This paper deals with the historical and philosophical background of the introduction of the notion of branching time in philosophical logic as it is revealed in the hitherto unpublished mail-correspondence between Saul Kripke and A.N. Prior in the late 1950s. The paper reveals that the idea was first suggested by Saul Kripke in a letter to A.N. Prior, dated September 3, 1958, and it is shown how the elaboration of the idea in the course of the correspondence was intimately (...) intervowen with considerations of how to represent indeterminism and of the adequacy of tensed logic in light of special relativity. The correspondence underpins the point that Prior's later development of branching time may be understood as a crucial part of his attempt at the formulating a conceptual framework integrating basic human notions of time and free choice. (shrink)

Mathematically, gauge theories are extraordinarily rich --- so rich, in fact, that it can become all too easy to lose track of the connections between results, and become lost in a mass of beautiful theorems and properties: indeterminism, constraints, Noether identities, local and global symmetries, and so on. -/- One purpose of this short article is to provide some sort of a guide through the mathematics, to the conceptual core of what is actually going on. Its focus is on the (...) Lagrangian, variational-problem description of classical mechanics, from which the link between gauge symmetry and the apparent violation of determinism is easy to understand; only towards the end will the Hamiltonian description be considered. -/- The other purpose is to warn against adopting too unified a perspective on gauge theories. It will be argued that the meaning of the gauge freedom in a theory like general relativity is (at least from the Lagrangian viewpoint) significantly different from its meaning in theories like electromagnetism. The Hamiltonian framework blurs this distinction, and orthodox methods of quantization obliterate it; this may, in fact, be genuine progress, but it is dangerous to be guided by mathematics into conflating two conceptually distinct notions without appreciating the physical consequences. (shrink)

Many phenomena in the world display a striking time-asymmetry: the forwards transition frequencies are approximately invariant while the backwards ones are not. I argue in this paper that theories of such phenomena will entail that time has a direction, and that quantum mechanics in particular entails that the future is objectively different from the past.

A recent proposal by Norton (2003) to show that a simple Newtonian system can exhibit stochastic acausal behavior by giving rise to spontaneous movements of a mass on the dome of a certain shape is examined. We discuss the physical significance of an often overlooked and yet important Lipschitz condition the violation of which leads to the existence of anomalous nontrivial solutions in this and similar cases. We show that the Lipschitz condition is closely linked with the time reversibility (...) of certain solutions in Newtonian mechanics and the failure to incorporate this condition within Newtonian mechanics may unsurprisingly lead to physically impossible solutions that have no serious metaphysical implications. ‡I thank Steven Savitt of the Philosophy Department at the University of British Columbia for drawing my attention to the Lipschitz condition, and Alexei Cheviakov of the Mathematics Department at the University of British Columbia for useful discussions. †To contact the author, please write to: Department of Philosophy, University of British Columbia, Vancouver, BC, V6T 1Z1, Canada; e-mail: [email protected]. (shrink)

Notoriously, the Einstein equations of general relativity have solutions in which closed timelike curves occur. On these curves time loops back onto itself, which has exotic consequences: for example, traveling back into one's own past becomes possible. However, in order to make time travel stories consistent constraints have to be satisfied, which prevents seemingly ordinary and plausible processes from occurring. This, and several other "unphysical" features, have motivated many authors to exclude solutions with CTCs from consideration, e.g. by (...) conjecturing a chronology protection law. In this contribution we shall investigate the nature of one particular class of exotic consequences of CTCs, namely those involving unexpected cases of indeterminism or determinism. Indeterminism arises even against the backdrop of the usual deterministic physical theories when CTCs do not cross spacelike hypersurfaces outside of a limited CTC-region|such hypersurfaces fail to be Cauchy surfaces. We shall compare this CTC-indeterminism with four other types of indeterminism that have been discussed in the philosophy of physics literature: quantum indeterminism, the indeterminism of the hole argument, non-uniqueness of solutions of differential equations and lack of predictability due to insuffcient data. By contrast, a certain kind of determinism appears to arise when an indeterministic theory is applied on a CTC: things cannot be different from what they already were. Again we shall make comparisons, this time with other cases of determination in physics. We shall argue that on further consideration both this indeterminism and determinism on CTCs turn out to possess analogues in other, familiar areas of physics. CTC- indeterminism is close to the epistemological indeterminism we know from statistical physics, while the "fixedness" typical of CTC-determinism is pervasive in physics. CTC- determinism and CTC-indeterminism therefore do not provide incontrovertible grounds for rejecting CTCs as conceptually inadmissible. (shrink)

There is no possible world in which someone travels back in time and kills herself as a baby. All possible worlds are internally consistent; the one just described would not be. For this reason, autoinfanticide is metaphysically impossible. This metaphysical impossibility is philosophically intriguing because unlike most impossible events, we can vividly picture how it might look. Time travel itself seems possible, and for those who arrive in the past with proper equipment and training, the actual infanticide should (...) not be difficult. The considerations in this paper have led me to conclude that there are indeterministic worlds in which instances of autoinfanticide have a chance of succeeding, sometimes even a high chance. Some may be tempted to resist this conclusion, uncomfortable with the notion that something metaphysically impossible can have a positive chance. Understandably, they expect something which happens at no world to also have no chance of happening. However, no plausible theory of chance fits these preconceptions. (shrink)

A set of axioms implicitly defining the standard, though not instant-based but interval-based, time topology is used as a basis to build a temporal modal logic of events. The whole apparatus contains neither past, present, and future operators nor indexicals, but only B-series relations and modal operators interpreted in the standard way. Determinism and indeterminism are then introduced into the logic of events via corresponding axioms. It is shown that, if determinism and indeterminism are understood in accordance with their (...) core meaning, the way in which they are formally introduced here represents the only right way to do this, given that we restrict ourselves to one real world and make no use of the many real worlds assumption. But then the result is that the very truth conditions for sentences about indeterministic events imply the existence of tensed truths, in spite of the fact that these conditions are formulated (in the indeterministic axiom) in terms of tenseless language. The tenseless theory of time implies determinism, while indeterminism requires the flow of time assumption. (shrink)

Branching space-times (BST; Belnap, Synthese 92:385–434, 1992 ) is the most advanced formal framework for representing indeterminism. BST is however based on continuous partial orderings, while our natural way of describing indeterministic scenarios may be called discrete. This paper establishes a theorem providing a discrete data format for BST: it is proved that a discrete representation of indeterministic scenarios leading to BST models is possible in an important subclass of cases. This result enables the representation of limited indeterminism in BST (...) and hopefully paves the way for the representation of substances with capacities in that framework. (shrink)

Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to “speak” of indeterminism, its inability to present us a worldview in which new information is created as time passes. In such a case, scientific determinism would only be an illusion due to the timeless mathematical language scientists use. To investigate this possibility it is (...) necessary to develop an alternative mathematical language that is both powerful enough to allow scientists to compute predictions and compatible with indeterminism and the passage of time. We suggest that intuitionistic mathematics provides such a language and we illustrate it in simple terms. (shrink)

On the observational equivalence of continuous-time deterministic and indeterministic descriptions Content Type Journal Article Pages 193-225 DOI 10.1007/s13194-010-0011-5 Authors Charlotte Werndl, Department of Philosophy, Logic and Scientific Method, London School of Economics, Houghton Street, London, WC2A 2AE UK Journal European Journal for Philosophy of Science Online ISSN 1879-4920 Print ISSN 1879-4912 Journal Volume Volume 1 Journal Issue Volume 1, Number 2.

“Branching space-times” (BST) is intended as a representation of objective, event-based indeterminism. As such, BST exhibits both a spatio-temporal aspect and an indeterministic “modal” aspect of alternative possible historical courses of events. An essential feature of BST is that it can also represent spatial or space-like relationships as part of its (more or less) relativistic theory of spatio-temporal relations; this ability is essential for the representation of local (in contrast with “global”) indeterminism. This essay indicates how BST might be seen (...) to grow out of Newton’s deterministic and non-relativistic theory by two independent moves: (1) Taking account of indeterminism, and (2) attending to spatio-temporal relationships in a spirit derived from Einstein’s theory of special relativity. Since (1) and (2) are independent, one can see that there is room for four theories: Newtonian determinism, branching time indeterminism, relativistic determinism, and (finally) branching space-times indeterminism. (shrink)

The paper defends an Aristotelian notion of indeterminism, as rigorously formulated in the framework of branching space-times (BST) of Belnap (1992), against the model-theoretic characterization of indeterminism that Montague (1962) introduced into the philosophy of science. It delineates BST branching against the background provided by Earman's (2008) distinction between individual vs. ensemble branching. It describes a construction of physically-motivated BST models, in which histories are isomorphic to Minkowski spacetime. Finally it responds to criticism leveled against BST by addressing some semantical (...) questions, a topological issue, and the past/future asymmetry. (shrink)

The aim of the paper is to prove the consistency of libertarianism. We examine the example of Jane, who deliberates at length over whether to vacation in Colorado (C) or Hawaii (H), weighing the costs and benefits, consulting travel brochures, etc. Underlying phenomenological deliberation is an indeterministic neural process in which nonactual motor neural states n(C) and n(H) corresponding to alternatives C and H remain physically possible up until the moment of decision. The neurophysiological probabilities pr(n(C)) and pr(n(H)) evolve continuously (...) according to the different weights Jane's judgement attaches to C and H at different times during the deliberation. The overall process is indeterministic, since Jane's exact judgemental weighting would vary slightly were the process to be repeated from the same initial conditions. The weighting is however rational, and entirely under Jane's control. This controlled, rational, indeterministic process shows that libertarianism is a consistent philosophical thesis. (shrink)

The aim of the paper is to prove the consistency of libertarianism. We examine the example of Jane, who deliberates at length over whether to vacation in Colorado (C) or Hawaii (H), weighing the costs and benefits, consulting travel brochures, etc. Underlying phenomenological deliberation is an indeterministic neural process in which nonactual motor neural states n(C) and n(H) corresponding to alternatives C and H remain physically possible up until the moment of decision. The neurophysiological probabilities pr(n(C)) and pr(n(H)) evolve continuously (...) according to the different weights Jane's judgement attaches to C and H at different times during the deliberation. The overall process is indeterministic, since Jane's exact judgemental weighting would vary slightly were the process to be repeated from the same initial conditions. The weighting is however rational, and entirely under Jane's control. This controlled, rational, indeterministic process shows that libertarianism is a consistent philosophical thesis. (shrink)

Indeterminism, understood as a notion that an event may be continued in a few alternative ways, invokes the question what a region of chanciness looks like. We concern ourselves with its topological and spatiotemporal aspects, abstracting from the nature or mechanism of chancy processes. We first argue that the question arises in Montague-Lewis-Earman conceptualization of indeterminism as well as in the branching tradition of Prior, Thomason and Belnap. As the resources of the former school are not rich enough to study (...) topological issues, we investigate the question in the framework of branching space-times of Belnap (Synthese 92:385–434, 1992). We introduce a topology on a branching model as well as a topology on a history in a branching model. We define light-cones and assume four conditions that guarantee the light-cones so defined behave like light-cones of physical space-times. From among various topological separation properties that are relevant to our question, we investigate the Hausdorff property. We prove that each history in a branching model satisfies the Hausdorff property. As for the satisfaction of the Hausdorff property in the entire branching model, we prove that it is related to the phenomenon of passive indeterminism, which we describe in detail. (shrink)

An informal sketch is offered of some chief ideas of the (formal) ``branching histories'' theory of objective possibility, free will and indeterminism. Reference is made to ``branching time'' and to ``branching space-times,'' with emphasis on a theme that they share: Objective possibilities are in Our World, organized by the relation of causal order.

Quantum mechanics studies physical phenomena on a microscopic scale. These phenomena are far beyond the reach of our observation, and the connection between QM's mathematical formalism and the experimental results is very indirect. Furthermore, quantum indeterminism defies common sense. Microphysical experiments have shown that, according to the empirical context, electrons and quanta of light behave as waves and other times as particles, even though it is impossible to design an experiment that manifests both behaviors at the same time. Unlike (...) Newtonian physics, the properties of quantum systems are not all well-defined simultaneously. Moreover, quantum systems are not characterized by their properties, but by a wave function. Although one of the principles of the theory is the uncertainty principle, the trajectory of the wave function is controlled by the deterministic Schrödinger equations. But what is the wave function? Like other theories of the physical sciences, quantum theory assigns states to systems. The wave function is a particular mathematical representation of the quantum state of a physical system, which contains information about the possible states of the system and the respective probabilities of each state. (shrink)

Quantum mechanics, and the micro level indeterminacy it implies, is generally accepted by philosophers. So too naturalism on which macro states are held to supervene on micro states is now orthodox in the philosophy of mind and science. Still, in both fields it is frequently assumed that macro systems evolve deterministically. This assumption is commonly implicit and undefended, though at times it is made explicit and given minimal defense. In neither case is the incompatability of quantum indeterminacy, macro-micro dependence, and (...) macro level determinism fully acknowledged. Even when incompatability is recognized, it is held that there is hope that quantum indeterminacy might be confined to micro levels. We argue that this is a vain hope. For certain standard quantum mechanical systems, micro indeterminism entails macro indeterminism unless macro states are effectively independent from micro states. This result obtains whether the relationship between supervenient and subvenient states is deterministic or indeterministic. (shrink)

The relationship between formal logic and general philosophy is discussed under headings such as A Re-examination of Our Tense-Logical Postulates, Modal Logic in the Style of Frege, and Intentional Logic and Indeterminism.

A theory of temporal passage is put forward which is "objective" in the sense that time flow characterizes the universe independently of the existence of conscious beings. The theory differs from Grunbaum's "mind-dependence" theory, and is designed to avoid Grunbaum's criticisms of an earlier theory of Reichenbach's. The representation of temporal becoming is accomplished by the introduction of indeterministic universe-models; each model representing the universe at a time. The models depict the past as a single four-dimensional manifold, and (...) the future as a branched structure of such manifolds. Time flow is relativistic in that it manifests itself in a frame-dependent (but not observer-dependent) way. The indeterministic character of the universe-models is mirrored in a "temporal" theory of truth which rejects the principle of bivalence, and suitable semantics are provided for this theory. Finally, an account of physical law is given which defines it in terms of physical possibility, rather than vice versa. (shrink)

According to Roman Ingarden, transcendental idealism prevented Kant from "even undertaking an attempt" at elucidating freedom "in terms of the causal structure of the world." I show that this claim requires qualification. In a remarkable series of Critical-period Reflexionen (5611-4, 5616-9), Kant sketches a defense of the possibility of freedom that differs radically from his published ones by incorporating an indeterministic account of the phenomena. Anticipating Łukasiewicz, he argues that universal causal determination is consistent with an open future: if an (...) action is contingent, there is an infinite regress of determining causes, yet there is a prior time at which this infinite series of causes has not yet commenced. However, he concedes that on this account the unity of experience "cannot fully obtain in the case of free beings." The fact that Kant even contemplated the indeterministic theory may carry implications for interpreting the argument of the Second Analogy. (shrink)

In this text the ancient philosophical question of determinism (“Does every event have a cause ?”) will be re-examined. In the philosophy of science and physics communities the orthodox position states that the physical world is indeterministic: quantum events would have no causes but happen by irreducible chance. Arguably the clearest theorem that leads to this conclusion is Bell’s theorem. The commonly accepted ‘solution’ to the theorem is ‘indeterminism’, in agreement with the Copenhagen interpretation. Here it is recalled that indeterminism (...) is not really a physical but rather a philosophical hypothesis, and that it has counterintuitive and far-reaching implications. At the same time another solution to Bell’s theorem exists, often termed ‘superdeterminism’ or ‘total determinism’. Superdeterminism appears to be a philosophical position that is centuries and probably millennia old: it is for instance Spinoza’s determinism. If Bell’s theorem has both indeterministic and deterministic solutions, choosing between determinism and indeterminism is a philosophical question, not a matter of physical experimentation, as is widely believed. If it is impossible to use physics for deciding between both positions, it is legitimate to ask which philosophical theories are of help. Here it is argued that probability theory – more precisely the interpretation of probability – is instrumental for advancing the debate. It appears that the hypothesis of determinism allows to answer a series of precise questions from probability theory, while indeterminism remains silent for these questions. From this point of view determinism appears to be the more reasonable assumption, after all. (shrink)

While the question of free will does not figure as prominently in Buddhist writings as it does in western theology, philosophy, and psychology, it is a topic that was addressed in the earliest Buddhist writings. According to these accounts, for pragmatic and ethical reasons, the Buddha rejected both determinism and indeterminism as understood at that time. Rather than asking the metaphysical question of whether already humans have free will, Buddhist tradition takes a more pragmatic approach, exploring ways in which (...) we can acquire greater freedom to make wise choices that are truly conducive to our own and others' genuine well-being. One key to achieving such freedom is the cultivation of attentional skills so that one can deliberately focus one's attention with continuity and clarity on one's chosen object. A second theme is the cultivation of insight into the manner in which our own attitudes shape experience, allowing for the possibility of altering not only the way we experience events in the present, but also how we are influenced by our memories of the past. Finally, the Great Perfection school of Tibetan Buddhism emphasizes the realization of the deepest dimension of consciousness -- pristine awareness -- which transcends the nexus of causality. This is regarded as the ultimate source of freedom and the ultimate nature of human identity. (shrink)

In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are (...) two sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe. (shrink)

In philosophical logic and metaphysics there is a long-standing debate around the most appropriate structures to represent indeterministic scenarios concerning the future. We reconstruct here such a debate in a computational setting, focusing on the fundamental difference between moment-based and history-based structures. Our presentation is centered around two versions of an indeterministic scenario in which a programmer wants a machine to perform a given task at some point after a specified time. One of the two versions includes an assumption (...) about the future behaviour of the machine that cannot be encoded in any programming instruction; such version has models over history-based structures but no model over a moment-based structure. Therefore, our work adds a new stance to the debate: moment-based structures can be said to rule out certain indeterministic scenarios that are computationally unfeasible. (shrink)

Against what is commonly accepted in many contexts, it has been recently suggested that both deterministic and indeterministic quantum theories are not time‐reversal invariant, and thus time is handed in a quantum world. In this paper, I analyze these arguments and evaluate possible reactions to them. In the context of deterministic theories, first I show that this conclusion depends on the controversial assumption that the wave‐function is a physically real scalar field in configuration space. Then I argue that (...) answers which restore invariance by assuming the wave‐function is a ray in Hilbert space fall short. Instead, I propose that one should deny that the wave‐function represents physical systems, along the lines proposed by the so‐called primitive ontology approach. Moreover, in the context of indeterministic theories, I argue that time‐reversal invariance can be restored suitably redefining its meaning. (shrink)

We suggest a rigorous theory of how objective single-case transition probabilities fit into our world. The theory combines indeterminism and relativity in the “branching space–times” pattern, and relies on the existing theory of causae causantes (originating causes). Its fundamental suggestion is that (at least in simple cases) the probabilities of all transitions can be computed from the basic probabilities attributed individually to their originating causes. The theory explains when and how one can reasonably infer from the probabilities of one “chance (...) set-up” to the probabilities of another such set-up that is located far away. (shrink)

We discuss two supertasks invented recently by Laraudogoitia [1996, 1997], Both involve an infinite number of particle collisions within a finite amount of time and both compromise determinism. We point out that the sources of the indeterminism are rather different in the two cases - one involves unbounded particle velocities, the other involves particles with no lower bound to their sizes - and consequently that the implications for determinism are rather different - one form of indeterminism affects Newtonian but (...) not relativistic physics, while the other form is insensitive to the classical vs relativistic distinction. We also note some interesting linkages among supertasks, indeterminism and foundations problems in the general theory of relativity. (shrink)

This paper presents two general results of decidability concerning logics based on an indeterministic metric tense logic, which can be applied to, among others, logics combining knowledge, time and agency. We provide a general Kripke semantics based on a variation of the notion of synchronized Ockhamist frames. Our proof of the decidability is by way of the finite frame property, applying subframe transformations and a variant of the filtration technique.

I shall argue that there is no such property of an event as its “probability.” This is why standard interpretations cannot give a sound definition in empirical terms of what “probability” is, and this is why empirical sciences like physics can manage without such a definition. “Probability” is a collective term, the meaning of which varies from context to context: it means different — dimensionless [0, 1]-valued — physical quantities characterising the different particular situations. In other words, probability is a (...) reducible concept, supervening on physical quantities characterising the state of affairs corresponding to the event in question. On the other hand, however, these “probability-like” physical quantities correspond to objective features of the physical world, and are objectively related to measurable quantities like relative frequencies of physical events based on finite samples — no matter whether the world is objectively deterministic or indeterministic. (shrink)

The paper re-evaluates Prior's tenets about indeterminism and relativity from the point of view of the current state of the debate. We first discuss Prior's claims about indeterministic tense logic and about relativity separately and confront them with new technical developments. Then we combine the two topics in a discussion of indeterministic approaches to space-time logics. Finally we show why Prior would not have to "dig his heels in" when it comes to relativity: We point out a way of (...) combining the existential import of the distinction between past, present, and future with a frame-relative notion of the present. (shrink)

Bergson's views on time are supported by the time operator qualifying complex systems with a concept of time that is essentially difierent from the clock time used to register the events. Irreversibility, unpredictability, and innovation characterize complex systems in contrast with the reversibility, predictability and lack of novelties of the regular motions of integrable systems. The idea for this work came from our teacher Ilya Prigogine who pointed out repeatedly that the time operator actually incorporates (...) Bergson's views on time. We construct a time operator which incorporates Bergson's intuitive views on durations, indeterminism, innovations and irreversibility and the significance of events in terms of inno- vation and aging. In addition, Bergson emphasized that the signif- icance of durations depends on consciousness and memory, a discussion beyond the proposed time operator. Moreover we discuss the relation of Bergson's time with the internal time concepts of Husserl and Heidegger. (shrink)

The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR experiment. That assumption is one of the premises of Bell’s theorem. I first argue that only a premise to the effect that what determines the choice of the measurement settings is independent of what determines the past state of the measured system is needed for (...) the derivation of Bell’s theorem. Determinism as such does not undermine that independence . Only entanglement could do so. However, generic entanglement without collapse on the level of the universal wave-function can go together with effective wave-functions for subsystems of the universe, as in Bohmian mechanics. The paper argues that such effective wave-functions are sufficient for the mentioned independence premise to hold. (shrink)

In this paper we describe a novel approach to defining an ontologically fundamental notion of co-presentness that does not go against the tenets of relativity theory. We survey the possible reactions to the problem of the present in relativity theory, introducing a terminological distinction between a static role of the present, which is served by the relation of simultaneity, and a dynamic role of the present, with the corresponding relation of co-presentness. We argue that both of these relations need to (...) be equivalence relations, but they need not coincide. Simultaneity, the sharing of a temporal coordinate, need not have fundamental ontological import, so that a relativizing strategy with respect to simultaneity seems promising. The notion of co-presentness, on the other hand, does have ontological import, and can therefore not be relativized to an observer or to an arbitrarily chosen frame. We argue that a formal representation of indeterminism can provide the structure needed to anchor the relation of co-presentness, and that this addition is in fact congenial to the notion of dynamic time as requiring real change. The resulting picture is one of an extended dynamic present, implying a formal distinction between static simultaneity and dynamic co-presentness. After working out the basics of our approach in the simpler framework of branching time, we provide our full analysis in the framework of branching space-times, which allows for a formal definition of modal correlations. The spatial extension of the dynamic present can reach as far as the modal correlations do. In the limit, the dynamic present could extend across a maximal space-like hypersurface. (shrink)

Alfred Mele and David Robb (1998, 2003) offer what they claim is a counter-example to the principle of alternative possibilities (PAP), the principle that a person is morally responsible for what he has done only if he could have done otherwise. In their example, a person makes a decision by his own indeterministic causal process though antecedent circumstances ensure he could not have done otherwise. Specifically, a simultaneously occurring process in him would deterministically cause the decision at the precise (...) class='Hi'>time it actually occurs if he were not to make it 'on his own' i.e. without being deterministically caused.Their case is designed to avoid a well-known dilemma that has plagued earlier apparent counterexamples of this sort. We argue, however, that Mele andRobb's example does not have all the features necessary in order for it to undermine PAP. It still fails to avoid the original dilemma. (shrink)

Earman and Norton argue that manifold realism leads to inequivalence of Leibniz-shifted space-time models, with undesirable consequences such as indeterminism. I respond that intrinsic axiomatization of space-time geometry shows the variant models to be isomorphic with respect to the physically meaningful geometric predicates, and therefore certainly physically equivalent because no theory can characterize its models more closely than this. The contrary philosophical arguments involve confusions about identity and representation of space-time points, fostered by extrinsic coordinate formulations and (...) irrelevant modal metaphysics. I conclude that neither the revived Einstein hole argument nor the original Leibniz indiscernibility argument have any force against manifold realism. (shrink)

Branching space-time is a simple blend of relativity and indeterminism. Postulates and definitions rigorously describe the causal order relation between possible point events. The key postulate is a version of everything has a causal origin; key defined terms include history and choice point. Some elementary but helpful facts are proved. Application is made to the status of causal contemporaries of indeterministic events, to how splitting of histories happens, to indeterminism without choice, and to Einstein-Podolsky-Rosen distant correlations.

In this paper we describe some first steps for bringing the framework of branching space-times (BST) to bear on quantum information theory. Our main application is quantum error correction. It is shown that BST offers a new perspective on quantum error correction: as a supplement to the orthodox slogan, “fight entanglement with entanglement”, we offer the new slogan, “fight indeterminism with indeterminism”.

It is common knowledge that the Aristotelian idea of an unmoved mover was abandoned definitively with the advent of modern science and, in particular, Newton’s precise formulation of mechanics. Here I show that the essential attribute of an unmoved mover is not incompatible with such mechanics; quite the contrary, it makes this possible. The unmoved mover model proposed does not involve supertasks, and leads both to an outrageous form of indeterminism and a new, accountable form of interaction. The process presents (...) a more precise characterization of the crucial going-to-the-limit operation. It has long been acknowledged in the existing literature that, theoretically, in infinite Newtonian systems, masses can move from rest to motion through supertasks. Numerous minor variations on the original schemes have already been published. Against this backdrop, this paper introduces three significant additions: 1) It formulates for the first time a limit postulate for systematically addressing infinite systems; 2) It shows that an Aristotelian unmoved mover is possible in systems of infinitely many particles that interact with each other solely by contact collision; 3) It shows how interaction at a distance can emerge in systems of infinitely many particles that interact with each other solely by contact. (shrink)

This paper gives an overview of logico-philosophical issues of time and determinism. After a brief review of historical roots and 20th century developments, three current research areas are discussed: the definition of determinism, space-time indeterminism, and the temporality of individual things and their possibilities.

In this paper, I present a new argument against the compatibility of human free will and divine timelessness when conceiving of eternity in terms of an additional dimension as presented by brian leftow. The paper is organized as follows: After giving a brief sketch of leftow’s model, I argue that assuming libertarianism, free will presupposes presentism, since metaphysical indeterminism is only compatible with a presentist A-theory of physical time. Given this result, I make a case for the incompatibility of (...) presentism and divine eternity modelled as a frame of reference, implying the incompatibility of the latter with human free will. (shrink)