Modal propositional logic; Modal predicate logic; A survey of modal logic.

The papers collected in this volume were written over a period of some eight or nine years, with some still earlier material incorporated in one of them. Publishing them under the same cover does not make a con tinuous book of them. The papers are thematically connected with each other, however, in a way which has led me to think that they can naturally be grouped together. In any list of philosophically important concepts, those falling within the range of application (...) of modal logic will rank high in interest. They include necessity, possibility, obligation, permission, knowledge, belief, perception, memory, hoping, and striving, to mention just a few of the more obvious ones. When a satisfactory semantics (in the sense of Tarski and Carnap) was first developed for modal logic, a fascinating new set of methods and ideas was thus made available for philosophical studies. The pioneers of this model theory of modality include prominently Stig Kanger and Saul Kripke. Several others were working in the same area independently and more or less concurrently. Some of the older papers in this collection, especially 'Quantification and Modality' and 'Modes of Modality', serve to clarify some of the main possibilities in the semantics of modal logics in general. (shrink)

This book, one of the handful of truly pathbreaking works in twentieth-century philosophical theology, presents Hartshorne's persuasive rehabilitation of Anselm's Ontological Argument, recast in neoclassical form as "the Modal Proof.".

A philosophy of shared creative experience.--What metaphysics is.--Present prospects for metaphysics.--Abstraction: the question of nominalism.--Some principles of method.--A logic of ultimate contrasts.--Wittgenstein and Tillich: reflections on metaphysics and language.--Non-restrictive existential statements.--Events, individuals and predication: a defence of event pluralism--The prejudice in favor of symmetry.--The principle of dual transcendence and its basis in ordinary language.--Can there be a priori knowledge of what exists?--Ideas of God: an exhaustive division.--Six theistic proofs.--Sensory qualities and ordinary language.--The aesthetic matrix of value.

The structure of the second, Or so-Called modal version of anselm's ontological argument is discussed in relation to various systems of alethic modal logic. It is argued that there are three current problems standing in the way of acceptance of the argument, Each related to its modal structure, And each an analogue of a traditional objection to anselm's original argument. Two of these problems can probably be solved, But the third remains recalcitrant.

In chapter one, I motivate the results to follow by discussing their impact on our conception of the nature of philosophy. ;In chapter two, I define, by way of a description of its rules of inference, a system of quantified modal logic. I then use this system in subsequent chapters to codify definitions of concepts and to construct formal derivations. ;Chapter three considers an essay by Nasser and Brown in which they attempt to answer our basic question: does an omniscient (...) being exist? I also evaluate their claim to be addressing an argument by Hartshorne . ;In chapter four I distinguish four traditional concepts of omniscience. Each is defined in terms of the formal system of chapter two, making use of only non-logical predicate, the dyadic relation 'x knows that p'. I then define adequacy conditions and prove that the definitions given meet them. ;In chapter five, I construct valid derivations of the existence of an omniscient being . ;In chapter six, I consider the premisses used in the Seven Epistemic Ways, and show that, with the exception of the premise that it is possible that there be an omniscient being, each of these premisses is a theorem when omniscience is construed as in the classical tradition . ;In chapter seven alternatives to the classical concepts of omniscience are defined formally . I then show which of the seven ways are sound when the premisses are interpreted in terms of these alternative concepts. (shrink)