It is a classical result of Mortimer that $L^2$ , first-order logic with two variables, is decidable for satisfiability. We show that going beyond $L^2$ by adding any one of the following leads to an undecidable logic:– very weak forms of recursion, viz.¶(i) transitive closure operations¶(ii) (restricted) monadic fixed-point operations¶– weak access to cardinalities, through the Härtig (or equicardinality) quantifier¶– a choice construct known as Hilbert's $\epsilon$ -operator.In fact all these extensions of $L^2$ prove to be undecidable both for satisfiability, (...) and for satisfiability in finite structures. Moreover most of them are hard for $\Sigma^1_1$ , the first level of the analytical hierachy, and thus have a much higher degree of undecidability than first-order logic. (shrink)

This book constitutes the outcome of an international conference held at the Otto-Mobes-Volkswirtschaftsschule, Graz-Stifting( Austria), from June 16 to 22, 1974. The conference was initiated by a project group working on determinants and controls of social science development at the In stitute for Advanced Studies and Scientific Research in Vienna and or ganized by the editors of this volume. It was held under the auspices of the Austrian Ministry of Science and Research. The main topics of the conference were (...) those at the forefront of the 'state of argumentation' (to borrow from one of our contributors) in philosophy and sociology of science ever since the controversy between Thomas S. Kuhn and Sir Karl R. Popper has sharpened our awareness for the methodological and substantial presuppositions involved with questions of growth and development in science. Let us give two examples of those topics. The borderline between sociology of science and philo sophy of science has become more and more unclear; while the work of at least some philosophers of science comes to have an empirical flavour, sociologists of science are increasingly apt to include logical and methodo logical components of the research process as their objects of examina tion. Papers included in this volume testify to both tendencies. (shrink)

Routledge is now re-issuing this prestigious series of 204 volumes originally published between 1910 and 1965. The titles include works by key figures such asC.G. Jung, Sigmund Freud, Jean Piaget, Otto Rank, James Hillman, Erich Fromm, Karen Horney and Susan Isaacs. Each volume is available on its own, as part of a themed mini-set, or as part of a specially-priced 204-volume set. A brochure listing each title in the "International Library of Psychology" series is available upon request.

Treatises on Indian philosophy have multiplied in the last thirty years, in the “West as well as in India itself. And in spite of the demanding nature of this subject—it exacts, so to speak, a uniform presentation; it entails a whole succession of systems, each one of which is elaborated in a more or less independent manner—this abundance is nonetheless profitable. Each author makes his contribution in the detailed account of new views and strives to rejuvenate a somewhat refractory material, (...) even if this involves the taking up of old views, discarded or neglected by the new generation of scholars. (shrink)

In this paper, I present an outline of the oppression account of cultural appropriation and argue that it offers the best explanation for the wrongfulness of the varied and complex cases of appropriation to which people often object. I then compare the oppression account with the intimacy account defended by C. Thi Nguyen and Matt Strohl. Though I believe that Nguyen and Strohl’s account offers important insight into an essential dimension of the cultural appropriation debate, I argue that justified objections (...) to cultural appropriation must ultimately be grounded in considerations of oppression as opposed to group intimacy. I present three primary objections to the intimacy account. First, I suggest that in its effort to explain expressive appropriation claims (those that purportedly lack an independent ground), the intimacy account doubles down on the boundary problem. Second, I question whether group intimacy possess the kind of bare normativity that Nguyen and Strohl claim for it. Finally, I argue that these objections give us reason to accept the importance of group intimacy to the cultural appropriation debate, but question the source of its significance as identified by Nguyen and Strohl. (shrink)

This translation of four of Plato's dialogues brings these classic texts alive for modern readers. Allen introduces and comments on the dialogues in an accessible way, inviting the reader to re-examine the issues Plato continually raises.

‘Heritage’ is a concept that often carries significant normative weight in moral and political argument. In this article, I present and critique a prevalent conception according to which heritage must have a positive valence. I argue that this view of heritage leads to two moral problems: Disowning Injustice and Embracing Injustice. In response, I argue for an alternative conception of heritage that promises superior moral and political consequences. In particular, this alternative jettisons the traditional focus on heritage as a primarily (...) positive relationship to the past, and thus offers resources for coming to terms with histories of injustice. (shrink)

Various contributors to recent philosophy of mathematics havetaken Richard Dedekind to be the founder of structuralismin mathematics. In this paper I examine whether Dedekind did, in fact, hold structuralist views and, insofar as that is the case, how they relate to the main contemporary variants. In addition, I argue that his writings contain philosophical insights that are worth reexamining and reviving. The discussion focusses on Dedekind''s classic essay Was sind und was sollen die Zahlen?, supplemented by evidence from Stetigkeit und (...) irrationale Zahlen, his scientific correspondence, and his Nachlaß. (shrink)

This chapter offers an overview of issues posed by the problem of immoral artists, artists who in word or deed violate commonly held moral principles. I briefly consider the question of whether the immorality of an artist can render their work aesthetically worse (making connections to chapters in the Theory section of the handbook), and then turn to questions about what the audience should do and feel in response to knowledge of these moral failings. I discuss questions such as whether (...) audiences have reason not to purchase or consume work by these artists, whether their shows and exhibitions should be canceled, and how fans might grapple with the emotional turmoil they feel when artists whom they love act or speak in ways that are morally condemnable. (shrink)

In recent philosophy of mathematics avariety of writers have presented ``structuralist''views and arguments. There are, however, a number ofsubstantive differences in what their proponents take``structuralism'' to be. In this paper we make explicitthese differences, as well as some underlyingsimilarities and common roots. We thus identifysystematically and in detail, several main variants ofstructuralism, including some not often recognized assuch. As a result the relations between thesevariants, and between the respective problems theyface, become manifest. Throughout our focus is onsemantic and metaphysical issues, (...) including what is orcould be meant by ``structure'' in this connection. (shrink)

Man : wolf or sheep? -- Different forms of violence -- Love of death and love of life -- Individual and social narcissism -- Incestuous ties -- Freedom, determinism, alternativism.

This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.

We identify the computational complexity of the satisfiability problem for FO 2 , the fragment of first-order logic consisting of all relational first-order sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity of its decision problem has not been pinpointed so far. In 1975 Mortimer proved that FO 2 has the finite-model property, which means that if an FO 2 -sentence is satisfiable, then it has a finite (...) model. Moreover, Mortimer showed that every satisfiable FO 2 -sentence has a model whose size is at most doubly exponential in the size of the sentence. In this paper, we improve Mortimer's bound by one exponential and show that every satisfiable FO 2 -sentence has a model whose size is at most exponential in the size of the sentence. As a consequence, we establish that the satisfiability problem for FO 2 is NEXPTIME-complete. (shrink)

Nothing less than a manifesto for a new social and psychological revolution to save our threatened planet, this book is a summary of the penetrating thought of ...

This paper has a two-fold objective: to provide a balanced, multi-faceted account of the origins of logicism; to rehabilitate Richard Dedekind as a main logicist. Logicism should be seen as more deeply rooted in the development of modern mathematics than typically assumed, and this becomes evident by reconsidering Dedekind's writings in relation to Frege's. Especially in its Dedekindian and Fregean versions, logicism constitutes the culmination of the rise of ?pure mathematics? in the nineteenth century; and this rise brought with it (...) an inter-weaving of methodological and epistemological considerations. The latter aspect illustrates how philosophical concerns can grow out of mathematical practice, as opposed to being imposed on it from outside. It also sheds new light on the legacy and the lasting significance of logicism today. (shrink)

During the last 25 years, a large number of publications on the history of analytic philosophy have appeared, significantly more than in the preceding period. As most of these works are by analytically trained authors, it is tempting to speak of a 'historical turn' in analytic philosophy. The present volume constitutes both a contribution to this body of work and a reflection on what is, or might be, achieved in it. The twelve new essays, by an international group of contributors, (...) range from case studies on individual philosophers through discussions of broader themes in the history of analytic philosophy to related methodological reflections. (shrink)

The problem of value disagreement and contextualist, relativist and metalinguistic attempts of solving it are laid out. Although the metalinguistic account seems to be on the right track, it is argued that it does not sufficiently explain why and how disagreements about the meaning of evaluative terms are based on and can be decided by appeal to existing social practices. As a remedy, it is argued that original suggestions from Putnam's 'The Meaning of "Meaning"' ought to be taken seriously. The (...) resulting dual aspect theory of meaning can explain value disagreement in much the same way as it deals with disagreement about general terms. However, the account goes beyond Putnam's by not just defending a version of social externalism, but also defending the thesis that the truth conditional meaning of many evaluative terms is not fixed by experts either and instead constantly contested as part of a normal function of language. (shrink)

In Frege's writings, the notions of truth, judgment, and objectivity are all prominent and important. This paper explores the close connections between them, together with their ties to further cognate notions, such as those of thought, assertion, inference, logical law, and reason. It is argued that, according to Frege, these notions can only be understood properly together, in their inter-relations. Along the way, interpretations of some especially cryptic Fregean remarks, about objectivity, laws of truth, and reason, are offered, and seemingly (...) opposed "realist" and "idealist" strands in his position reconciled. (shrink)

The philosophy of mathematics has long been an important part of philosophy in the analytic tradition, ever since the pioneering works of Frege and Russell. Richard Dedekind was roughly Frege's contemporary, and his contributions to the foundations of mathematics are widely acknowledged as well. The philosophical aspects of those contributions have been received more critically, however. In the present essay, Dedekind's philosophical reception is reconsidered. At the essay’s core lies a comparison of Frege's and Dedekind's legacies, within and outside of (...) analytic philosophy. While the comparison proceeds historically, it is shaped by current philosophical concerns, especially by debates about neo-logicist and neo-structuralist views. In fact, philosophical and historical considerations are intertwined thoroughly, to the benefit of both. The underlying motivation is to rehabilitate Dedekind as a major philosopher of mathematics, in relation, but not necessarily in opposition, to Frege. (shrink)

Routledge is now re-issuing this prestigious series of 204 volumes originally published between 1910 and 1965. The titles include works by key figures such asC.G. Jung, Sigmund Freud, Jean Piaget, Otto Rank, James Hillman, Erich Fromm, Karen Horney and Susan Isaacs. Each volume is available on its own, as part of a themed mini-set, or as part of a specially-priced 204-volume set. A brochure listing each title in the "International Library of Psychology" series is available upon request.

Every year since 1933 many of the world's leading intellectuals have met on Lake Maggiore to discuss the latest developments in philosophy, history, art and science and, in particular, to explore the mystical and symbolic in religion. The Eranos Meetings - named after the Greek word for a banquet where the guests bring the food - constitute one of the most important gatherings of scholars in the twentieth century. The book presents a set of portraits of some of the century's (...) most influential thinkers, all participants at Eranos: Carl Jung, Erich Neumann, Mircea Eliade, Martin Buber, Walter Otto, Paul Tillich, Gershom Scholem, Herbert Read, Joseph Campbell, Erwin Schrodinger, Karl Kereyni, D.T. Suzuki, and Adolph Portmann. The volume presents a critical appraisal of the views of these men, how the exchange of ideas encouraged by Eranos influenced each, and examines the attraction of these esotericists towards authoritarian politics. (shrink)

Hermeneutic studies of science locate a circle at the heart of scientific practice: scientists only gain knowledge of what they, in some sense, already know. This may seem to threaten the rational validity of science, but one can argue that this circle is a virtuous rather than a vicious one. A virtuous circle is one in which research conclusions are already present in the premises, but only in an indeterminate and underdeveloped way. In order to defend the validity of science, (...) the hermeneuticist must describe a method by which a vague and confused initial knowledge of nature gets transformed into a clear and determinate knowledge of nature. I consider three such methods. The first is regressus demonstrativa, favoured by the physicians of Padua during the fifteenth and sixteenth centuries. The second is mathēsis, introduced by Martin Heidegger in his discussion of seventeenth-century science. The third is Denkstil, a key concept in Ludwik Fleck’s history of syphilology. I conclude by listing three desiderata for a hermeneutic science studies: that it be anti-metaphysical, historical, and sociological. --- Reprinted in: Erich Otto Graf, Martin Schmid & Johannes Fehr (eds.), Fleck and the Hermeneutics of Science (Collegium Helveticum Heft 14) (Zürich, 2016), pp. 85-93. (shrink)

Gottlob Frege is often called a "platonist". In connection with his philosophy we can talk about platonism concerning three kinds of entities: numbers, or logical objects more generally; concepts, or functions more generally; thoughts, or senses more generally. I will only be concerned about the first of these three kinds here, in particular about the natural numbers. I will also focus mostly on Frege's corresponding remarks in The Foundations of Arithmetic (1884), supplemented by a few asides on Basic Laws of (...) Arithmetic (1893/1903) and "Thoughts" (1918). My goal is to clarify in which sense the Frege of Foundations and Basic Laws is a platonist concerning the natural numbers.1.. (shrink)

Bioethics and its offspring Health-care Ethics have a variety ofuses and obligations among which and perhaps most importantly istheir social obligation. This paper raises questions as toBioethics fulfilling the necessary criteria for a profession,suggests that it can serve as a link between individual andcommunal problems, discusses the task of health-care ethics as well as ways of teaching it, lists some of the obligationsof health-care ethics professionals and discusses the dangers to and failings of these health-care professionals today. Itconcludes that we (...) are at a crossroads in which we must choosebetween our own personal security and comfort and fulfilling our social role. (shrink)

In this paper I: (1) Describe something of the present situation in the United States and briefly contrast this with the state of affairs in other nations of the industrialised world. I emphasise health care but also allude to other social conditions: health care is merely one institution of a society and, just as do its other institutions, the system of health care reflects the basic world-view of that society. (2) Sketch the world-view and the philosophy which underwrites the use (...) of a market system in distributing what are acknowledged to be critically important social goods like health care and higher education. I show that a well-functioning market can indeed be useful when it comes to distributing some, but not when distributing other goods. (3) Suggest that when competition and the market are used to ‘regulate’ health care, technology—instead of being used to benefit patients—is apt to be used primarily to maximise individual profit: it becomes a weapon between what is often painted as ‘warfare’ among health care providers and institutions. I argue that this state of affairs is based on an undue emphasis upon the demands of individual freedom to the detriment of the community. Finally (4) I suggest an alternative approach to balancing individual with communal interests, an approach which is neither based on a predominance of one with neglect of the other, nor on a dialectic balance between them, but rather upon an approach which sees both individual and communal interests as modifying forces in a complex homeostatic balance. Individual success, in any civilised sense of the term, is possible only in a viable and well-functioning community, and a well-functioning community is not possible without individual success: the two are inevitably interdependent and linked. (shrink)

In this article, monist values are expressed as preferences like in economics and decision making. On the basis of this formalization, various ways of defining value disagreement of agents within a group are investigated. Twelve notions of categorical value disagreement are laid out. Since these are too coarse-grained for many purposes, known distance-based approaches like Kendall’s Tau and Spearman’s footrule are generalized from linear orders to preorders and position-sensitive variants are developed. The account is further generalized to allow for agents (...) with incomplete information. The article ends with a discussion of known limitations of preference-based accounts of values and how these might be overcome by accounting for parity and essential incompleteness. It is also shown that one intuitively compelling notion of disagreement does not give rise to a proper distance measure. (shrink)

We establish a general hierarchy theorem for quantifier classes in the infinitary logic L∞ωωon finite structures. In particular, it is shown that no infinitary formula with bounded number of universal quantifiers can express the negation of a transitive closure.This implies the solution of several open problems in finite model theory: On finite structures, positive transitive closure logic is not closed under negation. More generally the hierarchy defined by interleaving negation and transitive closure operators is strict. This proves a conjecture of (...) Immerman.We also separate the expressive power of several extensions of Datalog, giving new insight in the fine structure of stratified Datalog. (shrink)

In this book, one of the most distinguished scholars of German culture collects his essays on a figure who has long been one of his chief preoccupations.

Ordinal, interval, and ratio scales are discussed and arguments for the thesis that “better than” comparisons reside on interval or ratio scales are laid out. It is argued that linguistic arguments are not conclusive since alternative rank-based definitions can be given, and that in general “better than” comparisons do not have a common scale type. Some comparison dimensions reside on ratio scales, whereas others do not show any evidence of lying on a scale stronger than an ordinal scale.

We now have good reason to worry that many coastal cities will be flooded by the end of the century. How should we confront this possibility (or inevitability)? What attitudes should we adopt to impending inundation of such magnitude? In the case of place-loss due to anthropogenic climate change, I argue that there may ultimately be something fitting about letting go, both thinking prospectively, when the likelihood of preservation is bleak, and retrospectively, when we reflect on our inability to prevent (...) destruction. I then explore some of the ethical complications of this response. (shrink)

Nonindexical Context-Dependence and the Interpretation as Abduction Approach Inclusive nonindexical context-dependence occurs when the preferred interpretation of an utterance implies its lexically-derived meaning. It is argued that the corresponding processes of free or lexically mandated enrichment can be modeled as abductive inference. A form of abduction is implemented in Simple Type Theory on the basis of a notion of plausibility, which is in turn regarded a preference relation over possible worlds. Since a preordering of doxastic alternatives taken for itself only (...) amounts to a relatively vacuous ad hoc model, it needs to be combined with a rational way of learning from new evidence. Lexicographic upgrade is implemented as an example of how an agent might revise his plausibility ordering in light of new evidence. Various examples are given how this apparatus may be used to model the contextual resolution of context-dependent or semantically incomplete utterances. The described form of abduction is limited and merely serves as a proof of concept, but the idea in general has good potential as one among many ways to build a bridge between semantics and pragmatics since inclusive context-dependence is ubiquitous. (shrink)