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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.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.
Misak, Cheryl. Pragmatism and Deflationism2007, in New Pragmatists, ed. C.Misak. Oxford: Oxford University Press.-
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Added by: Jamie Collin
Summary: A contemporary defense of a pragmatist account of truth, which contrasts the view with various versions of deflationism. Misak defends the claim that to grasp the concept of truth by exploring its connections with practices we engage in - including assertion, believing, reason-giving, and inquiry. The pragmatist conception of truth, it is argued, helps to elucidate realism/anti-realism: inquiry is truth-apt when it aims at establishing propositions that are indefeasible.Comment: A clear and contemporary reading on pragmatist appraoches to truth in a course on theories of truth. Useful for both advanced undergraduate and postgraduate courses.
Cartwright, Nancy. Where Do Laws of Nature Come From?1997, Dialectica 51(1): 65-78.-
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Added by: Jamie Collin
Summary: Cartwright explains and defends the view that causal capacities are more fundamental than laws of nature. She does this by considering scientific practice: the kind of knowledge required to make experimental setups and predictions is knowledge of the causal capacities of the entities in those systems, not knowledge of laws of nature.Comment: A good introduction to Cartwright's views and the position that causal capacities are real and more fundamental than laws of nature. Useful reading for both undergraduate and graduate courses in philosophy of science and metaphysics.
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.
Leng, Mary. Mathematics and Reality2010, Oxford University Press, USA.-
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Added by: Jamie Collin
Publisher's Note: Mary Leng offers a defense of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at least approximately) true. But since claims whose truth would require the existence of mathematical objects are indispensable in formulating our best empirical theories, it follows that we have good reason to believe in the mathematical objects posited by those mathematical theories used in empirical science, and therefore to believe that the mathematical theories utilized in empirical science are true. Previous responses to the indispensability argument have focussed on arguing that mathematical assumptions can be dispensed with in formulating our empirical theories. Leng, by contrast, offers an account of the role of mathematics in empirical science according to which the successful use of mathematics in formulating our empirical theories need not rely on the truth of the mathematics utilized.Comment: This book presents the most developed account of mathematical fictionalism. The book, or chapters from it, would provide useful further reading in advanced undergraduate or postgraduate courses on metaphysics or philosophy of mathematics.
Douglas, Heather. Inductive Risk and Values in Science2000, Philosophy of Science 67(4): 559-579.-
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Added by: Nick Novelli
Abstract: Although epistemic values have become widely accepted as part of scientific reasoning, non-epistemic values have been largely relegated to the "external" parts of science (the selection of hypotheses, restrictions on methodologies, and the use of scientific technologies). I argue that because of inductive risk, or the risk of error, non-epistemic values are required in science wherever non-epistemic consequences of error should be considered. I use examples from dioxin studies to illustrate how non-epistemic consequences of error can and should be considered in the internal stages of science: choice of methodology, characterization of data, and interpretation of results.Comment: A good challenge to the "value-free" status of science, interrogating some of the assumptions about scientific methodology. Uses real-world examples effectively. Suitable for undergraduate teaching.
Franklin, L. R.. Exploratory Experiments2005, Philosophy of Science 72(5): 888-899.-
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Added by: Nick Novelli
Abstract: Philosophers of experiment have acknowledged that experiments are often more than mere hypothesis-tests, once thought to be an experiment's exclusive calling. Drawing on examples from contemporary biology, I make an additional amendment to our understanding of experiment by examining the way that `wide' instrumentation can, for reasons of efficiency, lead scientists away from traditional hypothesis-directed methods of experimentation and towards exploratory methods.Comment: Good exploration of the role of experiments, challenging the idea that they are solely useful for testing clearly defined hypotheses. Uses many practical examples, but is very concise and clear. Suitable for undergraduate teaching in an examination of scientific methods in a philosophy of science course.
Alexandrova, Anna. Making Models Count2008, Philosophy of Science 75(3): 383-404.-
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Added by: Nick Novelli
Abstract: What sort of claims do scientific models make and how do these claims then underwrite empirical successes such as explanations and reliable policy interventions? In this paper I propose answers to these questions for the class of models used throughout the social and biological sciences, namely idealized deductive ones with a causal interpretation. I argue that the two main existing accounts misrepresent how these models are actually used, and propose a new account.
Comment: A good exploration of the role of models in scientific practice. Provides a good overview of the main theories about models, and some objections to them, before suggesting an alternative. Good use of concrete examples, presented very clearly. Suitable for undergraduate teaching. Would form a useful part of an examination of modelling in philosophy of science.
Thalos, Mariam. Nonreductive physics2006, Synthese 149(1): 133-178.-
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Added by: Nick Novelli
Abstract: This paper documents a wide range of nonreductive scientific treatments of phenomena in the domain of physics. These treatments strongly resist characterization as explanations of macrobehavior exclusively in terms of behavior of microconstituents. For they are treatments in which macroquantities are cast in the role of genuine and irreducible degrees of freedom.Comment: A good argument against reduction, grounded in scientific practice. Would be useful in a philosophy of science or a metaphysics context to explore and challenge the idea of reduction. Does a good job of explaining some fairly technical concepts as clearly as possible, but still best suited to graduate or upper-level undergraduate teaching.
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Chihara, Charles. Nominalism
2005, in The Oxford Hanbook of Philosophy of Mathematics and Logic, ed. S. Shapiro. New York: Oxford University Press.
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.