We define two types of convergence for observables on a quantum logic which we call M-weak and uniform M-weak convergence. These convergence modes correspond to weak convergence of probability measures. They are motivated by the idea that two (in general unbounded) observables are “close” if bounded functions of them are “close.” We show that M-weak and uniform M-weak convergence generalize strong resolvent and norm resolvent convergence for self-adjoint operators on a Hilbert space. Also, these types of convergence strengthen the weak (...) operator convergence and operator norm convergence of bounded self-adjoint operators on a Hilbert space. Finally, we consider spectral perturbation by showing that the spectra of approximating observables approach the spectrum of the limit in a certain sense. (shrink)

1. IN the C.Q.xxxiv , pp. 118 ff., I wrote on ‘Some Uses of the Imperfect in Greek’ . It occurred tome to check the suggestions there made by examining all the instances in one author. I had no hesitation in choosing Herodotus, who of all authors, except perhaps Homer, presents the most baffling diversity of types . For purposes of comparison I also read Thucydides and Xenophon's Anabasis 1–4. It would appear that Thucydides retains something of Herodotus' freedom, Xenophon (...) comparatively little. (shrink)

1. IN the C.Q.xxxiv, pp. 118 ff., I wrote on ‘Some Uses of the Imperfect in Greek’. It occurred tome to check the suggestions there made by examining all the instances in one author. I had no hesitation in choosing Herodotus, who of all authors, except perhaps Homer, presents the most baffling diversity of types. For purposes of comparison I also read Thucydides and Xenophon's Anabasis 1–4. It would appear that Thucydides retains something of Herodotus' freedom, Xenophon comparatively little.

It is by no means unusual in works of philosophy for writers to make use of examples from literature or to bemoan the lack of literary examples in the work of other philosophers. Nor is it unusual for philosophers to write substantial tomes without ever mentioning any work of literature or to condemn the use of literary examples as a threat to clarity of thought. This contradiction in practice and principle might lead us to suspect that what we are here (...) dealing with is at least to some extent a philosophical disagreement, and I believe this to be the case. Unfortunately, what is extremely unusual is any direct discussion of the philosophical issues involved, that is to say any discussion of what philosophers are doing when they appeal in their writings to works of literature, and of what if anything is lost by those who fail to do so. (shrink)

It is by no means unusual in works of philosophy for writers to make use of examples from literature or to bemoan the lack of literary examples in the work of other philosophers. Nor is it unusual for philosophers to write substantial tomes without ever mentioning any work of literature or to condemn the use of literary examples as a threat to clarity of thought. This contradiction in practice and principle might lead us to suspect that what we are here (...) dealing with is at least to some extent a philosophical disagreement, and I believe this to be the case. Unfortunately, what is extremely unusual is any direct discussion of the philosophical issues involved, that is to say any discussion of what philosophers are doing when they appeal in their writings to works of literature, and of what if anything is lost by those who fail to do so. (shrink)

Medical practitioners of the sixteenth century had their own body of special terms, just like the doctors of this century. McConchie examines medical terminology used in a selection of thirteen medical works published between 1547 and 1612, and compares it with treatment of these words in the Oxford English Dictionary and other dictionaries of today, showing how well - or ill - the specialist terminology of sixteenth-century medical practitioners has been recorded. He compiles a corpus of new data from a (...) selection of medical texts ranging from scholarly tomes to homely handbooks. The study of this corpus reveals errors, omissions, and biases which raise questions for lexicographical tools in general. Are existing dictionaries adequate in their investigation of Renaissance English? Has current understanding been more biased and more deficient than we thought? If so, how are we to redress the problem? This book uses a specialist semantic domain to raise important issues for lexicographers, and historians of early modern English and medicine. (shrink)

This is a study of "three metaphysical naturalists" who, although minor figures in their own right, nonetheless substantially influenced the direction and cast of American naturalism. The theme that unites them, according to Delaney, is their reaction to the bifurcation of mind and corporeal nature bequeathed to modern philosophy by Descartes and Locke. Morris R. Cohen, as a logician and philosopher of science, saw such a bifurcation as engendering conventionalism and a type of nominalism in science, and he reacted against (...) these with his own "logical realism." Frederick J. E. Woodbridge, working out of the Aristotelian and Spinozistic traditions, saw it as entailing subjectivism and attempted to counteract this by reasserting an "experiential realism." Roy Wood Sellars, himself an evolutionist, viewed the duality of mind and nature as a stimulus for the imaginative projection of idealism and the quietistic escapism of spiritualism, and countered these with a thorough-going "materialistic humanism." Delaney elaborates his thesis with clarity and cogency, using it as a vehicle to reconstruct the metaphysical views of the three men under study. He concludes with a critical comparison of the resulting "naturalistic reintegrations" of the mind-nature bifurcation: Cohen's through a more adequate philosophy of science, Woodbridge's by a realistic theory of experience, and Sellars' by an emergent theory of evolution. Delaney's critique focuses on the fundamental notions of existence, nature, and man, using these to expose essential differences between the "metaphysics" of the New York naturalists and that of Sellars. Woodbridge emerges from Delaney's analysis as the most substantial philosopher of the group. This is not a ponderous tome--it can be read practically at one sitting--but it succeeds in throwing new light on American naturalism in terms of its positive contributions to both the philosophy of nature and the philosophy of mind.--W. A. W. (shrink)

This volume has a misleading title: one might think that the material in this long work is by the great Indian spiritual leader. But it is not. Rather it is a collection of essays by A. R. Wadia, M.P., and it is only the first essay in the tome which is about Gandhi. Wadia is obviously some kind of Renaissance man, an interpreter of all knowledge--philosophical and religious, western and eastern--to the Indian mind. In one volume can be found Wadia (...) on "Pragmatic Idealism," "Philosophy and Religion," "Science and Philosophy," "Buddha as a Revolutionary Force in Indian Culture," "The Psychological Background of Politics and Sociology," "The Problem of Population in India," and there is lots more.--W. A. J. (shrink)