Originally published between 1982 and 1991 the 3 volumes in this set Reflect the diversity in Hegelianism and every branch of philosophy which he contributed to. Examine Hegel's work in relation to Marx and Wittgenstein Discuss Hegel's social theory Examine British Hegelian thinking and the lines of its development Offer an interpretation of Hegelian theory that is relevant for the understanding of modern republican constitutions.

Reissuing works originally published between 1949 and ‘79, this set presents a rich selection of renowned scholarship across the subject, touching also on ethics, religion, and psychology and other behavioural science. Classic previously out-of-print works are brought back into print here in this set of important discourse and theory.

This 20 volume Routledge Revivals collection brings together a selection of groundbreaking Philosophy titles, from the rich and diverse Routledge backlist. With titles published between 1933 and 1991, this is a truly wide-ranging selection, encompassing works by distinguished authors such as: Simone Weil, Hilary Putnam, Franz Brentano, Anthony Kenny, Karl Jaspers and Israel Scheffler. Dealing with everything from the notion of freewill, to concepts of time and space, to theories of morality, this set offers a collection of the best of (...) Routledge publishing in the field of Philosophy from across the Twentieth Century. Please note that all titles have been previously available for sale individually through the Routledge Revivals programme. (shrink)

Since Darwin, the idea of psychological continuity between humans and other animals has dominated theory and research in investigating the minds of other species. Indeed, the field of comparative psychology was founded on two assumptions. First, it was assumed that introspection could provide humans with reliable knowledge about the causal connection between specific mental states and specific behaviors. Second, it was assumed that in those cases in which other species exhibited behaviors similar to our own, similar psychological causes were (...) at work. In this paper. we show how this argument by analogy is flowed with respect to the case of second-order mental states. As a test case, we focus on the question of how other species conceive of visual attention, and in particular whether chimpanzees interpret seeing as a mentalistic event involving internal states of perception, attention, and belief. We conclude that chimpanzees do not reason about seeing in this manner, and indeed, there is considerable reason to suppose that they do not harbor representations of mental states in general. We propose a reinterpretation model in which the majority of the rich social behaviors that humans and other primates share in common emerged long before the human lineage evolved the psychological means of interpreting those behaviors in mentalistic terms. Although humans, chimpanzees, and most other species may be said to possess mental states, humans alone may have evolved a cognitive specialization for reasoning about such states. (shrink)

La sapienza di partire da sè è una via che si sottrae alle molte contrapposizioni che sono iscritte nel simbolico dominante: quella tra soggettivo e oggettivo, tra individuo e comunità e tra locale e generale: apre un'altra strada.

This book starts from the premise that methodology has always dominated archaeology to the detriment of broader social theory.

There is currently much interest in bringing together the tradition of categorial grammar, and especially the Lambek calculus, with the recent paradigm of linear logic to which it has strong ties. One active research area is designing non-commutative versions of linear logic (Abrusci, 1995; Retoré, 1993) which can be sensitive to word order while retaining the hypothetical reasoning capabilities of standard (commutative) linear logic (Dalrymple et al., 1995). Some connections between the Lambek calculus and computations in groups have long been (...) known (van Benthem, 1986) but no serious attempt has been made to base a theory of linguistic processing solely on group structure. This paper presents such a model, and demonstrates the connection between linguistic processing and the classical algebraic notions of non-commutative free group, conjugacy, and group presentations. A grammar in this model, or G-grammar is a collection of lexical expressions which are products of logical forms, phonological forms, and inverses of those. Phrasal descriptions are obtained by forming products of lexical expressions and by cancelling contiguous elements which are inverses of each other. A G-grammar provides a symmetrical specification of the relation between a logical form and a phonological string that is neutral between parsing and generation modes. We show how the G-grammar can be oriented for each of the modes by reformulating the lexical expressions as rewriting rules adapted to parsing or generation, which then have strong decidability properties (inherent reversibility). We give examples showing the value of conjugacy for handling long-distance movement and quantifier scoping both in parsing and generation. The paper argues that by moving from the free monoid over a vocabulary V (standard in formal language theory) to the free group over V, deep affinities between linguistic phenomena and classical algebra come to the surface, and that the consequences of tapping the mathematical connections thus established can be considerable. (shrink)

We review some of the progress made in the past 27 years in understanding the group theoretic and path integral aspects of the hydrogen atom. The group theoretic development was triggered by A. O. Barut who suggested to me the search for a dynamical group larger than SO(4). In this way he became indirectly responsible also for important recent path integral developments.

The commentary is in general agreement with Roger Shepard's view of evolutionary internalization of certain procedural memories, but advocates the use of Lie groups to express the invariances of motion and color perception involved. For categorization, the dialectical pair is suggested. [Barlow; Hecht; Kubovy & Epstein; Schwartz; Shepard; Todorovic].

In this paper we investigate a number of analytical solutions to the polynomial class of nonlinear Klein-Gordon equations in multidimensional spacetime. This is done in the context of classical φ4 and φ6 field theory, the former with and without the inclusion of an external force field conjugate to φ. Both massive (m≠0) and massless (m=0) cases are considered, as well as tachyonic solutions allowed (v>c). We first present a complete set of translationally invariant solutions for the φ4 model and (...) demonstrate the role of external force fields in altering the form of these solutions. Next, spherically symmetric solutions are discussed in both φ4 and φ6 cases since they provide the most realistic models of elementary particles. (shrink)

This book is the first to systematically develop, explain, and apply diagrammatic projection operators to construct all semi-simple Lie algebras, both classical and exceptional.

To this day, a hundred and fifty years after Mendeleev's discovery, the overal structure of the periodic system remains unaccounted for in quantum-mechanical terms. Given this dire situation, a handful of scientists in the 1970s embarked on a quest for the symmetries that lie hidden in the periodic table. Their goal was to explain the table's structure in group-theoretical terms. We argue that this symmetry program required an important paradigm shift in the understanding of the nature of chemical elements. (...) The idea, in essence, consisted of treating the chemical elements, not as particles, but as states of a superparticle. We show that the inspiration for this came from elementary particle physics, and in particular from Heisenberg's suggestion to treat the proton and neutron as different states of the nucleon. We provide a careful study of Heisenberg's last paper on the nature of elementary particles, and explain why the Democritean picture of matter no longer applied in modern physics and a Platonic symmetry-based picture was called for instead. We show how Heisenberg's Platonic philosophy came to dominate the field of elementary particle physics, and how it found its culmination point in Gell-Mann's classification of the hadrons in the eightfold way. We argue that it was the success of Heisenberg's approach in elementary particle physics that sparked the group-theoretical approach to the periodic table. We explain how it was applied to the set of chemical elements via a critical examination of the work of the Russian mathematician Abram Ilyich Fet the Turkish-American physicist Asim Orhan Barut, before giving some final reflections. (shrink)

Symmetry is at the heart of our understanding of matter. This book tells the fascinating story of the constituents of matter from a common symmetry perspective. The standard model of elementary particles and the periodic table of chemical elements have the common goal to bring order in the bewildering chaos of the constituents of matter. Their success relies on the presence of fundamental symmetries in their core. -/- The purpose of Shattered Symmetry is to share the admiration for the power (...) and the beauty of these symmetries. The reader is taken on a journey from the basic geometric symmetry group of a circle to the sublime dynamic symmetries that govern the motions of the particles. Along the way the theory of symmetry groups is gradually introduced with special emphasis on its use as a classification tool and its graphical representations. This is applied to the unitary symmetry of the eightfold way of quarks, and to the four-dimensional symmetry of the hydrogen atom. The final challenge is to open up the structure of Mendeleev's table which goes beyond the symmetry of the hydrogen atom. Breaking this symmetry to accommodate the multi-electron atoms requires us to leave the common ground of linear algebras and explore the potential of non-linearity. (shrink)

Wigner famously referred to the `unreasonable effectiveness' of mathematics in its application to science. Using Wigner's own application of group theory to nuclear physics, I hope to indicate that this effectiveness can be seen to be not so unreasonable if attention is paid to the various idealising moves undertaken. The overall framework for analysing this relationship between mathematics and physics is that of da Costa's partial structures programme.

This article takes a fresh look at the Ardeners' muted group theory, originally applied in social anthropology and later taken up by the women's movement. The theory has wider applicability in aiding understanding of the communication processes between females and males but there is a need for a combination of disparate types of research extending the focus beyond mutedness as a structural product to the processes by which women are rendered mute, involving a broader analysis of the (...) political, economic and organizational context. The communications research arena is envisaged as one in which further work could be carried out. (shrink)

With the present paper I maintain that the group field theory (GFT) approach to quantum gravity can help us clarify and distinguish the problems of spacetime emergence from the questions about the nature of the quanta of space. I will show that the mechanism of phase transition suggests a form of indifference between scales (or phases) and that such an indifference allows us to black-box questions about the nature of the ontology of the fundamental levels of the (...) class='Hi'>theory. I consider the GFT approach to quantum gravity which derives spacetime as an emergent property from abstract non-geometrical tetrahedra through a processes of phase transition. Because the physical interpretation of the tetrahedra is problematic in view of their (non)-spatiotemporal nature, I will apply the considerations about phase transitions to GFT and conclude that the fundamental ontology of the theory and the mechanism of spacetime emergence can and should be treated separately. (shrink)

A. F. Bentley’s The Process of Government (1908) is widely accepted as an important source of contemporary interest group study. This paper argues to the contrary that Bentley’s arguments in this area are obscure and have contributed little to the programme of modern interest group research. His importance is as a contributor to the debate on the nature of social science and social science method and not as the starting-point for interest group analysis. The judgement about his (...) role as a social scientist should rest on consideration of his body of work and not simply the one book. In terms of his much cited book, Bentley, it is argued, is misread. The central purpose of this article is to explore the consequences of that misinterpretation. The misreading of The Process of Government, and the unmerited assumption that it is directly connected to modern interest group theory, has led to a misunderstanding of that contemporary theory. In particular his use of the term ‘group’ is much wider in scope than is now usually followed. This means that his claims are not so uni-dimensional as they appear when extracted from their context. Bentley used the term in a sociological sense that included informal social associations as ‘groups’: these are not the sort of formal, collective organizations of the interest group type as identified in political science. It is argued that the major sources of ideas current in the interest group field are Truman (1951) and the case-study authors of the 1930s such as Odegard, Childs, Herring and Schattschneider. Bentley’s contribution to political science is not as progenitor of interest group studies, but his emphasis on process anticipates the policy studies movement. (shrink)

Introduction. This survey is intended to introduce to logicians some notions, methods and theorems in set theory which arose—largely through the work of Saharon Shelah—out of attempts to solve problems in abelian group theory, principally the Whitehead problem and the closely related problem of the existence of almost free abelian groups. While Shelah's first independence result regarding the Whitehead problem used established set-theoretical methods, his later work required new ideas; it is on these that we focus. We (...) emphasize the nature of the new ideas and the historical context in which they arose, and we do not attempt to give precise technical definitions in all cases, nor to include a comprehensive survey of the algebraic results.In fact, very little algebraic background is needed beyond the definitions of group and group homomorphism. Unless otherwise specified, we will use the word “group” to refer to an abelian group, that is, the group operation is commutative. The group operation will be denoted by +, the identity element by 0, and the inverse of a by −a. We shall use na as an abbreviation for a + a + … + a [n times] if n is positive, and na = if n is negative. (shrink)

Klein’s Erlangen program contains the postulate to study thegroup of automorphisms instead of a structure itself. This postulate, takenliterally, sometimes means a substantial loss of information. For example, thegroup of automorphisms of the field of rational numbers is trivial. Howeverin the case of Euclidean plane geometry the situation is different. We shallprove that the plane Euclidean geometry is mutually interpretable with theelementary theory of the group of authomorphisms of its standard model.Thus both theories differ practically in the language (...) only. (shrink)

In this paper, we will prove the inevitable non-uniformity of two constructions from combinatorial group theory related to the word problem for finitely generated groups and the Higman—Neumann—Neumann Embedding Theorem.

A group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated “Groupthink”, Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever individual credences undergo Bayesian revision based on this information. To obtain a fully Bayesian group, one should often extend this requirement to non-public or even private information (learnt by (...) not all or just one individual), or to non-representable information (not representable by any event in the domain where credences are held). I pro- pose a taxonomy of six types of ‘group Bayesianism’. They differ in the information for which Bayesian revision of group credences is required: public representable information, private representable information, public non-representable information, etc. Six corre- sponding theorems establish how individual credences must (not) be aggregated to ensure group Bayesianism of any type, respectively. Aggregating through standard averaging is never permitted; instead, different forms of geometric averaging must be used. One theorem—that for public representable information—is essentially Russell et al.’s central result (with minor corrections). Another theorem—that for public non-representable information—fills a gap in the theory of externally Bayesian opinion pooling. (shrink)

In this paper, I shall discuss the heuristic role of symmetry in the mathematical formulation of quantum mechanics. I shall first set out the scene in terms of Bas van Fraassen’s elegant presentation of how symmetry principles can be used as problem-solving devices (see van Fraassen [1989] and [1991]). I will then examine in what ways Hermann Weyl and John von Neumann have used symmetry principles in their work as a crucial problem-solving tool. Finally, I shall explore one consequence of (...) this situation to recent debates about structural realism (SR) and empiricism in physics (Worrall [1989], Ladyman [1998], and French [1999]). (shrink)