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The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages are often insufficient to codify many concepts in contemporary mathematics, and thus that both first- and higher-order logics are needed to fully reflect current work. Throughout, the emphasis is on discussing the associated philosophical and historical issues and the implications they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic comparable to that provided in a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in the field today.

The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages are often insufficient to codify many concepts in contemporary mathematics, and thus that both first- and higher-order logics are needed to fully reflect current work. Throughout, the emphasis is on discussing the associated philosophical and historical issues and the implications they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic comparable to that provided in a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in the field today.

Such is the clarity of its exposition and interest of its argument, that it can be recommended to those seeking an introduction to recent work in [epistemology]. The interest of the book, however, is greater than that. For the discussion of foundationalism and of recent reactions to it is subtly interwoven into a discussion of recent and not so recent philosophy of religion. ― Colin Lyas Philosophy

By Good and Necessary Consequence presents a critical examination of the reasoning behind the "good and necessary consequence" clause in the Westminster Confession of Faith and makes five observations regarding its suitability for contemporary Reformed and evangelical adherents. 1) In the seventeenth century, religious leaders in every quarter were expected to respond to a thoroughgoing, cultural skepticism. 2) In response to the onslaught of cultural and epistemological skepticism, many looked to mimic as far as possible the deductive methods of mathematicians. 3) The use to which biblicist foundationalism was put by the Westminster divines is at variance with the classical invention, subsequent appropriation, and contemporary estimation of axiomatic and deductive methodology. 4) Although such methodological developments in theology might have seemed natural during the seventeenth century, their epistemological advantage is not evident today. 5) When a believer's faith is epistemologically ordered in a biblicist foundationalist way, once the foundation--the axiomatic use of a veracious scripture--is called into question, the entire faith is in serious danger of crashing down. In a nutshell, Bovell argues that it is not wise to structure the Christian faith in this biblicist foundationalist way, and that it is high time alternate approaches be sought.

Everyone knows that "postmodernism" implies pluralism, anti-foundationalism, and, generally,a postnormative view of the self and reality. While many embrace it, few bother to tell us what is wrong with modernity. What are the problems that brought about its crisis and ultimate demise as a philosophical and cultural movement? What are the lessons for the postmodern movement that can he drawn from them?James Mensch here explains why modernism failed as a viable philosophical enterprise and how postmodernism must be understood if it is to serve as a defensible intellectual project in its stead. The heart of Mensch's argument is a reversal of the modernist view of the unitary subject as a ground of epistemological and ethical normativity. He substitutes for modernism a view, beholden to Aristotle but adapted to for our present age, that sees subjectivity as temporality in a world where subject and object are interactive. The result is a pluralism of forms of subjectivity corresponding to the different modes of temporality brought about by the world. In a series of analyses on the nature knowing, Mensch shows how we can embrace both the perspectivism of postmodernism while avoiding the skepticism and relativism that have constantly threatened to undermine its insights.

Epistemology or the theory of knowledge is one of the cornerstones of analytic philosophy, and this book provides a clear and accessible introduction to the subject. It discusses some of the main theories of justification, including foundationalism, coherentism, reliabilism, and virtue epistemology. Other topics include the Gettier problem, internalism and externalism, skepticism, the problem of epistemic circularity, the problem of the criterion, a priori knowledge, and naturalized epistemology. Intended primarily for students taking a first class in epistemology, this lucid and well-written text would also provide an excellent introduction for anyone interested in knowing more about this important area of philosophy.

In this excellent treatment of the internalism-externalism debate in contemporary epistemology, Richard Fumerton explores its implications for traditional skeptical concerns. When one fully understands these implications, Fumerton argues, one will see philosophical usefulness of a foundationalism relying on acquaintance. Contending that the externalist response to skepticism is too quick and easy, Fumerton defends a version of internalism, but in doing so puts into stark relief the radically different alternatives for dealing with skepticism that our metaepistemological views force upon us.

In this wide-ranging, ambitious, and engaging study, Christian Thorne confronts the history and enduring legacy of anti-foundationalist thought. Anti-foundationalism―the skeptical line of thought that contends our beliefs cannot be authoritatively grounded and that most of what passes for knowledge is a sham―has become one of the dominant positions in contemporary criticism. Thorne argues that despite its ascendance, anti-foundationalism is wrong. In The Dialectic of Counter-Enlightenment, he uses deft readings of a range of texts to offer new perspectives on the ongoing clash between philosophy and comprehensive doubt. The problem with anti-foundationalism is not, as is often thought, that it radiates uncertainty or will unglue the university, but instead that it is a system of thought―with set habits that generate unearned certainties. The shelves are full of histories of modern philosophy, but the history of the resistance to philosophical thought remains to be told. At its heart, The Dialectic of Counter-Enlightenment is a plea not to take doubt at its word―a plea for the return of a vanished philosophical intelligence and for the retirement of an anti-Enlightenment thinking that commits, over and over again, the very crimes that it lays at Enlightenment’s door.

FOUNDATIONALISM IN PHILOSOPHY n his autobiographical work, The Education of Henry Adams, this I brooding and disillusioned offspring of American presidents confronted, at age sixty, his own perplexity concerning the new scientific world-view that was emerging at the end of the century. He noted that the unity of things, long guaranteed morally by the teachings of Christianity and scientifically by the Newtonian world-view, was being challenged by a newer vision of things that found only incomprehensible multiplicity at the root of the world: What happened if one dropped the sounder into the ab­ yss-let it go-frankly gave up Unity altogether? What was Unity? Why was one to be forced to affirm it? Here every­ body flatly refused help. . . . [Adams] got out his Descartes again; dipped into his Hume and Berkeley; wrestled anew with his Kant; pondered solemnly over his Hegel and Scho­ penhauer and Hartmann; strayed gaily away with his Greeks-all merely to ask what Unity meant, and what happened when one denied it. Apparently one never denied it. Every philosopher, whether sane or insane, naturally af­ firmed it. I Adams, then approaching with heavy pessimism a new century, felt instinc­ tively that, were one to attack the notion of unity, the entire edifice of human knowledge would quickly collapse. For understanding requires the unification of apparently different phenomena.

This text mixes Chisholm as a disseminator of others ideas, with his own theories of knowledge and perception, his defence of Cartesian dualism, foundationalism, his adverbial theory of sensory experience, and his immanent agent causation as a solution to the problem of personal freedom.

This text mixes Chisholm as a disseminator of others ideas, with his own theories of knowledge and perception, his defence of Cartesian dualism, foundationalism, his adverbial theory of sensory experience, and his immanent agent causation as a solution to the problem of personal freedom.

In this excellent treatment of the internalism-externalism debate in contemporary epistemology, Richard Fumerton explores its implications for traditional skeptical concerns. When one fully understands these implications, Fumerton argues, one will see philosophical usefulness of a foundationalism relying on acquaintance. Contending that the externalist response to skepticism is too quick and easy, Fumerton defends a version of internalism, but in doing so puts into stark relief the radically different alternatives for dealing with skepticism that our metaepistemological views force upon us.

Philosophy long sought to set knowledge on a firm foundation, through derivation of indubitable truths by infallible rules. For want of such truths and rules, the enterprise foundered. Nevertheless, foundationalism's heirs continue their forbears' quest, seeking security against epistemic misfortune, while their detractors typically espouse unbridled coherentism or facile relativism. Maintaining that neither stance is tenable, Catherine Elgin devises a via media between the absolute and the arbitrary, reconceiving the nature, goals, and methods of epistemology. In Considered Judgment, she argues for a reconception that takes reflective equilibrium as the standard of rational acceptability. A system of thought is in reflective equilibrium when its components are reasonable in light of one another, and the account they comprise is reasonable in light of our antecedent convictions about the subject it concerns. Many epistemologists now concede that certainty is a chimerical goal. But they continue to accept the traditional conception of epistemology's problematic. Elgin suggests that in abandoning the quest for certainty we gain opportunities for a broader epistemological purview--one that comprehends the arts and does justice to the sciences. She contends that metaphor, fiction, emotion, and exemplification often advance understanding in science as well as in art. The range of epistemology is broader and more variegated than is usually recognized. Tenable systems of thought are neither absolute nor arbitrary. Although they afford no guarantees, they are good in the way of belief.

This classic book by Theodor W. Adorno anticipates many of the themes that have since become common in contemporary philosophy: the critique of foundationalism, the illusions of idealism and the end of epistemology. It also foreshadows many of the key ideas that were developed by Adorno in his most important philosophical works, including Negative Dialectics. Against Epistemology is based on a manuscript Adorno originally wrote in Oxford in 1934-37 during his first years in exile and subsequently reworked in Frankfurt in 1955-56. The text was written as a critique of Husserl’s phenomenology, but the critique of phenomenology is used as the occasion for a much broader critique of epistemology. Adorno described this as a ‘metacritique’ which blends together the analysis of Husserl’s phenomenology as the most advanced instance of the decay of bourgeois idealism with an immanent critique of the tensions and contradictions internal to Husserl’s thought. The result is a powerful text which remains one of the most devastating critiques of Husserl’s work ever written and which heralded many of the ideas that have become commonplace in contemporary philosophy.

FOUNDATIONALISM IN PHILOSOPHY n his autobiographical work, The Education of Henry Adams, this I brooding and disillusioned offspring of American presidents confronted, at age sixty, his own perplexity concerning the new scientific world-view that was emerging at the end of the century. He noted that the unity of things, long guaranteed morally by the teachings of Christianity and scientifically by the Newtonian world-view, was being challenged by a newer vision of things that found only incomprehensible multiplicity at the root of the world: What happened if one dropped the sounder into the ab­ yss-let it go-frankly gave up Unity altogether? What was Unity? Why was one to be forced to affirm it? Here every­ body flatly refused help. . . . [Adams] got out his Descartes again; dipped into his Hume and Berkeley; wrestled anew with his Kant; pondered solemnly over his Hegel and Scho­ penhauer and Hartmann; strayed gaily away with his Greeks-all merely to ask what Unity meant, and what happened when one denied it. Apparently one never denied it. Every philosopher, whether sane or insane, naturally af­ firmed it. I Adams, then approaching with heavy pessimism a new century, felt instinc­ tively that, were one to attack the notion of unity, the entire edifice of human knowledge would quickly collapse. For understanding requires the unification of apparently different phenomena.

In this wide-ranging, ambitious, and engaging study, Christian Thorne confronts the history and enduring legacy of anti-foundationalist thought. Anti-foundationalism―the skeptical line of thought that contends our beliefs cannot be authoritatively grounded and that most of what passes for knowledge is a sham―has become one of the dominant positions in contemporary criticism. Thorne argues that despite its ascendance, anti-foundationalism is wrong. In The Dialectic of Counter-Enlightenment, he uses deft readings of a range of texts to offer new perspectives on the ongoing clash between philosophy and comprehensive doubt. The problem with anti-foundationalism is not, as is often thought, that it radiates uncertainty or will unglue the university, but instead that it is a system of thought―with set habits that generate unearned certainties. The shelves are full of histories of modern philosophy, but the history of the resistance to philosophical thought remains to be told. At its heart, The Dialectic of Counter-Enlightenment is a plea not to take doubt at its word―a plea for the return of a vanished philosophical intelligence and for the retirement of an anti-Enlightenment thinking that commits, over and over again, the very crimes that it lays at Enlightenment’s door.

Philosophy long sought to set knowledge on a firm foundation, through derivation of indubitable truths by infallible rules. For want of such truths and rules, the enterprise foundered. Nevertheless, foundationalism's heirs continue their forbears' quest, seeking security against epistemic misfortune, while their detractors typically espouse unbridled coherentism or facile relativism. Maintaining that neither stance is tenable, Catherine Elgin devises a via media between the absolute and the arbitrary, reconceiving the nature, goals, and methods of epistemology. In Considered Judgment, she argues for a reconception that takes reflective equilibrium as the standard of rational acceptability. A system of thought is in reflective equilibrium when its components are reasonable in light of one another, and the account they comprise is reasonable in light of our antecedent convictions about the subject it concerns. Many epistemologists now concede that certainty is a chimerical goal. But they continue to accept the traditional conception of epistemology's problematic. Elgin suggests that in abandoning the quest for certainty we gain opportunities for a broader epistemological purview--one that comprehends the arts and does justice to the sciences. She contends that metaphor, fiction, emotion, and exemplification often advance understanding in science as well as in art. The range of epistemology is broader and more variegated than is usually recognized. Tenable systems of thought are neither absolute nor arbitrary. Although they afford no guarantees, they are good in the way of belief.

This collection of papers (including three completely new ones) by one of the foremost philosophers in epistemology transcends two of the most widely misunderstood positions in philosophy--foundationalism and coherentism. Audi proposes a distinctively moderate, internalist foundationalism that incorporates some of the virtues of both coherentism and reliabilism. He develops important distinctions between positive and negative epistemic dependence, substantively and conceptually naturalistic theories, dispositional beliefs and dispositions to believe, episodically and structurally inferential beliefs, first and second order internalism, and rebutting as opposed to refuting skepticism. These contrasts are applied not only to rational belief, but to rational action and the rationality of desires and intentions. The overall position is a pluralist, moderately rationalistic, internalist theory of justification and a partly externalist conception of knowledge. However, by virtue of offering a theory of rationality as well as an account of knowledge and justified belief, it will interest philosophers of ethics, science, and the social sciences and teachers and students of epistemology.