For n≥3, define Tn to be the theory of the generic Kn-free graph, where Kn is the complete graph on n vertices. We prove a graph-theoretic characterization of dividing in Tn and use it to show that forking and dividing are the same for complete types. We then give an example of a forking and nondividing formula. Altogether, Tn provides a counterexample to a question of Chernikov and Kaplan.

We prove that in theories without the tree property of the second kind (which include dependent and simple theories) forking and dividing over models are the same, and in fact over any extension base. As an application we show that dependence is equivalent to bounded non-forking assuming NTP 2.

We consider existentially closed fields with several orderings, valuations, and [Formula: see text]-valuations. We show that these structures are NTP2 of finite burden, but usually have the independence property. Moreover, forking agrees with dividing, and forking can be characterized in terms of forking in ACVF, RCF, and [Formula: see text]CF.

We give three counterexamples to the folklore claim that in an arbitrary theory, if a complete type p over a set B does not divide over $C\subseteq B$, then no extension of p to a complete type over $\operatorname {acl}(B)$ divides over C. Two of our examples are also the first known theories where all sets are extension bases for nonforking, but forking and dividing differ for complete types (answering a question of Adler). One example is an $\mathrm (...) {NSOP}_1$ theory with a complete type that forks, but does not divide, over a model (answering a question of d’Elbée). Moreover, dividing independence fails to imply M-independence in this example (which refutes another folklore claim). In addition to these counterexamples, we summarize various related properties of dividing that are still true. We also address consequences for previous literature, including an earlier unpublished result about forking and dividing in free amalgamation theories, and some claims about dividing in the theory of generic $K_{m,n}$ -free incidence structures. (shrink)

The classes stable, simple, and NSOP $_1$ in the stability hierarchy for first-order theories can be characterised by the existence of a certain independence relation. For each of them there is a canonicity theorem: there can be at most one nice independence relation. Independence in stable and simple first-order theories must come from forking and dividing (which then coincide), and for NSOP $_1$ theories it must come from Kim-dividing. We generalise this work to the framework of Abstract (...) Elementary Categories (AECats) with the amalgamation property. These are a certain kind of accessible category generalising the category of (subsets of) models of some theory. We prove canonicity theorems for stable, simple, and NSOP $_1$ -like independence relations. The stable and simple cases have been done before in slightly different setups, but we provide them here as well so that we can recover part of the original stability hierarchy. We also provide abstract definitions for each of these independence relations as what we call isi-dividing, isi-forking, and long Kim-dividing. (shrink)

Twentieth-century Western philosophy divides untidily into two traditions, analytic and continental, and two figures stand tall at the forking of the ways—the philosophers Gottlob Frege and Edmund Husserl. However, the division is not reducible to this convenient alternative between two great contemporaries equally committed to the provision of firm foundations for the advancement of philosophy.

"What can we expect from the study of Chinese philosophy? « In the philosophical systems of the Hindoos and the Chinese there are still hidden treasures, in which the anticipation of scientific discoveries, the results of thousands of years of occidental research, is most striking. Such are the words of Edward von Hartmann, the most famous living German philosopher1. Much labour has been spent in Europe on the Indian Vedanta philosophy, which had such a marked influence on Arthur Schopenhauer. « (...) The Upanishads, says the author of the Parerga and Paralipomena, are the outcome of the highest human wisdom.... They afford the most remunerative and sublime reading possible in this world, which has been the consolation of my life, as it will be that of my death 2. I do not see why the many germs scattered over the vast field of Chinese philosophy should not have a similar fertilizing influence on some philosophical European mind also. The deep impression caused by the Tao-tê-king will support my view. But much work remains to be done before Chinese philosophy will take its proper place in the history of philosophy. The burden of this task lies with us who are living in China and studying her language and literature, for, while great care is bestowed on all her sister languages in Europe and America, Chinese, the oldest of all, but the youngest in the curriculum of our high-schools, is treated as a step-child by public opinion. This paper is meant as a move in the direction just indicated.". (shrink)

We investigate the notions of strict independence and strict non-forking, and establish basic properties and connections between the two. In particular, it follows from our investigation that in resilient theories strict non-forking is symmetric. Based on this study, we develop notions of weight which characterize NTP2, dependence and strong dependence. Many of our proofs rely on careful analysis of sequences that witness dividing. We prove simple characterizations of such sequences in resilient theories, as well as of Morley (...) sequences which are witnesses. As a by-product we obtain information on types co-dominated by generically stable types in dependent theories. For example, we prove that every Morley sequence in such a type is a witness. (shrink)

We argue against some of Reichenbach's claims about causal forks are incorrect. We do not see why the Second Law of Thermodynamics rules out the existence of conjunctive forks open to the past. In addition, we argue that a common effect rarely forms a conjunctive fork with its joint causes, but it sometimes does. Nevertheless, we think there is something to be said for Reichenbach's idea that forks of various kinds are relevant to explaining why we know more about the (...) past than about the future. And entropy turns out to play a role in the explanation, though not the determining role that Reichenbach envisions. (shrink)

We give a characterisation of forking in the context of simple theories in terms of the fundamental order.

We prove that a theory T has stable forking if and only if Teq has stable forking.

Let Δ be a set of formulas. In this paper we study the following question: under what assumptions on Δ, the concept “a complete Δ-type p over B does not fork over A ⊆ B” behaves well. We apply the results to the structure theory of ω1-saturated models.

This book explores the philosophical thought and praxis of Paul B. Thompson, who planted some of the first seeds of philosophy of agriculture and whose work inspires interdisciplinary scholarship in food ethics, biotechnology, and environmental philosophy. Landmark texts such as The Spirit of the Soil, The Agrarian Vision, and From Field to Fork revealed the fertility of food systems for inspiring reflection on our relationships to technology, the land, and one another. Rooted in philosophical traditions ranging from pragmatism to post-phenomenology, (...) Thompson’s work nourishes projects in ethics, epistemology, philosophy of science, and social and political theory, not only in academic philosophy departments but also in the social and natural sciences. This volume collects this diversity of thought in a tour of the many fields of food systems; from theorizing the sustainability of agroecological systems, to appreciating the quotidian practice of agrarian communities, to anticipating the impacts of emerging biotechnology, and to savoring the roles that food plays in forming our identities. Composed by an international crop of scholars working on the future of food ethics, the volume is a vital contribution to scholars and practitioners thinking through our relationships to the food systems that sustain us. (shrink)

Embodied Selves and Divided Minds examines how research in embodied cognition and enactivism can contribute to our understanding of the nature of self-consciousness, the metaphysics of personal identity, and the disruptions to self-awareness that occur in case of psychopathology. The book reveals how a critical dialogue between Philosophy and Psychiatry can lead to a better understanding of important issues surrounding self-consciousness, personal identity, and psychopathology.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

ABSTRACT Since the United Kingdom’s referendum on European Union (EU) membership in 2016, a new political cleavage of Remainers and Leavers has developed (Kelley, N. [2019]. British social attitudes survey: Britain’s shifting identities and attitudes. (36). National Centre for Research). This paper explores how five pro-Brexit newspapers discursively construct political division in Britain in relation to two key events in the final year of Britain’s EU membership: the extension of the withdrawal process past the original date of March, and the (...) introduction of the Benn Act in September. The paper reveals two primary discursive constructions of division in Britain: a divide between incompetent and arrogant political officials and an innocent, suffering public, and an identity cleavage between pro-Remain ‘elites’ and ‘ordinary’ Leave-voting citizens. The study argues that the construction of these divisions threatens a collective national identity in Britain at a time when it is most required. It concludes that by apportioning blame for socio-political divisions, the newspapers obfuscate their role in contributing to disunity in the UK. (shrink)

We prove in particular that, in a large class of dp-minimal theories including the p-adics, definable types are dense amongst nonforking types.

A ternary relation [Formula: see text] between subsets of the big model of a complete first-order theory T is called an independence relation if it satisfies a certain set of axioms. The primary example is forking in a simple theory, but o-minimal theories are also known to have an interesting independence relation. Our approach in this paper is to treat independence relations as mathematical objects worth studying. The main application is a better understanding of thorn-forking, which turns out (...) to be closely related to modular pairs in the lattice of algebraically closed sets. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

We study Kim-independence over arbitrary sets. Assuming that forking satisfies existence, we establish Kim's lemma for Kim-dividing over arbitrary sets in an NSOP1 theory. We deduce symmetry of Kim-independence and the independence theorem for Lascar strong types.

Given the sharp distinction that follows from Hume’s Fork, the proper epistemic status of propositions of mixed mathematics seems to be a mystery. On the one hand, mathematical propositions concern the relation of ideas. They are intuitive and demonstratively certain. On the other hand, propositions of mixed mathematics, such as in Hume’s own example, the law of conservation of momentum, are also matter of fact propositions. They concern causal relations between species of objects, and, in this sense, they are not (...) intuitive or demonstratively certain, but probable or provable. In this article, I argue that the epistemic status of propositions of mixed mathematics is that of matters of fact. I wish to show that their epistemic status is not a mystery. The reason for this is that the propositions of mixed mathematics are dependent on the Uniformity Principle, unlike the propositions of pure mathematics. (shrink)

The organisation of mammalian mitochondrial DNA (mtDNA) is more complex than usually assumed. Despite often being depicted as a simple circle, the topology of mtDNA can vary from supercoiled monomeric circles over catenanes and oligomers to complex multimeric networks. Replication of mtDNA is also not clear cut. Two different mechanisms of replication have been found in cultured cells and in most tissues: a strand‐asynchronous mode involving temporary RNA coverage of one strand, and a strand‐coupled mode rather resembling conventional nuclear DNA (...) replication. In addition, a recombination‐initiated replication mechanism is likely to be associated with the multimeric mtDNA networks found in human heart. Although an insight into the general principles and key factors of mtDNA organisation and maintenance has been gained over the last few years, there are many open questions regarding replication initiation, termination and physiological factors determining mtDNA organisation and replication mode. However, common themes in mtDNA maintenance across eukaryotic kingdoms can provide valuable lessons for future work. (shrink)

The notion of CM-triviality was introduced by Hrushovski, who showed that his new strongly minimal sets have this property. Recently Baudisch has shown that his new ω 1 -categorical group has this property. Here we show that any group of finite Morley rank definable in a CM-trivial theory is nilpotent-by-finite, or equivalently no simple group of finite Morley rank can be definable in a CM-trivial theory.

Food standards, which are used to signal adherence to sustainability goals or a specific origin, have deep political implications. Standards crafted by retailers, processors, or third-party actors such as non-governmental organizations (NGOs) often disempower farmers. Moreover, due to the liberalization and globalization of many food value chains, producer organizations (POs) lost some of their legal privileges and market protections. This paper analyzes how POs in the Global North sought to regain their control over food markets by establishing their own standards. (...) These strategies and their consequences are considered across three dimensions: the internal life of the PO, the relevant market institutions, and the relationship between the PO and the state. Our case studies (N = 5) performed in France and in Québec, a French-speaking province of Canada, span across a variety of food sectors. Drawing on qualitative material, we designed our explanatory framework through an abductive, iterative method. Although standards crafted by POs have, in some cases, reshaped market institutions to their advantage and have repositioned them in the governance of food markets, they come at a cost. They may create tensions within POs and clash with the agrarian values of solidarity, democracy, and autonomy. Overall, this article challenges the assumption that food standards are mainly governed by private actors and sheds light on the new alliances and new identities of POs. (shrink)

In this article I look at CR (critical realism)1 as chiefly exhibited in the seminal theory of Ron Bhaskar – in particular, his early theory of transcendental realism. I examine its mechanisms of thought and pick out some difficulties with the theorisation relative to its deployment by OS theorists and relative to recent attempts to deploy CR as a theory which can bridge the fork in the constructivist and realist areas known as a form of ‘divide’ in the discipline (fault (...) line). I also try and attempt a more in-depth philosophical analysis of the ideas of CR to gain an insight into its nature and what it can offer both as an apodictic system of philosophical insights with aspects of a belief system – but also relative to its realist-related claims towards veridical knowledge of kinds. I make comparisons with other theorists and philosophers including Kant, Derrida, Hume and Aristotle. I close with insights into how a closer scrutiny of CR thought as it is entering OS is necessary to understand the evolving nature of the inter-relationship of ontology and the ontic, in relation to the fault line described. (shrink)

In this essay, it is submitted that consent comes in degrees and the wrongfulness and harmfulness of conduct is contingent on the degree of voluntariness underwriting the particular consent decision. A fully free decision to consent changes the normative nature of the act: genuine gift-giving is not theft. Lovemaking is not rape. Partially free decisions to consent can change the nature of the act if it makes the act less harmful and thus less wrongful. Partial consent is not about claiming (...) that the conduct was partially justified, but rather about demonstrating the particular act was less harmful and thus deserving of a less serious crime label than is found in the label rape simpliciter. A second theme picked up in this essay is the issue of conditional consent. It is submitted that breaching a condition (conditions such as D is rich, D is a pacifist, D does not have HIV and so on) of consent to sexual intercourse will not change otherwise consensual nature of the sexual intercourse itself, but it may give rise to criminal liability for the collateral harm caused such as HIV infection. (shrink)

I explore connections between social divisions and diversity within the self, while striving to differentiate internal diversity and multiplicity. When the person is understood as composite or multiple, she is seen as divided into several distinct agent-like aspects. This view is found in ancient, modern, and postmodern philosophy, psychology, poetry, and lay people's accounts of their experience. I argue for a conception of the self as diverse but not composite or multiple.

We discuss the role of weakly normal formulas in the theory of thorn forking, as part of a commentary on the paper [5]. We also give a counterexample to Corollary 4.2 from that paper, and in the process discuss “theories with selectors.”.

​​This book explores the philosophical thought and praxis of Paul B. Thompson, who planted some of the first seeds of philosophy of agriculture and whose work inspires interdisciplinary scholarship in food ethics, biotechnology, and environmental philosophy. Landmark texts such as The Spirit of the Soil, The Agrarian Vision, and From Field to Fork revealed the fertility of food systems for inspiring reflection on our relationships to technology, the land, and one another. Rooted in philosophical traditions ranging from pragmatism to post-phenomenology, (...) Thompson’s work nourishes projects in ethics, epistemology, philosophy of science, and social and political theory, not only in academic philosophy departments but also in the social and natural sciences. This volume collects this diversity of thought in a tour of the many fields of food systems; from theorizing the sustainability of agroecological systems, to appreciating the quotidian practice of agrarian communities, to anticipating the impacts of emerging biotechnology, and to savoring the roles that food plays in forming our identities. Composed by an international crop of scholars working on the future of food ethics, the volume is a vital contribution to scholars and practitioners thinking through our relationships to the food systems that sustain us. (shrink)

We present a self-contained exposition of the basic aspects of simple theories while developing the fundamentals of forking calculus. We expound also the deeper aspects of S. Shelah's 1980 paper Simple unstable theories. The concept of weak dividing has been replaced with that of forking. The exposition is from a contemporary perspective and takes into account contributions due to S. Buechler, E. Hrushovski, B. Kim, O. Lessmann, S. Shelah and A. Pillay.

Anna Lappé: Diet for a Hot Planet: The Climate Crisis at the End of Your Fork and What You Can Do About it Content Type Journal Article Pages 1-2 DOI 10.1007/s10806-011-9326-2 Authors Diane Veale Jones, College of Saint Benedict/Saint John’s University Environmental Studies Department, 112 New Science Center, Saint John’s University, Collegeville, MN 56321, USA Journal Journal of Agricultural and Environmental Ethics Online ISSN 1573-322X Print ISSN 1187-7863.