Many macroscopic physical processes are known to occur in a time-directed way despite the apparent time-symmetry of the known fundamental laws. A popular explanation is to postulate an unimaginably atypical state for the early universe — a ‘Past Hypothesis’ (PH) — that seeds the time-asymmetry from which all others follow. I will argue that such a PH faces serious new difficulties. First I strengthen the grounds for existing criticism by providing a systematic analytic framework for assessing the status of the PH. I outline three broad categories of criticism that put into question a list of essential requirements of the proposal. The resulting analysis paints a grim picture for the prospects of providing an adequate formulation for an explicit PH. I then provide a new argument that substantively extends this criticism by showing that any time-independent measure on the space of models of the universe must necessarily break one of its gauge symmetries. The PH then faces a new dilemma: reject a gauge symmetry of the universe and introduce a distinction without difference or reject the time-independence of the measure and lose explanatory power.

The Free Choice e↵ect—whereby ⌃(p or q) seems to entail both ⌃p and ⌃q—has traditionally been characterized as a phenomenon a↵ecting the deontic modal ‘may’. This paper presents an extension of the semantic account of free choice defended in Fusco (2015) to the agentive modal ‘can’, the ‘can’ which, intuitively, describes an agent’s powers. On this account, free choice is a nonspecific de re phenomenon (Fodor, 1970; Bauerle, 1983) that—unlike typical cases— a↵ects disjunction. I begin by sketching a model of inexact ability, which grounds a modal approach to agency (Belnap and Perlo↵, 1998; Belnap et al., 2001) in a Williamson ( , 2014)-style margin of error. A classical propositional semantics combined with this framework can reflect the intuitions highlighted by Kenny (1976)’s dartboard cases, as well as the counterexamples to simple conditional views recently discussed by Mandelkern et al. (2017). In §3, I turn to an independently motivated actual-world-sensitive account of disjunction, and show how it extends free choice inferences into an object language for propositional modal logic.

The assertion by Yu and Nikolic that the delayed choice quantum eraser experiment of Kim et al. empirically falsifies the consciousness-causes-collapse hypothesis of quantum mechanics is based on the unfounded and false assumption that the failure of a quantum wave function to collapse implies not be surprising, as confirmed by [3], that the distribution recorded at D is the sum of two closely-spaced single-slit Fraunhofer distributions. In other words, the detection of which-path information by detectors D1 and D2 guarantees no interference distribution at D . FIG. 1. When which-path information of idler photons is recorded by detectors D1 and D2 , detector D does not produce an interference pattern.

In this talk, I propose to sketch the contents of Noether’s 1918 article, “Invariante Variationsprobleme”, as it may be seen against the background of the work of her predecessors and in the context of the debate on the conservation of energy that had arisen in the general theory of relativity.

This article is about the ontological dispute between finitists, who claim that only finitely many numbers exist, and infinitists, who claim that infinitely many numbers exist. Van Bendegem set out to solve the ‘general problem’ for finitism: how can one recast finite fragments of classical mathematics in finitist terms? To solve this problem Van Bendegem comes up with a new brand of finitism, namely so-called ‘apophatic finitism’. In this article it will be argued that apophatic finitism is unable to represent the negative ontological commitments of infinitism or, in other words, that which does not exist according to infinitism. However, there is a brand of infinitism, so-called ‘apophatic infinitism’, that is able to represent both the positive and the negative ontological commitments of apophatic finitism.

We argue that permissibility-based solutions to the paradox of supererogation encounter a nested dilemma. Such approaches solve the paradox by distinguishing moral and rational permissions. If they do not also include a bridge condition that relates these two permissions, then they violate a very plausible monotonicity condition. If they do include a bridge condition, then permissibility-based solutions either amount to rational satisficing or they collapse back into the classical account of supererogation and fail to resolve the paradox.

The concept of emergence is commonly invoked in modern physics but rarely defined. Building on recent influential work by Butterfield (2011a,b), I provide precise definitions of emergence concepts as they pertain to properties represented in models, applying them to some basic examples from spacetime and thermostatistical physics. The chief formal innovation I employ, similarity structure, consists in a structured set of similarity relations among those models under analysis—and their properties—and is a generalization of topological structure. Although motivated from physics, this similarity-structure-based account of emergence applies to any science that represents its possibilia with (mathematical) models.

Merely approximate symmetry is mundane enough in physics that one rarely finds any explication of it. Among philosophers it has also received scant attention compared to exact symmetries. Herein I invite further consideration of this concept that is so essential to the practice of physics and interpretation of physical theory. After motivating why it deserves such scrutiny, I propose a minimal definition of approximate symmetry—that is, one that presupposes as little structure on a physical theory to which it is applied as seems needed. Then I apply this definition to three topics: first, accounting for or explaining the symmetries of a theory emeritus in intertheoretic reduction; second, explicating and evaluating the Curie-Post principle; and third, a new account of accidental symmetry.

I provide a formally precise account of diachronic emergence of properties as described within scientific theories, extending a recent account of synchronic emergence using similarity structure on the theories’ models. This similarity structure approach to emergent properties unifies the synchronic and diachronic types by revealing that they only differ in how they delineate the domains of application of theories. This allows it to apply also to cases where the synchronic/diachronic distinction is unclear, such as spacetime emergence from theories of quantum gravity. In addition, I discuss two further case studies—finite periodicity in van der Pol oscillators and two-dimensional quasiparticles in the fractional quantum Hall effect—to facilitate comparison of this approach to others in the literature on concepts of emergence applicable to the sciences. My discussion of the fractional quantum Hall effect in particular may be of independent interest to philosophers of physics concerned with its interpretation.

The Rawlsian veil of ignorance should induce agents to behave fairly in a distributive context. This work tried to re-propose, through a dictator game with giving and taking options, a sort of original position in which reasoning behind the veil should have constituted a moral cue for subjects involved in the distribution of a common output with unequal means of production. However, our experimental context would unwittingly recall more the Hobbesian state of nature than the Rawlsian original position, showing that the heuristic resource to the Rawlsian idea of a choice behind the veil is inefficacious in distributive contexts.

The basic axioms or formal conditions of decision theory, especially the ordering condition put on preferences and the axioms underlying the expected utility (EU) formula, are subject to a number of counter-examples, some of which can be endowed with normative value and thus fall within the ambit of a philosophical reflection on practical rationality. Against such counter-examples, a defensive strategy has been developed which consists in redescribing the outcomes of the available options in such a way that the threatened axioms or conditions continue to hold. We examine how this strategy performs in three major cases: Sen's counterexamples to the binariness property of preferences, the Allais paradox of EU theory under risk, and the Ellsberg paradox of EU theory under uncertainty. We find that the strategy typically proves to be lacking in several major respects, suffering from logical triviality, incompleteness, and theoretical insularity (i.e., being cut off from the methods and results of decision theory). To give the strategy more structure, philosophers have developed "principles of individuation"; but we observe that these do not address the aforementioned defects. Instead, we propose the method of checking whether the strategy can overcome its typical defects once it is given a proper theoretical expansion (i.e., it is duly developed using the available tools of decision theory). We find that the strategy passes the test imperfectly in Sen's case and not at all in Allais's. In Ellsberg's case, however, it comes close to meeting our requirement. But even the analysis of this more promising application suggests that the strategy ought to address the decision problem as a whole, rather than just the outcomes, and that it should extend its revision process to the very statements it is meant to protect. Thus, by and large, the same cautionary tale against redescription practices runs through the analysis of all three cases. A more general lesson, simply put, is that there is no easy way out from the paradoxes of decision theory.

I survey from a modern perspective what spacetime structure there is according to the general theory of relativity, and what of it determines what else. I describe in some detail both the “standard” and various alternative answers to these questions. Besides bringing many underexplored topics to the attention of philosophers of physics and of science, metaphysicians of science, and foundationally minded physicists, I also aim to cast other, more familiar ones in a new light.

In physics the concept of reduction is often used to describe how features of one theory can be approximated by those of another under specific circumstances. In such circumstances physicists say the former theory reduces to the latter, and often the reduction will induce a simplification of the features in question. (By contrast, the standard terminology in philosophy is to say that the less encompassing, approximating theory reduces the more encompassing theory being approximated.) Accounts of reductive relationships aspire to generality, as broader accounts provide a more systematic understanding of the relationships between theories and which of their features are relevant under which circumstances.

Surplus structure arguments famously identify elements of a theory regarded as excess or superfluous. If there is an otherwise analogous theory that does without such elements, a surplus structure argument prompts adopting it over the one with those elements. Despite their prominence, the form, justification, and range of applicability of such arguments is disputed. I provide an account of these, following Dasgupta ([2016]) for the form, which makes plain the role of observables and observational equivalence. However, I diverge on the justification: instead of demanding that the symmetries of the theory relevant for surplus structure arguments be defined without recourse to any interpretation of those theories, I suggest that the process of identifying what is observable and its consequences for symmetries work in dialog. They settle through a reflective equilibrium that is responsible to new experiments, arguments, and examples. Besides better aligning with paradigmatic uses of the surplus structure argument, this position also has some broader consequences for scope of these arguments and the relationship between symmetry and interpretation more generally.

Based on three common interpretive commitments in general relativity, I raise a conceptual problem for the usual identification, in that theory, of timelike curves as those that represent the possible histories of (test) particles in spacetime. This problem affords at least three different solutions, depending on different representational and ontological assumptions one makes about the nature of (test) particles, fields, and their modal structure. While I advocate for a cautious pluralism regarding these options, I also suggest that re-interpreting (test) particles as field processes offers the most promising route for natural integration with the physics of material phenomena, including quantum theory.

Christian List [24] has recently proposed a category-theoretic model of a system of levels, applying it to various pertinent metaphysical questions. We modify and extend this framework to correct some minor defects and better adapt it to application in philosophy of science. This includes a richer use of category theoretic ideas and some illustrations using social choice theory.

Recently, Horsman et al. (2014) have proposed a new framework, Abstraction/Representation (AR) theory, for understanding and evaluating claims about unconventional or non-standard computation. Among its attractive features, the theory in particular implies a novel account of what is means to be a computer. After expounding on this account, I compare it with other accounts of concrete computation, finding that it does not quite fit in the standard categorization: while it is most similar to some semantic accounts, it is not itself a semantic account. Then I evaluate it according to the six desiderata for accounts of concrete computation proposed by Piccinini (2015). Finding that it does not clearly satisfy some of them, I propose a modification, which I call Agential AR theory, that does, yielding an account that could be a serious competitor to other leading account of concrete computation.

If one is interested in reasoning counterfactually within a physical theory, one cannot adequately use the standard possible world semantics. As developed by Lewis and others, this semantics depends on entertaining possible worlds with miracles, worlds in which laws of nature, as described by physical theory, are violated. Van Fraassen suggested instead to use the models of a theory as worlds, but gave up on determining the needed comparative similarity relation for the semantics objectively. I present a third way, in which this similarity relation is determined from properties of the models contextually relevant to the truth of the counterfactual under evaluation. After illustrating this with a simple example from thermodynamics, I draw some implications for future work, including a renewed possibility for a viable deflationary account of laws of nature.

A “stopping rule” in a sequential experiment is a rule or procedure for determining when the experiment should end. For example, consider a pair of experiments designed to obtain evidence about the proportion of fruit flies in a given population with red eyes [Savage, 1962, pp. 17–8]. In both experiments, flies are caught, observed, and released sequentially and fairly, reporting in the end the number of red-eyed flies. In the first, the experiment is designed to stop after observing 100 flies, while the second is designed to stop after observing 6 red-eyed flies. In general the data from these experiments could be very different, but it is also possible that they be the same: in this case, 100 total flies would be observed in both experiments, of which 6 (including the last) would have red eyes. Is the evidence that each of the two would then provide for or against an hypothesis about the proportion of red-eyed flies the same? The stopping rule principle (SRP) states that this is so: Stopping Rule Principle: The evidential relationship between the data from a completed sequential experiment and a statistical hypothesis does not ever depend on the experiment’s stopping rule.

Amalgamating evidence from heterogeneous sources and across levels of inquiry is becoming increasingly important in many pure and applied sciences. This special issue provides a forum for researchers from diverse scientific and philosophical perspectives to discuss evidence amalgamation, its methodologies, its history, its pitfalls and its potential. We situate the contributions therein within six themes from the broad literature on this subject: the variety-of-evidence thesis, the philosophy of meta-analysis, the role of robustness/sensitivity analysis for evidence amalgamation, its bearing on questions of extrapolation and external validity of experiments, its connection with theory development, and its interface with causal inference, especially regarding causal theories of cancer.

This review concerns the notions of physical possibility and necessity as they are informed by contemporary physical theories and the reconstructive explications of past physical theories according to present standards. Its primary goal is twofold: first, to motivate and introduce a range of accessible issues of philosophical relevance around these notions; and second, to provide extensive references to the research literature on them. Although I will have occasion to comment on the direction and shape of this literature, pointing out certain lacunae in argument or scholarly attention, I intend to advance no overriding thesis or point of view, aside from the selection of issues I deem most interesting.

Recent work on the hole argument in general relativity by Weatherall (2016b) has drawn attention to the neglected concept of (mathematical) models’ representational capacities. I argue for several theses about the structure of these capacities, including that they should be understood not as many-to-one relations from models to the world, but in general as many-to-many relations constrained by the models’ isomorphisms. I then compare these ideas with a recent argument by Belot (2017) for the claim that some isometries “generate new possibilities” in general relativity. Philosophical orthodoxy, by contrast, denies this. Properly understanding the role of representational capacities, I argue, reveals how Belot’s rejection of orthodoxy does not go far enough, and makes better sense of our practices in theorizing about spacetime.

In this chapter we will see how string theory contains some surprising symmetries – ‘dualities’ – which, we will argue, put pressure on the view that the spacetime in which strings are described can be literally identified with classical, physical spacetime – instead it is ‘emergent’ from the theory. While the following stands on the previous chapter, and exemplifies its physics, it can be read on its own to understand the essential conclusions. We focus on one such symmetry, ‘T-duality’, but at the end review others.

Archimedes’ statics is considered as an example of ancient Greek applied mathematics; it is even seen as the beginning of mechanics. Wilbur Knorr made the case regarding this work, as other works by him or other mathematicians from ancient Greece, that it lacks references to the physical phenomena it is supposed to address. According to Knorr, this is understandable if we consider the propositions of the treatise in terms of purely mathematical elaborations suggested by quantitative aspects of the phenomena. In this paper, we challenge Knorr’s view, and address propositions of Archimedes’ statics in their relation to physical phenomena.

The notions of time and causality are revisited, as well as the A- and B-theories of time, in order to determine which theory of time is most compatible with relativistic spacetimes. Using time-orientation as one of the fundamental parameters in our manifold, we will describe the concept of time and time-series (the ordering of events in time) in Special and General Relativity and their intrinsic differences. The notions of A-theory and B-theory will be given mathematical interpretations within the scheme of General Relativity. As result, in time-orientable spacetimes, the notions of events being in the future and past, which are notions of A-thoery, are more fundamental than the notions of events being earlier than or later than than other events, which are notions of B-theory. This supports the A-theory of time vs. the B-theory of time. Furthermore, we find that B-theory notions are are incompatible with some structures found in globally hyperbolic spacetimes, namely past and future inextendible curves.

Leonard Savage famously contravened his own theory when first confronting the Allais Paradox, but then convinced himself that he had made an error. We examine the formal structure of Savage’s ‘error-correcting’ reasoning in the light of (i) behavioural economists’ claims to identify the latent preferences of individuals who violate conventional rationality requirements and (ii) John Broome’s critique of arguments which presuppose that rationality requirements can be achieved through reasoning. We argue that Savage’s reasoning is not vulnerable to Broome’s critique, but does not provide support for the view that behavioural scientists can identify and counteract errors in people’s choices.

This paper argues that the theory of structured propositions is not undermined by the Russell-Myhill paradox. I develop a theory of structured propositions in which the Russell- Myhill paradox doesn’t arise: the theory does not involve ramification or compromises to the underlying logic, but rather rejects common assumptions, encoded in the notation of the λ-calculus, about what properties and relations can be built out of others. I argue that the structuralist had independent reasons to reject these underlying assumptions. The theory is given both a diagrammatic representation, and a logical representation in a special purpose language.

We show that there is a mathematical obstruction to complete Turing computability of intelligence. This obstruction can be circumvented only if human reasoning is fundamentally unsound, with the latter formally interpreted here as certain stable soundness. To this end, we first develop in a specific setting a certain analogue of a Gödel statement, which has universality with respect to a certain class of Turing machines / formal systems. As a partial consequence of this universality, this Gödel statement, or Gödel string G as we call it in the language of Turing machines, does not require soundness but only stable soundness. Moreover, this G is constructed explicitly, given the general form of our class of Turing machines.

“Signals” are a conceptual apparatus in many scientific disciplines. Biologists inquire about the evolution of signals, economists talk about the signaling function of purchases and prices, and philosophers discuss the conditions under which signals acquire meaning. However, little attention has been paid to what is a signal. This paper is an attempt to fill this gap with a definition of signal that avoids reference to form or purpose. Along the way we introduce novel notions of “information revealing” and “information concealing” moves in games. In the end, our account offers an alternative to teleological accounts of communication.

This chapter builds on the results of the previous two to investigate the extent to which spacetime might be said to ‘emerge’ in perturbative string theory. Our starting point is the string theoretic derivation of general relativity explained in depth in the previous chapter, and reviewed in §1 below (so that the philosophical conclusions of this chapter can be understood by those who are less concerned with formal detail, and so skip the previous one). The result is that the consistency of string theory requires that the ‘background’ spacetime obeys the Einstein Field Equation (EFE) – plus string theoretic corrections. But their derivation, while necessary, is not sufficient for spacetime emergence. So we will next, in §2, identify spacetime structures whose derivation would justify us in saying that a generally relativistic spacetime ‘emerges’: this section will be important for establishing a fruitful way of approaching the question. The remainder of the chapter, §3-5, will investigate how these structures arise as empirical phenomena in string theory: at this point we will also draw on the results concerning T-duality from chapter 7 (again summarizing the essential ideas). A critical question is the recurring one of this book: whether these structures are indeed emergent, or just features already present in the more fundamental string theory. Insofar as they are emergent, the goal is of course to try to understand the physical principles underwriting their formal derivation.