What are empirical consequences? On dispensability and composite objects

Philosophers sometimes give arguments that presuppose the following principle: two theories can fail to be empirically equivalent on the sole basis that they present different “thick” metaphysical pictures of the world. Recently, a version of this principle has been invoked to respond to the argument that composite objects are dispensable to our best scientific theories. This response claims that our empirical evidence distinguishes between ordinary and composite-free theories, and it empirically favors the ordinary ones (Hofweber 2016, 2018). In this paper, I ask whether this response to the dispensability argument is tenable. I claim that it is not. This is because it presupposes an indefensible thesis about when two empirical consequences are distinct or the same. My argument provides some insight into what our empirical consequences are, and I conclude that empirical evidence is radically metaphysically neutral. This gives us some insight into the significant content of our scientific theories—the content that a scientific realist is committed to—and I show how this insight relates to questions about theoretical equivalence more broadly.

On Dualities and Equivalences between Physical Theories

The main aim of this paper is to make a remark about the relation between (i) dualities between theories, as ‘duality’ is understood in physics and (ii) equivalence of theories, as ‘equivalence’ is understood in logic and philosophy. The remark is that in physics, two theories can be dual, and accordingly get called ‘the same theory’, though we interpret them as disagreeing—so that they are certainly not equivalent, as ‘equivalent’ is normally understood. So the remark is simple, but, I shall argue, worth stressing, since often neglected. My argument for this is based on the account of duality developed by De Haro. I also spell out how this remark implies a limitation of proposals (both traditional and recent) to understand theoretical equivalence as either logical equivalence or a weakening of it.

On the Costs of Classical Logic

This article compares classical (or -like) and nonclassical (or -like) axiomatisations of the fixed-point semantics developed by Kripke (J Philos 72(19): 690–716, 1975). Following the line of investigation of Halbach and Nicolai (J Philos Logic 47(2): 227–257, 2018), we do not compare and qua theories of truth simpliciter, but rather qua axiomatisations of the Kripkean conception of truth. We strengthen the central results of Halbach and Nicolai (2018) and Nicolai (Stud Log 106(1): 101–130, 2018), showing that, on the one hand, there is a stronger sense in which some variants of and some variants of can be taken to be, truth-theoretically, equivalent. On the other hand, we show that this truth-theoretical equivalence is not preserved by some other variants of and , arguing that the variants are more adequate axiomatisations of the fixed-point semantics than the corresponding variants.

On the Equivalence of Physical Theories

This chapter argues against formal accounts of theoretical equivalence in physics. It defends the importance of a theory’s picture of the world and its explanations of the phenomena, drawing on examples from classical physics, Newtonian gravitation, classical electromagnetism, special relativity, and quantum mechanics. The discussion draws a distinction between metaphysical equivalence and informational equivalence and argues that these are equally important to the equivalence of physical theories. The chapter concludes that there are fewer cases of wholly equivalent theories in physics than usually thought. However, this is not a problem, for it is still possible to talk about the various respects in which physical theories are, or are not, equivalent to one another.

Realism about Structure

This chapter rebuts objections to the account, dispelling concerns about taking the mathematical structures of our best physical theories seriously. It outlines further aspects of the book’s realism about structure and explains what this realism is, and what it is not, committed to. It discusses the ideas of reasonably straightforward interpretations of physics; of perspicuous formulations of physics; and of direct and indirect representations. It argues against a different kind of realism about structure in physics, which is at once both stronger and weaker than the realism about structure defended in the book. It ends by arguing against focusing on the structure of a theory’s models in our physical theorizing in general, and the model isomorphism criterion for theoretical equivalence in particular.

Introduction

This chapter provides an overview of the book: its aims, scope, and key themes. The chief project is to unearth how we figure out what our mathematically formulated, best physical theories tell us about the nature of the world, and how we figure out what these theories tell us when they can be mathematically formulated in different ways. The chapter outlines the core theme of taking the mathematics in which our best physical theories are formulated seriously; notes the background assumption of scientific realism; outlines the idea that direct formulations of physical theories are preferable; explains the idea of taking a theory’s metaphysical aspects seriously; and notes that one upshot of the account will be fewer cases of theoretical equivalence than usually thought.

Theoretical equivalence and duality

Theoretical equivalence and duality are two closely related notions: but their interconnection has so far not been well understood. In this paper I explicate the contribution of a recent schema for duality to discussions of theoretical equivalence. I argue that duality suggests a construal of theoretical equivalence in the physical sciences. The construal is in terms of the isomorphism of models, as defined by the schema. This construal gives interpretative constraints that should be useful for discussions of theoretical equivalence more generally. I illustrate the construal in various formulations of Maxwell’s electromagnetic theory.

ON MORITA EQUIVALENCE AND INTERPRETABILITY

In a recent article, Barrett & Halvorson (2016) define a notion of equivalence for first-order theories, which they call “Morita equivalence.” To argue that Morita equivalence is a reasonable measure of “theoretical equivalence,” they make use of the claim that Morita extensions “say no more” than the theories they are extending. The goal of this article is to challenge this central claim by raising objections to their argument for it and by showing why there is good reason to think that the claim itself is false. In light of these criticisms, this article develops a natural way for the advocate of Morita equivalence to respond. I prove that this response makes her criterion a special case of bi-interpretability, an already well-established barometer of theoretical equivalence. I conclude by providing reasons why the advocate of Morita equivalence should opt for a notion of theoretical equivalence that is defined in terms of interpretability rather than Morita extensions.