We show that versions of the prime number theorem as well as equivalent statements hold in an arbitrary model ofIΔ 0+exp.

We present a comprehensive study of the axiom schemas IΣ - n , BΣ - n (induction and collection schemas for parameter free Σ n formulas) and some closely related schemas.

In this paper, we prove results concerning the existence of proper end extensions of arbitrary models of fragments of Peano arithmetic. In particular, we give alternative proofs that concern a result of Clote :163–170, 1986); :301–302, 1998), on the end extendability of arbitrary models of \-induction, for \, and the fact that every model of \-induction has a proper end extension satisfying \-induction; although this fact was not explicitly stated before, it follows by earlier results of Enayat and Wong and (...) Wong. (shrink)

We study the strength (over bounded induction) of axioms expressing particular cases of the Chinese Remainder Theorem with respect to the axiom ∀ x, y∃ z (z = xy).

. We provide an alternative proof of a theorem of P. Clote concerning end extensions of models of $\Sigma_n$ -induction, for $n \geq 2$.

We study problems of Clote and Paris, concerning the existence of end extensions of models of Σ n -collection. We continue the study of the notion of ‘Γ-fullness’, begun by Wilkie and Paris (Logic, Methodology and Philosophy of Science VIII (Moscow, 1987). Stud. Logic Found. Math., vol. 126, pp. 143–161. North- Holland, Amsterdam, 1989) and introduce and study a generalization of it, to be used in connection with the existence of Σ n -elementary end extensions (instead of plain end extensions). (...) We obtain (a) alternative proofs of results (Adamowicz in Fund. Math. 136, 133–145, 1990) and (Wilkie and Paris in Logic, Methodology and Philosophy of Science VIII (Moscow, 1987). Stud. Logic Found. Math., vol. 126, pp. 143–161. North-Holland, Amsterdam, 1989) related to the problem of Paris and (b) a partial solution to the problem of Clote. (shrink)

In June 2012, the conference Trends in Logic XI, whose main theme was Advances in Philosophical Logic, took place at the Ruhr University in Bochum. Eight of the invited papers were published in a special issue of the journal Studia Logica. The present volume contains fourteen papers, which the editors selected out of the contributed papers presented at the conference, in order to offer a panorama of the themes developed in philosophical logic in the last two decades or so, as (...) well as to indicate some promising directions for further research. In what follows, we give a brief description of each contribution, following the order in the list of contents.In the first paper, B. Armour-Garb and J.A. Woodbridge discuss a manner in which one can treat semantic pathologies, such as the Liar Paradox. According to their approach, semantically pathological sentences are s-defective, i.e. they can be understood in a sense, but they bear no content, which we can accept or reject. The a .. (shrink)

De Interpretatione is among Aristotle's most influential and widely read writings; C. W. A. Whitaker presents the first systematic study of this work, and offers a radical new view of its aims, its structure, and its place in Aristotle's system. He shows that De Interpretatione is not a disjointed essay on ill-connected subjects, as traditionally thought, but a highly organized and systematic treatise on logic, argument, and dialectic.

We give alternative proofs of results due to Paris and Wilkie concerning the existence of end extensions of countable models of $B\Sigma_{1}$, that is, the theory of $\Sigma_{1}$ collection.

Both Carnap and Quine made significant contributions to the philosophy of mathematics despite their diversedviews. Carnap endorsed the dichotomy between analytic and synthetic knowledge and classified certainmathematical questions as internal questions appealing to logic and convention. On the contrary, Quine wasopposed to the analytic-synthetic distinction and promoted a holistic view of scientific inquiry. The purpose of thispaper is to argue that in light of the recent advancement of experimental mathematics such as Monte Carlosimulations, limiting mathematical inquiry to the domain of (...) logic is unjustified. Robustness studies implemented inMonte Carlo Studies demonstrate that mathematics is on par with other experimental-based sciences. (shrink)

On the basis of recent work concerning the meaning of the term stoicheion in Aristotle’s Analytics, we strengthen the view that this treatise can be viewed as a precursor of Euclid’s Elements.

The volume under review contains work dedicated to the memory of Leo Esakia, who died in 2010, after having worked for over 40 years towards developing duality theory for modal and intuitionistic logics. The collection comprises ten technical contributions that follow the first chapter, in which the reader can find information on Esakia’s studies and career, as well as a complete list of his research publications. In the sequel, we will refer briefly to each of these ten chapters, following the (...) order in the list of contents.B. Jónsson and A. Tarski, in two papers they published in the early 1950s in the American Journal of Mathematics, initiated the study of duality for Boolean algebras with additional operations, via the theory of canonical extensions. Esakia was among the first researchers who studied duality for lattices with additional operations [Topological Kripke models. Soviet Math.Dokl. 15 , 147–151], in particular for Heyting algebras and S4 modal algebras. M. Gehrke, a .. (shrink)

Postcolonial science studies entails ostensibly contradictory critical and empirical commitments. Science studies scholars influenced by Bruno Latour and Isabelle Stengers embrace forms of realist, radical empiricism, while postcolonial studies scholars influenced by Jacques Derrida trace the limits of the knowable. This essay takes their common use of the term cosmopolitics as an unexpected point of departure for reconciling Derrida’s program with Stengers’s and Latour’s. I read Derrida’s critique of hospitality and Stengers’s and Latour’s ontological politics as necessary complements for conceiving (...) a care-oriented subalternist cosmopolitics, a process of composing common worlds that remains attentive to the limits of representation. (shrink)

Biologists studying complex causal systems typically identify some factors as causes and treat other factors as background conditions. For example, when geneticists explain biological phenomena, they often foreground genes and relegate the cellular milieu to the background. But factors in the milieu are as causally necessary as genes for the production of phenotypic traits, even traits at the molecular level such as amino acid sequences. Gene-centered biology has been criticized on the grounds that because there is parity among causes, the (...) “privileging” of genes reflects a reductionist bias, not an ontological difference. The idea that there is an ontological parity among causes is related to a philosophical puzzle identified by John Stuart Mill: what, other than our interests or biases, could possibly justify identifying some causes as the actual or operative ones, and other causes as mere background? The aim of this paper is to solve this conceptual puzzle and to explain why there is not an ontological parity among genes and the other factors. It turns out that solving this puzzle helps answer a seemingly unrelated philosophical question: what kind of causal generality matters in biology? (shrink)

Bazzocchi disposes the text of the Tractatus in a user-friendly manner, exactly as Wittgenstein's decimals advise. This discloses the logical form of the book by distinct reading units, linked into a fashioned hierarchical tree. The text becomes much clearer and every reader can enjoy, finally, its formal and literary qualities.

The authors present a case study involving truth telling responsibilities in the setting of nonepileptic seizures. Specifically, over the course of several suspected nonepileptic seizures, a patient’s seizures stopped after he received a saline flush meant to precede the administration of anti-seizure medication. The patient and his surrogate believed he had received the medication each time, and the team wondered whether they should disclose the truth. Some worried that disclosure would reinforce the suspected psychogenic behavior, exacerbating the patient’s condition. In (...) this way, the case study presents a twist on the traditional truth telling archetype. While most truth telling cases center on navigating cultural differences or worries about emotional harm, this case presented concerns about medical harm in the form of exacerbating the patient’s condition. The authors describe the complex patient-family-team dynamic that preceded this ethical dilemma, describe the case, analyze the ethical issue, and describe the outcome. (shrink)

This paper investigates the emotional import of literary devices deployed in fiction. Reflecting on the often-favored approach in the analytic tradition that locates fictional characters, events, and narratives as sources of readers’ emotions, I attempt to broaden the scope of analysis by accounting for how literary devices trigger non-cognitive emotions. I argue that giving more expansive consideration to literary devices by which authors present content facilitates a better understanding of how fiction engages emotion. In doing so, I also explore the (...) somatic dimension of reading fiction. (shrink)

This paper investigates what molecular biology has done for our understanding of the gene. I base a new account of the gene concept of classical genetics on the classical dogma that gene differences cause phenotypic differences. Although contemporary biologists often think of genes in terms of this concept, molecular biology provides a second way to understand genes. I clarify this second way by articulating a molecular gene concept. This concept unifies our understanding of the molecular basis of a wide variety (...) of phenomena, including the phenomena that classical genetics explains in terms of gene differences causing phenotypic differences. (shrink)

In ancient China, a revered Taoist sage named Zhuangzi told many parables. In Existential Psychology and the Way of the Tao, a selection of these parables will be featured. Following each parable, an eminent existential psychologist will share a personal and scholarly reflection on the meaning and relevance of the parable for psychotherapy and contemporary life. The major tenets of Zhuangzi's philosophy are featured. Taoist concepts of emptiness, stillness, Wu Wei (i.e. intentional non-intentionality), epistemology, dreams and the nature of reality, (...) character building in the midst of pain, meaning and the centrality of relationships, authenticity, self-care, the freedom that can come from one's willingness to confront death, spiritual freedom, and gradations of therapeutic care are topics highlighted in this book. (shrink)

An examination of David Hume's philosophy of religion that situates his conception "true religion" within the context of his overall science of human nature, his rejection of popular religion, and his Ciceronian influence"--Provided by publisher.

This reconsideration of Hume’s classic essay “Of Miracles” via the lens of American pragmatist ways of thinking about history and power shifts our attention from Hume’s epistemic concerns about the legitimacy of witnesses and testimony to his distaste for sacred history, his critical stance regarding the social force of revelation, and his disdain for religious authority. To view Hume’s essay both as an articulation of a critical philosophy of history and as an exercise in moral dynamism (social power or, authority, (...) is a result of epistemic transactions), is to intervene in both Hume studies and Contemporary Pragmatism. (shrink)

Under what circumstances if ever ought we to grant that Artificial Intelligences (AI) are persons? The question of whether AI could have the high degree of moral status that is attributed to human persons has received little attention. What little work there is employs western conceptions of personhood, while non-western approaches are neglected. In this article, I discuss African conceptions of personhood and their implications for the possibility of AI persons. I focus on an African account of personhood that is (...) prima facie inimical to the idea that AI could ever be ‘persons’ in the sense typically attributed to humans. I argue that despite its apparent anthropocentrism, this African account could admit AI as persons. (shrink)