We work in the context of ω-stable theories. We obtain a natural, algebraic equivalent of ENI-NDOP and discuss recent joint proofs with Shelah that if an ω-stable theory has either ENI-DOP or is ENI-NDOP and is ENI-deep, then the set of models of T with universe ω is Borel complete.

We define an easily verifiable notion of an atomic formula having uniformly bounded arrays in a structure M. We prove that if T is a complete L-theory, then T is mutually algebraic if and only if there is some model M of T for which every atomic formula has uniformly bounded arrays. Moreover, an incomplete theory T is mutually algebraic if and only if every atomic formula has uniformly bounded arrays in every model M of T.

A countable, atomically stable structure U in a finite, relational language has fewer than 2 ω non-isomorphic substructures if and only if U is cellular. An example shows that the finiteness of the language is necessary.

We describe the Ax-Kochen definable subsets of the value group of a Hensel field and apply our results to a problem on identifying invariant factors in Hecke algebras.

We prove that if M is any model of a trivial, weakly minimal theory, then the elementary diagram T(M) eliminates quantifiers down to Boolean combinations of certain existential formulas.

We introduce the notions of a mutually algebraic structures and theories and prove many equivalents. A theory $T$ is mutually algebraic if and only if it is weakly minimal and trivial if and only if no model $M$ of $T$ has an expansion $(M,A)$ by a unary predicate with the finite cover property. We show that every structure has a maximal mutually algebraic reduct, and give a strong structure theorem for the class of elementary extensions of a fixed mutually algebraic (...) structure. (shrink)

We sharpen Hájek’s Completeness Theorem for theories extending predicate product logic, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi\forall}$$\end{document}. By relating provability in this system to embedding properties of ordered abelian groups we construct a universal BL-chain L in the sense that a sentence is provable from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi\forall}$$\end{document} if and only if it is an L-tautology. As well we characterize the class of lexicographic sums that have this universality property.

We study o-minimal expansions of Archimedean totally ordered groups. We first prove that any such expansion must be elementarily embeddable via a unique (provided some nonzero element is 0-definable) elementary embedding into a unique o-minimal expansion of the additive ordered group of real numbers R. We then show that a definable function in an o-minimal expansion of R enjoys good differentiability properties and use this to prove that an Archimedean real closed field is definable in any nonsemilinear expansion of R. (...) Combining these results, we obtain several restrictions on possible o-minimal expansions of arbitrary Archimedean ordered groups and in particular of the rational ordered group. (shrink)

We study classes of atomic models \ of a countable, complete first-order theory T. We prove that if \ is not \-small, i.e., there is an atomic model N that realizes uncountably many types over \\) for some finite \ from N, then there are \ non-isomorphic atomic models of T, each of size \.

Fix a weakly minimal (i.e. superstable U-rank 1) structure M. Let M∗ be an expansion by constants for an elementary substructure, and let A be an arbitrary subset of the universe M. We show that all formulas in the expansion (M∗,A) are equivalent to bounded formulas, and so (M,A) is stable (or NIP) if and only if the M-induced structure AM on A is stable (or NIP). We then restrict to the case that M is a pure abelian group with (...) a weakly minimal theory, and AM is mutually algebraic (equivalently, weakly minimal with trivial forking). This setting encompasses most of the recent research on stable expansions of (Z,+). Using various characterizations of mutual algebraicity, we give new examples of stable structures of the form (M,A). Most notably, we show that if (G,+) is a weakly minimal additive subgroup of the algebraic numbers, A⊆G is enumerated by a homogeneous linear recurrence relation with algebraic coefficients, and no repeated root of the characteristic polynomial of A is a root of unity, then (G,+,B) is superstable for any B⊆A. (shrink)

We characterize when the elementary diagram of a mutually algebraic structure has a model complete theory, and give an explicit description of a set of existential formulas to which every formula is equivalent. This characterization yields a new, more constructive proof that the elementary diagram of any model of a strongly minimal, trivial theory is model complete.

We prove that many seemingly simple theories have Borel complete reducts. Specifically, if a countable theory has uncountably many complete one-types, then it has a Borel complete reduct. Similarly, if $Th(M)$ is not small, then $M^{eq}$ has a Borel complete reduct, and if a theory T is not $\omega $ -stable, then the elementary diagram of some countable model of T has a Borel complete reduct.

We show that if a countable structure M in a finite relational language is not cellular, then there is an age-preserving $N \supseteq M$ such that $2^{\aleph _0}$ many structures are bi-embeddable with N. The proof proceeds by a case division based on mutual algebraicity.

We show that if T is a trivial uncountably categorical theory of Morley Rank 1 then T is model complete after naming constants for a model.

We prove two results intended to streamline proofs about cellularity that pass through mutual algebraicity. First, we show that a countable structure M is cellular if and only if M is \-categorical and mutually algebraic. Second, if a countable structure M in a finite relational language is mutually algebraic non-cellular, we show it admits an elementary extension adding infinitely many infinite MA-connected components. Towards these results, we introduce MA-presentations of a mutually algebraic structure, in which every atomic formula is mutually (...) algebraic. This allows for an improved quantifier elimination and a decomposition of the structure into independent pieces. We also show this decomposition is largely independent of the MA-presentation chosen. (shrink)

In this paper, we study VC-minimal theories and explore related concepts. We first define the notion of convex orderablity and show that this lies strictly between VC-minimality and dp-minimality. To do this we prove a general result about set systems with independence dimension ≤ 1. Next, we define the notion of weak VC-minimality, show it lies strictly between VC-minimality and dependence, and show that all unstable weakly VC-minimal theories interpret an infinite linear order. Finally, we define the notion full VC-minimality, (...) show that this lies strictly between weak o-minimality and VC-minimality, and show that theories that are fully VC-minimal have low VC-density. (shrink)

We describe techniques for constructing models of size continuum inωsteps by simultaneously building a perfect set of enmeshed countable Henkin sets. Such models have perfect, asymptotically similar subsets. We survey applications involving Borel models, atomic models, two-cardinal transfers and models respecting various closure relations.

We consider the question of when, given a subset A of M, the setwise stabilizer of the group of automorphisms induces a closed subgroup on Sym(A). We define s-homogeneity to be the analogue of homogeneity relative to strong embeddings and show that any subset of a countable, s-homogeneous, ω-stable structure induces a closed subgroup and contrast this with a number of negative results. We also show that for ω-stable structures s-homogeneity is preserved under naming countably many constants, but under slightly (...) weaker conditions it can be lost by naming a single point. (shrink)

Abstract: In this article, I offer a proposal to clarify what I believe is the proper relation between value maximization and stakeholder theory, which I call enlightened value maximization. Enlightened value maximization utilizes much of the structure of stakeholder theory but accepts maximization of the long-run value of the firm as the criterion for making the requisite tradeoffs among its stakeholders, and specifies long-term value maximization or value seeking as the firm’s objective. This proposal therefore solves the problems that arise (...) from the multiple objectives that accompany traditional stakeholder theory. I also discuss the Balanced Scorecard, which is the managerial equivalent of stakeholder theory, explaining how this theory is flawed because it presents managers with a scorecard that gives no score—that is, no single-valued measure of how they have performed. Thus managers evaluated with such a system (which can easily have two dozen measures and provides no information on the tradeoffs between them) have no way to make principled or purposeful decisions. The solution is to define a true (single dimensional) score for measuring performance for the organization or division (and it must be consistent with the organization’s strategy), and as long as their score is defined properly, (and for lower levels in the organization it will generally not be value) this will enhance their contribution to the firm. (shrink)

The arguments for redistribution of wealth, and for prohibiting certain transactions such as price-gouging, both are based in mistaken conceptions of exchange. This paper proposes a neologism, “euvoluntary” exchange, meaning both that the exchange is truly voluntary and that it benefits both parties to the transaction. The argument has two parts: First, all euvoluntary exchanges should be permitted, and there is no justification for redistribution of wealth if disparities result only from euvoluntary exchanges. Second, even exchanges that are not euvoluntary (...) should generally be permitted, because access to market exchange may be the only means by which people in desperate circumstances can improve their position. (shrink)

This paper defends Mereological Universalism(the thesis that, for any set S of disjoint objects, there is an object that the members of S compose. Universalism is unpalatable to many philosophers because it entails that if there are such things as my left tennis shoe, W. V. Quine, and the Taj Mahal, then there is another object that those three things compose. This paper presents and criticizes Peter van Inwagen's argument against Universalism and then presents a new argument in favor of (...) Universalism. It turns out that the most reasonable way to resist the argument for Universalism is to deny the existence of artifacts; thus, if we believe in artifacts, we have no real choice other than to embrace Universalism. (shrink)

This paper defends Mereological Universalism (the thesis that, for any set S of disjoint objects, there is an object that the members of S compose. Universalism is unpalatable to many philosophers because it entails that if there are such things as my left tennis shoe, W. V. Quine, and the Taj Mahal, then there is another object that those three things compose. This paper presents and criticizes Peter van Inwagen’s argument against Universalism and then presents a new argument in favor (...) of Universalism. It turns out that the most reasonable way to resist the argument for Universalism is to deny the existence of artifacts; thus, if we believe in artifacts, we have no real choice other than to embrace Universalism. (shrink)

There are five individually plausible and jointly incompatible assumptions underlying four familiar puzzles about material constitution. The problem of material constitution just is the fact that these five assumptions are both plausible and incompatible. I will begin by providing a very general statement of the problem. I will present the five assumptions and provide a short argument showing how they conflict with one another. Then, in subsequent sections, I will go on to show how these assumptions underlie each of the (...) four puzzles. I will conclude by providing an exhaustive taxonomy of possible solutions to the problem. (shrink)

The European Legacy, Volume 17, Issue 4, Page 568-569, July 2012.

In debate about the nature of persistence over time, the view that material objects endure has played the role of "champion" and the view that they perdure has played the role of the "challenger." It has fallen to the perdurantists rather than the endurantists to motivate their view, to provide reasons for accepting it that override whatever initial presumption there is against it. Perdurantists have sought to discharge their burden in several ways. For example, perdurantism has been recommend on the (...) grounds that: (i) it solves several of the puzzles that raise the problem of material constitution; (ii) it is (at least) suggested by the special theory of relativity (hereafter "SR"); (iii) it is the only view that makes sense out of the possibility of intrinsic change; (iv) it is the only view consistent with the doctrine of Humean supervenience; and (v) it makes better sense than its competitor out of the possibility of fission. There are primary and most powerful claims that have been made on behalf of perdurantism. They are individually persuasive and together they constitute a formidable assault upon the hegemony of endurantism. Endurantists of course, have not been without reply. However, since endurantists typically respond to these claims one at a time and in different ways, it is easy to get the impression that perdurantism offers a single, neat solution to a host of problems whereas endurantism requires a patchwork of different strategies. But this impression is an illusion. In Rea 1995, I argued that though perdurantism does solve some of the puzzles that raise the problem of material constitution, it does not solve the problem of material constitution itself. Thus, the problem of material constitution really has no bearing on the debate between endurantists and perdurantists. In his paper, I will show that the same is true with respect to SR, the problem of intrinsic change, the doctrine of Humean supervenience, and the possibility of fission. In short, I will argue that none of (ii-v) is true and that therefore the doctrine of temporal parts stands unmotivated. (shrink)

There are various puzzles that set our intuitions about composition and identity against one another. Four that are particularly well known are the Growing Argument, the Ship of Theseus Puzzle, the Body-minus Argument, and Allan Gibbard’s puzzle about Lumpl and Goliath. Such puzzles have received a great deal of attention in the literature over the past thirty years, and there is an impressive and growing variety of solutions available for each of them. Surprisingly, however, no one has really discussed how (...) all of the different puzzles, and their solutions, are interrelated. On the surface, they seem to raise different problems; but clearly the puzzles are related somehow. They raise similar questions and generate similar sets of possible solutions. But, as yet, nothing has been said about how far the similarities extend. (shrink)

In debate about the nature of persistence over time, the view that material objects endure has played the role of “champion” and the view that they perdure has played the role of “challenger.” As in other contests, the champion’s job is merely to defend her title, whereas the challenger’s job is to prove herself worthy. I have no view about how these roles came to be assigned; but the historical fact is that perdurantists have traditionally borne the proverbial burden of (...) proof in this debate. It has fallen to the perdurantists rather than the endurantists to motivate their view, to provide reasons for accepting it that override whatever initial presumption there is against it. (shrink)

Griffiths and Tenenbaum (2006) asked individuals to make predictions about the duration or extent of everyday events (e.g., cake baking times), and reported that predictions were optimal, employing Bayesian inference based on veridical prior distributions. Although the predictions conformed strikingly to statistics of the world, they reflect averages over many individuals. On the conjecture that the accuracy of the group response is chiefly a consequence of aggregating across individuals, we constructed simple, heuristic approximations to the Bayesian model premised on the (...) hypothesis that individuals have access merely to a sample of k instances drawn from the relevant distribution. The accuracy of the group response reported by Griffiths and Tenenbaum could be accounted for by supposing that individuals each utilize only two instances. Moreover, the variability of the group data is more consistent with this small‐sample hypothesis than with the hypothesis that people utilize veridical or nearly veridical representations of the underlying prior distributions. Our analyses lead to a qualitatively different view of how individuals reason from past experience than the view espoused by Griffiths and Tenenbaum. (shrink)

The strong predominance of right-handedness appears to be a uniquely human characteristic, whereas the left-cerebral dominance for vocalization occurs in many species, including frogs, birds, and mammals. Right-handedness may have arisen because of an association between manual gestures and vocalization in the evolution of language. I argue that language evolved from manual gestures, gradually incorporating vocal elements. The transition may be traced through changes in the function of Broca's area. Its homologue in monkeys has nothing to do with vocal control, (...) but contains the so-called “mirror neurons,” the code for both the production of manual reaching movements and the perception of the same movements performed by others. This system is bilateral in monkeys, but predominantly left-hemispheric in humans, and in humans is involved with vocalization as well as manual actions. There is evidence that Broca's area is enlarged on the left side in Homo habilis, suggesting that a link between gesture and vocalization may go back at least two million years, although other evidence suggests that speech may not have become fully autonomous until Homo sapiens appeared some 170,000 years ago, or perhaps even later. The removal of manual gesture as a necessary component of language may explain the rapid advance of technology, allowing late migrations of Homo sapiens from Africa to replace all other hominids in other parts of the world, including the Neanderthals in Europe and Homo erectus in Asia. Nevertheless, the long association of vocalization with manual gesture left us a legacy of right-handedness. Key Words: cerebral dominance; gestures; handedness; hominids; language evolution; primates; speech; vocalization. (shrink)

In the UK, current policies and services for people with mental disorders, including those with intellectual disabilities (ID), presume that these men and women can, do, and should, make decisions for themselves. The new Mental Capacity Act (England and Wales) 2005 (MCA) sets this presumption into statute, and codifies how decisions relating to health and welfare should be made for those adults judged unable to make one or more such decisions autonomously. The MCA uses a procedural checklist to guide this (...) process of substitute decision-making. The personal experiences of providing direct support to seven men and women with ID living in residential care, however, showed that substitute decision-making took two forms, depending on the type of decision to be made. The first process, ‘strategic substitute decision-making’, paralleled the MCA’s legal and ethical framework, whilst the second process, ‘relational substitute decision-making’, was markedly different from these statutory procedures. In this setting, ‘relational substitute decision-making’ underpinned everyday personal and social interventions connected with residents’ daily living, and was situated within a framework of interpersonal and interdependent care relationships. The implications of these findings for residential services and the implementation of the MCA are discussed. (shrink)

For over two decades, the philosophical literature on divine hiddenness has been concerned with just one problem about divine hiddenness that arises out of one very particular concept of God. The problem - I'll call it the Schellenberg problem - has J. L. Schellenberg as both its inventor and its most prominent defender. The concept of God in question construes God as a perfect heavenly parent, and seems to be the product of perfect being theology deployed within the constraints imposed (...) by modern ideals of parenthood. In this paper, I argue that the Schellenberg problem is an attack on a straw deity. More specifically, I argue that Schellenberg's argument against the existence of God depends on certain theological claims that are not commitments of traditional Christian theology and that would, furthermore, be repudiated by many of the most important and influential theologians in the Christian tradition. I close with some very brief remarks about the implications of this conclusion for what I take to be the real import of the Schellenberg problem. (shrink)

In this paper, I present an Aristotelian solution to the problem of material constitution. The problem of material constitution arises whenever it appears that an object a and an object b share all of the same parts and yet are essentially related to their parts in different ways. (A familiar example: A lump of bronze constitutes a statue of Athena. The lump and the statue share all of the same parts, but it appears that the lump can, whereas the statue (...) cannot, survive radical rearrangements of those parts.) I argue that if we are prepared to follow Aristotle in making a distinction between numerical sameness and identity, we can solve the problem of material constitution without recourse to co-location or contingent identity and without repudiating any of the familiar objects of common sense (such as lumps and statues) or denying that these objects have the essential properties we ordinarily think that they have. (shrink)

Originally published by the Center for Hellenic Studies, this book investigates the extent to which the Presocratics were hamstrung by their lack of detailed conceptual framework in the case of the words "one" and "many." This investigation is based on Aristotle's analyses.

A detailed account of human language and evolution, reconciling the apparent dichotomy between humans and all other animals. Focuses on the speculative presence of a Generative Assembly Device, unique to Homo sapiens.

Conservation policy in New Zealand is centred around an objective to totally eradicate three invasive species; the ship rat, the brushtail possum and the stoat, by 2050. The preferred control method to achieve this is large scale poisoning operations with 1080 and similar toxins. This project is backed up by governmental and non-governmental agencies and surrounded with discourse of ‘war’ and ‘invasion’. The ‘Big Three’ predators are endowed with sinister motives as a means of mobilising support. This self-described ‘war’ is (...) evaluated in terms of ‘just war’ theory and found wanting. In particular there are issues with the recruitment of children for killing, humiliation of combatants, questionable economic motives for the ‘war’, deception by government agencies, lack of consultation, a lack of consideration of alternatives, the use of excessive suffering, and unrealistic expectations. An alternative paradigm of ‘compassionate conservation’ is proposed for New Zealand. Instead of trying to get back to a stable pre-colonial state of nature, I propose a holistic approach that respects both ecosystems and their members and takes into account new understandings of ecosystems as dynamic processes. (shrink)

In this paper I defend two conclusions: that time travel journeys to the past are not undertaken freely and, more generally, that nobody is free between the earliest arrival time and the latest departure time of a time travel journey to the past. Time travel to the past destroys freedom on a global scale.