Steven French

Wave function realism has attracted considerable attention. Interestingly, it has served both as the focus of metaphysically inspired criticism and as support for certain metaphysical views. On one hand it has been criticized for its supposed inability to accommodate our judgments concerning "everyday" objects and, on the other, it has been invoked as support for the apparent restoration of intrinsic properties within the quantum context. Both the criticisms and deployment of wave function realism assume certain relationships between physics and metaphysics. This chapter exposes these relationships in the context of a broad understanding of both the impact of physics and metaphysics and the manner in which the latter might inform the former. In that context I aim to articulate an appropriate understanding of this position that will be appropriately and metaphysically realist.

This chapter presents a model-theoretic account in which regarding theories in terms of partial structures offers a straightforward and natural way of accommodating inconsistency. In particular, it draws attention to the heuristic importance of inconsistency in science. Shifting to the epistemic perspective, inconsistent theories can then be regarded as quasi-true and accepted as such, just like any other theory in science. This common epistemic framework forces a blurring of the standard discovery-justification distinction. A form of paraconsistent logic is introduced at the epistemic level as a logic of quasi truth.

This chapter considers the “vertical” relationship between theory and evidence. In particular, it considers the impact of the conception of “partial” truth on the dynamics of belief change. A new basis for a logic of induction is developed which is faithful to the central principles of induction as set down by Russell, and which can handle various well-known problems that are taken to beset standard Bayesian approaches. It is shown that the standard, but implausible, assumption of “logical omniscience” can be appropriately weakened through a formal modification of the notion of “quasi truth”.

It has long been argued that the model-theoretic approach acquires a certain plausibility from the fact that models are also extensively used in science itself. However, the sense of “model” here is apparently quite different from that discussed in the previous chapter. This chapter starts by discussing the models of model theory and the models of science. It presents various arguments around this subject. The chapter goes on to discuss icons and analogies, in other words the fundamental idea that a model is an icon. The chapter continues by discussing partial structures and partial isomorphisms. The question is asked: Can we construct an overarching account of models in science? The criticisms and ideas of Achinstein are described in great detail in relation to this topic.

Tarski's innovation performed a double duty in both mathematics and philosophy. In formalizing an intuitive notion of truth-as-correspondence in terms of “sentence _s_ is true in a structure” and suggesting that other semantic notions could be defined similarly, he brought model theory into mathematics and was therefore largely responsible for the explosion of developments that resulted. Motivated by Tarski's work, it has been argued that the semantic counterpart of scientific theories is of fundamental importance, and that scientific theories should be viewed not as axiomatized sets of sentences in some suitable formal language but as classes of _models_. This chapter presents a “semantic” or “model-theoretic” approach in the philosophy of science based on this theory.

The focus on the models or, more generally, the structures in which sentences are satisfied encourages a shift to a broadly _representational_ and nonpropositional account of the objects of belief. The consequences of such a move have yet to be fully explored in this context. This chapter sets out a possible doxastic framework for understanding this shift in epistemic attention. It draws on Sperber's account of the difference between “factual” and “representational” beliefs, where the object of the latter is a “semipropositional” representation of incomplete conceptual content. It is argued that the fundamental idea behind this notion can be conveniently grasped in terms of partial structures: a “representational” belief that _p_ is then understood as a belief that _p_ is partially true only, whereas a factual belief that _p_ is a belief that _p_ is true in the correspondence sense.

Ladyman has incorporated partial structures into his version of “structural realism” which he sees as realism's best hope in the face of the ontological perplexities presented by modern physics. On the other side of the divide, Bueno has also used partial structures to elaborate a form of “structural empiricism”, which extends van Fraassen's antirealist “constructive empiricism” in significant respects. This chapter does not aim to defend either realism or antirealism, but to indicate how both sides in the debate can benefit from the partial structures approach. This debate needs just the kind of detailed articulation that structural realism and empiricism offer, and that these positions represent at least two of the more interesting hopes for the future.

This chapter reviews the formalism of “pragmatic” or “quasi” truth. Just as Tarski's formalization attempted to capture what he called the “intentions” of the correspondence view of truth, the formalism outlined here attempts to represent the “intentions” of the pragmatists, notably Peirce and James. Of these, perhaps the most significant is a concern with representations of the world that are not perfect copies but are, in certain respects, incomplete and partial. The nature of the agreement between such representations and the world is then spelled out in pragmatic terms, which emphasize the set of empirical consequences of a particular idea or “concept”. The fundamental formal device behind this formalism is that of a “partial structure” and it is upon this that our epistemic construction rests.

The physics and metaphysics of identity and individuality Content Type Journal Article DOI 10.1007/s11016-010-9463-7 Authors Don Howard, Department of Philosophy and Graduate Program in History and Philosophy of Science, University of Notre Dame, Notre Dame, IN 46556, USA Bas C. van Fraassen, Philosophy Department, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132, USA Otávio Bueno, Department of Philosophy, University of Miami, Coral Gables, FL 33124, USA Elena Castellani, Department of Philosophy, University of Florence, Via Bolognese 52, 50139 Florence, Italy Laura Crosilla, Department of Pure Mathematics, School of Mathematics, University of Leeds, Leeds, LS2 9JT UK Steven French, Department of Philosophy, University of Leeds, Leeds, UK Décio Krause, Department of Philosophy, Federal University of Santa Catarina, 88040-900 Campus Trindade, Florianópolis, SC Brazil Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796

What has been called ‘the unreasonable effectiveness of mathematics’ sets a challenge for philosophers. Some have responded to that challenge by arguing that mathematics is essentially anthropocentric in character whereas others have pointed to the range of structures that mathematics offers. Here a middle way is offered that focuses on the moves that have to be made in both the mathematics and the relevant physics in order to bring the two into appropriate relation. This relation can be captured via the inferential conception of the applicability of mathematics which is formulated in terms of immersion inference and interpretation. In particular the roles of idealizations and of surplus structure in science and mathematics respectively are brought to the fore and captured via an approach to models and theories that emphasizes the partiality of the available information: the partial structures approach. The discussion as a whole is grounded in a number of case studies drawn from the history of quantum physics and extended to contest recent claims that the explanatory role of certain mathematical structures in scientific practice supports a realist attitude towards them. The overall conclusion is that the effectiveness of mathematics does not seem unreasonable at all once close attention is paid to how it is actually applied in practice.

The view that quantum particles cannot be regarded as individuals was articulated in the early days of the ‘quantum revolution’ and became so well-entrenched that French and Krause (Identity in Physics: A Historical, Philosophical and Formal Analysis. Oxford University Press, Oxford, 2006) called it ‘the Received View’. However it was subsequently shown that quantum statistics is in fact compatible with a metaphysics of particle individuality, subject to certain caveats. As a consequence it has been claimed that there exists a kind of underdetermination of the metaphysics by the physics which in turn has been used to motivate a form of ‘ontic’ structural realism (Ladyman, 1998; French, 2014). In this essay I will review this underdetermination and the motivation for structural realism that it purportedly provides in the context of recent developments in both the philosophy of physics (specifically the work of Saunders) and metaphysics (specifically the work of Dasgupta). I aim to conclude that such developments reinforce the underdetermination and allow one to respond to certain critical concerns regarding its motivational power.

Stein once urged us not to confuse the means of representation with that which is being represented. Yet that is precisely what philosophers of science appear to have done at the meta-level when it comes to representing the practice of science. Proponents of the so-called ‘syntactic’ view identify theories as logically closed sets of sentences or propositions and models as idealised interpretations, or ‘theoruncula, as Braithwaite called them. Adherents of the ‘semantic’ approach, on the other hand, are typically characterised as taking them to be families of models that are set-theoretic, according to Suppes and others, or abstract, as Giere has argued. da Costa and French (Science and Partial Truth. OUP, Oxford, 2003) suggested that we should refrain from ontological speculation as to the nature of scientific theories and models and focus on their appropriate representation for various purposes within the philosophy of science. Such an approach allows both linguistic and non-linguistic resources to play their appropriate role (see also French and Saatsi, Philosophy of Science, Proceedings of the 2004 PSA Meeting, 78:548–559, 2006) and can be supported by recent case studies illustrating the heterogeneity of scientific practice. My aim in this paper is to further develop this ‘quietist’ view, and to indicate how it offers a fruitful way forward for the philosophy of science.