Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.

Quantum mechanics is a subject that has captured the imagination of a surprisingly broad range of thinkers, including many philosophers of science. Quantum field theory, however, is a subject that has been discussed mostly by physicists. This is the first book to present quantum field theory in a manner that makes it accessible to philosophers. Because it presents a lucid view of the theory and debates that surround the theory, An Interpretive Introduction to Quantum Field Theory will interest students of (...) physics as well as students of philosophy. -/- Paul Teller presents the basic ideas of quantum field theory in a way that is understandable to readers who are familiar with non-relativistic quantum mechanics. He provides information about the physics of the theory without calculational detail, and he enlightens readers on how to think about the theory physically. Along the way, he dismantles some popular myths and clarifies the novel ways in which quantum field theory is both a theory about fields and about particles. His goal is to raise questions about the philosophical implications of the theory and to offer some tentative interpretive views of his own. This provocative and thoughtful book challenges philosophers to extend their thinking beyond the realm of quantum mechanics and it challenges physicists to consider the philosophical issues that their explorations have encouraged. (shrink)

Every Thing Must Go aruges that the only kind of metaphysics that can contribute to objective knowledge is one based specifically on contemporary science as it ...

According to 'Ontic Structural Realism' (OSR), physical objects—qua metaphysical entities—should be reconceptualised, or, more strongly, eliminated in favour of the relevant structures. In this paper I shall attempt to articulate the relationship between these putative objects and structures in terms of certain accounts of metaphysical dependence currently available. This will allow me to articulate the differences between the different forms of OSR and to argue in favour of the 'eliminativist' version. A useful context is provided by Floridi's account of the (...) relationship between 'ontic' and 'epistemic' structural realisms and I shall conclude with some brief remarks on possible extensions of OSR into other scientific domains. (shrink)

Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic (...) problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians. (shrink)

This paper has two goals. The first goal is to show that the structuralists’ claims about dependence are more significant to their view than is generally recognized. I argue that these dependence claims play an essential role in the most interesting and plausible characterization of this brand of structuralism. The second goal is to defend a compromise view concerning the dependence relations that obtain between mathematical objects. Two extreme views have tended to dominate the debate, namely the view that all (...) mathematical objects depend on the structures to which they belong and the view that none do. I present counterexamples to each of these extreme views. I defend instead a compromise view according to which the structuralists are right about many kinds of mathematical objects (roughly, the algebraic ones), whereas the anti-structuralists are right about others (in particular, the sets). I end with some remarks about how to understand the crucial notion of dependence, which despite being at the heart of the debate is rarely examined in any detail. (shrink)

This paper distinguishes two kinds of realist issue -- the issue of whether the propositions of a given domain are factual and the issue of whether they are fundamental. It criticizes previous accounts of what these issues come to and suggests that they are to be understood in terms of a basic metaphysical concept of reality. This leaves open the question of how such issues are to be resolved; and it is argued that this may be done through consideration of (...) what grounds the facts of a given domain, when fundamentality is in question, and what grounds our engagement with the putative facts, when factuality is in question. (shrink)

Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.

Kit Fine; XIV*—Ontological Dependence, Proceedings of the Aristotelian Society, Volume 95, Issue 1, 1 June 1995, Pages 269–290, https://doi.org/10.1093/aristote.

Ontological dependence is a relation—or, more accurately, a family of relations—between entities or beings. For there are various ways in which one being may be said to depend upon one or more other beings, in a sense of “depend” that is distinctly metaphysical in character and that may be contrasted, thus, with various causal senses of this word. More specifically, a being may be said to depend, in such a sense, upon one or more other beings for its existence or (...) for its identity. Some varieties of ontological dependence may be analyzed in modal terms—that is, in terms of distinctly metaphysical notions of possibility and necessity—while others seem to demand an analysis in terms of the notion of essence. The latter varieties of ontological dependence may accordingly be called species of essential dependence. Notions of ontological dependence are frequently called upon by metaphysicians in their proposed analyses of other metaphysically important notions, such as the notion of substance. (shrink)

We outline Ladyman's 'metaphysical' or 'ontic' form of structuralrealism and defend it against various objections. Cao, in particular, has questioned theview of ontology presupposed by this approach and we argue that by reconceptualisingobjects in structural terms it offers the best hope for the realist in thecontext of modern physics.

This book argues that the only kind of metaphysics that can contribute to objective knowledge is one based specifically on contemporary science as it really is, and not on philosophers' a priori intuitions, common sense, or simplifications of science. In addition to showing how recent metaphysics has drifted away from connection with all other serious scholarly inquiry as a result of not heeding this restriction, this book demonstrates how to build a metaphysics compatible with current fundamental physics, which, when combined (...) with metaphysics of the special sciences, can be used to unify physics with the other sciences without reducing these sciences to physics itself. Taking science metaphysically seriously, this book argues, means that metaphysicians must abandon the picture of the world as composed of self-subsistent individual objects, and the paradigm of causation as the collision of such objects. The text assesses the role of information theory and complex systems theory in attempts to explain the relationship between the special sciences and physics, treading a middle road between the grand synthesis of thermodynamics and information, and eliminativism about information. The consequences of the books' metaphysical theory for central issues in the philosophy of science are explored, including the implications for the realism versus empiricism debate, the role of causation in scientific explanations, the nature of causation and laws, the status of abstract and virtual objects, and the objective reality of natural kinds. (shrink)

means exhaust the insults. This is unfortunate as their attitude turns a useful book, with valuable contributions from a number of writers, into a polemic.

This paper explores the consequences of the two most prominent forms of contemporary structural realism for the notion of objecthood. Epistemic structuralists hold that we can know structural aspects of reality, but nothing about the natures of unobservable relata whose relations define structures. Ontic structuralists hold that we can know structural aspects of reality, and that there is nothing else to know—objects are useful heuristic posits, but are ultimately ontologically dispensable. I argue that structuralism does not succeed in ridding a (...) structuralist ontology of objects. (shrink)

This paper examines in detail two paths that lead to Structural Realism (SR), viz. a substantive philosophical position which asserts that only the structure of the world is knowable. The upward path is any attempt to begin with empiricist premises and reach a sustainable realist position. (It has been advocated by Russell, Weyl, and Maxwell among others.) The downward path is any attempt to start from realist premises and construct a weaker realist position. (It has been recently advocated by Worrall, (...) French, and Ladyman.) This paper unravels and criticizes the metaphysical presuppositions of both paths to SR. It questions its very possibility as a substantive-and viable-realist thesis. (shrink)

This paper examines in detail two paths that lead to Structural Realism, viz. a substantive philosophical position which asserts that only the structure of the world is knowable. The upward path is any attempt to begin with empiricist premises and reach a sustainable realist position. The downward path is any attempt to start from realist premises and construct a weaker realist position. This paper unravels and criticizes the metaphysical presuppositions of both paths to SR. It questions its very possibility as (...) a substantive—and viable—realist thesis. (shrink)

In this paper, I try to decipher the role of internal symmetries in the ontological maze of particle physics. The relationship between internal symmetries and laws of nature is discussed within the framework of “Platonic realism.” The notion of physical “structure” is introduced as representing a deeper ontological layer behind the observable world. I argue that an internal symmetry is a structure encompassing laws of nature. The application of internal symmetry groups to particle physics came about in two revolutionary steps. (...) The first was the introduction of the internal symmetries of hadrons in the early 1960s. These global and approximate symmetries served as means of bypassing the dynamics. I argue that the realist could interpret these symmetries as ontologically prior to the hadrons. The second step was the gauge revolution in the 1970s, where symmetries became local and exact and were integrated with the dynamics. I argue that the symmetries of the second generation are fundamental in the following two respects: According to the so-called “gauge argument,” gauge symmetry dictates the existence of gauge bosons, which determine the nature of the forces. This view, which has been recently criticized by some philosophers, is widely accepted in particle physics at least as a heuristic principle. In view of grand unified theories, the new symmetries can be interpreted as ontologically prior to baryon matter. (shrink)