The connections between mathematical logic and combinatorics have a rich history. This paper focuses on one aspect of this relationship: understanding the strength, measured using the tools of computability theory and reverse mathematics, of various partition theorems. To set the stage, recall two of the most fundamental combinatorial principles, König's Lemma and Ramsey's Theorem. We denote the set of natural numbers by ω and the set of finite sequences of natural numbers by ω<ω. We also identify each n ∈ ω (...) with its set of predecessors, so n = {0, 1, 2, …, n − 1}. (shrink)

We study the computational content of the Brouwer Fixed Point Theorem in the Weihrauch lattice. Connected choice is the operation that finds a point in a non-empty connected closed set given by negative information. One of our main results is that for any fixed dimension the Brouwer Fixed Point Theorem of that dimension is computably equivalent to connected choice of the Euclidean unit cube of the same dimension. Another main result is that connected choice is complete for dimension greater than (...) or equal to two in the sense that it is computably equivalent to Weak Kőnig’s Lemma. While we can present two independent proofs for dimension three and upward that are either based on a simple geometric construction or a combinatorial argument, the proof for dimension two is based on a more involved inverse limit construction. The connected choice operation in dimension one is known to be equivalent to the Intermediate Value Theorem; we prove that this problem is not idempotent in contrast to the case of dimension two and upward. We also prove that Lipschitz continuity with Lipschitz constants strictly larger than one does not simplify finding fixed points. Finally, we prove that finding a connectedness component of a closed subset of the Euclidean unit cube of any dimension greater than or equal to one is equivalent to Weak Kőnig’s Lemma. In order to describe these results, we introduce a representation of closed subsets of the unit cube by trees of rational complexes. (shrink)

Theories of discourse bring to realism new ideas about how knowledge develops and how representations of reality are influenced. We gain an understanding of the conceptual aspect of social life and the processes by which meaning is produced. This collection reflects the growing interest realist critics have shown towards forms of discourse theory and deconstruction. The diverse range of contributions address such issues as the work of Derrida and deconstruction, discourse theory, Eurocentrism and poststructuralism. What unites all of the contributions (...) is a sense that it is essential to provide a realist alternative to the hitherto dominance of social constructionism, hermeneutics and postmodernism, over many of the issues discussed. By developing a realist perspective the different authors attempt to embed discourse within the structured nature of the reality of the world. Realism can situate language, discourse and ideology within context specific, or 'causally efficacious' circumstances. Realism can help to uncover issues of power, representation, and subjectivity and how discursive and other social practices produce real effects. This can help us understand the manner in which social structures are reproduced through various forms of ideology and discourse. And by knowing this, we can start to address questions concerning human emancipation and how the world is to be transformed. (shrink)

Topics covered in Discrete Mathematics have become essential tools in many areas of studies in recent years. This is primarily due to the revolution in technology, communications, and cyber security. The book treats major themes in a typical introductory modern Discrete Mathematics course: Propositional and predicate logic, proof techniques, set theory (including Boolean algebra, functions and relations), introduction to number theory, combinatorics and graph theory. An accessible, precise, and comprehensive approach is adopted in the treatment of each topic. The ability (...) of abstract thinking and the art of writing valid arguments are emphasized through detailed proof of (almost) every result. Developing the ability to think abstractly and roguishly is key in any areas of science, information technology and engineering. Every result presented in the book is followed by examples and applications to consolidate its comprehension. The hope is that the reader ends up developing both the abstract reasoning as well as acquiring practical skills. All efforts are made to write the book at a level accessible to first-year students and to present each topic in a way that facilitates self-directed learning. Each chapter starts with basic concepts of the subject at hand and progresses gradually to cover more ground on the subject. Chapters are divided into sections and subsections to facilitate readings. Each section ends with its own carefully chosen set of practice exercises to reenforce comprehension and to challenge and stimulate readers. As an introduction to Discrete Mathematics, the book is written with the smallest set of prerequisites possible. Familiarity with basic mathematical concepts (usually acquired in high school) is sufficient for most chapters. However, some mathematical maturity comes in handy to grasp some harder concepts presented in the book. (shrink)

Ranging over central issues of morals and politics and the nature of freedom and authority, this study examines the role of value-neutrality, rights, equality, ...

Various theorems for the preservation of set-theoretic axioms under forcing are proved, regarding both forcing axioms and axioms true in the Lévy collapse. These show in particular that certain applications of forcing axioms require to add generic countable sequences high up in the set-theoretic hierarchy even before collapsing everything down to ‮א‬₁. Later we give applications, among them the consistency of MM with ‮א‬ω not being Jónsson which answers a question raised in the set theory meeting at Oberwolfach in 2005.

Jennifer Hornsby has defended the Reasons-Knowledge Thesis : the claim that \-ing because p requires knowing that p, where the ‘because’ at issue is a rationalising ‘because’. She defends by appeal to the thought that it provides the best explanation of why the subject in a certain sort of Gettier case fails to be in a position to \ because p. Dustin Locke and, separately, Nick Hughes, present some modified barn-façade cases which seem to constitute counterexamples to and undermine Hornsby’s (...) way of motivating it by rendering their alternative Reasons-Explanation Thesis a better explanation of Hornsby’s datum. This paper defends and Hornsby’s argument for it against those objections. First, I point out that their supposedly intuitive verdict about the relevant barn-façade cases is not as intuitive as they think. Second, I point out that even if we share the intuition: we have strong reason to doubt the verdict anyway. And finally, I point out that since is independently implausible, the two problems can be tackled anyway. (shrink)

According to standard comparativist views, death is bad insofar as it deprives someone of goods she would otherwise have had. In The Ethics of Killing, Jeff McMahan argues against such views and in favor of a gradualist account according to which how bad it is to die is a function of both the future goods of which the decedent is deprived and her cognitive development when she dies. Comparativists and gradualists therefore disagree about how bad it is to die at (...) different ages. In this paper I examine two prominent criticisms of gradualism and show that both misconstrue McMahan. I develop a related criticism that seems to show that a gradualist cannot coherently relate morbidity and mortality. This criticism also fails, but has an instructive implication for how policy-makers setting priorities for health care investments should regard choices between life-saving interventions and interventions against non-fatal diseases in the very young. (shrink)

Over the last few decades, multiple studies have examined the understanding of participants in clinical research. They show variable and often poor understanding of key elements of disclosure, such as expected risks and the experimental nature of treatments. Did the participants in these studies give valid consent? According to the standard view of informed consent they did not. The standard view holds that the recipient of consent has a duty to disclose certain information to the profferer of consent because valid (...) consent requires that information to be understood. The contents of the understanding and disclosure requirements are therefore conceptually linked. In this paper, we argue that the standard view is mistaken. The disclosure and understanding requirements have distinct grounds tied to two different ways in which a token of consent can be rendered invalid. Analysis of these grounds allows us to derive the contents of the two requirements. It also implies that it is sometimes permissible to enroll willing participants who have not understood everything that they ought to be told about their clinical trials. (shrink)

To attribute confusion to someone is to take up a paternalistic stance in evaluating his reasoning.

We argue that there is a conflict among classical theism's commitments to divine simplicity, divine creative freedom, and omniscience. We start by defining key terms for the debate related to classical theism. Then we articulate a new argument, the Aloneness Argument, aiming to establish a conflict among these attributes. In broad outline, the argument proceeds as follows. Under classical theism, it's possible that God exists without anything apart from Him. Any knowledge God has in such a world would be wholly (...) intrinsic. But there are contingent truths in every world, including the world in which God exists alone. So, it's possible that God contingently has wholly intrinsic knowledge. But whatever is contingent and wholly intrinsic is an accident. So, God possibly has an accident. This is incompatible with classical theism. Finally, we consider and rebut several objections. (shrink)

CONTEMPORARY ISSUES IN BUSINESS ETHICS, 6E introduces readers to business ethics by focusing on the influence of market mechanisms and social values on workplace norms. And because business is increasingly a global enterprise, this edition emphasizes the role of ethics both at home and abroad.

The point of Hegel's dissatisfaction with Kant -- Rethinking Peirce's fallibilism -- Pragmatism's future : a touch of prophecy.

The central issue here concerns whether Being as explored by Martin Heidegger in Being and Time is constituted spatiotemporally. As such this project has two interlinked objectives. One objective is to supply conceptually plausible answers to Heidegger’s unanswered questions regarding the temporality of Being, which he raised at the very end of Being and Time. In response I argue that each individual human being is constituted as a Space-Time-Event-Motion (STEM) containment-field embodied entity. Heidegger situates Dasein (human existence) in a temporal (...) stream moving towards the nothingness of death but all the while separating being and time as two distinct phenomena rather than coexistent. I demonstrate why this was a crucial error in Heidegger’s thinking. The second objective deals with the sense of authentic being developed by Heidegger. The spatiotemporal nature of one’s life for Heidegger is understood from the standpoint of Being-in-the-world, as an engaged participant, coexistent with the world, so that contextually it is through this engagement in recognition of this facticity or thrownness that one comes to recognise one’s own authentic self. Somewhat problematic is the coexistent phenomenological recognition that one does not live in isolation and as such one may question what of the contingent, constraining and influencing factors that shape one’s sense of self particularly against the backdrop of self-other relations. This project is situated methodologically within Process Philosophy, and it is from this perspective that draws attention to the role of human agency in which individuals are spatiotemporally construed in terms of Space-Time-Event-Motion (STEM) entities. (shrink)

Particularism's model of explanation is challenged on the ground that a sensible intelligibility principle requires that there must be an explanation for the difference between a good and a bad action. Raz is concerned with what it is to be guided by reason, as well as with the results of the fact that reason can often undermine particular outcomes. What determines the moral status of an action must extend beyond what the agent's reason for acting is. It is argued that (...) there is a clear distinction between the evaluative and guiding functions of reasons. (shrink)

There is a growing body of empirical evidence which shows that infants and non-human primates have the ability to represent the mental states of other agents, i.e. that they possess a Theory of Mind. We will argue that this evidence also suggests that infants and non-human primates possess the concept of truth, which, as we will explain, is good news for primitivists about truth. First, we will offer a brief overview of alethic primitivism, focusing on Jamin Asay’s conceptual version of (...) the view. Next, we will survey relevant work on Theory of Mind which indicates that children younger than two and non-human primates are able to attribute false beliefs. Then, we will bring these false-belief data to bear on Asay’s form of primitivism, arguing that the data support two of the four distinctive theses of this view and offering some remarks about the empirical evaluability of the two remaining theses. We hope that our discussion will help to bridge the gap between psychological and philosophical inquiry and that it will encourage further empirical research on the cognitive significance of the concept of truth for humans and other thinking creatures. (shrink)

Joseph J. Fins calls for a reconsideration of severe brain injury treatment, including discussion of public policy and physician advocacy.

This paper provides a sketch of a fresh conception of the “metaphysics” of culture and a sense of its conceptual power and advantages, based on a post-Darwinian account of the artifactual, hybrid nature of a person, chiefly in terms of (what I treat as terms of art) Bildung (“external” and “internal”), Sittlichkeit (both descriptive and normative), and interpretation (diversely manifested in different sectors of inquiry). I consider the (“metaphysical”) relationship between membership in the species Homo sapiens sapiens and functioning as (...) a person the generic distinction of human cultures (enlanguaged cultures), which I call Intentionality (that is, whatever is culturally significant or significative); and the bearing of the thesis on familiar philosophical quarrels and theory of the sciences. (shrink)

The target articles by Dixon (2012), Scarantino (2012), and Mulligan and Scherer (2012) explore the nature of emotion from philosophical and psychological perspectives. I discuss how neuroscience can also contribute to debates about the nature of emotion. I focus on the aspects of emotion that usually fall within the topic of basic emotions, but conclude that we may need to revise how we conceive and study these kinds of emotional states in relation to the brain.

Schlusslogische Letztbegründung is a collection of essays in honor of Kurt Walter Zeidler. Mr. Zeidler is a distinguished Kant- and Neo-Kantian-scholar who has reconstructed Kant's concept of transcendental logic in connection with the logic of the concept of Hegel and the logic of symbolization of Peirce. (cf. Zeidler: Grundriss der transzendentalen Logik, 3rd ed., Wien 2017) He has most notably inquired intensively into the relation of transcendental logic to philosophy of science (cf. Zeidler: Prolegomena zur Wissenschaftstheorie, Wien 2000) and to (...) phenomenology (cf. Zeidler: Vermittlungen. Zum antiken und neueren Idealismus, Wien 2016). He has also published several studies on Neo-Kantianism (cf. Zeidler: Provokationen. Zu Problemen des Neukantianismus, Wien 2018). This is refelected in the collection of essays by distinguished scholars who discuss and critically examine Zeidler's work. It includes contributions by Steinar Mathisen (Oslo), Wolfdietrich Schmied-Kowarzik (Vienna), Werner Flach (Lichtenau), Thomas Knoppe (Straberg), Geert Edel (Wyk/Föhr), Martin Bunte (Münster), Reinhard Hiltscher (Dresden), Walter Tydecks (Bensheim), Christian Krijnen (Amsterdam), Hartwig Wiedebach (Zürich), Max Gottschlich (Linz), Thomas Sören Hoffmann (Hagen), Rudolf Meer (Kaliningrad), Hans-Jürgen Müller (Frankfurt am Main), Robert König (Vienna), Ulrich Blau (Marburg), Karen Gloy (Luzern/Munich), Reinhold Breil (Aachen), Erhard Oeser (Vienna), Hans-Dieter Klein (Vienna), Hans Martin Dober (Tübingen), Kurt Walter Zeidler (Vienna) and Lois Marie Rendl (Vienna). (shrink)

Belief storage is often modeled as having the structure of a single, unified web. This model of belief storage is attractive and widely assumed because it appears to provide an explanation of the flexibility of cognition and the complicated dynamics of belief revision. However, when one scrutinizes human cognition, one finds strong evidence against a unified web of belief and for a fragmented model of belief storage. Using the best available evidence from cognitive science, we develop this fragmented model into (...) a nascent theory of the cognitive architecture of belief storage. (shrink)

In the current paper we re-examine the concepts of attack semantics and collective attacks in abstract argumentation, and examine how these concepts interact with each other. For this, we systematically map the space of possibilities. Starting with standard argumentation frameworks (which consist of a directed graph with nodes and arrows) we briefly state both node semantics and arrow semantics (the latter a.k.a. attack semantics) in both their extensions-based form and labellings-based form. We then proceed with SETAFs (which consist of a (...) directed hypergraph of nodes and arrows, to take into account the notion of collective attacks) and state both node semantics and arrow semantics, in both their extensions-based and labellings-based form. We then show equivalence between the extensions-based and labellings-based form, for node semantics and arrow semantics of AFs, as well as for node semantics and arrow semantics of SETAFs. Moreover, we show equivalence between node semantics and arrow semantics for AFs, and equivalence between node semantics and arrow semantics for SETAFs (with the notable exception of semi-stable). We also provide a novel way of converting a SETAF to an AF such that semantics are preserved, without the use of any “meta arguments”. Although the main part of our work is on the level of abstract argumentation, we do provide an application of our theory on the instantiated level. More specifically, we show that the classical characterisation of Assumption-Based Argumentation (ABA) can be seen as an instantiation based on a SETAF, whereas the contemporary characterisation of ABA can be seen as an instantiation based on a standard AF. Our theory of how to convert a SETAF to an AF can then be used to account for both the similarities and the differences between the classical and contemporary characterisations of ABA. Most prominently, our theory is able to explain the semantic mismatch for semi-stable semantics that arises in the ABA instantiation process. (shrink)

The early modern period in Western philosophy is the source of many of our most powerful and seductive intellectual commitments. While we may disagree with philosophers of this period, the terms of philosophical inquiry and our standards of rational argumentation are in part derived from the work of Descartes, Leibniz, Locke, Berkeley, Hume and Kant. For this reason, we will pursue a rigorous and sustained introduction to this episode of human intellectual history. We will cover topics in Metaphysics, Epistemology and (...) Philosophy of Mind. (shrink)

This book addresses the mid-rank of the soul theme as it emerges in Plotinus and Augustine in the context of their respective interpretations of universal order. They both use the journey metaphor to describe the soul's progress through the turbulent "sea" of earthly existence.

Frankfurt‐style action cases have been immensely influential in the free will and moral responsibility literatures because they arguably show that an agent can be morally responsible for a behavior despite lacking the ability to do otherwise. However, even among the philosophers who accept Frankfurt‐style action cases, there remains significant disagreement about whether also to accept Frankfurt‐style omission cases – cases in which an agent omits to do something, is unable to do otherwise, and is allegedly morally responsible for that omission. (...) Settling this debate about Frankfurt‐style omission cases is significant because the resolution entails an important fact about moral responsibility: whether there is there a moral asymmetry between actions and omissions with respect to the ability to do otherwise. My proposal is that both Frankfurt‐style action cases and omission cases involve the same type of causal structure: causal preemption. However, the preemptor and the preemptee differ. In action cases, the Frankfurted agent preempts the neuroscientist and is causally and morally responsibility for the effect. In omission cases, Frankfurted agent is neither causally nor morally responsible for the effect. Instead, the neuroscientist preempts the Frankfurted agent. Thus, there are no Frankfurt‐style omission cases. (shrink)