Krynicki, M. and M. Mostowski, Decidability problems in languages with Henkin quantifiers, Annals of Pure and Applied Logic 58 149–172.We consider the language L with all Henkin quantifiers Hn defined as follows: Hnx1…xny1…yn φ iff f1…fnx1. ..xn φ, ...,fn). We show that the theory of equality in L is undecidable. The proof of this result goes by interpretation of the word problem for semigroups.Henkin quantifiers are strictly related to the function quantifiers Fn defined as follows: Fnx1…xny1…yn φ iff fx1…xn (...) φ,...,f). In contrast with the first result we show that the theory of equality with all quantifiers Fn is decidable.We also consider decidability problems for other theories in languages L and L. (shrink)

We say that a semantical function is correlated with a syntactical function F iff for any structure A and any sentence we have A F A .It is proved that for a syntactical function F there is a semantical function correlated with F iff F preserves propositional connectives up to logical equivalence. For a semantical function there is a syntactical function F correlated with iff for any finitely axiomatizable class X the class –1X is also finitely axiomatizable (i.e. iff is (...) continuous in model class topology). (shrink)

Connections between partially ordered connectives and Henkin quantifiers are considered. It is proved that the logic with all partially ordered connectives and the logic with all Henkin quantifiers coincide. This implies that the hierarchy of partially ordered connectives is strongly hierarchical and gives several nondefinability results between some of them. It is also deduced that each Henkin quantifier can be defined by a quantifier of the form equation imagewhat is a strengthening of the Walkoe result. MSC: 03C80.

A fundamental notion in a large part of mathematics is the notion of equicardinality. The language with Hartig quantifier is, roughly speaking, a first-order language in which the notion of equicardinality is expressible. Thus this language, denoted by LI, is in some sense very natural and has in consequence special interest. Properties of LI are studied in many papers. In [BF, Chapter VI] there is a short survey of some known results about LI. We feel that a more extensive exposition (...) of these results is needed. The aim of this paper is to give an overview of the present knowledge about the language LI and list a selection of open problems concerning it. After the Introduction $(\S1)$ , in $\S\S2$ and 3 we give the fundamental results about LI. In $\S4$ the known model-theoretic properties are discussed. The next section is devoted to properties of mathematical theories in LI. In $\S6$ the spectra of sentences of LI are discussed, and $\S7$ is devoted to properties of LI which depend on set-theoretic assumptions. The paper finishes with a list of open problem and an extensive bibliography. The bibliography contains not only papers we refer to but also all papers known to us containing results about the language with Hartig quantifier. Contents. $\S1$ . Introduction. $\S2$ . Preliminaries. $\S3$ . Basic results. $\S4$ . Model-theoretic properties of $LI. \S5$ . Decidability of theories with $I. \S6$ . Spectra of LI- sentences. $\S7$ . Independence results. $\S8$ . What is not yet known about LI. Bibliography. (shrink)

We investigate theories of initial segments of the standard models for arithmetics. It is easy to see that if the ordering relation is definable in the standard model then the decidability results can be transferred from the infinite model into the finite models. On the contrary we show that the Σ₂—theory of multiplication is undecidable in finite models. We show that this result is optimal by proving that the Σ₁—theory of multiplication and order is decidable in finite models as well (...) as in the standard model. We show also that the exponentiation function is definable in finite models by a formula of arithmetic with multiplication and that one can define in finite models the arithmetic of addition and multiplication with the concatenation operation. We consider also the spectrum problem. We show that the spectrum of arithmetic with multiplication and arithmetic with exponentiation is strictly contained in the spectrum of arithmetic with addition and multiplication. (shrink)

Simple formula should contain only few quantifiers. In the paper the methods to estimate quantity and quality of quantifiers needed to express a sentence equivalent to given one.

The theorem to the effect that the languageL introduced in [2] is mutually interpretable with the first order language is proved. This yields several model-theoretical results concerningL.

Writing from a scientifically and philosophically informed perspective, the authors provide a critical overview of the conceptual difficulties encountered in many current neuroscientific and psychological theories.

A long-standing theme in discussion of perception and thought has been that our primary cognitive contact with individual objects and events in the world derives from our perceptual contact with them. When I look at a duck in front of me, I am not merely presented with the fact that there is at least one duck in the area, rather I seem to be presented withthisthing (as one might put it from my perspective) in front of me, which looks to (...) me to be a duck. Furthermore, such a perception would seem to put me in a position not merely to make the existential judgment that there is some duck or other present, but rather to make a singular, demonstrative judgment, that that is a duck. My grounds for an existential judgment in this case derives from my apprehension of the demonstrative thought and not vice versa. (shrink)

This book defends antitheodicism, arguing that theodicies, seeking to excuse God for evil and suffering in the world, fail to ethically acknowledge the victims of suffering. The authors argue for this view using literary and philosophical resources, commencing with Immanuel Kant's 1791 "Theodicy Essay" and its reading of the Book of Job. Three important twentieth century antitheodicist positions are explored, including "Jewish" post-Holocaust ethical antitheodicism, Wittgensteinian antitheodicism exemplified by D.Z. Phillips and pragmatist antitheodicism defended by William James. The authors argue (...) that these approaches to evil and suffering are fundamentally Kantian. Literary works such as Franz Kafka'sThe Trial, Samuel Beckett's Waiting for Godot, and George Orwell's Nineteen Eighty-Four, are examined in order to crucially advance the philosophical case for antitheodicism. (shrink)

In his last book, David Armstrong sets out his metaphysical system in a set of concise and lively chapters each dealing with one aspect of the world. He begins with the assumption that all that exists is the physical world of space-time. On this foundation he constructs a coherent metaphysical scheme that gives plausible answers to many of the great problems of metaphysics. He gives accounts of properties, relations, and particulars; laws of nature; modality; abstract objects such as numbers; and (...) time and mind. (shrink)

Is consciousness a purely physical phenomenon? Most contemporary philosophers and theorists hold that it is, and take this to be supported by modern science. But a significant minority endorse non-physicalist theories such as dualism, idealism and panpsychism, among other reasons because it may seem impossible to fully explain consciousness, or capture what it's like to be in conscious states (such as seeing red, or being in pain), in physical terms. This Element will introduce the main non-physicalist theories of consciousness and (...) explain the most important arguments for them, and consider how they each respond to the scientific and other arguments in support of physicalism. This title is also available as Open Access on Cambridge Core. (shrink)

Western democracy is now at a critical juncture. Some worry that power has been wrested from the people and placed in the hands of a small political elite. Others argue that the democratic system gives too much power to a populace that is largely ill-informed and easily swayed by demagogues. This classic study of democratic principles is thus now more relevant than ever. A renowned historian of antiquity and political philosophy, Sir M.I. Finley offers a comparative analysis of Greek and (...) modern conceptions of democracy. As he puts the ancient Greeks in dialogue with their contemporary counterparts, Finley tackles some of the most pressing issues of our day, including public apathy, partisanship, consensus politics, distrust of professional politicians, and the limits of free speech. Including three lectures that Finley delivered at Rutgers University, plus two additional essays that further illuminate his thinking, _Democracy Ancient and Modern _explores the dramatic differences between the close-knit civil society of the ancient Greeks and our own atomized mass societies. By mapping out democracy’s past and its present manifestations, this book helps us plot a course for democracy’s future. (shrink)

This book presents a collection of essays on institutional theory written by the German sociologist and Weber-expert M. Rainer Lepsius. Based on Weber's work, the author develops concepts of institutional theory, which he subsequently applies to topics such as National Socialism, democratization processes, German unification, and the institutionalization of the European Union. By showing how charismatic leadership can under certain circumstances threaten democratic structures and curtail individual freedoms, and by analyzing the structural and cultural conditions under which people develop trust (...) in political and social structures and ultimately come to support and comply with them, the author provides a sound analytical understanding of the development of democratic institutions and a democratic political culture. This collection of essays was edited, translated and commented on by Claus Wendt. (shrink)

The Ismaili Imam and Imamat -- Ethical foundations -- Tradition and modernity -- The ethos of modernism -- Pluralism and cosmopolitan ethics -- Cohesion within the Umma -- Islam and the West -- Cultivating and enabling environment -- Living the ethics of Islam -- Global convergence.

The socialist construction in Vietnam, aspect of human role.

The given is the state of a mind in its primary engagement with the world. A satisfactory epistemology—one, it turns out, that is foundationalist and includes a naïve realist view of perception—requires a certain account of the given. Moreover, knowledge based on the given requires both a particular view of the world itself and a heterodox account of judgment. These admittedly controversial claims are supported by basic ontological considerations. I begin, then, with two contradictory views of the world per se (...) and the structure one experiences. I draw out the consequences of these two views for what intentionality is. The two views yield incompatible accounts of the given. The definitive spontaneity of the one account, and passivity of the other, can be understood in terms of the structure (or lack thereof) in the given. In defense of the claim that a structured given is not an apt epistemic basis, I examine an attempt to found an epistemology on such an account in light of the so-called myth of the given. I maintain that the given, if it is to provide some justification for taking the world to be a particular way, must be unstructured. To support this, I first discuss a significant problem with traditional foundationalism. I then argue that a satisfactory (foundationalist) epistemology requires the rejection of the orthodox propositional view of judgment in favor of a non-propositional, reistic view. (shrink)

A selection of important writings which together suggest that legal philosophy is the nerve of legal reasoning.

On Avicenna, 980-1037, a Muslim philosopher.

Philosophical Thought in Russia in the Second Half of the 20th Century is the first book of its kind that offers a systematic overview of an often misrepresented period in Russia's philosophy. Focusing on philosophical ideas produced during the late 1950s – early 1990s, it reconstructs the development of genuine philosophical thought in the Soviet period and introduces those non-dogmatic Russian thinkers who saw in philosophy a means of reforming social and intellectual life. Covering such areas of philosophical inquiry as (...) philosophy of science, philosophical anthropology, the history of philosophy, activity approach as well as communication and dialogue studies, the volume presents and thoroughly discusses central topics and concepts developed by Soviet thinkers in that particular fields. Written by a team of internationally recognized scholars from Russia and abroad, it examines the work of well-known Soviet philosophers (such as Mikhail Bakhtin, Evald Ilyenkov and Merab Mamardashvili) as well as those important figures (such as Vladimir Bibler, Alexander Zinoviev, Yury Lotman, Georgy Shchedrovitsky, Genrich Batishchev, Sergey Rubinstein, and others) who have often been overlooked. By introducing and examining original philosophical ideas that evolved in the Soviet period, the book confirms that not all Soviet philosophy was dogmatic and tied to orthodox Marxism and the ideology of Marxism-Leninism. It shows Russian philosophical development of the Soviet period in a new light, as a philosophy defined by a genuine discourse of exploration and intellectual progress, rather than stagnation and dogmatism. In addition to providing the historical and cultural background that explains the development of the 20th-century Russian philosophy, the book also puts the discussed ideas and theories in the context of contemporary philosophical discussions showing their relevance to nowadays debates in Western philosophy. With short biographies of key thinkers, an extensive current bibliography and a detailed chronology of Soviet philosophy, this research resource provides a new understanding of the Soviet period and its intellectual legacy 100 years after the Russian Revolution. (shrink)

Thomas Aquinas's Disputed Questions on Evil is a careful and detailed analysis of the general topic of evil, including discussions on evil as privation, human free choice, the cause of moral evil, moral failure, and the so-called seven deadly sins. This collection of ten, specially commissioned new essays, the first book-length English-language study of Disputed Questions on Evil, examines the most interesting and philosophically relevant aspects of Aquinas's work, highlighting what is distinctive about it and situating it in relation not (...) only to Aquinas's other works but also to contemporary philosophical debates in metaphysics, ethics, and philosophy of action. The essays also explore the history of the work's interpretation. The volume will be of interest to researchers in a broad range of philosophical disciplines including medieval philosophy and history of philosophy, as well as to theologians. (shrink)