Graduate-level historical study is ideal for students intending to specialize in the topic, as well as those who only need a general treatment. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics, emphasizing Hilbert’s metamathematics. Part III focuses on the philosophy of mathematics. Each chapter has extensive supplementary notes; a detailed appendix charts modern developments.

Croc lattices are of central importance in the mathematical foundation of quantum mechanics. They reflect the structure of the logical calculus of propositions concerning microphenomena. In this context, the mathematical consequences resulting from the special structure of the lattice are of particular interest. Beginning with the notion of hemimorphism of a croc lattice, we get, in a natural way, an extension of the structure of the lattice by the Baer *-semigroup. We embed the Baer *-semigroup in an algebra with generalized (...) *- and ′-operations and prove some theorems as consequences of the particular properties of the underlying croc lattice. (shrink)

This classic textbook focuses on medical law and its relationship with medical practice and modern ethics. It provides thorough coverage of all of the topics found on medical law courses, and in depth analysis of recent court decisions, encouraging students to think analytically about the subject.

In a short article, published in an earlier volume of Philosophy 1 under the title “Philosophy and Mathematics,” I tried to explain the current conception of pure mathematics as the study of abstract structure by construction and elaboration of appropriate axiomatic formalisms. In the present paper I propose to consider certain philosophical problems, of interest to philosophers and mathematicians alike, which have their origin in the relation between such formalisms and any applications to experience that they may possess. Consideration of (...) problems of this kind is no new undertaking, and in Reichenbach's Wahrscheinlichkeitslehre , for instance, a considerable amount of space is devoted to the Anwendungsproblem or problem of application of the formal calculus under consideration. Most such discussions, however, are at bottom an appendage to an account of the formalism itself, and the author's interest is primarily mathematical. The result is that the philosophical issues involved are not given due weight; and it is these philosophical issues that I wish to discuss in the present paper. (shrink)

Healey et al. use experiments with chat dialogues to test the hypothesis that language co‐ordination is driven by ‘running repairs’. They replace signals of understanding such as “okay” with weaker, ‘spoof’ signals like “ummm”, and replace specific requests for clarification like “on the left?” with signals that suggest a higher degree of misunderstanding like “what?”. The latter manipulation causes participants to switch rapidly to more abstract forms of referring expression.