Different religious traditions offer apparently very different pictures of the world. How are we to make sense of this radical diversity of religious belief? In this book, Professor Godlove argues that religions are alternative conceptual frameworks, the categories of which organise experience in diverse ways. He traces the history of this idea from Kant to Durkheim, and then proceeds to discuss two constraints on the diversity of all human judgment and belief: first that human experience is made possible by shared, (...) a priori rules, and second, that as language-users we must presuppose that we hold the vast bulk of our beliefs in common. Given these unavoidable constraints, it is clear how religions may offer encompassing symbolic systems that often diverge dramatically from one another. 'An original and brilliant critique of Durkheim and Kant from within the framework of Davidson's semantic theory. This book is required reading for anyone interested in the academic study of religion, and the problems of relativism and the diversity of belief.' -- Hans H. Penner, Dartmouth CollegeDifferent religious traditions offer apparently very different pictures of the world. How are we to make sense of this radical diversity of religious belief? In this book, Professor Godlove argues that religions are alternative conceptual frameworks, the categories of which organise experience in diverse ways. He traces the history of this idea from Kant to Durkheim, and then proceeds to discuss two constraints on the diversity of all human judgment and belief: first that human experience is made possible by shared, a priori rules, and second, that as language-users we must presuppose that we hold the vast bulk of our beliefs in common. Given these unavoidable constraints, it is clear how religions may offer encompassing symbolic systems that often diverge dramatically from one another. 'An original and brilliant critique of Durkheim and Kant from within the framework of Davidson's semantic theory. This book is required reading for anyone interested in the academic study of religion, and the problems of relativism and the diversity of belief.' -- Hans H. Penner, Dartmouth College. (shrink)

Davidson attacks the intelligibility of conceptual relativism, i.e. of truth relative to a conceptual scheme. He defines the notion of a conceptual scheme as something ordering, organizing, and rendering intelligible empirical content, and calls the position that employs both notions scheme-content dualism. He argues that such dualism is untenable since: not only can we not parcel out empirical content sentence per sentence but also the notion of uninterpreted content to which several schemes are relative, and the related notion of a (...) theory ”fitting the evidence’, can be shown to lack intelligibility too. Davidson argues further that belief in incommensurable schemes or non-intertranslatable languages is possible only on violating a correct understanding of interpretability : if we succeed in interpreting someone else then we have shown there is no need to speak of two conceptual schemes, while if we fail ”there is no ground for speaking of two.’. (shrink)

Church’s type theory, aka simple type theory, is a formal logical language which includes classical first-order and propositional logic, but is more expressive in a practical sense. It is used, with some modifications and enhancements, in most modern applications of type theory. It is particularly well suited to the formalization of mathematics and other disciplines and to specifying and verifying hardware and software. It also plays an important role in the study of the formal semantics of natural language. When utilizing (...) it as a meta-logic to semantically embed expressive non-classical logics further topical applications are enabled in artificial intelligence and philosophy. A great wealth of technical knowledge can be expressed very naturally in it. With possible enhancements, Church’s type theory constitutes an excellent formal language for representing the knowledge in automated information systems, sophisticated automated reasoning systems, systems for verifying the correctness of mathematical proofs, and a range of projects involving logic and artificial intelligence. Some examples and further references are given in Sections 1.2.2 and 5 below. Type theories are also called higher-order logics, since they allow quantification not only over individual variables, but also over function, predicate, and even higher order variables. Type theories characteristically assign types to entities, distinguishing, for example, between numbers, sets of numbers, functions from numbers to sets of numbers, and sets of such functions. As illustrated in Section 1.2.2 below, these distinctions allow one to discuss the conceptually rich world of sets and functions without encountering the paradoxes of naive set theory. Church’s type theory is a formulation of type theory that was introduced by Alonzo Church in Church 1940. In certain respects, it is simpler and more general than the type theory introduced by Bertrand Russell in Russell 1908 and Whitehead & Russell 1927a. Since properties and relations can be regarded as functions from entities to truth values, the concept of a function is taken as primitive in Church’s type theory, and the λ-notation which Church introduced in Church 1932 and Church 1941 is incorporated into the formal language. Moreover, quantifiers and description operators are introduced in a way so that additional binding mechanisms can be avoided, λ-notation is reused instead. λ-notation is thus the only binding mechanism employed in Church’s type theory. (shrink)

The authors investigated the ontological argument computationally. The premises and conclusion of the argument are represented in the syntax understood by the automated reasoning engine PROVER9. Using the logic of definite descriptions, the authors developed a valid representation of the argument that required three non-logical premises. PROVER9, however, discovered a simpler valid argument for God's existence from a single non-logical premise. Reducing the argument to one non-logical premise brings the investigation of the soundness of the argument into better focus. Also, (...) the simpler representation of the argument brings out clearly how the ontological argument constitutes an early example of a ?diagonal argument? and, moreover, one used to establish a positive conclusion rather than a paradox. (shrink)

This is a wide-ranging 2004 book about arguments for and against beliefs in God. The arguments for the belief are analysed in the first six chapters and include ontological arguments from Anselm to Gödel, the cosmological arguments of Aquinas and Leibniz, and arguments from evidence for design and miracles. The next two chapters consider arguments against belief. The last chapter examines Pascalian arguments for and against belief in God. There are discussions of Cantorian problems for omniscience, of challenges to divine (...) omnipotence, and of the compatibility of everlasting complete knowledge of the world with free-will. There are appendices that present formal proofs in a system for quantified modal logic, a theory of possible worlds, notes on Cantorian set theory, and remarks concerning non-standard hyperreal numbers. This book will be a valuable resource for philosophers of religion and theologians and will interest logicians and mathematicians as well. (shrink)

In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this paper, we describe what we have discovered when the theory of abstract objects is implemented in PROVER9 (a first-order automated reasoning system which is the successor to OTTER). After reviewing the second-order, axiomatic theory of abstract objects, we show (1) how to represent a fragment of that theory in PROVER9's first-order syntax, and (2) how (...) PROVER9 then finds proofs of interesting theorems of metaphysics, such as that every possible world is maximal. We conclude the paper by discussing some issues for further research. (shrink)

Kurt Gödel’s version of the ontological argument was shown by J. Howard Sobel to be defective, but some plausible modifications in the argument result in a version which is immune to Sobel’s objection. A definition is suggested which permits the proof of some of Godel’s axioms.