The problem of finding irreducible representations of a simple Lie group that decompose into just pure replications of a representation of a subgroup is considered. Replications involving tensor representations of the orthogonal groups are studied in detail using counting groups whose representation dimensions correspond to branching multiplicities. Replications involving spinor and mixed tensor representations are briefly considered.

Do we remember what pain feels like? Investigations into this question have sometimes led to ambiguous or apparently contradictory results. Building on research on pain memory by Rohini Terry and colleagues, I argue that this lack of agreement may be due in part to the difficulty researchers face when trying to convey to their study's participants the type of memory they are being tasked with recalling. To address this difficulty, I introduce the concept of 'qualitative memory', which, arguably, is the (...) sort of memory we have of what red looks like yet lack with respect to pain. I also briefly address a number of consequences the acknowledgment of qualitative memory would potentially have for philosophy, arguing that if we fail to have qualitative memories of certain sensations, such as pain, the standard philosophical accounts of experience, rational choice, and the sources of moral action may all need revision. (shrink)

An implication is a proposition, a consequence is a relation between propositions, and an inference is act of passage from certain premise-judgements to another conclusion-judgement: a proposition is true, a consequence holds, whereas an inference is valid. The paper examines interrelations, differences, refinements and linguistic renderings of these notions, as well as their history. The truth of propositions, respectively the holding of consequences, are treated constructively in terms of verification-objects. The validity of an inference is elucidated in terms of the (...) existence of a chain of immediately evident steps linking premises and conclusion. (shrink)

Susan Schneider argues that physicalism must be false if abstracta are part of the physicalist's dependence base. In opposition to her view, here I set out some reasons to think that abstracta in general, including abstracta that are woven into the dependence base, are something physicalists can countenance with consistency.

The genesis of classical science was accompanied by a transition from logical to mathematical analysis. This change did not mean a rejection of Aristotle's canons of logic; it was simply that these canons became inadequate. They underwent a certain generalization and, in the course of this, came closely to approximate mathematical analysis, the foundations of the calculus of the infinitesimal. Classical science no longer took as its point of departure the notion of motion from "something" into "something," as did Peripatetic (...) physics and cosmology . The initial concept is motion, considered from point to point and instant to instant. This kind of differential notion of motion was clearly expressed by Kepler when he wrote: "Where Aristotle sees direct oppositeness between two things, with no mediating links, there I, looking at geometry philosophically, find a mediated opposition; so that where Aristotle employs a single term, ‘other,’ I use two: ‘larger’ and ‘smaller.’". (shrink)

A vast literature has been devoted to the Dialectics of Nature and dialectics in Capital. There is a considerable number of works in which the connection between the philosophical generalization of natural science in the Dialectics of Nature and the philosophical aspects of the economic categories in Capital are analyzed. I should like to touch upon only one aspect of the problem — that aspect which pertains to certain new problems in philosophical and economic thought. Reference is, first, to the (...) new, unprecedented role of philosophy and natural science in the period of the scientific and technological revolution under the conditions of the unification and planning of science and, second, to the unprecedented dynamism of the economy today. This dynamism requires a radical rethinking of categories, and that rethinking, in turn, requires a return to the fundamental categories of Capital. (shrink)

A vast literature has been devoted to the Dialectics of Nature and dialectics in Capital. There is a considerable number of works in which the connection between the philosophical generalization of natural science in the Dialectics of Nature and the philosophical aspects of the economic categories in Capital are analyzed. I should like to touch upon only one aspect of the problem — that aspect which pertains to certain new problems in philosophical and economic thought. Reference is, first, to the (...) new, unprecedented role of philosophy and natural science in the period of the scientific and technological revolution under the conditions of the unification and planning of science and, second, to the unprecedented dynamism of the economy today. This dynamism requires a radical rethinking of categories, and that rethinking, in turn, requires a return to the fundamental categories of Capital. (shrink)

This chapter contains sections titled: I II III IV V VI VII VIII IX X.

В книге собраны статьи по актуальным вопросам политической теории, которые находятся в центре дискуссий отечественных и зарубежных философов и обществоведов. Книга имеет полемический характер и предназначена всем.