Thomas Müller

Anscombe’s 1971 inaugural lecture at Cambridge, entitled ‘Causality and Determination’, has had a lasting influence on a remarkably broad range of philosophers and philosophical debates, touching on fundamental topics in philosophy of science, action theory, the free will debate, epistemology, philosophy of mind, and metaphysics. Especially where anti-reductionist or pluralist strands of philosophical thought are being seriously considered, one should not be surprised to find references to Anscombe’s lecture. Moreover, there appears to be a growing interest in Anscombe’s comprehensive philosophical outlook, as attested by the recent publication of a weighty collection of essays spanning that outlook in its full breadth in the prestigious Routledge Philosophical Minds series. Against this background it is apt that now, 50 years after the original lecture, a Topical Collection sees the light, circling around the most central themes from Anscombe’s lecture, with a particular emphasis on the question how these hang together, how they form part of the larger philosophical project that Anscombe obviously intended the lecture to highlight. This Introduction motivates the Topical Collection, and introduces the various contributions against that background.

This chapter introduces a variety of events that are definable in BST and discusses in which histories these events occur. This gives rise to the concept of the occurrence proposition for events of various kinds. Of particular interest are transitions, defined as pairs of events, one of which is appropriately below the other. Transitions play a crucial role in later chapters. The chapter then discusses the topological aspects of BST, which are picked up again in Chapter 9. It defines a natural topology for BST: the diamond topology, and describes some important facts about it, focusing on the Hausdorff property and local Euclidicity. The chapter also gives an overview of how BST structures may be used to build semantic models for languages with temporal and modal operators.

The chapter constructs a notion of the present that is both relativity-friendly and serves the metaphysical role required by presentism. It draws a distinction between a static present based on simultaneity and a dynamic present based on co-presentness. Co-presentness points to a dynamic role of the present in separating a fixed past from an open future. That dynamical role is linked to the idea that dynamic change must be based on the indeterministic realization of possibilities for the future. In working out the formal details of this idea, the chapter makes use of the rich notion of modal correlations that BST offers. Depending on what exactly the modal correlations are like, the analysis delivers different regions of the past, present, and future of a given event.

The chapter shows how local indeterminism underlying BST combines with relativistic space-times. First it defines particular BST structures in which histories are isomorphic to Minkowski space-times. It further argues that many general relativistic space-times are one-history structures of BST. It introduces the notion of non-Hausdorff differential manifolds and investigates if they can be interpreted modally, as structures of BST with multiple histories. It investigates bifurcating curves in non-Hausdorff manifolds, which are natural representations of alternative evolutions of point-like objects. As the required bifurcating curves are unlikely in General Relativity, whereas there are cases of indeterministic general relativistic space-times, the chapter concludes that General Relativity is globally indeterministic, but locally deterministic.

This chapter analyzes the phenomenon of quantum mechanical correlations using the BST notions of transitions, propensities, and funny business. It considers two ways of understanding such correlations: First, as modal correlations (exhibited, e.g., in the GHZ setup) and, second, as probabilistic correlations (exhibited, e.g., in the Bell-Aspect setup). Having introduced the notion of structure extensions, it asks if it is possible to extend an initial BST structure harboring correlations (modal or probabilistic) in such a way that the resulting extended structure harbors no such correlations. An important distinction, rigorously stated in BST, is that between agents-induced indeterminism and Nature-induced indeterminism. A main result concerning structure extensions is that in the mentioned cases, the procedure is not possible unless the extended structure violates the initially given division between cases of agents-induced indeterminism and cases of Nature-induced indeterminism.

This chapter offers a BST theory of propensities (i.e., of objective single-case probabilities), which builds on the account of indeterministic causation developed in Chapter 6. Propensities are shown to deliver classical (Kolmogorovian) probability spaces. The chapter draws a distinction between propensities and probability measures. The former are assigned to sets of BST transitions, in particular to sets of _causae causantes_ of transitions, and are interpreted as degrees of possibility of these transitions. The latter are defined in terms of propensities and are measures of Komogorovian probability spaces. Features of propensities are derived from a logico-causal analysis. Finally, the chapter discusses how the theory developed here handles well-known objections to propensities due to Humphreys and to Salmon, especially Humphreys’s paradox.

The chapter analyses singular causation within an indeterministic context. It assumes that effects are transitions and causes are basic indeterministic transitions, called _causae causantes_. It considers a variety of transitions as effects, depending on what their outcomes are (outcome chains, scattered outcomes, or disjunctive outcomes). By this analysis, a _causa causans_ for a given transition occurs at a risky junction, where alternative basic transitions could prohibit the occurrence of the given transition. The _causa causans_ keeps the occurrence of this transition possible. As an argument for the adequacy of this analysis, the chapter offers a few theorems showing that _causae causantes_ satisfy inus-like conditions as proposed by Mackie.

The focus of this chapter is modal correlations, rigorously analysed in terms of BST transitions. In the simplest case, two transitions are modally correlated if each is possible, but their joint occurrence is not possible. The chapter singles out a class of “interesting” modal correlations, called modal funny business, and offers two approaches to them. On the first analysis, a set of basic transition exhibits modal funny business if it is combinatorially consistent but not consistent as a whole. The other approach draws on explanation: in a set of transitions harboring modal funny business there is no pair of blatantly inconsistent transitions that could explain why the whole set is inconsistent. These two analyses yield precise definitions of combinatorial and explanatory funny business. The main result consists of theorems showing that the two concepts are co-extensive, which stresses the stability of the notion of modal funny business.

The chapter discusses how the histories in a common BST structure are related. By the axioms of the core theory of BST, any two histories share some past, but there are different ways to implement this. These are distinguished by the so-called prior choice principles, which make specific demands on the way in which histories branch. On one option (which yields structures of BST 92 ), histories branch, or remain undivided, at points, which means that there is a maximal element in the overlap of any two histories. The other option (which yields BST NF structures) prohibits the existence of such maximal elements and works with so-called choice sets. The chapter discusses the pattern of branching in the two theories, BST 92 and BST NF, also with respect to topology. As it turns out, the two theories are are intertranslatable. The chapter ends with a sketch of these translatability results.

In this chapter the reader is guided through the construction of the core theory of Branching Space-Times. This discursive approach culminates in proposing a set of postulates that a structure of the core theory of Branching Space-Times (common BST) has to satisfy. The theory’s basic notion is that of a set of events, partially ordered by a pre-causal relation. Histories are then defined as maximal directed subsets of the base set. The chapter proves essential facts about histories and the postulates that the core of BST is assumed to satisfy. Among other things, it proves the so-called M-property that determines how any two point event in a common BST structure are related.

This introductory chapter explains the aim of the book: the analysis of real possibilities as anchored in a spatio-temporal world that is rudimentarily relativistic. It contrasts real possibilities to other possibilities discussed in the philosophical literature. It explains how branching is related to the possible worlds framework made popular, e.g., by David Lewis’s works. It offers philosophical comments on crucial notions and assumptions of BST, such as events, histories, and temporal directedness. It ends up with some hints about how the BST project is situated in modal metaphysics, touching themes such as the concept of actuality or the distinction between possibilities as “alternatives to” vs. “alternatives for”.

We address the philosophical problem of agency via an explication of the notion of agency that defines a useful target for our modelling efforts. We start with an initial explication as offered in the groundbreaking and influential study A Metaphysics for Freedom by Steward (2012), which centres on animal agency and its basis in what our world is like. We agree with Steward’s metaphysical outlook and discuss the agency question not as one of epistemology, but as a question of ontology. The general ontological question is how nature can leave room for real higher-level ontological categories. Agency is just one such higher category. Life is another important one—but both have a somewhat contentious status in philosophy. Using the example of the sun as a real higher-level entity, we discuss the interdependence of levels of organisation and argue for a specific notion of ontologically emergent individuals. Such entities must be based on lower-level open possibilities. From that general basis we work our way towards a refined explication of agency, taking inspiration from our practices of agency attribution and tackling the possibility of artificial agents along the way. We characterise agency as free agency that requires open possibilities for the flexible configuration of the agent’s body. In our resulting explication, we also stress one of the most neglected, but crucially important aspects of agency: agents have to be able to learn and to adapt over time. To model agency is, therefore, to model a specific kind of flexible decision making and learning.

We discuss a phenomenological approach to agency based on Heidegger’s analysis of Dasein, the human way of being-in-the-world. Inspired by the works of Dreyfus, we understand the human way of being-in-the-world as acting in the world, and we seek to isolate general structures (existentiales) of agency by transposing the structures identified through the analysis of Dasein downwards. The most basic such structure is circumspect coping, through which an agent encounters its environment’s sensible possibilities in the form of equipment, or more generally, affordances. Our agency reading confronts the phenomenological analysis with two crucial questions. First: how to anchor the sensible agential possibilities that sustain an agent’s coping with the environment in the world as described by science? Second: how do development and learning find a place in the analysis? We claim that both issues can be successfully addressed in terms of our general account of agency (Chap. 2) and of the agency model of Projective Simulation (Chap. 5). We give three reasons for a phenomenological view on agency. First, it links to our individual experience as human agents. Second, Dreyfus’s critique of AI is a challenge for the conceptual possibility of artificial agency, which we defended by the project of agency modelling. Third, we believe that the phenomenological reading that we provide for the agency model of Projective Simulation strengthens our explication of agency from Chap. 2.

The introduction gives an overview of the philosophical problem of agency: How does agency fit into the natural world as described by the sciences? We introduce the general methodology of modelling and specify what that means in the case of agency, where an initial explication of the notion is required. We briefly introduce the agency model of Projective Simulation to be discussed later in the book. We mention that the notion of experiment takes on a special role in quantum mechanics, because the experimenter’s active role is ineliminable there. The introduction also includes a per-chapter overview of the five main chapters of the book.

The approach to quantum mechanics that we present in this book aligns fairly well with the QBist position in quantum foundations, which takes quantum mechanics as describing the interaction of an agent with the world: A theory mainly offers a way for the agent to manage her expectations about the outcomes of her interactions, not a picture of what nature is really like. We introduce QBism briefly and situate the framework within a range of options for integrating agency and quantum mechanics. We agree with QBism on many fundamental issues, but we do not subscribe to QBism wholesale. We agree with QBism’s pragmatic outlook that takes scientific theories to be tools for agents to use, and with the QBist goal of developing a participatory realism. But we are critical of the particular idealisations that QBism in its present form subscribes to. Most importantly, we are critical of the structural choice not to resolve the agent nor the world in any detail. In our view, scientific agents learn by modelling. Models are tools that agents can use and develop in dealing with the world. Guided by concrete examples, we describe a scientific modelling framework that allows for loops of three different degrees of difficulty and complexity. These range from quantum state updating, which neatly fits the QBist approach of working within a fixed probability space, via a broader class of updates including so-called Hamiltonian learning, up to the most difficult cases in which true scientific creativity is at play. All three levels of difficulty need to be acknowledged for a full picture of real scientific agency.At the end of the chapter, we describe the project of modelling scientific agency itself, which leads to the topics of Chaps. 5 and 6.

Projective Simulation (PS) is a model for agency that incorporates aspects of reinforcement learning, an indeterministic basic dynamics inspired by physical hopping processes as studied in quantum optics, and an overall orientation towards agency as a continuous process of interaction with the environment as described by phenomenology. We explain the formal structure of PS in detail and compare it to the more standard paradigm of reinforcement learning. PS stands out mostly due to its specific memory structure (Episodic and Compositional Memory, ECM) and its openness, which makes it apt as an agency model rather than just a learning model: PS does not start from a fixed environment model to be “solved”. The focus is, rather, on the internal dynamics of deliberation, which is resolved as a stochastic process within the ECM, as well as on learning and adaptation over a long time, allowing for significant and even disruptive changes in the environment to be incorporated. After discussing the model, we showcase several applications of PS, prominently in basic research in quantum mechanics and especially in quantum information. This strengthens our claim about the intimate connection between agency and quantum physics that we already defended in Chaps. 3 and 4. We also consider quantum versions of PS, which promise to show quantum advantages in machine learning while retaining a maximum of transparency. These applications motivate a separate discussion of transparency and traceability in the context of explainable (quantum) AI.

This open access monograph presents an in-depth study of the problem of how agency fits into the physical world. In particular, the authors focus on agency as a precondition of free will. They present a detailed and physically well motivated formal model to anchor their philosophical discussion. Coverage brings together perspectives from physics, computer science, and different branches of philosophy. The book describes the agency model of Projective Simulation, its physical realisability and its quantum extensions. It situates this model within the discussion of agency in philosophy and in Artificial Intelligence. In addition, the authors highlight the role of agency in Quantum Mechanics itself, recently stressed by the Bayesian-inspired interpretation of Quantum Mechanics, QBism. They provide a comprehensive exposition of Quantum Mechanics and a reflection on the embodied nature of agents. (Quantum) indeterminism turns out to be a key resource for Projective Simulation, and for agency in general. This establishes a novel connection between agency and phenomenology. Overall, the book provides a coherent picture of agents as persisting physical entities endowed with active capacities. Such an explanation does not necessarily settle the question of the actual empirical basis of our human agency. It does, however, show that a coherent notion of agency is possible within a modern scientific world-view.

We provide a formally rigorous framework for integrating singular causation, as understood by Nuel Belnap's theory of causae causantes, and objective single case probabilities. The central notion is that of a causal probability space whose sample space consists of causal alternatives. Such a probability space is generally not isomorphic to a product space. We give a causally motivated statement of the Markov condition and an analysis of the concept of screening-off. 1. Causal dependencies and probabilities1.1Background: causation in branching space-times1.2What are probabilities defined for?2. Basic transitions2.1Basics of basic transitions2.2Sets of basic transitions3. Causal probability theory3.1Some simple cases3.2General causal probabilities3.3Application: probability of suprema of a chain.

This paper aims at bringing together two debates in metaphysics that so far have been kept separate: the debate about determinism vs. indeterminism as de re modality on the one hand, and the debate about persistence on the other hand. Both debates significantly involve talk of things. We will show that working out a proper semantics for singular terms and an accompanying theory of things, motivated by considerations of quantified modal logic, can significantly further the persistence debate. We will use our semantic framework to give an argument in support of the endurantist position as the best theory of persistence

Theories of free agency based on indeterminism -- that is, libertarian theories -- are often accused of undermining an agent's integrity: If an action is due to indeterministic happenings, how can it be called the agent's action to begin with? Isn't a deterministic connection between an agent's circumstances and her action needed to maintain her integrity? We claim that a meaningful notion of agency does not need determinism. In this paper we introduce stochastic libertarianism, a novel theory of free agency under indeterminism. Based on a physically motivated, stochastic model of the temporal evolution of a deliberation process, stochastic libertarianism views indeterminism as a core resource for meaningful agency rather than as a threat. We counter the supposed threat by explicitly discussing Van Inwagen's replay argument, exposing a flaw in the argument that is due to insufficient attention to temporal details. Our approach can also explain how a stochastically libertarian agent developing over time can exhibit highly realiable behavior. We claim, therefore, that integrity in action does not need determinism.

We show that truth conditions for counterfactuals need not always be given in terms of a vague notion of similarity. To this end, we single out the important class of historical counterfactuals and give formally rigorous truth conditions for these counterfactuals, employing a partial ordering relation called "comparative closeness" that is defined in the framework of branching space-times. Among other applications, we provide a detailed analysis of counterfactuals uttered in the context of lost bets. In an appendix we compare our theory with the branching space-times based reading of counterfactuals recently proposed by Belnap.

Branching theories are popular frameworks for modeling objective indeterminism in the form of a future of open possibilities. In such theories, the notion of a history plays a crucial role: it is both a basic ingredient in the axiomatic definition of the framework, and it is used as a parameter of truth in semantics for languages with a future tense. Furthermore, histories—complete possible courses of events—ground the notion of modal consistency: a set of events is modally consistent iff there is a history containing that set. We will explain these roles of histories and highlight some critical aspects having to do with the fact that histories are global and, in a relevant sense, “big” objects. The notion of modal consistency, on the other hand, has both local and global aspects. We ask in how far a local notion of modal consistency can serve as an alternative to the common uses of histories, and work out two recent approaches to alternatives to histories. Combining these approaches, we develop a novel semantics for branching time.

The article puts forward a branching-style framework for the analysis of determinism and indeterminism of scientific theories, starting from the core idea that an indeterministic system is one whose present allows for more than one alternative possible future. We describe how a definition of determinism stated in terms of branching models supplements and improves current treatments of determinism of theories of physics. In these treatments, we identify three main approaches: one based on the study of equations, one based on mappings between temporal realizations, and one based on branching models. We first give an overview of these approaches and show that current orthodoxy advocates a combination of the mapping- and the equations-based approaches. After giving a detailed formal explication of a branching-based definition of determinism, we consider three concrete applications and end with a formal comparison of the branching- and the mapping-based approach. We conclude that the branching-based definition of determinism most usefully combines formal clarity, connection with an underlying philosophical notion of determinism, and relevance for the practical assessment of theories. 1 Introduction2 Determinism in Philosophy of Science: Three Approaches2.1 Determinism: The core idea and how to spell it out2.2 The three approaches in more detail2.3 Representing indeterminism3 Orthodoxy: DMAP, with Invocations of DEQN4 Branching-Style Determinism 4.1 Models and realizations4.2 Faithfulness4.3 Two types of branching topologies 5 Comparing the Approaches5.1 Case studies5.2 Formal comparison of the DMAP and DBRN frameworks6 Conclusions.