Whenever a structure with a particularly interesting computability-theoretic property is found, it is natural to ask whether similar examples can be found within well-known classes of algebraic structures, such as groups, rings, lattices, and so forth. One way to give positive answers to this question is to adapt the original proof to the new setting. However, this can be an unnecessary duplication of effort, and lacks generality. Another method is to code the original structure into a structure in the given (...) class in a way that is effective enough to preserve the property in which we are interested. In this paper, we show how to transfer a number of computability-theoretic properties from directed graphs to structures in the following classes: symmetric, irreflexive graphs; partial orderings; lattices; rings ; integral domains of arbitrary characteristic; commutative semigroups; and 2-step nilpotent groups. This allows us to show that several theorems about degree spectra of relations on computable structures, nonpreservation of computable categoricity, and degree spectra of structures remain true when we restrict our attention to structures in any of the classes on this list. The codings we present are general enough to be viewed as establishing that the theories mentioned above are computably complete in the sense that, for a wide range of computability-theoretic nonstructure type properties, if there are any examples of structures with such properties then there are such examples that are models of each of these theories. (shrink)

Cholak, Goncharov, Khoussainov, and Shore [1] showed that for each k > 0 there is a computably categorical structure whose expansion by a constant has computable dimension k. We show that the same is true with k replaced by ω. Our proof uses a version of Goncharov's method of left and right operations.

Originally published in 1958.The history of Morley College provides an illuminating case-history of the growth and spread of adult education in the second half of the nineteenth and early years of the twentieth centuries. Morley College is unique in that it was one of the first of such institutions to proclaim and inculcate absolute sex and class equality. It has always been guided by democratic principles in the sense that the students have been encouraged to play a definite part in (...) the administration of the college – an ethos which continues to this day. (shrink)

Originally published in 1958.The history of Morley College provides an illuminating case-history of the growth and spread of adult education in the second half of the nineteenth and early years of the twentieth centuries. Morley College is unique in that it was one of the first of such institutions to proclaim and inculcate absolute sex and class equality. It has always been guided by democratic principles in the sense that the students have been encouraged to play a definite part in (...) the administration of the college – an ethos which continues to this day. (shrink)

We investigate the complexity of various combinatorial theorems about linear and partial orders, from the points of view of computability theory and reverse mathematics. We focus in particular on the principles ADS (Ascending or Descending Sequence), which states that every infinite linear order has either an infinite descending sequence or an infinite ascending sequence, and CAC (Chain-AntiChain), which states that every infinite partial order has either an infinite chain or an infinite antichain. It is well-known that Ramsey's Theorem for pairs (...) (RT₂²) splits into a stable version (SRT₂²) and a cohesive principle (COH). We show that the same is true of ADS and CAC, and that in their cases the stable versions are strictly weaker than the full ones (which is not known to be the case for RT₂² and SRT₂²). We also analyze the relationships between these principles and other systems and principles previously studied by reverse mathematics, such as WKL₀, DNR, and BΣ₂. We show, for instance, that WKL₀ is incomparable with all of the systems we study. We also prove computability-theoretic and conservation results for them. Among these results are a strengthening of the fact, proved by Cholak, Jockusch, and Slaman, that COH is Π₁¹-conservative over the base system RCA₀. We also prove that CAC does not imply DNR which, combined with a recent result of Hirschfeldt, Jockusch, Kjos-Hanssen, Lempp, and Slaman, shows that CAC does not imply SRT₂² (and so does not imply RT₂²). This answers a question of Cholak, Jockusch, and Slaman. Our proofs suggest that the essential distinction between ADS and CAC on the one hand and RT₂² on the other is that the colorings needed for our analysis are in some way transitive. We formalize this intuition as the notions of transitive and semitransitive colorings and show that the existence of homogeneous sets for such colorings is equivalent to ADS and CAC, respectively. We finish with several open questions. (shrink)

Using coding devices based on a theorem due to Zsigmondy, Birkhoff and Vandiver, we first define in terms of successor S and coprimeness predicate $\perp$ a full arithmetic over the set of powers of some fixed prime, then we define in the same terms a restriction of the exponentiation. Hence we prove the main result insuring that all arithmetical relations and functions over prime powers and their opposite are $\{S, \perp\}$ -definable over Z. Applications to definability over Z and N (...) are stated as corollaries of the main theorem. (shrink)

Human control of action in routine situations involves a flexible interplay between (a) task-dependent serial ordering constraints; (b) top-down, or intentional, control processes; and (c) bottom-up, or environmentally triggered, affordances. In addition, the interaction between these influences is modulated by learning mechanisms that, over time, appear to reduce the need for top-down control processes while still allowing those processes to intervene at any point if necessary or if desired. We present a model of the acquisition and control of goal-directed action (...) that goes beyond existing models by operationalizing an interface between two putative systems—a routine and a non-routine system—thereby demonstrating how explicitly represented goals can interact with the emergent task representations that develop through learning in the routine system. The gradual emergence of task representations offers an explanation for the transfer of control with experience from the non-routine goal-based system to the routine system. At the same time it allows action selection to be sensitive both to environmental triggers and to biasing from multiple levels within the goal system. (shrink)

In this paper we give a positive answer to Julia Robinson's question whether the definability of + and · from S and ∣ that she proved in the case of positive integers is extendible to arbitrary integers (cf. [JR, p. 102]).

Let $ be the restriction of usual order relation to integers which are primes or squares of primes, and let ⊥ denote the coprimeness predicate. The elementary theory of $\langle\mathbb{N};\bot, , is undecidable. Now denote by $ the restriction of order to primary numbers. All arithmetical relations restricted to primary numbers are definable in the structure $\langle\mathbb{N};\bot, . Furthermore, the structures $\langle\mathbb{N};\mid, and $\langle\mathbb{N};=,+,x\rangle$ are interdefinable.

We show that the theory of the partial ordering of the computably enumerable degrees in any given nontrivial interval is undecidable and has uncountably many 1-types.

The development of analogical reasoning has traditionally been understood in terms of theories of adult competence. This approach emphasizes structured representations and structure mapping. In contrast, we argue that by taking a developmental perspective, analogical reasoning can be viewed as the product of a substantially different cognitive ability – relational priming. To illustrate this, we present a computational (here connectionist) account where analogy arises gradually as a by-product of pattern completion in a recurrent network. Initial exposure to a situation primes (...) a relation that can then be applied to a novel situation to make an analogy. Relations are represented as transformations between states. The network exhibits behaviors consistent with a broad range of key phenomena from the developmental literature, lending support to the appropriateness of this approach (using low-level cognitive mechanisms) for investigating a domain that has normally been the preserve of high-level models. Furthermore, we present an additional simulation that integrates the relational priming mechanism with deliberative controlled use of inhibition to demonstrate how the framework can be extended to complex analogical reasoning, such as the data from explicit mapping studies in the literature on adults. This account highlights how taking a developmental perspective constrains the theory construction and cognitive modeling processes in a way that differs substantially from that based purely on adult studies, and illustrates how a putative complex cognitive skill can emerge out of a simple mechanism. (shrink)

Let M be a first-order structure; we denote by DEF(M) the set of all first-order definable relations and functions within M. Let π be any one-to-one function from N into the set of prime integers. Let ∣ and $\bullet$ be respectively the divisibility relation and multiplication as function. We show that the sets DEF(N,π,∣) and $\mathrm{DEF}(\mathbb{N},\pi,\bullet)$ are equal. However there exists function π such that the set DEF(N,π,∣), or, equivalently, $\mathrm{DEF}(\mathbb{N},\pi,\bullet)$ is not equal to $\mathrm{DEF}(\mathbb{N},+,\bullet)$ . Nevertheless, in all cases (...) there is an $\{\pi,\bullet\}$ -definable and hence also {π,∣}-definable structure over N which is isomorphic to $\langle\mathbb{N},+,\bullet\rangle$ . Hence theories TH(N,π,∣) and $\mathrm{TH}(\mathbb{N},\pi,\bullet)$ are undecidable. The binary relation of equipotence between two positive integers saying that they have equal number of prime divisors is not definable within the divisibility lattice over positive integers. We prove it first by comparing the lower bound of the computational complexity of the additive theory of positive integers and of the upper bound of the computational complexity of the theory of the mentioned lattice. The last section provides a self-contained alternative proof of this latter result based on a decision method linked to an elimination of quantifiers via specific tables. (shrink)

In this response, we reiterate the importance of development (both ontogenetic and phylogenetic) in the understanding of a complex cognitive skill – analogical reasoning. Four key questions structure the response: Does relational priming exist, and is it sufficient for analogy? What do we mean by relations as transformations? Could all or any relations be represented as transformations? And what about the challenge of more complex analogies? In addressing these questions we bring together a number of supportive commentaries, strengthening our emergentist (...) case for analogy (in particular with insights from comparative psychology), and review new supportive evidence. We also rebut those commentaries that ignore development at their peril. Along the way, we revisit the main assumptions underlying the analogy as relational priming (ARP) account of analogy, clarifying and elaborating as necessary. (shrink)

Which entities should be accepted as part of the furniture of the world, and which not? What are pseudo-objects, if they are not properly objects? This collection explores the answers given to these questions by some key philosophers throughout the 20th century. It brings together essays by leading scholars on a subject of central importance to both metaphysics and the history of philosophy.".

Contemporary conversations about religion and culture are framed by two reductive definitions of secularity. In one, multiple faiths and nonfaiths coexist free from a dominant belief in God. In the other, we deny the sacred altogether and exclude religion from rational thought and behavior. But is there a third way for those who wish to rediscover the sacred in a skeptical society? What kind of faith, if any, can be proclaimed after the ravages of the Holocaust and the many religion-based (...) terrors since? Richard Kearney explores these questions with a host of philosophers known for their inclusive, forward-thinking work on the intersection of secularism, politics, and religion. An interreligious dialogue that refuses to paper over religious difference, these conversations locate the sacred within secular society and affirm a positive role for religion in human reflection and action. Drawing on his own philosophical formulations, literary analysis, and personal interreligious experiences, Kearney develops through these engagements a basic gesture of hospitality for approaching the question of God. His work facilitates a fresh encounter with our best-known voices in continental philosophy and their views on issues of importance to all spiritually minded individuals and skeptics: how to reconcile God's goodness with human evil, how to believe in both God and natural science, how to talk about God without indulging in fundamentalist rhetoric, and how to balance God's sovereignty with God's love. (shrink)

This note argues that the charge of reductionism levelled against Richard Dawkins is false. It does so by examining the development of his notion of the genes in his books The Selfish Gene (TSG), and The Extended Phenotype (TEP).

Embodied approaches to cognition conceive of mental life as emerging from the ongoing relationship between neural and extra-neural resources. The latter include, first and foremost, our entire body, but also the activity patterns enacted within a contingent milieu, cultural norms, social factors, and the features of the environment that can be used to enhance our cognitive capacities (e.g., tools, devices, etc.). Recent work in music education and sport psychology has applied general principles of embodiment to a number of social contexts (...) relevant to their respective fields. In particular, both disciplines have contributed fascinating perspectives to our understanding of how skills are acquired and developed in groups; how musicians, athletes, teachers, and coaches experience their interactions; and how empathy and social action participate in shaping effective performance. In this paper, we aim to provide additional grounding for this research by comparing and further developing original themes emerging from this cross-disciplinary literature and empirical works on how performative skills are acquired and optimized. In doing so, our discussion will focus on: (1) the feeling of being together, as meaningfully enacted in collective musical and sport events; (2) the capacity to skillfully adapt to the contextual demands arising from the social environment; and (3) the development of distributed forms of bodily memory. These categories will be discussed from the perspective of embodied cognitive science and with regard to their relevance for music education and sport psychology. It is argued that because they play a key role in the acquisition and development of relevant skills, they can offer important tools to help teachers and coaches develop novel strategies to enhance learning and foster new conceptual and practical research in the domains of music and sport. (shrink)

The conceptual and technical difficulties involved in creating a quantum theory of gravity have led some physicists to question, and even in some cases to deny, the reality of time. More surprisingly, this denial has found a sympathetic audience among certain philosophers of physics. What should we make of these wild ideas? Does it even make sense to deny the reality of time? In fact physical science has been chipping away at common sense aspects of time ever since its inception. (...) Section 1 offers a brief survey of the demolition process. Section 2 distinguishes a tempered from an extremely radical form that a denial of time might take, and argues that extreme radicalism is empirically self-refuting. Section 3 begins an investigation of the prospects for tempered radicalism in a timeless theory of quantum gravity. (shrink)

This book builds on the idea that pragmatics and philosophy are strictly interconnected and that advances in one area will generate consequential advantages in the other area. The first part of the book, entitled ‘Theoretical Approaches to Philosophy of Language’, contains contributions by philosophers of language on connectives, intensional contexts, demonstratives, subsententials, and implicit indirect reports. The second part, ‘Pragmatics in Discourse’, presents contributions that are more empirically based or of a more applicative nature and that deal with the pragmatics (...) of discourse, argumentation, pragmatics and law, and context. The book presents perspectives which, generally, make most of the Gricean idea of the centrality of a speaker’s intention in attribution of meaning to utterances, whether one is interested in the level of sentence-like units or larger chunks of discourse. (shrink)

Michael A. PetersBeijing Normal UniversityMy deepest condolences to Pepe, Dom and Marcus and to Jim’s grandchildren. Tina and I spent a lot of time at the Marshall family home, often attending dinn...

Few philosophers have left a legacy like that of Gottfried Wilhelm Leibniz. He has been credited not only with inventing the differential calculus, but also with anticipating the basic ideas of modern logic, information science, and fractal geometry. He made important contributions to such diverse fields as jurisprudence, geology and etymology, while sketching designs for calculating machines, wind pumps, and submarines. But the common presentation of his philosophy as a kind of unworldly idealism is at odds with all this bustling (...) practical activity. In this book Richard. T. W. Arthur offers a fresh reading of Leibniz’s philosophy, clearly situating it in its scientific, political and theological contexts. He argues that Leibniz aimed to provide an improved foundation for the mechanical philosophy based on a new kind of universal language. His contributions to natural philosophy are an integral part of this programme, which his metaphysics, dynamics and organic philosophy were designed to support. Rather than denying that substances really exist in space and time, as the idealist reading proposes, Leibniz sought to provide a deeper understanding of substance and body, and a correct understanding of space as an order of situations and time as an order of successive things. This lively and approachable book will appeal to students of philosophy, as well as anyone seeking a stimulating introduction to Leibniz's thought and its continuing relevance. (shrink)

Richard Jeffrey espoused an antifoundationalist variant of Bayesian thinking that he termed ‘Radical Probabilism’. Radical Probabilism denies both the existence of an ideal, unbiased starting point for our attempts to learn about the world and the dogma of classical Bayesianism that the only justified change of belief is one based on the learning of certainties. Probabilistic judgment is basic and irreducible. Bayesian conditioning is appropriate when interaction with the environment yields new certainty of belief in some proposition but leaves one’s (...) conditional beliefs untouched (the ‘Rigidity’ condition). Although Richard Jeffrey denied the general applicability of this condition, one of his main contributions to probabilistic thinking is a form of belief updating—now typically called ‘Jeffrey conditioning’ or ‘probability kinematics’—that is appropriate in circumstances in which Rigidity is satisfied, but where the interaction causes one to reevaluate one’s probability judgments over some partition of the possibility space without conferring certainty on any particular element. The most familiar occasion for Jeffrey conditioning is receipt of uncertain evidence: things partially perceived or remembered. But it also serves to illuminate belief updating occasioned by a change in one’s degrees of conditional belief, a kind of belief change largely ignored by classical Bayesianism. I argue that such changes in conditional belief can also be basic (in the sense of not being analyzable as a consequence of conditioning on factual information) and offer a kinematical model for a particular kind change in conditional belief. Both are applied to changes in preference. Finally, I argue that Rigidity can fail when changes of belief give inferential grounds for changes in conditional belief (and vice versa). These failures show that conditioning methods are properly regarded, not as valid rules of inference, but as tools in the ‘art of judgment’. (shrink)

Choix d’articles. By Gérard Fussman. Edited by Denis Matringe, Éric Ollivier, and Isabelle Szelagowski. École française d’Extrême-Orient, Réimpressions no. 14. Paris: École Française d’Extrême-Orient, 2014. Pp. 598. €40.

Richard A. Watson - Augustinian-Cartesian Index: Texts and Commentary - Journal of the History of Philosophy 43:3 Journal of the History of Philosophy 43.3 359-361 Zbigniew Janowski. Augustinian-Cartesian Index: Texts and Commentary. South Bend, IN: St. Augustine's Press, 2004. Pp. xv + 275. Cloth, $35.00. This is an English translation and substantial expansion of the French edition . Besides augmenting Augustinian citations, Janowski has added indices and commentaries for Saint Thomas Aquinas, John Duns Scotus, Francis Bacon, and Montaigne. The result (...) is a crucial compilation and analysis of the major textual sources of Descartes's philosophy. Janowski demonstrates that Descartes's metaphysics is foundationally Augustinian, particularly in his dependence on the doctrine of God's creation of eternal truths: "the idea that God creates by an act of understanding" . This doctrine was, in fact, left out of the Meditations. Janowski argues that it logically belongs in the fourth Meditation but was deleted because it was almost universally denied by the.. (shrink)

The standard Kripkean semantic theories for quantified modal logic allow the individuals that exist at other worlds to vary from those that exist at the actual world. This causes a problem for those who deny the existence of non-actual individuals. I focus on two prominent strategies for solving this problem, due respectively to Bernard Linsky and Edward Zalta (who identify the possible individuals with the actual individuals) and Alvin Plantinga (who identifies the possible individuals with the individual essences). I argue, (...) contra various commentators, that both of these solutions are acceptable by the lights of those who deny the existence of mere possibilia. (shrink)

I.WhatVintage ofCivilRights?In this paper I wish to compare and contrast two separate conceptions of civil rights and to argue that the older, more libertarian conception of the subject is preferable to the more widely accepted version used in the modern civil rights movement. The first conception of civil rights focuses on the question of individual capacity. The antithesis of a person with civil rights is the slave. But even if individuals are declared free, they are nonetheless denied their civil rights (...) if they are unable to own property, to enter into contracts, to make wills, to give evidence, and to sue (and be sued) in courts. With all these civil rights claims, the target of the individual grievance is the state; it has denied large classes of individuals the formal capacities that it recognized and protected in others. The Civil War was fought largely over slavery. In its aftermath, civil rights claims protecting individual capacity received explicit, if imperfect, statutory and constitutional protection. The postbellum protections didnotguarantee these rights in absolute fashion – that is, in a way that would not be susceptible to abridgment under any circumstances. Instead, civil rights were protected in what might be called a relative fashion: whatever rights of this sort were enjoyed by white citizens were to be enjoyed by the newly freed black citizens as well. (shrink)