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.

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)

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.

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.

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.

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)

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)

The official model of explanation proposed by the logical empiricists, the covering law model, is subject to familiar objections. The goal of the present paper is to explore an unofficial view of explanation which logical empiricists have sometimes suggested, the view of explanation as unification. I try to show that this view can be developed so as to provide insight into major episodes in the history of science, and that it can overcome some of the most serious difficulties besetting the (...) covering law model. (shrink)

In this work, the prominent political philosopher Philip Pettit embarks on a massive undertaking to offers major new accounts of the foundations of the state and the nature of justice. In doing so Pettit builds a new theory of what the state is and what it ought to be, addresses the normative question of how justice serves as a measure of the success of a state, and the way it should operate in relation to its citizens and other people.

A person presented with adequate but not conclusive evidence for a proposition is in a position voluntarily to acquire a belief in that proposition, or to suspend judgment about it. The availability of doxastic options in such cases grounds a moderate form of doxastic voluntarism not based on practical motives, and therefore distinct from pragmatism. In such cases, belief-acquisition or suspension of judgment meets standard conditions on willing: it can express stable character traits of the agent, it can be responsive (...) to reasons, and it is compatible with a subjective awareness of the available options. (shrink)

How Galileo created the problem of consciousness -- Is there a ghost in the machine? -- Can physical science explain consciousness? -- How to solve the problem of consciousness -- Consciousness and the meaning of life.

What's the Use of Philosophy? aims to answer the question posed in its title, whether the questioner intends to dismiss philosophy, or seeks a positive answer. The first three chapters explore the grounds for dismissal. Chapter 1 expresses skepticism about the value of much professional Anglophone philosophy, while recognizing virtues in work often viewed as peripheral. Chapter 2 studies a philosophical subfield, the philosophy of science, arguing that, while its condition may be better than the norm, it is far from (...) perfect. In Chapter 3, a more systematic critique is offered, in the form of a pathology report. Its diagnosis identifies six justifiable philosophical impulses that, when pursued obsessively, generate distortions and diseases: clarity becomes a fetish, formalism becomes obfuscation, "intuition" is given burdens it cannot bear, appeals to the a priori sprinkle fairy dust on controversial claims, ideas grabbed from other fields are used in cartoon forms, and questions no longer relevant are treated as if they were "timeless." Chapter 4 attempts to identify the legitimate goals of philosophy. It sees value in attempts to respond to questions arising from the difficulties of the age, in attempts to reform methods of inquiry, and, above all, in the construction of syntheses capable of helping people as they struggle to make sense of their lives. Philosophy is renewed when these traditional goals once again become central to its discussions. The final chapter responds to a frequently voiced worry in a letter to young philosophers who wonder how they can align their aspirations with the hyper-professionalism expected of them. (shrink)

This paper argues for a Husserlian account of phenomenal intentionality. Experience is intentional insofar as it presents a mind-independent, objective world. Its doing so is a matter of the way it hangs together, its having a certain structure. But in order for the intentionality in question to be properly understood as phenomenal intentionality, this structure must inhere in experience as a phenomenal feature. Husserl’s concept of horizon designates this intentionality-bestowing experiential structure, while his concept of motivation designates the unique phenomenal (...) character of this structure as it is experientially lived through. The way experience hangs together is itself a phenomenal feature of experience. (shrink)

Engineers are traditionally regarded as trustworthy professionals who meet exacting standards. In this chapter I begin by explicating our trust relationship towards engineers, arguing that it is a linear but indirect relationship in which engineers “stand behind” the artifacts and technological systems that we rely on directly. The chapter goes on to explain how this relationship has become more complex as engineers have taken on two additional aims: the aim of social engineering to create and steer trust between people, and (...) the aim of creating automated systems that take over human tasks and are meant to invite the trust of those who rely on and interact with them. (shrink)

An esteemed philosopher discusses his theory of universal freedom, describing how even those who are members of free societies may find their liberties curtailed and includes tests of freedom including the eyeball test and the tough-luck test.

Good reasoning can lead to success; bad reasoning can lead to catastrophe. Yet, it's not obvious how we reason, and why we make mistakes. This new book by one of the pioneers of the field, Philip Johnson-Laird, looks at the mental processes that underlie our reasoning. It provides the most accessible account yet of the science of reasoning.

This paper has two goals: (1) to defend a particular response to the problem of resultant moral luck and (2) to defend the claim that we are only responsible for what we could have avoided. Cases of overdetermination threaten to undermine the claim that we are only responsible for what we could have avoided. To deal with this issue, I will motivate a particular way of responding to the problem of resultant moral luck. I defend the view that one's degree (...) of responsibility is immune to moral luck but the scope of events for which one is responsible is subject to moral luck. I will then argue that this view allows us to explain away certain intuitions about responsibility and overdetermination (as well as similar intuitions regarding Frankfurt Cases). As a result, the claim that we are only responsible for what we could have avoided becomes significantly more plausible. (shrink)

Cognitive neuropsychiatry (CN) is the explanation of psychiatric disorder by the methods of cognitive neuropsychology. Within CN there are, broadly speaking, two approaches to delusion. The first uses a one-stage model, in which delusions are explained as rationalizations of anomalous experiences via reasoning strategies that are not, in themselves, abnormal. Two-stage models invoke additional hypotheses about abnormalities of reasoning. In this paper, I examine what appears to be a very strong argument, developed within CN, in favor of a twostage explanation (...) of the difference in content between the Capgras and Cotard delusions. That explanation treats them as alternative rationalizations of essentially the same phenomenology. I show, however, that once we distinguish the phenomenology (and the neuroetiology), a one-stage model is adequate. In the final section I make some more general remarks on the oneand two-stage models. (shrink)

Wisdom is peculiarly abstract, ineffable, and yet perennial. It is also temporal, stretching forwards as well is backwards in time. Wisdom is often treated as the outcome of life experience, reflection, discipline, and equanimity. Capturing the Ineffable aims to establish wisdom as an area if inquiry within anthropology and an analytic account of wisdom and its role and focus in anthropology. In addition to developing theories for an anthropology (and excavation) of wisdom, this volume argues collectively that anthropology is especially (...) well suited to engage in questioning what it is that is called wisdom, and how wisdom, as a concept, and an enacted activity, functions in metaphysical and interpersonal experiences, values, and judgements. The contributors include many key US and UK thinkers. (shrink)

This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik, with introduction and annotation. The importance of Frege's ideas within contemporary philosophy would be hard to exaggerate. He was, to all intents and purposes, the inventor of mathematical logic, and the influence exerted on modern philosophy of language and logic, and indeed on general epistemology, by the philosophical framework.

The early nineteenth century saw the demise of the Italian-Atlantic tradition of republicanism and the rise of classical liberalism. A distinct Franco-German tradition of republicanism emerged from the time of Jean-Jacques Rousseau and Immanuel Kant, which differs from the older way of thinking associated with neo-republicanism. This chapter examines the key differences between the Italian-Atlantic and Franco-German traditions of republicanism and places them in a historical context. It first considers classical republicanism and how the ideological ideal of equal freedom as (...) nondomination differs from the twin institutional ideals of a mixed constitution and a contestatory citizenry. It then looks at the classical liberal opposition that arose in response to Italian-Atlantic republicanism. It also discusses the views of Kant and Rousseau about freedom and the role of the citizenry, as well as their theory of the constitution. The absolutist opposition in Jean Bodin and Thomas Hobbes to the institutional ideals of republicanism is also explored. (shrink)

Trusting someone in an intuitive, rich sense of the term involves not just relying on that person, but manifesting reliance on them in the expectation that this manifestation of reliance will increase their reason and motive to prove reliable. Can trust between people be formed on the basis of Internet contact alone? Forming the required expectation in regard to another person, and so trusting them on some matter, may be due to believing that they are trustworthy; to believing that they (...) seek es teem and will be rationally responsive to the good opinion communicated or promised by an act of trust; or to both factors at once. Neither mechanism can rationally command confidence, however, in the case where people are related only via the Internet. On the Internet everyone wears the ring of Gyges; everyone is invisible, in their personal identity, to others. (shrink)

This chapter contains section titled: Rawls's Anti‐Cosmopolitanism Rawls's Ontology of Peoples Reconstructing Rawls's Rejection of Cosmopolitanism Acknowledgments Notes.

There has recently been a revival of interest in panpsychism as a theory of consciousness. The hope of the contemporary proponents of panpsychism is that the view enables us to integrate consciousness into our overall theory of reality in a way that avoids the deep difficulties that plague the more conventional options of physicalism on the one hand and dualism on the other. However, panpsychism comes in two forms — strong and weak emergentist — and there are arguments that seem (...) to show that weak emergentist panpsychism faces problems analogous to those of physicalism whilst strong emergentist panpsychism faces problems analogous to those of dualism. In this paper, I will develop a new hybrid of the strong and weak emergentist forms of panpsychism, a view according to which subjects of experience are strongly emergent but their phenomenal properties are weakly emergent. I will argue that this hybrid view manages to avoid the challenges facing both physicalism and dualism, and the analogues of those challenges that seem to undermine standard forms of panpsychism. (shrink)