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Added by: Jamie Collin
Summary: Thomasson argues that merely verbal disputes arise in metaphysics when ontologists misuse the words 'thing' and 'object'. Application conditions fix the conditions under which a claim can be applied or refused, but some ontological disputes involve using the terms 'thing' and 'object' in such a way that they lack application conditions. When this happens there is no way to determine the truth values of the claims being made.Ahmed, Arif. Saul Kripke (Contemporary American Thinkers)2007, Bloomsbury.-
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Added by: Jamie CollinPublisher’s Note:
Saul Kripke is one of the most important and original post-war analytic philosophers. His work has undeniably had a profound impact on the philosophy of language and the philosophy of mind. Yet his ideas are amongst the most challenging frequently encountered by students of philosophy. In this informative and accessible book, Arif Ahmed provides a clear and thorough account of Kripke's philosophy, his major works and ideas, providing an ideal guide to the important and complex thought of this key philosopher. The book offers a detailed review of his two major works, Naming and Necessity and Wittgenstein on Rules and Private Language, and explores how Kripke's ideas often seem to overturn widely accepted views and even perceptions of common sense. Geared towards the specific requirements of students who need to reach a sound understanding of Kripke's thought, the book provides a cogent and reliable survey of the nature and significance of Kripke's contribution to philosophy. This is the ideal companion to the study of this most influential and challenging of philosophers.Comment: This book would be very useful in any course on Philosophy of Language, Philosophical Logic, and/or Metaphysics which incorporated the work of Saul Kripke. There are separate chapters on names, necessity, rule-following, and private languages; so a syllabus could make use of these individually depending on need, rather than the entire book. This is an excellent survey which covers Kripke's work in depth. As such, it is suitable for undergraduates and graduates.
Leng, Mary. What’s there to know?2007, In M. Leng, A. Paseau, and M. Potter (eds.), Mathematical Knowledge. OUP-
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Added by: Jamie Collin
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.
Wetzel, Linda. Types and Tokens: On Abstract Objects2009, MIT Press.-
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Added by: Jamie Collin
Publisher's Note: There is a widely recognized but infrequently discussed distinction between the spatiotemporal furniture of the world (tokens) and the types of which they are instances. Words come in both types and tokens - for example, there is only one word type 'the' but there are numerous tokens of it on this page - as do symphonies, bears, chess games, and many other types of things. In this book, Linda Wetzel examines the distinction between types and tokens and argues that types exist (as abstract objects, since they lack a unique spatiotemporal location). Wetzel demonstrates the ubiquity of references to (and quantifications over) types in science and ordinary language; types have to be reckoned with, and cannot simply be swept under the rug. Wetzel argues that there are such things as types by undermining the epistemological arguments against abstract objects and offering extended original arguments demonstrating the failure of nominalistic attempts to paraphrase away such references to (and quantifications over) types. She then focuses on the relation between types and their tokens, especially for words, showing for the first time that there is nothing that all tokens of a type need have in common other than being tokens of that type. Finally, she considers an often-overlooked problem for realism having to do with types occurring in other types (such as words in a sentence) and proposes an important and original solution, extending her discussion from words and expressions to other types that structurally involve other types (flags and stars and stripes; molecules and atoms; sonatas and notes).Comment: The book, or extracts from the book, could be used in advanced undergraduate or postgraduate courses on metaphysics, nominalism or philosophy of language. Chapter 2 of the book provides a clear account of the ways Quine and Frege thought about ontological commitment and language. Chapters 3-5 are also useful for students who want to understand nominalism better, though more recent nominalist strategies, such as the kinds of fictionalism developed by Mark Balaguer and Mary Leng, are not addressed.
Beebee, Helen. The non-governing conception of laws of nature2000, Philosophy and Phenomenological Research 56: 571-594.-
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Added by: Jamie Collin
Abstract: Recently several thought experiments have been developed (by John Carroll amongst others) which have been alleged to refute the Ramsey-Lewis view of laws of nature. The paper aims to show that two such thought experiments fail to establish that the Ramsey-Lewis view is false, since they presuppose a conception of laws of nature that is radically at odds with the Humean conception of laws embodied by the Ramsey- Lewis view. In particular, the thought experiments presuppose that laws of nature govern the behavior of objects. The paper argues that the claim that laws govern should not be regarded as a conceptual truth, and shows how the governing conception of laws manifests itself in the thought experiments. Hence the thought experiments do not constitute genuine counter-examples to the Ramsey-Lewis view, since the Humean is free to reject the conception of laws which the thought experiments presuppose.Comment: Good primary or secondary reading for advanced undergraduate or graduate philosophy of science or metaphysics courses; or any course where laws of nature are relevant (for instance, a course considering the contemporary impact of Hume).
Maddy, Penelope. Three Forms of Naturalism2005, in The Oxford Handbook of Philosophy of Mathematics and Logic, (ed.) S. Shapiro. New York: Oxford University Press.-
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Added by: Jamie Collin
Summary: A clear introduction to mathematical naturalism and its Quinean roots; developing and defending Maddy's own naturalist philosophy of mathematics. Maddy claims that the Quinian ignores some nuances of scientific practice that have a bearing on what the naturalist should take to be the real scientific standards of evidence. Historical studies show that scientists sometimes do not take themselves to be committed to entities that are indispensably quantified over in their best scientific theories, hence the Quinian position that naturalism dictates that we are committed to entities that are indispensably quantified over in our best scientific theories is incorrect.Comment: Good primary reading in advanced undergraduate or postgraduate courses on metaphysics, naturalism or philosophy of mathematics. This would serve well both as a clear and fairly concise introduction to Quinean naturalism and to the indispensability argument in the philosophy of mathematics.
Maddy, Penelope. Naturalism in Mathematics1997, Oxford: Oxford University Press.-
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Added by: Jamie Collin
Publisher's Note: Our much-valued mathematical knowledge rests on two supports: the logic of proof and the axioms from which those proofs begin. Naturalism in Mathematics investigates the status of the latter, the fundamental assumptions of mathematics. These were once held to be self-evident, but progress in work on the foundations of mathematics, especially in set theory, has rendered that comforting notion obsolete. Given that candidates for axiomatic status cannot be proved, what sorts of considerations can be offered for or against them? That is the central question addressed in this book. One answer is that mathematics aims to describe an objective world of mathematical objects, and that axiom candidates should be judged by their truth or falsity in that world. This promising view - realism - is assessed and finally rejected in favour of another - naturalism - which attends less to metaphysical considerations of objective truth and falsity, and more to practical considerations drawn from within mathematics itself. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be helpfully applied in the assessment of candidates for axiomatic status in set theory. Maddy's clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.Comment: Good further reading in advanced undergraduate or postgraduate courses on metaphysics, naturalism or philosophy of mathematics. Sections from the book - for instance, the chapters in Part II on indispensability considerations in scientific and mathematical practice - could be profitably read on their own. These sections may also be of interest in philosophy of science courses, as they provide a careful analysis of scientific practice (as it relates to what scientists take themselves to be ontologically committed to).
Chihara, Charles. Nominalism2005, in The Oxford Hanbook of Philosophy of Mathematics and Logic, ed. S. Shapiro. New York: Oxford University Press.-
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Added by: Jamie Collin
Summary: Introduction to mathematical nominalism, with special attention to Chihara's own development of the position and the objections of John Burgess and Gideon Rosen. Chihara provides an outline of his constructibility theory, which avoids quantification over abstract objects by making use of contructibility quantifiers which instead of making assertions about what exists, make assertions about what sentences can be constructed.Comment: This chapter would be a good primary or secondary reading in a course on philosophy of mathematics or metaphysics. Chihara is very good at conveying difficult ideas in clear and concise prose. It is worth noting however that, despite the title, this is not really an introduction to nominalism generally but to Chihara's own (important) development of a nominalist philosophy of mathematics / metaphysics.
Chihara, Charles. A Structural Account of Mathematics2004, Oxford: Oxford University Press.-
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Added by: Jamie Collin
Publisher's Note: Charles Chihara's new book develops and defends a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that, in order to understand how mathematical systems are applied in science and everyday life, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true. Chihara builds upon his previous work, in which he presented a new system of mathematics, the constructibility theory, which did not make reference to, or presuppose, mathematical objects. Now he develops the project further by analysing mathematical systems currently used by scientists to show how such systems are compatible with this nominalistic outlook. He advances several new ways of undermining the heavily discussed indispensability argument for the existence of mathematical objects made famous by Willard Quine and Hilary Putnam. And Chihara presents a rationale for the nominalistic outlook that is quite different from those generally put forward, which he maintains have led to serious misunderstandings. A Structural Account of Mathematics will be required reading for anyone working in this field. generally put forward, which he maintains have led to serious misunderstandings.Comment: This book, or chapters from it, would provide useful further reading on nominalism in courses on metaphysics or the philosophy of mathematics. The book does a very good job of summarising and critiquing other positions in the debate. As such individual chapters on (e.g.) mathematical structuralism, Platonism and Field and Balaguer's respective developments of fictionalism could be helpful. The chapter on his own contructibility theory is also a good introduction to that position: shorter and less technical than his earlier (1991) book Constructibility and Mathematical Existence, but longer and more developed than his chapter on Nominalism in the Oxford Handbook of the Philosophy of Mathematics and Logic.
Leng, Mary. “Algebraic” Approaches to Mathematics2009, In Otávio Bueno & Øystein Linnebo (eds.). New Waves in Philosophy of Mathematics. Palgrave Macmillan.-
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Added by: Jamie Collin
Summary: Surveys the opposition between views of mathematics which take mathematics to represent a independent mathematical reality and views which take mathematical axioms to define or circumscribe their subject matter; and defends the latter view against influential objections.Comment: A very clear and useful survey text for advanced undergraduate or postgraduate courses on metaphysics or philosophy of mathematics.
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Thomasson, Amie. Answerable and Unanswerable Questions
2009, In MetaMetaphysics, eds. David Chalmers, Ryan Wasserman, and David Manley. Oxford: Oxford University Press. 444-471.
Comment: This would be useful in a course on metaphysics, ontology or metametaphysics. It gives an interesting and plausible articulation of the idea that some metaphysical disputes are illegitimate in some sense (an intution that some students share). This isn't an easy paper, but it is clearly written and suitable for advanced undergraduates or graduates.