We show that the stabilizer of an element a of a countable recursively saturated model of arithmetic M is a maximal subgroup of Aut iff the type of a is selective. This is a point of departure for a more detailed study of the relationship between pointwise and setwise stabilizers of certain subsets of M and the types of elements in those subsets. We also show that a complete type of PA is 2-indiscernible iff it is minimal in the sense (...) of Gaifman. (shrink)

Let M be a countable recursively saturated model of Th(), and let GAut(M), considered as a topological group. We examine connections between initial segments of M and subgroups of G. In particular, for each of the following classes of subgroups HG, we give characterizations of the class of terms of the topological group structure of H as a subgroup of G. (a) for some (b) for some (c) for some (d) for some (Here, M(a) denotes the smallest M containing a, (...) , , and .). (shrink)

Let M be a countable recursively saturated model of PA and H an open subgroup of G = Aut. We prove that I = sup {b ∈ M : ∀u < bfu = u and J = inf{b ∈ MH} may be invariant, i. e. fixed by all automorphisms of M.

Continuing the earlier research from [T. Bigorajska, H. Kotlarski, Partitioning α-large sets: some lower bounds, Trans. Amer. Math. Soc. 358 4981–5001] we show that for the price of multiplying the number of parts by 3 we may construct partitions all of whose homogeneous sets are much smaller than in [T. Bigorajska, H. Kotlarski, Partitioning α-large sets: some lower bounds, Trans. Amer. Math. Soc. 358 4981–5001]. We also show that the Paris–Harrington independent statement remains unprovable if the number of (...) colors is restricted to 2, in fact, the statement is unprovable in IΣb. Other results concern some lower bounds for partitions of pairs. (shrink)

In a countable, recursively saturated model of Peano Arithmetic, an interstice is a maximal convex set which does not contain any definable elements. The interstices are partitioned into intersticial gaps in a way that generalizes the partition of the unbounded interstice into gaps. Continuing work of Bamber and Kotlarski [1], we investigate extensions of Kotlarski's Moving Gaps Lemma to the moving of intersticial gaps.

We give a survey of automorphisms of countable recursively saturated models of Peano Arithmetic.

Continuing the earlier research in [14] we give some more information about nonmaximal open subgroups of G = Aut with unique maximal extension, where ℳ is a countable recursively saturated model of True Arithmetic.

We give some information about the action of Aut on M, where M is a countable arithmetically saturated model of Peano Arithmetic. We concentrate on analogues of moving gaps and covering gaps inside M.

We give some information about new proofs of the incompleteness theorems, found in 1990s. Some of them do not require the diagonal lemma as a method of construction of an independent statement.

We give an examination of the automorphism group Aut of a countable recursively saturated model M of PA. The main result is a characterisation of strong elementary initial segments of M as the initial segments consisting of fixed points of automorphisms of M. As a corollary we prove that, for any consistent completion T of PA, there are recursively saturated countable models M1, M2 of T, such that Aut[ncong]Aut, as topological groups with a natural topology. Other results include a classification (...) of the normal subgroups of Aut of the form [lcub]g: g [uharr] A = idA[rcub], for sets A M, and a highly homogeneous representation of Aut as a subgroup of Aut. (shrink)

For a primitive recursive consistent and strong enough theory T we construct an independent statement which has some clear metamathematical meaning.

We give new proofs of both incompleteness theorems. We do not use the diagonalization lemma, but work with some quickly growing functions instead.

We transform the proof of the second incompleteness theorem given in [3] to a proof-theoretic version, avoiding the use of the arithmetized completeness theorem. We give also new proofs of old results: The Arithmetical Hierarchy Theorem and Tarski's Theorem on undefinability of truth; the proofs in which the construction of a sentence by means of diagonalization lemma is not needed.

We show that if M is a countable recursively saturated model of True Arithmetic, then G = Aut has nonmaximal open subgroups with unique extension to a maximal subgroup of Aut.

In this philosophically sophisticated and historically significant work, John H. Zammito reconstructs Kant's composition of The Critique of Judgment and reveals that it underwent three major transformations before publication. He shows that Kant not only made his "cognitive" turn, expanding the project from a "Critique of Taste" to a Critique of Judgment but he also made an "ethical" turn. This "ethical" turn was provoked by controversies in German philosophical and religious culture, in particular the writings of Johann Herder and the (...) Sturm und Drang movement in art and science, as well as the related pantheism controversy. Such topicality made the Third Critique pivotal in creating a "Kantian" movement in the 1790s, leading directly to German Idealism and Romanticism. The austerity and grandeur of Kant's philosophical writings sometimes make it hard to recognize them as the products of a historical individual situated in the particular constellation of his time and society. Here Kant emerges as a concrete historical figure struggling to preserve the achievements of cosmopolitan Aufkl-rung against challenges in natural science, religion, and politics in the late 1780s. More specifically Zammito suggests that Kant's Third Critique was animated throughout by a fierce personal rivalry with Herder and by a strong commitment to traditional Christian ideas of God and human moral freedom. "A work of extraordinary erudition. Zammito's study is both comprehensive and novel, connecting Kant's work with the aesthetic and religious controversies of the late eighteenth century. He seems to have read everything. I know of no comparable historical study of Kant's Third Critique."-Arnulf Zweig, translator and editor of Kant's ;IPhilosophical Correspondence, 1759-1799;X "An intricate, subtle, and exciting explanation of how Kant's thinking developed and adjusted to new challenges over the decade from the first edition of the Critique of Pure Reason to the appearance of the Critique of Judgment. "--John W. Burbidge, Review of Metaphysics "There has been for a long time a serious gap in English commentary on Kant's Critique of Judgment Zammito's book finally fills it. All students and scholars of Kant will want to consult it."--Frederick Beiser, Times Literary Supplement. (shrink)

This book presents a detailed treatment of ordinal combinatorics of large sets tailored for independence results. It uses model theoretic and combinatorial methods to obtain results in proof theory, such as incompleteness theorems or a description of the provably total functions of a theory. In the first chapter, the authors first discusses ordinal combinatorics of finite sets in the style of Ketonen and Solovay. This provides a background for an analysis of subsystems of Peano Arithmetic as well as for combinatorial (...) independence results. Next, the volume examines a variety of proofs of Gödel's incompleteness theorems. The presented proofs differ strongly in nature. They show various aspects of incompleteness phenomena. In additon, coverage introduces some classical methods like the arithmetized completeness theorem, satisfaction predicates or partial satisfaction classes. It also applies them in many contexts. The fourth chapter defines the method of indicators for obtaining independence results. It shows what amount of transfinite induction we have in fragments of Peano arithmetic. Then, it uses combinatorics of large sets of the first chapter to show independence results. The last chapter considers nonstandard satisfaction classes. It presents some of the classical theorems related to them. In particular, it covers the results by S. Smith on definability in the language with a satisfaction class and on models without a satisfaction class. Overall, the book's content lies on the border between combinatorics, proof theory, and model theory of arithmetic. It offers readers a distinctive approach towards independence results by model-theoretic methods. (shrink)

If $M \models PA (= Peano Arithmetic)$ , we set $A^M = \{N \subset_e M: N \models PA\}$ and study this family.

We study cofinal extensions of models of arithmetic, in particular we show that some properties near to expandability are preserved under cofinal extensions.

In 'Een handvol filosofen' staan de filosofen centraal die sinds de oprichting van de Vrije Universiteit in 1880 aan deze instelling verbonden zijn geweest. Het gaat hierbij niet alleen om de inhoud van hun werk, maar ook om de personen zelf. Er waren filosofiedocenten die zich met de universiteit identificeerden en zich volledig konden ontplooien. Er waren er echter ook voor wie dit niet gold, die geïsoleerd of in gewetensnood raakten. Veel filosofiestudenten waren actief betrokken bij wat er in hun (...) faculteit gebeurde. Zij namen initiatieven, protesteerden soms tegen de gang van zaken en kozen partij in conflictsituaties. Sinds het eind van de jaren zestig van de twintigste eeuw verloor de Vrije Universiteit geleidelijk haar christelijk karakter. Tegenwoordig werken alle stafleden vanuit hun eigen motivatie mee aan een hoofdzakelijk seculier geworden universiteit, die ruimte biedt voor religieuze en levensbeschouwelijke diversiteit. (shrink)

We prove that for each β, γ < ε0 there existsα < ε0 such that whenever A ⊆ ω is α ‐large and G: A → β is such that (∀a ∈ A)(psn(G (a)) ≤ a), then there exists a γ ‐large C ⊆ A on which G is nondecreasing. Moreover, we give upper bounds for α for small ordinals β ≤ ω (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim).

We study some variations of the so-called Hardy hierarchy of quickly growing functions, known from the literature, and obtain analogues of Ratajczyk's approximation lemma for them.

In this paper we study the model theory of extensions of models of first-order Peano Arithmetic by means of the arithmetized completeness theorem applied to a definable complete extension of PA in the original model. This leads us to many interesting model theoretic properties equivalent to reflection principles and ω-consistency, and these properties together with the associated first-order schemes extending PA are studied.

Introduction: Platonic dramatology -- The political and philosophical problems. Using pre-Socratic philosophy to support political reform: the Athenian stranger ; Plato's Parmenides: Parmenides' critique of Socrates and Plato's critique of Parmenides ; Becoming Socrates ; Socrates interrogates his contemporaries about the noble and good -- Paradigms of philosophy. Socrates' positive teaching ; Timaeus-Critias: completing or challenging Socratic political philosophy? ; Socratic practice -- The trial and death of Socrates. The limits of human intelligence ; The Eleatic challenge ; The trial (...) and death of Socrates -- Conclusion: Why Plato made Socrates his hero. (shrink)

Many people are worried about the harmful effects of climate change but nevertheless enjoy some activities that contribute to the emission of greenhouse gas (driving, flying, eating meat, etc.), the main cause of climate change. How should such people make choices between engaging in and refraining from enjoyable greenhouse-gas-emitting activities? In this chapter, we look at the answer provided by decision theory. Some scholars think that the right answer is given by interactive decision theory, or game theory; and moreover think (...) that since private climate decisions are instances of the prisoner’s dilemma, one rationally should engage in these activities provided that one enjoys them. Others think that the right answer is given by expected utility theory, the best-known version of individual decision theory under risk and uncertainty. In this chapter, we review these different answers, with a special focus on the latter answer and the debate it has generated. (shrink)

Background: The factors influencing parents’ willingness to enroll their children in biobanks are poorly understood. This study sought to assess parents’ willingness to enroll their children, and their perceived benefits, concerns, and information needs under different consent and data-sharing scenarios, and to identify factors associated with willingness. Methods: This large, experimental survey of patients at the 11 eMERGE Network sites used a disproportionate stratified sampling scheme to enrich the sample with historically underrepresented groups. Participants were randomized to receive one of (...) three consent and data-sharing scenarios. Results: In total, 90,000 surveys were mailed and 13,000 individuals responded (15.8% response rate). 5737 respondents were parents of minor children. Overall, 55% (95% confidence interval 50–59%) of parents were willing to enroll their youngest minor child in a hypothetical biobank; willingness did not differ between consent and data-sharing scenarios. Lower educational attainment, higher religiosity, lower trust, worries about privacy, and attitudes about benefits, concerns, and information needs were independently associated with less willingness to allow their child to participate. Of parents who were willing to participate themselves, 25% were not willing to allow their child to participate. Being willing to participate but not willing to allow one’s child to participate was independently associated with multiple factors, including race, lower educational attainment, lower annual household income, public health care insurance, and higher religiosity. Conclusions: Fifty-five percent of parents were willing to allow their youngest minor child to participate in a hypothetical biobank. Building trust, protecting privacy, and addressing attitudes may increase enrollment and diversity in pediatric biobanks. (shrink)

Abstract:During recent years, the principle and practice of employment-at-will have been under attack. While progress has been made in eroding the practice, the principle still governs the philosophical assumptions underlying employment practices in the United States, and, indeed, EAW has been promulgated as one of the ways to address economic ills in other countries. This paper will briefly review the major critiques of EAW. Given the failure of these arguments to erode the underpinnings of EAW, we shall suggest new avenues (...) for approaching employment issues to achieve the desirable goal of employee dignity and respect. (shrink)

This article presents a response to Richard Rorty's paper "Is Philosophy Relevant to Business Ethics?" The author questions Rorty's views on the depreciation of the role of philosophy in applied ethics, and outlines four reasons why philosophy retains its relevance. The author addresses the role of moral reasoning in the development of the moral imagination. The author also concludes that humans have the means necessary to make moral progress and are capable of moral reasoning, and need only to develop a (...) strong moral imagination. (shrink)

Human nature is enigmatic. Are we cruel, selfish creatures or good merciful Samaritans? This book takes you on a journey into the complexities of human mind and kind, from altruism, sharing, and large-scale cooperation, to cheating, distrust, and warfare. What are the building blocks of morality and sociality? Featuring contributions from leading researchers, such as Christophe Boesch, Leda Cosmides and John Tooby, Azar Gat, Dennis Krebs, Ara Norenzayan, and Frans B. M. de Waal, this fascinating interdisciplinary reader draws on evolutionary (...) and comparative perspectives, and is essential reading for any students interested in the unique characteristics that define humanity and society. (shrink)

This groundbreaking volume casts light on the long shadow of naturalistic monism in modern thought and culture. When monism's philosophical proposition - the unity of all matter and thought in a single, universal substance - fused with scientific empiricism and Darwinism in the mid-nineteenth century, it led to the formation of a powerful worldview articulated in the work of figures such as Ernst Haeckel. The compelling essays collected here, written by leading international scholars, investigate the articulation of monism in science, (...) philosophy, and religion and its impact on a range of social movements, from socialism and early feminism to imperialism and eugenics. The result is a broad and comprehensive chronological, disciplinary, and geographic map of a century of monism, as well as a bellwether for innovative new directions in the interdisciplinary study of science, religion, philosophy, and culture. (shrink)

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)

This article sheds new light on late-19th-century debates about the organization of knowledge through its emphasis on German orientalism and comparative linguistics. Centering on Friedrich Carl Andreas’ (1846–1930) controversial reconstruction of the Avestan language and its sacred literary corpus, I highlight a shift from the history of texts to an engagement with ‘living’ language in the decades around 1900. Andreas is shown to have inherited aspects of two schools, which collectively defined the landscape of 19th-century philological research – one traditional (...) and the other comparative. The long-standing struggle between these schools demonstrates that ‘the humanities’ were no monolithic foil to the rise of natural sciences during the second half of the 19thcentury. Instead, I argue that alternative conceptual frameworks were cultivated within German philology – concepts that were taken up in broader disciplinary debates, though they were not narrowly the products of them. (shrink)