imposed on these sets. However, although key in determining the benchmark or best practice possibilities, these sets are not practical for determining the performance of individual entities relative to the benchmark. More practical are functional representations of these multidimensional sets that are easy to estimate, which include distance functions and their dual value functions. These functions inherit properties from their respective technology sets, which in turn require certain specifications of their functional form if they are to be estimated parametrically.

Chapter 7 publishes the text of Pitcairneana, MS Eng 1114 in the Houghton Library, Harvard. In it, a spokesman for atheism, ‘Incredulous’, argues against ‘Credulous’, a spokesman for Christian orthodoxy, and makes various points, notably concerning the relationship between spiritual and non-spiritual bodies and the issue of motion being intrinsic to matter; he also argues in favour of the world’s being eternal rather than the result of a divine act of creation and offers a cyclical rather than progressive view of human development. The authors referred to in the dialogue include Samuel Clarke, Henry More, John Toland and Robert Hooke, while the treatise ends by invoking ‘axioms’ in an essentially Newtonian mode.

We introduce the two axioms on which SR is based, namely the Principle of Relativity and the constancy of the speed of light.

By the turn of the twentieth century, many philosophers claimed that Kant’s philosophy of mathematics (and, indeed, his entire philosophy) was undermined by the real possibility of geometries in which Euclid’s axiom of parallels is false. It is surprisingly not well known that Kant – though never discussing parallel lines in his published work – did write a series of unpublished notes on the philosophical problems posed by parallel lines. This paper presents the argument and chief issues of these notes. Kant’s main point in these notes is that neither Euclid’s definition of parallel lines, nor the alternative definition proposed by Leibniz and Christian Wolff, fulfills the requirements on mathematical definitions that Kant explicates in the Critique of Pure Reason. Thus, these notes show that Kant did reflect on the problems posed by the theory of parallel lines and recognized that it was uniquely problematic. Moreover, Kant’s reflections yield new insights about his philosophy of mathematics. In particular, Kant’s attitude toward the theory of parallels demonstrates that he had a novel theory of mathematical definitions, axioms, and postulates – a theory that Kant’s contemporary readers have largely misunderstood.