It is usually assumed that the modal ontological argument is valid. However, the logical system in which the argument is analyzed can require different assumptions to secure validity. Some strategies for the both critics and proponents of the modal ontological argument are examined in different logical systems. For agnostics, statements involving a perfect being may have a truth value other than true or false. A many-valued modal logic may be a more suitable framework for agnostics, and the modal ontological argument (...) will be invalid in some many-valued modal logics. These considerations show that defenders of the modal ontological argument must also defend the choice of a particular logic (or class of logics) as the appropriate setting where the argument should be evaluated. (shrink)

It is usually assumed that the modal ontological argument is valid. However, the logical system in which the argument is analyzed can require different assumptions to secure validity. Some strategies for the both critics and proponents of the modal ontological argument are examined in different logical systems. For agnostics, statements involving a perfect being may have a truth value other than true or false. A many-valued modal logic may be a more suitable framework for agnostics, and the modal ontological argument (...) will be invalid in some many-valued modal logics. These considerations show that defenders of the modal ontological argument must also defend the choice of a particular logic (or class of logics) as the appropriate setting where the argument should be evaluated. (shrink)

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.

This volume succeeds the same authors' well-known An Introduction to Modal Logic and A Companion to Modal Logic. We designate the three books and their authors NIML, IML, CML and H&C respectively. Sadly, George Hughes died partway through the writing of NIML.

This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: _An Introduction to Modal Logic_ and _A Companion to Modal Logic_. _A New Introduction to Modal Logic_ is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works. The book takes (...) readers from the most basic systems of modal propositional logic right up to systems of modal predicate with identity. It covers both technical developments such as completeness and incompleteness, and finite and infinite models, and their philosophical applications, especially in the area of modal predicate logic. (shrink)