This is a book that every enthusiast for Gödel’s proofs of his incompleteness theorems will want to own. It gives an up-to-date account of connections between systems of modal logic and results on provability in formal systems for arithmetic, analysis, and set theory.

This paper obtains lower and upper bounds for the number of alternations of bounded quantifiers needed to express all formulas in certain ordered Abelian groups admitting elimination of unbounded quantifiers. The paper also establishes model-theoretic tests for equivalence to a formula with a given number of alternations of bounded quantifiers.

If are structures for a first-order language , is said to be algebraically closed in just in case every positive existential -sentence true in is true in . In 1976 Elliott showed that unital AF algebras are classified up to isomorphism by corresponding dimension groups with order unit. This paper shows that one dimension group with order unit is algebraically closed in another just in case the corresponding AF algebras, viewed as metric structures, fall in the same relation.

The study of existentially closed closure algebras begins with Lipparini’s 1982 paper. After presenting new nonelementary axioms for algebraically closed and existentially closed closure algebras and showing that these nonelementary classes are different, this paper shows that the classes of finitely generic and infinitely generic closure algebras are closed under finite products and bounded Boolean powers, extends part of Hausdorff’s theory of reducible sets to existentially closed closure algebras, and shows that finitely generic and infinitely generic closure algebras are elementarily (...) inequivalent. Special properties of algebraically closed, existentially closed, finitely generic, and infinitely generic closure algebras are established along the way. (shrink)

A nontrivial ring with unit eliminates imaginaries just in case its complete theory has the following property: every definable m-ary equivalence relation E may be defined by a formula f = f, where f is an m-ary definable function. We show that for certain natural expansions of the field of p-adic numbers, elimination of imaginaries fails or is independent of ZPC. Similar results hold for certain fields of formal power series.

If one builds a topological model, analogous to that of Moschovakis , over the product of uncountably many copies of the Cantor set, one obtains a structure elementarily equivalent to Krol's model . In an intuitionistic metatheory Moschovakis's original model satisfies all the axioms of intuitionistic analysis, including the unrestricted version of weak continuity for numbers.

In the context of continuous logic, this paper axiomatizes both the class \ of lattice-ordered groups isomorphic to C for X compact and the subclass \ of structures existentially closed in \; shows that the theory of \ is \-categorical and admits elimination of quantifiers; establishes a Nullstellensatz for \ and \; shows that \\in \mathcal {C}\) has a prime-model extension in \ just in case X is Boolean; and proves that in a sense relevant to continuous logic, positive formulas (...) admit in \ elimination of quantifiers to positive formulas. (shrink)

There is a model, for a system of intuitionistic analysis including Brouwer's principle for numbers and Kripke's schema, in which math formula ø-definable discrete sets of choice sequences are subcountable.

In a dimension group, the projection of a finite intersection of generalized halfspaces is a finite intersection of generalized halfspaces. The dimension groups obeying a stronger version of this result, true in dense Archimedean ordered groups, are characterized algebraically and provided with a simple set of axioms.

This paper extends theorems of Belegradek about poly-regular groups of finite rank to certain poly-regular groups of infinite rank. A model-theoretic property aiding these investigations is the elimination of unbounded quantifiers, and the paper establishes both a general model-theoretic test for this property and results about bounded quantifiers in the special context of ordered Abelian groups.

In the ordered Abelian group of reals with the integers as a distinguished subgroup, the projection of a finite intersection of generalized halfspaces is a finite intersection of generalized halfspaces. The result is uniform in the integer coefficients and moduli of the initial generalized halfspaces.

While finitely generic dimension groups are known to admit no proper self-embeddings, these groups also have no automorphisms other than scalar multiplications, and every countable infinitely generic dimension group admits proper self-embeddings and has automorphisms other than scalar multiplications. The finite-forcing companion of the theory of dimension groups is recursively isomorphic to first-order arithmetic, the infinite-forcing companion of the theory of dimension groups is recursively isomorphic to second-order arithmetic, and the first-order theory of existentially closed dimension groups is a complete (...) $\Pi_{1}^{1}$-set. While many special properties of f.g. dimension groups may be realized in recursive e.c. dimension groups, and many special properties of i.g. dimension groups may be realized in hyperarithmetic e.c. dimension groups, no f.g. dimension group is arithmetic and no i.g. dimension group is analytical. Yet there is an f.g. dimension group recursive in first-order arithmetic, and there is an i.g. dimension group recursive in second-order arithmetic. (shrink)

Husserlian phenomenology, as the study of conscious experience, has often been accused of solipsism. Husserl’s method, it is argued, does not have the resources to provide an account of consciousness of other minds. This chapter will address this issue by providing a brief overview of the multiple angles from which Husserl approached the theme of intersubjectivity, with specific focus on the details of his account of the concrete interpersonal encounter – “empathy.” Husserl understood empathy as a direct, quasi-perceptual form of (...) intentionality through which the sense of the Other is constituted. Furthermore, his account of empathy is holistically integrated with his overall theory of intersubjectivity, including his discussions of the objectivity of nature, and the social, historical, and communal aspects of subjectivity. Husserl’s theory of empathy continues to cast a long shadow, influencing both the analytic and continental approaches to the problem of other minds, as well as contemporary account of social cognition in the cognitive sciences. (shrink)

This article draws on the antebellum political thought of Black abolitionists Frederick Douglass and Martin Delany in critically assessing the efficacy of reasonableness in advancing the aims of emancipatory politics in political discourse. I argue, through a reading of Douglass and Delany, that comporting oneself reasonably in the face of oppressive ideology can be counterproductive, if one’s aim is to undermine such ideology and the institutions it supports. Douglass and Delany, I argue, also provide us with a framework for evaluating (...) alternative discursive strategies we might wish to employ in light of the limited value of reasonableness for emancipatory politics. (shrink)

For liberal contractarians, moral and political principles are justified if agreeable to persons as free and equals. But for critics of liberal contractarianism, this justification applies only to those capable of agreement. Understanding why contractarianism suffers from the problem of exclusion helps up understand the distinctive character of contractarianism and the importance of agreement in particular. I suggest contractarianism need not be objectionably exclusive. I first consider why agreement is important in contractarianism, and then introduce the main versions of contemporary (...) contractarianism and their different understandings of agreement. I discuss how agreement results in exclusion in each, and distinguish two kinds of response to the problem of exclusion: differential inclusion and permissive inclusion. Differential inclusion is unsuccessful because it offers those not fully capable of agreement unequal status. Permissive inclusion may either make the circumstances of agreement more open, or characterize the capacities required for inclusion more permissively. I advocate the latter as the most promising response to the problem of exclusion. I outline a more inclusive contractualism based on the capacity to share goals. (shrink)

The _Platform Sutra_ records the teachings of Hui-neng, the Sixth Patriarch, who is revered as one of the two great figures in the founding of Ch'an (Zen) Buddhism. This translation is the definitive English version of the eighth-century Ch'an classic. Phillip B. Yampolsky has based his translation on the Tun-huang manuscript, the earliest extant version of the work. A critical edition of the Chinese text is given at the end of the volume. Dr. Yampolsky also furnishes a lengthy and detailed (...) historical introduction which contains much information hitherto unavailable even to scholars, and provides the context essential to an understanding of Hui-neng's work. He gives an account of the history and legends of Ch'an Buddhism, with particular attention to the traditions associated with Hui-neng, quoting or summarizing the most important narratives. He then discusses the various texts of the _Platform Sutra_, and analyzes its contents. (shrink)

ABSTRACT Constitutive panpsychism is the doctrine that macro-level consciousness—that is, consciousness of the sort possessed by certain composite things such as humans—is built out of irreducibly mental features had by some or all of the basic physical constituents of reality. On constitutive panpsychism, changes in macro-level consciousness amount to changes in either the way that micro-conscious entities ‘bond’ or the way that micro-conscious qualities ‘blend’. I pose the ‘Selection Problem’ for constitutive panpsychism—the problem of explaining how high-level functional states of (...) the brain ‘select’ micro-conscious qualities for bonding or blending. I argue that there are no empirically plausible solutions to this problem. (shrink)

The questions -- The purpose of morality and law -- The past and the future -- What is religion? -- What is the rule of law? -- The families of religion : western religions -- The families of religion : eastern religions -- The families of law -- A brief tour of secular law -- Money, banks and corporations -- Secularisation and religious decline -- Reasons for the decline of religiosity -- Secularisation of government -- The rise of the lawyers (...) -- Who rules the world : lawyers or economists? -- What is wrong with the law? -- Scientific progress and the law -- A way of living -- A billion years from now. (shrink)

It is intuitive that free action depends on consciousness in some way, since behavior that is unconsciously generated is widely regarded as un-free. But there is no clear consensus as to what such dependence comes to, in part because there is no clear consensus about either the cognitive role of consciousness or about the essential components of free action. I divide the space of possible views into four: the Constitution View (on which free actions metaphysically consist, at least in part, (...) in phenomenally conscious episodes of a special sort), the Causal-Dependence View (on which free actions are necessarily caused by conscious episodes), the Counterfactaul-Dependence View (on which free actions necessarily counterfactually dependent on conscious episodes of certain types), and the Independence View (on which there are no necessary dependence-relations that hold between free action and conscious episodes). After surveying recent empirical literature that purports to show that consciousness plays a smaller role in generating action than is usually supposed, I conclude that it is plausible that free action depends on consciousness in two ways. First, free action causally depends on consciousness control. Second, free action counterfactually depends on the agent's being responsive to certain reasons. (shrink)

I discuss three tiers of technological innovation: mild innovation, or the acceleration by technology of a human activity aimed at a good; moderate innovation, or the obviation by technology of an activity aimed at a good; and radical innovation, or the altering by technology of the human condition so as to change what counts as a good. I argue that it is impossible to morally assess proposed innovations within any of these three tiers unless we rehabilitate a natural-law ethical framework. (...) And I offer some moral starting points within such a framework, in connection with innovations of each of the three types. (shrink)

Breaking off the ordinary flow of experience, the passions create a state of exception. In their suddenness and intensity, they map a personal world, fix and qualify our attention, and impel our actions. Outraged anger drives us to write laws that will later be enforced by impersonal justice. Intense grief at the death of someone in our life discloses the contours of that life to us. Wonder spurs scientific inquiry. The strong current of Western thought that idealizes a dispassionate world (...) has ostracized the passions as quaint, even dangerous. Intense states have come to be seen as symptoms of pathology. A fondness for irony along with our civic ideal of tolerance lead us to prefer the diluted emotional life of feelings and moods. Demonstrating enormous intellectual originality and generosity, Philip Fisher meditates on whether this victory is permanent-and how it might diminish us. From Aristotle to Hume to contemporary biology, Fisher finds evidence that the passions have defined a core of human nature no less important than reason or desire. Traversing the Iliad, King Lear, Moby Dick, and other great works, he discerns the properties of the high-spirited states we call the passions. Are vehement states compatible with a culture that values private, selectively shared experiences? How do passions differ from emotions? Does anger have an opposite? Do the passions give scale, shape, and significance to our experience of time? Is a person incapable of anger more dangerous than someone who is irascible? In reintroducing us to our own vehemence, Fisher reminds us that it is only through our strongest passions that we feel the contours of injustice, mortality, loss, and knowledge. It is only through our personal worlds that we can know the world. (shrink)

In Working Virtue: Virtue Ethics and Contemporary Moral Problems, leading figures in the fields of virtue ethics and ethics come together to present the first ...

This volume is dedicated to the drawing of the implications of the contemporary 'post-secular' social transformation for education. Contributions discuss such topics as the mystical tradition and its social and pedagogic implications; transformative and ecological education; and the relations between secular and religious education in different local contexts.

Examines rationality from Aristotle to Foucault, seeking to place reason in a historical context within the Western tradition.

Husserl introduces a phenomenological concept called “motivation” early in the First Investigation of his magnum opus, the Logical Investigations. The importance of this concept has been overlooked since Husserl passes over it rather quickly on his way to an analysis of the meaningful nature of expression. I argue, however, that motivation is essential to Husserl’s overall project, even if it is not essen- tial for defining expression in the First Investigation. For Husserl, motivation is a relation between mental acts whereby (...) the content of one act make some fur- ther meaningful content probable. I explicate the nature of this relation in terms of “evidentiary weight” and differentiate it from Husserl’s notion of Evidenz, often translated as “self-evidence”. I elucidate the importance of motivation in Husserl’s overall phenomenological project by focusing on his analyses of thing-perception and empathy. Through these examples, we can better understand the continuity between the Logical Investigations and Husserl’s later work. (shrink)

Arendt Contra Sociology re-assesses the relationship between Hannah Arendt's work and the theoretical foundations of sociology, bringing her insights to bear on key themes within contemporary theoretical sociology. Departing from the view of Arendt as a political theorist who sought to rescue politics from society, and political theory from the social sciences, this book re-examines her distinctions between labour, fabrication and action as a theory of the fundamental ontology of human societies, revisiting her criticism of the tendency of many sociological (...) paradigms to conflate the activity of fabrication with that of action. (shrink)

From the legendary inventor Daedalus to Goethe's tragic Faust, from the automata-making magicians of E.T.A Hoffmann to Mary Shelley's Victor Frankenstein – ...