Ever since Bertrand Russell, logic is not merely to be taken as the study of correct reasoning - checking the validity of arguments and/or vindicating the legitimacy of the process of reasoning, so as to produce more truth. ‘Logic is fundamental in philosophy’, to put in Russell’s words. In particular, the development of modal logic equipped with Kripke models since the middle of the 20th century has expand the scope of axiomatization (of a logical theory) to cover a variety of philosophical issues/topics, e.g. metaphysical modality, knowledge and belief, time, and some others. It is them tempting for philosophers to illustrate some philosophical concepts by virtue of proposing certain appropriate theses which can be further theorized as some sort of logical systems. At present, a large family of so called non-classical logics have been well established, such as logics of metaphysical modality (including necessity and possibility), epistemic logics (including knowing and believing and some other epistemic attitudes), temporal logic, logic of justification, to mention a few.
Following along this approach, in Modal Logic as Metaphysics (Oxford University Press, 2013), Timothy Williamson proposes an axiomatization of some main metaphysical doctrines, taken as modal truths of some sort, in a well-constructed framework of higher order modal logic, and argues that the resulting axiomatization, taken as a whole, can be treated as a theory of metaphysics. Williamson rejects the search for a metaphysically neutral logic as futile. Instead, he holds a positive path in searching for satisfactory answers to some noticeably metaphysical questions on the basis of an integrated approach to the issues under investigation, applying the technical resources of modal logic to provide structural cores for metaphysical theories.
As is well-known, a variety of issues/debates/problems involving metaphysical modality have been playing a dominating part not only in metaphysics but also in philosophical logic since the second half of the twenty century. Questions of this kind raise deep issues about both the nature of being and its logical relations with contingency and change.
In Modal Logic as Metaphysics, Williamson offers detailed historical discussions of how the metaphysical issues emerged in the twentieth century development of quantified modal logic, through the work of a group of distinguished philosophers/logicians, such as Rudolf Carnap, Ruth Barcan Marcus, Arthur Prior, and Saul Kripke. Williamson proposes a kind of higher-order modal logic as a new setting in which such metaphysical questions can be dealt with scientifically, by the construction of systematic logical theories embodying rival answers and their comparison by normal scientific standards.
The book also contains some of Williamson’s original and precise treatments of a wide range of topics: the relation between logic and metaphysics; the methodology of theory choice in philosophical theorization, the nature of possible worlds and their role in semantics, plural quantification vs. quantification into predicate position, communication across metaphysical disagreement, and problems for truth-maker theory. It is striking that the book deserves a serious study and examination for any students who are interested in modal logic, metaphysics, philosophical logic, and the development of analytic philosophy.