Leng, Mary, and . What’s there to know?

2007, In M. Leng, A. Paseau, and M. Potter (eds.), Mathematical Knowledge. OUP

Summary: Defends an account of mathematical knowledge in which mathematical knowledge is a kind of modal knowledge. Leng argues that nominalists should take mathematical knowledge to consist in knowledge of the consistency of mathematical axiomatic systems, and knowledge of what necessarily follows from those axioms. She defends this view against objections that modal knowledge requires knowledge of abstract objects, and argues that we should understand possibility and necessity in a primative way.

Comment: This would be useful in an advanced undergraduate course on metaphysics, epistemology or philosophy of logic and mathematics. This is not an easy paper, but Leng does an excellent job of making clear some difficult ideas. The view defended is an important one in both philosophy of logic and philosophy of mathematics. Any reasonably comprehensive treatment of nominalism should include this paper.

Sullivan, Meghan, and Peter Van Inwagen. Metaphysics

2016, The Stanford Encyclopedia of Philosophy.

Introduction: It is not easy to say what metaphysics is. Ancient and Medieval philosophers might have said that metaphysics was, like chemistry or astrology, to be defined by its subject matter: metaphysics was the ‘science’ that studied ‘being as such’ or ‘the first causes of things’ or ‘things that do not change’. It is no longer possible to define metaphysics that way. First, a philosopher who denied the existence of those things that had once been seen as constituting the subject-matter of metaphysics – first causes or unchanging things – would now be considered to be making thereby a metaphysical assertion. Second, there are many philosophical problems that are now considered to be metaphysical problems (or at least partly metaphysical problems) that are in no way related to first causes or unchanging things – the problem of free will, for example, or the problem of the mental and the physical.

The first three sections of this entry examine a broad selection of problems considered to be metaphysical and discuss ways in which the purview of metaphysics has expanded over time. The central problems of metaphysics were significantly more unified in the Ancient and Medieval eras. Which raises a question – is there any common feature that unites the problems of contemporary metaphysics? The final two sections of the entry discuss some recent theories of the nature and methodology of metaphysics, including those that consider metaphysics as an impossible enterprise.

Comment: Essential article for introducing metaphysics to undergraduete students.The article offers a clear overview of the main problems of metaphysics as well as of the historical evolution from antient to contemporary metaphysics.

Vetter, Barbara, and . Potentiality: From Dispositions to Modality

2015, Oxford: Oxford University Press.

Publisher’s Note: This book develops and defends dispositionalism about modality: the view that metaphysical modality is a matter of the dispositions that objects have. Dispositionalism is an attractive view for actualists about modality, and for anyone who embraces an anti-Humean metaphysics of powers. This book shows in detail how such a view is to be formulated, which challenges it faces, and how they may be met. The metaphysics of potentiality is examined in detail to show that the view meets the three main challenges for a metaphysics of modality: (1) Extensional correctness: providing the right truth-values for statements of possibility and necessity; (2) formal adequacy: providing the right logic for metaphysical modality; and (3) semantic utility: providing a semantics that links ordinary modal language to the metaphysics of modality.

Comment: The book develops the dispositionalist view in a way that takes account of contemporary developments in metaphysics, logic, and semantics. It can be used as a main reading in metaphysics and as further reading in many other fields. Recommendable in principle for postgraduate courses.