We explore analogues of o-minimality and weak o-minimality for circularly ordered sets. Much of the theory goes through almost unchanged, since over a parameter the circular order yields a definable linear order. Working over ∅ there are differences. Our main result is a structure theory for ℵ0-categorical weakly circularly minimal structures. There is a 5-homogeneous example which is not 6-homogeneous, but any example which is k-homogeneous for some k ≥ 6 is k-homogeneous for all k.

We classify countable metrically homogeneous graphs of diameter 3.

I hope you have had no trouble identifying this issue of our journal, even if the cover has been changed slightly. I would like to draw your attention to a more essential improvement in the journal's affairs: namely, that the Editorial Board has been enlarged by four new members. These are the following: Douglas Bridges , Ulrich Kohlenbach , H. Dugald Macpherson , and Pavel Pudlak . Please don't hesitate to contact a fellow editor, in particular the managing (...) editor, if you have suggestions for improving either the editorial procedures or the content and form of MLQ.The aims and scope of our journal are unchanged from the original ones developed by Günter Asser. His name is indissolubly connected with the former “Zeitschrift für Mathematische Logik und Grundlagen der Mathematik ”, now known as “Mathematical Logic Quarterly ”. He was one of the two founding editors and then the editor-in-chief of the journal until the 50th volume appeared about one year ago. Single-handedly, and almost incredibly, he showed that it is possible for one man to be the main editor of a successful highlevel scientific journal throughout half a century. He remains involved in and concerned with the editorial process of MLQ. For example, he carefully looks at every article to be published, faithfully checking almost every line of the final layout.On 26 February 2006, Professor Dr. Günter Asser celebrates his 80th birthday. I would like to take this opportunity, on behalf of the whole readership and of all fellow editors of ZML and MLQ throughout the last 51 years, to congratulate him cordially and to wish him good health and all the best for the future.The present issue starts with a paper directly related to G. Asser's spectrum conjecture. Then there are some papers specially dedicated to him, as well as further contributions, as always scrutinised and then recommended by expert referees. So this turns out to be an appropriate birthday issue. (shrink)

This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first-order theory of finite groups. The focus is on concepts from stability theory and generalisations in the context of pseudofinite groups, and on the information this might provide for finite group theory.

It is shown that if is an o-minimal structure such that is a dense total order and ≾ is a parameter-definable partial order on M, then ≾ has an extension to a definable total order.

We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity of the underlying theory, and that a drop in pseudofinite dimension is equivalent to forking. Under a suitable assumption, a measure-theoretic condition is shown to be equivalent to local stability. Many examples are explored, including vector spaces over finite fields viewed as 2-sorted finite structures, and homocyclic groups. Connections are (...) made to products of sets in finite groups, in particular to word maps, and a generalization of Tao's Algebraic Regularity Lemma is noted. (shrink)

It is shown that no infinite group is interpretable in any structure which is homogeneous in a finite relational language. Related questions are discussed for other ω-categorical structures.

C-minimality is a variant of o-minimality in which structures carry, instead of a linear ordering, a ternary relation interpretable in a natural way on set of maximal chains of a tree. This notion is discussed, a cell-decomposition theorem for C-minimal structures is proved, and a notion of dimension is introduced. It is shown that C-minimal fields are precisely valued algebraically closed fields. It is also shown that, if certain specific ‘bad’ functions are not definable, then algebraic closure has the exchange (...) property, and for definable sets dimension coincides with the rank obtained from algebraic closure. (shrink)

We explore the interplay between $\omega $ -categoricity and pseudofiniteness for groups, and we conjecture that $\omega $ -categorical pseudofinite groups are finite-by-abelian-by-finite. We show that the conjecture reduces to nilpotent p-groups of class 2, and give a proof that several of the known examples of $\omega $ -categorical p-groups satisfy the conjecture. In particular, we show by a direct counting argument that for any odd prime p the ( $\omega $ -categorical) model companion of the theory of nilpotent class (...) 2 exponent p groups, constructed by Saracino and Wood, is not pseudofinite, and that an $\omega $ -categorical group constructed by Baudisch with supersimple rank 1 theory is not pseudofinite. We also survey some scattered literature on $\omega $ -categorical groups over 50 years. (shrink)

The notion of a strongly determined type over A extending p is introduced, where p .S. A strongly determined extension of p over A assigns, for any model M )- A, a type q S extending p such that, if realises q, then any elementary partial map M → M which fixes acleq pointwise is elementary over . This gives a crude notion of independence which arises very frequently. Examples are provided of many different kinds of theories with strongly determined (...) types, and some without. We investigate a notion of multiplicity for strongly determined types with applications to ‘involved’ finite simple groups, and an analogue of the Finite Equivalence Relation Theorem. Lifting of strongly determined types to covers of a structure is discussed, and an application to finite covers is given. (shrink)

We give an example of an imaginary defined in certain valued fields with analytic structure which cannot be coded in the ‘geometric' sorts which suffice to code all imaginaries in the corresponding algebraic setting.

A partially ordered set is called k-homogeneous if any isomorphism between k-element subsets extends to an automorphism of . Assuming the set-theoretic assumption ⋄, it is shown that for each k, there exist partially ordered sets of size ϰ1 which embed each countable partial order and are k-homogeneous, but not -homogeneous. This is impossible in the countable case for k ≥ 4.

Let L be a finite relational language. The age of a structure M over L is the set of isomorphism types of finite substructures of M. We classify those ages U for which there are less than 2ω countably infinite pairwise nonisomorphic L-structures of age U.

We study the Vapnik–Chervonenkis density of definable families in certain stable first-order theories. In particular, we obtain uniform bounds on the VC density of definable families in finite $\mathrm {U}$-rank theories without the finite cover property, and we characterize those abelian groups for which there exist uniform bounds on the VC density of definable families.

0-categorical o-minimal structures were completely described by Pillay and Steinhorn 565–592), and are essentially built up from copies of the rationals as an ordered set by ‘cutting and copying’. Here we investigate the possible structures which an 0-categorical weakly o-minimal set may carry, and find that there are some rather more interesting examples. We show that even here the possibilities are limited. We subdivide our study into the following principal cases: the structure is 1-indiscernible, in which case all possibilities are (...) classified up to binary structure; the structure is 2-indiscernible, classified up to ternary structure; the structure is 3-indiscernible, in which case we show that it is k-indiscernible for every finite k. We also make some remarks about the possible structures of higher arities which an 0-categorical weakly o-minimal structure may carry. (shrink)

This essay is an introduction to the Routledge Handbook of Philosophy of Colour. Why has the examination of many different aspects of colour been a prominent feature in philosophy, to such an extent that the topic is worthy of a handbook? Here are two related answers. First, colours are exceedingly familiar, seemingly simple features that become enigmatic under scrutiny, and they are difficult to capture in any familiar-sounding, unsophisticated theory. Second, through colour one can confront various problems that span the (...) breadth of philosophy, including problems pertaining to perception, the mind-body relation, the nature of science, scepticism, vagueness, meta-ethics, and aesthetics. In this introduction we elaborate and guide the reader to the essays in the rest of this volume. (shrink)

A countably infinite relational structure M is called absolutely ubiquitous if the following holds: whenever N is a countably infinite structure, and M and N have the same isomorphism types of finite induced substructures, there is an isomorphism from M to N. Here a characterisation is given of absolutely ubiquitous structures over languages with finitely many relation symbols. A corresponding result is proved for uncountable structures.

This policy report arises from the research project Augmented Reality: Ethics, Perception, Metaphysics, conducted at the University of Glasgow’s Centre for the Study of Perceptual Experience between November 2021 and November 2023. It was funded by a grant from the Royal Society of Edinburgh. The project brought together experts in various academic fields, with partners from industry and regulatory bodies, to explore the nature of augmented and mixed reality technology, the theories underpinning them, and the ethical and legal questions prompted (...) by new technology in this domain. (shrink)

IN the recent past there has been a resurgence of interest in the work of Thomas Reid; several new editions of his work have appeared as well as a series of articles concerning various aspects of his systematic philosophy. Interest has generalized to the whole Scottish tradition, including numerous figures in the history of American philosophy who were deeply influenced by Reid and Dugald Stewart. In addition, several recent and contemporary philosophers have used Reid's epistemic views as a point (...) of departure in developing their own adverbial theories of sensing and appearing. Others have used Reid's theory of agency in formulating their own views on freedom and responsibility. (shrink)

Though some of the critical reviews of Frank M. Coleman's Hobbes and America have alluded to the affinities of his work to that of Strauss, Macpherson, Laslett, and Oakeshott, most have ignored Coleman's specifically philosophic treatment of Hobbes as the foundational thinker most responsive to political realities which emerge in the seventeenth century and still characterize American politics. Coleman's purpose is to demonstrate how the operative American constitutional philosophy can be recognized clearly only when understood in the context of (...) its Hobbesian origins. But, Coleman suggests, this does not necessarily exclude the possibility of gaining insight into the thought of Hobbes, Locke, and Madison in virtue of reflection on contemporary American political experience. (shrink)

Was Green a utilitarian? At least two studies suggest that he was, at least in some sense. One claim is inspired by Macpherson's association of nineteenth-century liberalism with utilitarianism. Drawing on this argument, Greengarten and Hansen claim that Green's departure from utilitarianism is only partial. His commitment to capitalism indicates a subscription to utilitarianism since the latter is the justificatory force of capitalist institutions.

Over the last several years, C. B. Macpherson has attempted to present a far-reaching critique of the theories underlying and justifying capitalist social systems. Beginning with a critique of the classical theories of capitalism, he has extended it to the later formulations offered by j. S. Mill and T. H. Green, along with the most recent formulation offered by john Rawls. The guiding thread throughout his writing has been the critique of the model of persons which underpin the various (...) formulations of capitalist theory. What I would like to do in this paper is to present what I think to be a stronger defense of Macpherson's argument than Macpherson has himself given, since I think it can be shown that at certain crucial points his argument is necessarily flawed for the point which he is trying to make. (shrink)

The sustained and critical attention that Hobbes commands from twentieth century scholars proves the relevance of his philosophy to our concerns, but it cannot explain the occasion for such an attention. The chief aim of the present work is to provide an account of the reason for the sudden emergence of diverse interpretations of Hobbes that had cropped up in the twentieth century. This work argues that the arrival of the diverse interpretations cannot be answered only by looking at the (...) developments within Hobbes’s political philosophy. We have to go outside Hobbes’s political philosophy to account for their arrival. The tenability of Hobbesian philosophy which is founded on Newtonian and Galilean theories that were subsequently contended by Einstein's Theory of Relativity is discussed in the light of the interpretations of four scholars – Leo Strauss, A E Taylor, J H Warrender, C B Macpherson – that attempted to provide alternative foundations such as Self-observation, Moral Imperative, Moral Obligation, Possessive Individualism, respectively. This book will be of considerable interest not only to the scholars of Hobbes, but also to those interested in the relationship between philosophy and science. (shrink)

How many senses do humans possess? Five external senses, as most cultures have it—sight, hearing, touch, smell, and taste? Should proprioception, kinaesthesia, thirst, and pain be included, under the rubric bodily sense? What about the perception of time and the sense of number? Such questions reduce to two. 1. How do we distinguish a sense from other sorts of information-receiving faculties? 2. By what principle do we distinguish the senses? Aristotle discussed these questions in the De Anima. H. P. Grice (...) revived them in 1967. More recently, they have taken on fresh interest as a result of a collection of essays edited by Fiona Macpherson. This entry reviews some approaches to these questions and advances some new ideas for the reader’s consideration. It proposes that the senses constitute an integrated learning system, membership in which answers question 1. It also proposes that the modalities can be distinguished from one another in two ways, by the means of information pick-up and by the kinds of activity that a perceiver undertakes to make use of them. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The “Figure” of God and the Limits to Liberalism: A Rereading of Locke’s Essay and Two TreatisesVivienne BrownI. A current interpretative issue in reading John Locke’s texts is the relationship between Locke’s theology and political philosophy. 1 Reacting against the secular interpretations of C. B. Macpherson and Leo Strauss, John Dunn argued that Locke’s theology was axiomatic for the political philosophy of the Two Treatises of Government in (...) that Locke’s liberalism was based on a religious individualism. 2 Dunn thus decisively reoriented Lockean scholarship away from seeing Locke as an apologist for a new capitalist economic order, and James Tully and Richard Ashcraft have since substantiated the view that theological presuppositions were foundational for Locke’s political writings but they emphasized the radical nature of Locke’s political position. 3 This view has in turn been challenged by more recent contextual studies of the development of Locke’s thought. John Marshall has argued that the political argument in the Two Treatises of Government is not dependent on religious individualism in [End Page 83] that Locke’s natural theology was itself driven by epistemological investigations, and that it was this epistemological impetus which inclined the Christian Locke towards the Socinian tendencies of his later years. 4 Ian Harris accepts that theological explanation was central to Locke’s writings in ethics and government, but he also emphasizes the reverse process of determination where Locke’s theology, particularly with respect to revealed religion, is in turn reliant upon Locke’s broader thinking. Harris argues therefore that there is a continuity of substantive thought such that theological concerns mesh into, rather than exclusively determine, the broader pattern of Locke’s political and moral ideas. 5 Recent studies thus share a considerable common ground in their recognition of the importance of the relationship between Locke’s theology and political philosophy, but disagreements remain over the precise nature of this relationship and its implications for Locke’s writings.This paper will address the question of the relationship between Locke’s theology and political philosophy by examining the figurative expressions by means of which God is represented in Locke’s Essay Concerning Human Understanding and Two Treatises of Government. 6 The paper will argue that the ways in which this metaphorical “figure” of God is inscribed in Locke’s epistemology and political philosophy 7 suggest a different approach to reading the intricate relationship between God and mankind, and that this casts doubt on the widely-received understanding of Locke’s contribution to classic liberal arguments within political philosophy. It will be argued further that the different formulations of the figure of God in these two texts result in problematizing the historiographic notions of theoretical determination and historicized authorial intent which have so far largely informed the interpretative debate in this area. 8 [End Page 84]II. In the Essay it is argued that mankind has no knowledge of real essences, even of such a simple thing as a pebble or a fly, and certainly cannot know the real essence of God which is immeasurably more inaccessible. 9 Descriptions of God in the Essay are not, therefore, literal statements of God’s characteristics but necessarily inadequate attempts to conceptualize him from within the linguistic and mental constraints of the finite world of men. Two possibilities are available to mankind in its attempt to mediate this fundamental state of ignorance. One is to try to form a complex idea made up of the simple ideas received from sensation or reflection upon itself and then to magnify this to an infinite degree:And even the most advanced Notion we have of God, is but attributing the same simple Ideas which we have got from Reflection on what we find in our selves, and which we conceive to have more Perfection in them, than would be in their absence, attributing, I say, those simple Ideas to him in an unlimited degree. 10God’s postulated qualities are thus valued human qualities writ infinitely large, even though elsewhere the anthropomorphism of the “ignorant and uninstructed” is rejected: 11[H]aving from what we experiment in our selves, got the Ideas of Existence and Duration; of... (shrink)

If $G$ is a group with a supersimple theory having a finite $SU$-rank, then the subgroup of $G$ generated by all of its normal nilpotent subgroups is definable and nilpotent. This answers a question asked by Elwes, Jaligot, Macpherson and Ryten. If $H$ is any group with a supersimple theory, then the subgroup of $H$ generated by all of its normal soluble subgroups is definable and soluble.

al-majmūʻah 1. Kayfa naʻmal lil-Islām -- Muqawwimāt shakhṣīyat al-Muslim -- al-Tawāzun wa-al-iʻtidāl fī ḥayāt al-Muslim.