Symmetry-based inferences have permeated many discussions in philosophy of physics and metaphysics of science. It is claimed that symmetries in our physical theories would allow us to draw metaphysical conclusions about the world, a view that I call ‘symmetry inferentialism’. This paper is critical to this view. I claim that (a) it assumes a philosophically questionable characterization of the relevant validity domain of physical symmetries, and (b) it overlooks a distinction between two opposing ways through which relevant physical symmetries become (...) established. My conclusion is that symmetry inferentialism loses persuasive force when these two points are taken into consideration. (shrink)

Symmetry fundamentalism claims that symmetries should be taken metaphysically seriously as part of the fundamental ontology. The main aim of this paper is to bring some novel objections against this view. I make two points. The first places symmetry fundamentalism within a broader network of philosophical commitments. I claim that symmetry fundamentalism entails idealization realism which, in turn, entails the reification of further theoretical structures. This might lead to an overloaded ontology as well as open the way to criticisms from (...) metaphysical frameworks that reject such reifications. The second point contrasts symmetry fundamentalism with the now common view that regards symmetries as stipulations guiding empirical research and theory construction. I claim that both views clash each other and cannot be held together. I finish the paper with a more positive prospect that will be developed in future work—symmetry deflationism. (shrink)

A number of metaphysicians and philosophers of science have raised the issue of themodalityof the fundamental structures of the world. Although the debate so far has been largely focused on the (alleged) inherent causal character of fundamental structures, one aspect of it has naturally taken its place as part of the dispositional/categorical debate. In this paper, I focus on the latter in the case of the fundamentalsymmetrystructures. After putting forward the necessary metaphysical presuppositions for the debate to make sense, I (...) offer an argument which undermines the plausibility of a dispositionalist account of fundamental symmetry structures. (shrink)

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. 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. (shrink)

This paper examines some recent attempts that use counterfactuals to understand the asymmetry of non-causal scientific explanations. These attempts recognize that even when there is explanatory asymmetry, there may be symmetry in counterfactual dependence. Therefore, something more than mere counterfactual dependence is needed to account for explanatory asymmetry. Whether that further ingredient, even if applicable to causal explanation, can fit non-causal explanation is the challenge that explanatory asymmetry poses for counterfactual accounts of non-causal explanation. This paper argues that several recent (...) accounts Explanation beyond causation: philosophical perspectives on non-causal explanations, Oxford University Press, Oxford, pp 117–140, 2018; Jansson and Saatsi in Br J Philos Sci, forthcoming; Jansson in J Philos 112:7–599, 2015; Saatsi and Pexton in Philos Sci 80: 613–624, 2013; French and Saatsi, in: Reutlinger and Saatsi Explanation beyond causation: philosophical perspectives on non-causal explanations, Oxford University Press, Oxford, pp 185–205, 2018) fail to meet this challenge. The paper then sketches a more positive proposal for dealing with explanatory asymmetry in non-causal explanations. (shrink)

The concept of process is ubiquitous in science, engineering and everyday life. Category theory, and monoidal categories in particular, provide an abstract framework for modelling processes of many kinds. In this paper, we concentrate on sequential and parallel decomposability of processes in the framework of monoidal categories: We will give a precise definition, what it means for processes to be decomposable. Moreover, through examples, we argue that viewing parallel processes as coupled in this framework can be seen as a category (...) mistake or a misinterpretation. We highlight the suitability of category theory for a structuralistic interpretation of mathematical modelling and argue that for appliers of mathematics, such as engineers, there is a pragmatic advantage from this. (shrink)

Virtually all philosophers of science have construed fundamental theories as descriptions of entities, properties, and/or structures. Call this the “descriptive-ontological” view. I argue that this view is incorrect, at least insofar as physical theories are concerned. I propose a novel construal of theories that I call the “prescriptive-dynamical” view. The central tenet of this view, roughly put, is that the _essential_ content of fundamental physical theories is a _prescription for interfacing with natural systems and translating local data into compact theoretical (...) language_. The descriptive-ontological aspects of theories, if any, are taken as _inessential_ content on this view: they do not contribute to the predictive success of the theory. Rather than describing _what is there_, the essence of a physical theory is to tell us _what to do_ when interfacing with a physical system. (shrink)

Mathematics is often taken to play one of two roles in the empirical sciences: either it represents empirical phenomena or it explains these phenomena by imposing constraints on them. This article identifies a third and distinct role that has not been fully appreciated in the literature on applicability of mathematics and may be pervasive in scientific practice. I call this the “bridging” role of mathematics, according to which mathematics acts as a connecting scheme in our explanatory reasoning about why and (...) how two different descriptions of an empirical phenomenon relate to each other. I discuss two bridging roles appearing in biological and physical explanations. (shrink)

Reformulating a scientific theory often leads to a significantly different way of understanding the world. Nevertheless, accounts of both theoretical equivalence and scientific understanding have neglected this important aspect of scientific theorizing. This essay provides a positive account of how reformulation changes our understanding. My account simultaneously addresses a serious challenge facing existing accounts of scientific understanding. These accounts have failed to characterize understanding in a way that goes beyond the epistemology of scientific explanation. By focusing on cases in which (...) we have differences in understanding without differences in explanation, I show that understanding does not reduce to explanation. (shrink)

We argue that Hamiltonian mechanics is more fundamental than Lagrangian mechanics. Our argument provides a non-metaphysical strategy for privileging one formulation of a theory over another: ceteris paribus, a more general formulation is more fundamental. We illustrate this criterion through a novel interpretation of classical mechanics, based on three physical conditions. Two of these conditions suffice for recovering Hamiltonian mechanics. A third condition is necessary for Lagrangian mechanics. Hence, Lagrangian systems are a proper subset of Hamiltonian systems. Finally, we provide (...) a geometric interpretation of the principle of stationary action and rebut arguments for privileging Lagrangian mechanics. (shrink)

Orthodoxy has it that only metaphysically elite properties can be invoked in scientifically elite laws. We argue that this claim does not fit scientific practice. An examination of candidate scientifically elite laws like Newton’s F = ma reveals properties invoked that are irreversibly defined and thus metaphysically non-elite by the lights of the surrounding theory: Newtonian acceleration is irreversibly defined as the second derivative of position, and Newtonian resultant force is irreversibly defined as the sum of the component forces. We (...) think that scientists are happy to invoke metaphysically non-elite properties in scientifically elite laws for reasons of convenience, such as to simplify the equations and to make them more modular. On this basis, we draw a deflationary moral about laws themselves, as being merely convenient summaries. 1 Introduction2 Orthodoxy2.1 Orthodoxy stated2.2 Orthodoxy explained2.3 A worrisome commitment: Term objectivism3 The Loose View3.1 The argument from practice3.2 Finding the scientifically elite equations3.3 Diagnosing the metaphysically non-elite properties3.4 Situating our challenge4 Newtonian Mechanics4.1 Newtonian acceleration4.2 Newtonian resultant force4.3 A metaphysical discovery?5 Objections5.1 Metaphysically elite after all?5.2 Scientifically non-elite after all?5.3 But our world is not Newtonian!6 Consequences6.1 Consequences for the motivations for link6.2 Consequences for metaphysically elite properties6.3 Consequences for lawhood. (shrink)

According to the semantic view of scientific theories, theories are classes of models. I show that this view -- if taken seriously as a formal explication -- leads to absurdities. In particular, this view equates theories that are truly distinct, and it distinguishes theories that are truly equivalent. Furthermore, the semantic view lacks the resources to explicate interesting theoretical relations, such as embeddability of one theory into another. The untenability of the semantic view -- as currently formulated -- threatens to (...) undermine scientific structuralism. (shrink)

In this paper I elicit a prediction from structural realism and compare it, not to a historical case, but to a contemporary scientific theory. If structural realism is correct, then we should expect physics to develop theories that fail to provide an ontology of the sort sought by traditional realists. If structure alone is responsible for instrumental success, we should expect surplus ontology to be eliminated. Quantum field theory (QFT) provides the framework for some of the best confirmed theories in (...) science, but debates over its ontology are vexed. Rather than taking a stand on these matters, the structural realist can embrace QFT as an example of just the kind of theory SR should lead us to expect. Yet, it is not clear that QFT meets the structuralist's positive expectation by providing a structure for the world. In particular, the problem of unitarily inequivalent representations threatens to undermine the possibility of QFT providing a unique structure for the world. In response to this problem, I suggest that the structuralist should endorse pluralism about structure. (shrink)

Howard argues that the existence of unitarily inequivalent representations in Quantum Field Theory presents a problem for structural realism in this context. I consider two potential ways round this problem: 1), follow Wallace in adopting the 'naive' Lagrangian form of QFT with cut-offs; 2), adapt Ruetsche's 'Swiss Army Knife' approach. The first takes us into the current debate between Wallace and Fraser on conventional vs. algebraic QFT. The second involves consideration of the role of inequivalent representations in understanding spontaneous symmetry (...) breaking and quantum statistics. In both cases, I suggest, the structural realist has sufficient room to manoeuvre. (shrink)

According to one prominent view, current metaphysics is hopelessly disconnected from the implications of modern science and as a result should be abandoned fort.

According to one prominent view, current metaphysics is hopelessly disconnected from the implications of modern science and as a result should be abandoned forthwith (Ladyman and Ross 2007). Others have taken a more conciliatory stance, suggesting that the metaphysicians’ toolbox may yet yield devices that could prove useful to the philosopher of science (French and McKenzie 2012). In this book, Sider aims to contribute to the metaphysics of science by setting out an array of such tools and indicating which are (...) up to the job. More particularly, he wants to demonstrate the usefulness of certain ‘postmodal’ concepts, such as fundamentality, which is a promising tack, given that (Callender 2011), for example, has argued that it was the modal turn initiated by the likes of Kripke that is ultimately responsible for the disconnect. To illustrate his overall claim that the tools we deploy may help frame the issues that we take to be central to the metaphysics of science, Sider chooses to analyse various forms of structuralism, the view that we should take structure to be primary and the relevant entities to be secondary : nomic essentialism, which takes properties to be ‘bound up’ with laws (ibid., p. 23); structural realism, which holds, in its epistemic form, that all that we know about the world is its structure and, in the ontic alternative, that the world is, in some sense, structure; and comparativism about quantities, whereby quantities are ascribed to objects comparatively or relationally (ibid., p. 122). His conclusions are that no postmodal sense can be made of the first two, and so much the worse for them, whereas comparativism about quantities can unproblematically be stated in such terms (ibid., p. 119), and indeed, when it comes to ‘fundamentality’, at least, may well be this concept’s ‘Waterloo’ (ibid., p. 166). The worry some philosophers of science will have is that Sider’s arguments are driven more by his metaphysics than the relevant science and the issues that he identifies don’t quite map onto those they take to be central. (shrink)

Within the philosophy of science, the realism debate has been revitalised by the development of forms of structural realism. These urge a shift in focus from the object oriented ontologies that come and go through the history of science to the structures that remain through theory change. Such views have typically been elaborated in the context of theories of physics and are motivated by, first of all, the presence within such theories of mathematical equations that allow straightforward representation of the (...) relevant structures; and secondly, the implications of such theories for the individuality and identity of putative objects. My aim in this talk is to explore the possibility of extending such views to biological theories. An obvious concern is that within the context of the latter it is typically insisted that we cannot find the kinds of highly mathematised structures that structural realism can point to in physics. I shall indicate how the model-theoretic approach to theories might help allay such concerns. Furthermore, issues of identity and individuality also arise within biology. Thus Dupre has recently noted that there exists a ‘General Problem of Biological Individuality’ which relates to the issue of how one divides ‘massively integrated and interconnected’ systems into discrete components. In response Dupre advocates a form of ‘Promiscuous Realism’ that holds, for example, that there is no unique way of dividing the phylogenetic tree into kinds. Instead I shall urge serious consideration of those aspects of the work of Dupre and others that lean towards a structuralist interpretation. By doing so I hope to suggest possible ways in which a structuralist stance might be extended to biology. (shrink)

Various forms of underdetermination that might threaten the realist stance are examined. That which holds between different 'formulations' of a theory (such as the Hamiltonian and Lagrangian formulations of classical mechanics) is considered in some detail, as is the 'metaphysical' underdetermination invoked to support 'ontic structural realism'. The problematic roles of heuristic fruitfulness and surplus structure in attempts to break these forms of underdetermination are discussed and an approach emphasizing the relevant structural commonalities is defended.

In this paper I begin with a recent challenge to the Semantic Approach and identify an underlying assumption, namely that identity conditions for theories should be provided. Drawing on previous work, I suggest that this demand should be resisted and that the Semantic Approach should be seen as a philosophical device that we may use to represent certain features of scientific practice. Focussing on the partial structures variant of that approach, I then consider a further challenge that arises from a (...) concern with the role of idealisations in that practice. I argue that the partial structures approach is capable of meeting this challenge and I conclude with some broader observations about the role of such formal accounts within the philosophy of science. (shrink)

Actualism is the view that only actually existing things exist. Presentism is the view that only presently existing things exist. In this paper, I argue that being an actualist without also being a presentist is not as easy as many philosophers seem to think. A common objection to presentism is that there is an unavoidable conflict between presentism and relativity theory. But actualists who do not wish to be presentists cannot point to this relativity objection alone to support their position. (...) Unless they have some antecedent reason for thinking that actualism is more plausible than presentism, anyone who is moved by the relativity objection to give up presentism should be moved by a related objection to give up actualism as well. If there is a reason to be an actualist without also being a presentist, it must go beyond the relativity objection to presentism. (shrink)

By briefly reviewing three well-known scientific revolutions in fundamental physics (the discovery of inertia, of special relativity and of general relativity), I claim that problems that were supposed to be crying for a dynamical explanation in the old paradigm ended up receiving a structural explanation in the new one. This claim is meant to give more substance to Kuhn’s view that revolutions are accompanied by a shift in what needs to be explained, while suggesting at the same time the existence (...) of a pattern that is common to all of the discussed case-studies. It remains to be seen whether also quantum mechanics, in particular entanglement, conforms to this pattern. (shrink)

In this paper a symmetry argument against quantity absolutism is amended. Rather than arguing against the fundamentality of intrinsic quantities on the basis of transformations of basic quantities, a class of symmetries defined by the Π-theorem is used. This theorem is a fundamental result of dimensional analysis and shows that all unit-invariant equations which adequately represent physical systems can be put into the form of a function of dimensionless quantities. Quantity transformations that leave those dimensionless quantities invariant are empirical and (...) dynamical symmetries. The proposed symmetries of the original argument fail to be both dynamical and empirical symmetries and are open to counterexamples. The amendment of the original argument requires consideration of the relationships between quantity dimensions. The discussion raises a pertinent issue: what is the modal status of the constants of nature which figure in the laws? Two positions, constant necessitism and constant contingentism, are introduced and their relationships to absolutism and comparativism undergo preliminary investigation. It is argued that the absolutist can only reject the amended symmetry argument by accepting constant necessitism. I argue that the truth of an epistemically open empirical hypothesis would make the acceptance of constant necessitism costly: together they entail that the facts are nomically necessary. (shrink)

⦿ In my dissertation I introduce, motivate and take the first steps in the implementation of, the project of naturalising modal metaphysics: the transformation of the field into a chapter of the philosophy of science rather than speculative, autonomous metaphysics. -/- ⦿ In the introduction, I explain the concept of naturalisation that I apply throughout the dissertation, which I argue to be an improvement on Ladyman and Ross' proposal for naturalised metaphysics. I also object to Williamson's proposal that modal metaphysics (...) --- or some view in the area --- is already a quasi-scientific discipline. -/- ⦿ Recently, some philosophers have argued that the notion of metaphysical modality is as ill defined as to be of little theoretical utility. In the second chapter I intend to contribute to such skepticism. First, I observe that each of the proposed marks of the concept, except for factivity, is highly controversial; thus, its logical structure is deeply obscure. With the failure of the "first principles" approach, I examine the paradigmatic intended applications of the concept, and argue that each makes it a device for a very specific and controversial project: a device, therefore, for which a naturalist will find no use for. I conclude that there is no well-defined or theoretically useful notion of objective necessity other than logical or physical necessity, and I suggest that naturalising modal metaphysics can provide more stable methodological foundations. -/- ⦿ In the third chapter I answer a possible objection against the in-principle viability of the project: that the concept of metaphysical modality cannot be understood through the philosophical analysis of any scientific theory, since metaphysical necessity "transcends'' natural necessity, and science only deals with the latter. I argue that the most important arguments for this transcendence thesis fail or face problems that, as of today, remain unsolved. -/- ⦿ Call the idea that science doesn't need modality, "demodalism''. Demodalism is a first step in a naturalistic argument for modal antirealism. In the fourth chapter I examine six versions of demodalism to explain why a family of formalisms, that I call "spaces of possibility'', are (i) used in a quasi-ubiquitous way in mathematised sciences (I provide examples from theoretical computer science to microeconomics), (ii) scientifically interpreted in modal terms, and (iii) used for at least six important tasks: (1) defining laws and theories; (2) defining important concepts from different sciences (I give several examples); (3) making essential classifications; (4) providing different types of explanations; (5) providing the connection between theory and statistics, and (6) understanding the transition between a theory and its successor (as is the case with quantisation). -/- ⦿ In fifth chapter I propose and defend a naturalised modal ontology. This is a realism about modal structure: my realism about constraints. The modal structure of a system are the relationships between its possible states and between its possible states and those of other systems. It is given by the plurality of restrictions to which said system is subject. A constraint is a factor that explains the impossibility of a class of states; I explain this concept further. First, I defend my point of view by rejecting some of its main rivals: constructive empiricism, Humean conventionalism, and wave function realism, as they fail to make sense of quantum chaos. This is because the field requires the notion of objective modal structure, and the mentioned views have trouble explaining the modal facts of quantum dynamics. Then, I argue that constraint realism supersedes these views in the context of Bohm's standard theory and mechanics, and underpins the study of quantum chaos. Finally, I consider and reject two possible problems for my point of view. -/- ⦿ A central concern of modal metaphysicians has been to understand the logical system that best characterises necessity. In the sixth chapter I intend to recover the logical project applied to my naturalistic modal metaphysics. Scientists and philosophers of science accept different degrees of physical necessity, ranging from purely mathematically necessary facts that restrict physical behaviour, to kinetic principles, to particular dynamical constraints. I argue that this motivates a multimodal approach to modal logic, and that the time dependence of dynamics motivates a logic of historical necessity. I propose multimodal propositional (classical) logics for Bohmian mechanics and the Everettian theory of many divergent worlds, and I close with a criticism of Williamson's approach to the logic of state spaces of dynamic systems. (shrink)

Mereological nihilism says that there do not exist (in the fundamental sense) any objects with proper parts. A reason to accept it is that we can thereby eliminate 'part' from fundamental ideology. Many purported reasons to reject it - based on common sense, perception, and the possibility of gunk, for example - are weak. A more powerful reason is that composite objects seem needed for spacetime physics; but sets suffice instead.

I review the philosophical literature on the question of when two physical theories are equivalent. This includes a discussion of empirical equivalence, which is often taken to be necessary, and sometimes taken to be sufficient, for theoretical equivalence; and "interpretational" equivalence, which is the idea that two theories are equivalent just in case they have the same interpretation. It also includes a discussion of several formal notions of equivalence that have been considered in the recent philosophical literature, including definitional equivalence (...) and categorical equivalence. The article concludes with a brief discussion of the relationship between equivalence and duality. (shrink)

In this paper, I introduce an intrinsic account of the quantum state. This account contains three desirable features that the standard platonistic account lacks: (1) it does not refer to any abstract mathematical objects such as complex numbers, (2) it is independent of the usual arbitrary conventions in the wave function representation, and (3) it explains why the quantum state has its amplitude and phase degrees of freedom. -/- Consequently, this account extends Hartry Field’s program outlined in Science Without Numbers (...) (1980), responds to David Malament’s long-standing impossibility conjecture (1982), and establishes an important first step towards a genuinely intrinsic and nominalistic account of quantum mechanics. I will also compare the present account to Mark Balaguer’s (1996) nominalization of quantum mechanics and discuss how it might bear on the debate about “wave function realism.” In closing, I will suggest some possible ways to extend this account to accommodate spinorial degrees of freedom and a variable number of particles (e.g. for particle creation and annihilation). -/- Along the way, I axiomatize the quantum phase structure as what I shall call a “periodic difference structure” and prove a representation theorem as well as a uniqueness theorem. These formal results could prove fruitful for further investigation into the metaphysics of phase and theoretical structure. -/- (For a more recent version of this paper, please see "The Intrinsic Structure of Quantum Mechanics" available on PhilPapers.). (shrink)

A new argument is given for the thesis that only symmetry-invariant physical quantities are real. Non-invariant quantities are dynamically epiphenomenal in that they have no effect on the evolution of invariant quantities, and it is a significant theoretical vice to posit epiphenomenal quantities.

What is the proper metaphysics of quantum mechanics? In this dissertation, I approach the question from three different but related angles. First, I suggest that the quantum state can be understood intrinsically as relations holding among regions in ordinary space-time, from which we can recover the wave function uniquely up to an equivalence class (by representation and uniqueness theorems). The intrinsic account eliminates certain conventional elements (e.g. overall phase) in the representation of the quantum state. It also dispenses with first-order (...) quantification over mathematical objects, which goes some way towards making the quantum world safe for a nominalistic metaphysics suggested in Field (1980, 2016). Second, I argue that the fundamental space of the quantum world is the low-dimensional physical space and not the high-dimensional space isomorphic to the ``configuration space.'' My arguments are based on considerations about dynamics, empirical adequacy, and symmetries of the quantum mechanics. Third, I show that, when we consider quantum mechanics in a time-asymmetric universe (with a large entropy gradient), we obtain new theoretical and conceptual possibilities. In such a model, we can use the low-entropy boundary condition known as the Past Hypothesis (Albert, 2000) to pin down a natural initial quantum state of the universe. However, the universal quantum state is not a pure state but a mixed state, represented by a density matrix that is the normalized projection onto the Past Hypothesis subspace. This particular choice has interesting consequences for Humean supervenience, statistical mechanical probabilities, and theoretical unity. (shrink)

I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang-Mills theories.

The wave function in quantum mechanics presents an interesting challenge to our understanding of the physical world. In this paper, I show that the wave function can be understood as four intrinsic relations on physical space. My account has three desirable features that the standard account lacks: it does not refer to any abstract mathematical objects, it is free from the usual arbitrary conventions, and it explains why the wave function has its gauge degrees of freedom, something that are usually (...) put into the theory by hand. Hence, this account has implications for debates in philosophy of mathematics and philosophy of science. First, by removing references to mathematical objects, it provides a framework for nominalizing quantum mechanics. Second, by excising superfluous structure such as overall phase, it reveals the intrinsic structure postulated by quantum mechanics. Moreover, it also removes a major obstacle to ``wave function realism.''. (shrink)

The impetus theory of motion states that to be in motion is to have a non-zero velocity. The at-at theory of motion states that to be in motion is to be at different places at different times, which in classical physics is naturally understood as the reduction of velocities to position developments. I first defend the at-at theory against the criticism raised by Arntzenius that it renders determinism impossible. I then develop a novel impetus theory of motion that reduces positions (...) to velocity developments. As this impetus theory of motion is by construction a mirror image of the at-at theory of motion, I claim that the two theories of motion are in fact epistemically on par—despite the unfamiliar metaphysical picture of the world furnished by the impetus version. (shrink)