God and Abstract Objects

Author: William Lane Craig
Publisher: Springer
ISBN: 9783319553849
Release Date: 2017-09-05
Genre: Philosophy

This book is an exploration and defense of the coherence of classical theism’s doctrine of divine aseity in the face of the challenge posed by Platonism with respect to abstract objects. A synoptic work in analytic philosophy of religion, the book engages discussions in philosophy of mathematics, philosophy of language, metaphysics, and metaontology. It addresses absolute creationism, non-Platonic realism, fictionalism, neutralism, and alternative logics and semantics, among other topics. The book offers a helpful taxonomy of the wide range of options available to the classical theist for dealing with the challenge of Platonism. It probes in detail the diverse views on the reality of abstract objects and their compatibility with classical theism. It contains a most thorough discussion, rooted in careful exegesis, of the biblical and patristic basis of the doctrine of divine aseity. Finally, it challenges the influential Quinean metaontological theses concerning the way in which we make ontological commitments.

God Over All

Author: William Lane Craig
Publisher: Oxford University Press
ISBN: 9780191090554
Release Date: 2016-10-20
Genre: Religion

God Over All: Divine Aseity and the Challenge of Platonism is a defense of God's aseity and unique status as the Creator of all things apart from Himself in the face of the challenge posed by mathematical Platonism. After providing the biblical, theological, and philosophical basis for the traditional doctrine of divine aseity, William Lane Craig explains the challenge presented to that doctrine by the Indispensability Argument for Platonism, which postulates the existence of uncreated abstract objects. Craig provides detailed examination of a wide range of responses to that argument, both realist and anti-realist, with a view toward assessing the most promising options for the theist. A synoptic work in analytic philosophy of religion, this groundbreaking volume engages discussions in philosophy of mathematics, philosophy of language, metaphysics, and metaontology.

Divine Foreknowledge and Human Freedom

Author: William Lane Craig
Publisher: BRILL
ISBN: 9004092501
Release Date: 1991
Genre: Religion

The ancient problem of fatalism, more particularly theological fatalism, has resurfaced with surprising vigour in the second half of the twentieth century. Two questions predominate in the debate: (1) Is divine foreknowledge compatible with human freedom and (2) How can God foreknow future free acts? Having surveyed the historical background of this debate in "The Problem of Divine Foreknowledge" and "Future Contingents from Aristotle to Suarez" (Brill: 1988), William Lane Craig now attempts to address these issues critically. His wide-ranging discussion brings together a thought- provoking array of related topics such as logical fatalism, multivalent logic, backward causation, precognition, time travel, counterfactual logic, temporal necessity, Newcomb's Problem, middle knowledge, and relativity theory. The present work serves both as a useful survey of the extensive literature on theological fatalism and related fields and as a stimulating assessment of the possibility of divine foreknowledge of future free acts.

God Time and Eternity

Author: W.L. Craig
Publisher: Springer Science & Business Media
ISBN: 9789401717151
Release Date: 2013-03-14
Genre: Philosophy

In this highly original and ground-breaking work, the author brings together discussions in the philosophy of time and space, philosophy of language, phenomenology, philosophy of science, Special and General Relativity, classical cosmology, quantum mechanics, and so forth, with the concerns of philosophy of religion and theology, in order to craft a philosophically informed and scientifically tenable doctrine of divine eternity and God's relationship to time.

God and Necessity

Author: Brian Leftow
Publisher: OUP Oxford
ISBN: 9780191654879
Release Date: 2012-09-06
Genre: Philosophy

Brian Leftow offers a theory of the possible and the necessary in which God plays the chief role, and a new sort of argument for God's existence. It has become usual to say that a proposition is possible just in case it is true in some 'possible world' (roughly, some complete history a universe might have) and necessary just if it is true in all. Thus much discussion of possibility and necessity since the 1960s has focussed on the nature and existence (or not) of possible worlds. God and Necessity holds that there are no such things, nor any sort of abstract entity. It assigns the metaphysical 'work' such items usually do to God and events in God's mind, and reduces 'broadly logical' modalities to causal modalities, replacing possible worlds in the semantics of modal logic with God and His mental events. Leftow argues that theists are committed to theist modal theories, and that the merits of a theist modal theory provide an argument for God's existence. Historically, almost all theist modal theories base all necessary truth on God's nature. Leftow disagrees: he argues that necessary truths about possible creatures and kinds of creatures are due ultimately to God's unconstrained imagination and choice. On his theory, it is in no sense part of the nature of God that normal zebras have stripes (if that is a necessary truth). Stripy zebras are simply things God thought up, and they have the nature they do simply because that is how God thought of them. Thus Leftow's essay in metaphysics takes a half-step toward Descartes' view of modal truth, and presents a compelling theist theory of necessity and possibility.

Beyond the Control of God

Author: Paul Gould
Publisher: Bloomsbury Publishing USA
ISBN: 9781623569372
Release Date: 2014-03-27
Genre: Religion

The question of God's relationship to abstract objects touches on a number of perennial concerns related to the nature of God. God is typically thought to be an independent and self-sufficient being. Further, God is typically thought to be supremely sovereign such that all reality distinct from God is dependent on God's creative and sustaining activity. However, the view that there are abstract objects seems to be a repudiation of this traditional understanding of God. Abstract objects are typically thought to exist necessarily and it is natural to think that if something exists necessarily, it does so because it is its nature to exist. Thus, abstract objects exist independently of God. Philosophers have called this the problem of God and abstract objects. In this book, six contemporary solutions to the problem are set out and defended against objections. It will be valuable for all students or scholars who are interested in the concept and nature of God.

Deflating Existential Consequence

Author: Jody Azzouni
Publisher: Oxford University Press
ISBN: 9780190289454
Release Date: 2004-01-08
Genre: Philosophy

If we must take mathematical statements to be true, must we also believe in the existence of abstracta eternal invisible mathematical objects accessible only by the power of pure thought? Jody Azzouni says no, and he claims that the way to escape such commitments is to accept (as an essential part of scientific doctrine) true statements which are about objects that don't exist in any sense at all. Azzouni illustrates what the metaphysical landscape looks like once we avoid a militant Realism which forces our commitment to anything that our theories quantify. Escaping metaphysical straitjackets (such as the correspondence theory of truth), while retaining the insight that some truths are about objects that do exist, Azzouni says that we can sort scientifically-given objects into two categories: ones which exist, and to which we forge instrumental access in order to learn their properties, and ones which do not, that is, which are made up in exactly the same sense that fictional objects are. He offers as a case study a small portion of Newtonian physics, and one result of his classification of its ontological commitments, is that it does not commit us to absolute space and time.

Tool and Object

Author: Ralph Krömer
Publisher: Springer Science & Business Media
ISBN: 9783764375249
Release Date: 2007-06-25
Genre: Mathematics

Category theory is a general mathematical theory of structures and of structures of structures. It occupied a central position in contemporary mathematics as well as computer science. This book describes the history of category theory whereby illuminating its symbiotic relationship to algebraic topology, homological algebra, algebraic geometry and mathematical logic and elaboratively develops the connections with the epistemological significance.

The Coherence of Theism

Author: Richard Swinburne
Publisher: Oxford University Press
ISBN: 9780191085321
Release Date: 2016-05-05
Genre: Philosophy

The Coherence of Theism investigates what it means, and whether it is coherent, to say that there is a God. Richard Swinburne concludes that despite philosophical objections, most traditional claims about God are coherent (that is, do not involve contradictions); and although some of the most important claims are coherent only if the words by which they are expressed are being used in analogical senses, this is the way in which theologians have usually claimed that they are being used. When the first edition of this book was published in 1977, it was the first book in the new 'analytic' tradition of philosophy of religion to discuss these issues. Since that time there have been very many books and discussions devoted to them, and this new, substantially rewritten, second edition takes account of these discussions and of new developments in philosophy generally over the past 40 years. These discussions have concerned how to analyse the claim that God is 'omnipotent', whether God can foreknow human free actions, whether God is everlasting or timeless, and what it is for God to be a 'necessary being'. On all these issues this new edition has new things to say.

Strict Finitism and the Logic of Mathematical Applications

Author: Feng Ye
Publisher: Springer Science & Business Media
ISBN: 9400713479
Release Date: 2011-07-06
Genre: Science

This book intends to show that radical naturalism (or physicalism), nominalism and strict finitism account for the applications of classical mathematics in current scientific theories. The applied mathematical theories developed in the book include the basics of calculus, metric space theory, complex analysis, Lebesgue integration, Hilbert spaces, and semi-Riemann geometry (sufficient for the applications in classical quantum mechanics and general relativity). The fact that so much applied mathematics can be developed within such a weak, strictly finitistic system, is surprising in itself. It also shows that the applications of those classical theories to the finite physical world can be translated into the applications of strict finitism, which demonstrates the applicability of those classical theories without assuming the literal truth of those theories or the reality of infinity. Both professional researchers and students of philosophy of mathematics will benefit greatly from reading this book.

Philosophy and Probability

Author: Timothy Childers
Publisher: Oxford University Press
ISBN: 9780199661824
Release Date: 2013-05-30
Genre: Philosophy

Probability is increasingly important for our understanding of the world. What is probability? How do we model it, and how do we use it? Timothy Childers presents a lively introduction to the foundations of probability and to philosophical issues it raises. He keeps technicalities to a minimum, and assumes no prior knowledge of the subject. He explains the main interpretations of probability-frequentist, propensity, classical, Bayesian, and objective Bayesian-and uses stimulating examples to bring the subject to life. All students of philosophy will benefit from an understanding of probability, and this is the book to provide it.

Epistemic Friction

Author: Gila Sher
Publisher: Oxford University Press
ISBN: 9780198768685
Release Date: 2016-06-09
Genre:

Gila Sher approaches knowledge from the perspective of the basic human epistemic situation - the situation of limited yet resourceful beings, living in a complex world and aspiring to know it in its full complexity. What principles should guide them? Two fundamental principles of knowledge areepistemic friction and freedom. Knowledge must be substantially constrained by the world (friction), but without active participation of the knower in accessing the world (freedom) theoretical knowledge is impossible. This requires a grounding of all knowledge, empirical and abstract, in both mindand world, but the fall of traditional foundationalism has led many to doubt the viability of this "classical" project. The book challenges this skepticism, charting a new foundational methodology, foundational holism, that differs from others in being holistic, world-oriented, and universal (i.e., applicable to all fields of knowledge). Using this methodology, Epistemic Friction develops an integrated theory ofknowledge, truth, and logic. This includes (i) a dynamic model of knowledge, incorporating some of Quine's revolutionary ideas while rejecting his narrow empiricism, (ii) a substantivist, non-traditional correspondence theory of truth, and (iii) an outline of a joint grounding of logic in mind andworld. The model of knowledge subjects all disciplines to robust norms of both veridicality and conceptualization. The correspondence theory is at once robust, universal, and flexible, allowing multiple patterns of correspondence, including complex and indirect patterns. Logic's systematic groundingbrings it in line with other disciplines without neglecting its strong necessity, generality, and normativity, which are explained by its semantic formality.

Space Number and Geometry from Helmholtz to Cassirer

Author: Francesca Biagioli
Publisher: Springer
ISBN: 9783319317793
Release Date: 2016-08-22
Genre: Philosophy

This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of intuitions, which lie at the foundation of mathematical knowledge. The success of his philosophical account of space was due not least to the fact that Euclidean geometry was widely considered to be a model of certainty at his time. However, such later scientific developments as non-Euclidean geometries and Einstein’s general theory of relativity called into question the certainty of Euclidean geometry and posed the problem of reconsidering space as an open question for empirical research. The transformation of the concept of space from a source of knowledge to an object of research can be traced back to a tradition, which includes such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincaré, and which finds one of its clearest expressions in Hermann von Helmholtz’s epistemological works. Although Helmholtz formulated compelling objections to Kant, the author reconsiders different strategies for a philosophical account of the same transformation from a neo-Kantian perspective, and especially Hermann Cohen’s account of the aprioricity of mathematics in terms of applicability and Ernst Cassirer’s reformulation of the a priori of space in terms of a system of hypotheses. This book is ideal for students, scholars and researchers who wish to broaden their knowledge of non-Euclidean geometry or neo-Kantianism.

The Divine Attributes

Author: Joshua Hoffman
Publisher: John Wiley & Sons
ISBN: 9780470692714
Release Date: 2008-04-15
Genre: Philosophy

The Divine Attributesis an engaging analysis of the God of Judaism, Christianity, and Islam from the perspective of rational theology.