The theory of branching space-times, put forward by Belnap, considers indeterminism as local in space and time. In the axiomatic foundations of that theory, so-called choice points mark the points at which the possible future can turn out in different ways. Working under the assumption of choice points is suitable for many applications, but has an unwelcome topological consequence that makes it difficult to employ branching space-times to represent a range of possible physical space-times. Therefore it is interesting to develop (...) a branching space-times theory without choice points. This is what we set out to do in this paper, providing new foundations for branching space-times in terms of choice sets rather than choice points. After motivating and developing the resulting theory in formal detail, we show that it is possible to translate structures of one style into structures of the other style and vice versa. This result shows that the underlying idea of indeterminism as the branching of spatio-temporal histories is robust with respect to different implementations, making a choice between them a matter of expediency rather than of principle. (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)

"This book develops a rigorous theory of indeterminism as a local and modal concept. Its crucial insight is that our world contains events or processes with alternative, really possible outcomes. The theory aims at clarifying what this assumption involves, and it does it in two ways. First, it provides a mathematically rigorous framework for local and modal indeterminism. Second, we support that theory by spelling out the philosophically relevant consequences of this formulation and by showing its fruitful applications in metaphysics. (...) To this end, we offer a formal analysis of modal correlations and of causation, which is applicable in indeterministic and non-local contexts as well. We also propose a rigorous theory of objective single-case probabilities, intended to represent degrees of possibility. In a third step, we link our theory to current physics, investigating how local and modal indeterminism relates to issues in the foundations of physics, in particular, quantum non-locality and spatio-temporal relativity. The book also ventures into the philosophy of time, showing how the theory's resources can be used to explicate the dynamic concept of the past, present, and future based on local indeterminism"--. (shrink)

The objectives of this paper are twofold. The first is to present a differentiation between two kinds of deferred uses of indexicals: those in which indexical utterances express singular propositions (I term them deferred reference proper) and those where they express general propositions (called descriptive uses of indexicals). The second objective is the analysis of the descriptive uses of indexicals. In contrast to Nunberg, who treats descriptive uses as a special case of deferred reference in which a property contributes to (...) the proposition expressed, I argue that examples in which a general proposition is indeed expressed by an indexical cannot be treated by assuming that the property is a deferred referent of the pronoun. I propose an analysis of descriptive uses of indexicals by means of a pragmatic mechanism of ‘descriptive anaphora’, which attempts to explain the special kind of contribution of the property retrieved from the context to the proposition that is characteristic of the descriptive interpretation. (shrink)

Paul Horwich is aware of the fact that his theory as stated in his works is directly applicable only to a language in which a word, understood as a syntactic type, is connected with exactly one literal meaning. Yet he claims that the theory is expandable to include homonymy and indexicality and thus may be considered as applicable to natural language. My concern in this paper is with yet another kind of ambiguity—systematic polysemy—that assigns multiple meanings to one linguistic type. (...) I want to combine the characteristics of systematic polysemy with the Kaplanian insight that meanings of expressions may be defined by semantic rules which assign content in context and to ask the question if minimalism about truth and meaning is compatible with such rule-based systematic polysemy. I will first explain why the expressions that exhibit rule-based systematic polysemy are difficult to combine with a truth theory that is based on a use theory of meaning before proceeding to argue that indexicals and proper names are such expressions. (shrink)

The thesis advanced in this paper is that the proper names of cities or countries inherit the linguistic types of the nouns which denote the basic category of the objects the names refer to. As a result, in the case of the proper names of cities or countries, a reference by those names may select particular aspects of those objects, in the same way that book or newspaper selects the physical or informational aspects of objects in the extension of the (...) nouns. This view is based on Asher’s and Pustejovsky’s conception of dot type semantics. (shrink)

We introduce the notion of a Minkowskian Branching Structure ("MBS" for short). Then we prove some results concerning the phenomenon of funny business in its finitary and infinitary variants.

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. (shrink)

In this paper I argue for a non-referential interpretation of some uses of indexicals embedded under epistemic modals. The so-called descriptive uses of indexicals come in several types and it is argued that those embedded within the scope of modal operators do not require non-referential interpretation, provided the modality is interpreted as epistemic. I endeavor to show that even if we allow an epistemic interpretation of modalities, the resulting interpretation will still be inadequate as long as we retain a referential (...) interpretation of indexicals. I then propose an analysis of descriptive indexicals that combines an epistemic interpretation of modality with a non-referential interpretation of indexicals. (shrink)

The article investigates the relations between Hausdorff and non-Hausdorff manifolds as objects of general relativity. We show that every non-Hausdorff manifold can be seen as a result of gluing together some Hausdorff manifolds. In the light of this result, we investigate a modal interpretation of a non-Hausdorff differential manifold, according to which it represents a bundle of alternative space-times, all of which are compatible with a given initial data set.

This paper offers an analysis of indexical expressions and proper names as they are used in proverbs. Both indexicals and proper names contribute properties rather than objects to the propositions expressed when they are used in sentences interpreted as proverbs. According to the proposal, their contribution is accounted for by the mechanism of descriptive anaphora. Indexicals with rich linguistic meaning, such as ‘I’, ‘you’ or ‘today’, turn out to be cases of the attributive uses of indexicals, i.e. uses whose contribution (...) relies on the linguistic meaning of the word. Third person pronouns, names of locations as well as surnames are analyzed as non-attributive descriptive uses. (shrink)

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. (shrink)

The paper extends the framework of outcomes in branching space-time (Kowalski and Placek [1999]) by assigning probabilities to outcomes of events, where these probabilities are interpreted either epistemically or as weighted possibilities. In resulting models I define the notion of common cause of correlated outcomes of a single event, and investigate which setups allow for the introduction of common causes. It turns out that a deterministic common cause can always be introduced, but (surprisingly) only special setups permit the introduction (...) of truly stochastic common causes. I analyse next the Bell-Aspect experiment and derive the Bell-CH inequalities. I observe that we postulate there not a common cause for outcomes of a single event but rather a common common cause that accounts for outcomes of many events, where 'events' mean 'measurements with (different) directions of polarization'. Since the inequalities are violated, I claim that no causal story can be told about the Bell correlations, where causality is subliminal and restricted by screening-off condition. Similarly, given certain intuitive principles, no deterministic story can be told about these correlations. (shrink)

The paper investigates, in the framework of branching space–times, whether an infinite EPR-like correlation which does not involve finite EPR-like correlations is possible.

Since the validity of Bell's inequalities implies the existence of joint probabilities for non-commuting observables, there is no universal consensus as to what the violation of these inequalities signifies. While the majority view is that the violation teaches us an important lesson about the possibility of explanations, if not about metaphysical issues, there is also a minimalist position claiming that the violation is to be expected from simple facts about probability theory. This minimalist position is backed by theorems due to (...) A. Fine and I. Pitowsky.Our paper shows that the minimalist position cannot be sustained. To this end,we give a formally rigorous interpretation of joint probabilities in thecombined modal and spatiotemporal framework of `stochastic outcomes inbranching space-time' (SOBST) (Kowalski and Placek, 1999; Placek, 2000). We show in this framework that the claim that there can be no joint probabilities fornon-commuting observables is incorrect. The lesson from Fine's theorem is notthat Bell's inequalities will be violated anyhow, but that an adequate modelfor the Bell/Aspect experiment must not define global joint probabilities. Thus we investigate the class of stochastic hidden variable models, whichprima facie do not define such joint probabilities. The reasonwhy these models fail supports the majority view: Bell's inequalities are notjust a mathematical artifact. (shrink)

This collection celebrates the centenary of the Lvov-Warsaw school, established by Kazimierz Twardowski in Lvov in 1895.

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)

The paper puts forward a theory of historical modalities that is framed in terms of possible continuations rather than possible worlds or histories. The proposal is tested as a semantic theory for a language with historical modalities, tenses, and indexicals.

Proper names are usually considered devices of singular reference but, when considered as word-types, they also exhibit other kinds of uses. In this paper I intend to show that systematic kinds of uses of proper names considered as word-types can be accounted for by a generalized rule-based conception of systematic polysemy, one which not only postulates a multiplicity of stable senses for an expression, but also a multiplicity of content generating rules, each of which determines potentially different contents in different (...) contexts. In contrast to the currently extant polysemous conceptions of proper names (Leckie in Philos Stud 165:1139–1160, 2013), which only encompass individual and predicative uses, the presented proposal concerns all systematic uses of proper names considered in the literature, i.e., individual, predicative, deferred, descriptive, anaphoric, and bound uses of proper names. The resulting conception accommodates referential intuition about the default individual uses of proper names while also admitting other kinds of uses without generating homonymy. It transpires that proper names are semantically underdetermined and context-sensitive expressions. (shrink)

Since the validity of Bell's inequalities implies the existence of joint probabilities for non-commuting observables, there is no universal consensus as to what the violation of these inequalities signifies. While the majority view is that the violation teaches us an important lesson about the possibility of explanations, if not about metaphysical issues, there is also a minimalist position claiming that the violation is to be expected from simple facts about probability theory. This minimalist position is backed by theorems due to (...) A. Fine and I. Pitowsky.Our paper shows that the minimalist position cannot be sustained. To this end,we give a formally rigorous interpretation of joint probabilities in thecombined modal and spatiotemporal framework of `stochastic outcomes inbranching space-time' (SOBST) (Kowalski and Placek, 1999; Placek, 2000). We show in this framework that the claim that there can be no joint probabilities fornon-commuting observables is incorrect. The lesson from Fine's theorem is notthat Bell's inequalities will be violated anyhow, but that an adequate modelfor the Bell/aspect experiment must not define global joint probabilities. Thus we investigate the class of stochastic hidden variable models, whichprima facie do not define such joint probabilities. The reasonwhy these models fail supports the majority view: Bell's inequalities are notjust a mathematical artifact. (shrink)

Its interpretation, however, is as unsettled now as in the heroic days of Einstein and Bohr.This book focuses on quantum non-locality, the curious quantum ...

The paper develops a theory of branching spatiotemporal histories that accommodates indeterminism and the insights of general relativity. A model of this theory can be viewed as a collection of overlapping histories, where histories are defined as maximal consistent subsets of the model's base set. Subsequently, generalized manifolds are constructed on the theory's models, and the manifold topology is introduced. The set of histories in a model turns out to be identical with the set of maximal subsets of the model's (...) base set with respect to being Hausdorff and downward closed. Further postulates ensure that the topology is connected, locally Euclidean, and satisfies the countable sub-cover condition. (shrink)

Pregnancy involves puzzling aversions to nutritious foods. Although studies generally support the hypotheses that such aversions are evolved mechanisms to protect the fetus from toxins and/or pathogens, other factors, such as resource scarcity and psychological distress, have not been investigated as often. In addition, many studies have focused on populations with high-quality diets and low infectious disease burden, conditions that diverge from the putative evolutionary environment favoring fetal protection mechanisms. This study tests the fetal protection, resource scarcity, and psychological distress (...) hypotheses of food aversions in a resource-constrained population with high infectious disease burden. The role of culture is also explored. In the first of two studies in Tamil Nadu, India, we investigated cultural explanations of pregnancy diet among non-pregnant women (N = 54). In the second study, we conducted structured interviews with pregnant women (N = 94) to determine their cravings and aversions, resource scarcity, indices of pathogen exposure, immune activation, psychological distress, and emic causes of aversions. Study 1 found that fruits were the most commonly reported food that pregnant women should avoid because of their harmful effects on infants. Study 2 found modest support for the fetal protection hypothesis for food aversions. It also found that pregnant women most commonly avoided fruits as well as “black” and “hot” foods. Aversions were primarily acquired through learning and focused on protecting the infant from harm. Our findings provide modest support for the fetal protection hypothesis and surprisingly strong support for the influence of cultural norms and learning on dietary aversions in pregnancy. (shrink)

Descriptive uses of indexicals result in expressing a general proposition instead of a singular proposition, which is typical for indexicals. In contrast to Nunberg's and Recanati's proposals, who treat such uses of indexicals as referring, the conception developed in the paper is a quasi-anaphoric interpretation of descriptive uses of indexicals. In the quasi-anaphoric mechanism an indexical expression inherits its semantic properties from its antecedent, but - in contrast to classical anaphora - that antecedent comes from extra-linguistic context: it is a (...) salient property of the individual in question. Since indexicals are quasi-anaphoric with respect to properties instead of being anaphoric with respect to referring expressions, the propositions generated are general. Three types of descriptive uses of indexicals are distinguished. In the first type the quasi-anaphoric mechanism is triggered by the conflict at the semantic level between the singularity of an indexical and the generality of a quantifier. In the second type (luck of reference in the context) the proposition is generated at the level of primary pragmatic processes. In both cases the propositions in question are the propositions expressed. In the third type the quasi-anaphoric mechanism is triggered by the conflict between the proposition expressed and the purpose of expressing it. As a result the proposition generated quasi-anaphorically is the Gricean proposition implicated. (shrink)

Contains papers from a November 1995 conference held in Eastern Europe, celebrating the centenary of the Lvov-Warsaw school of analytic philosophy. Papers deal with all directions of research undertaken by Polish analytic philosophers. Special attention is paid to logic and comparisons with other philosophical movements, particularly with brentanism. Contains sections on history and comparisons, the ideas of Lesniewski, philosophy of language, logic and the foundations of mathematics, logic and philosophy, and the ontology, epistemology, and philosophy of science. No index. Annotation (...) copyrighted by Book News, Inc., Portland, OR. (shrink)

The paper describes two approaches to determinism: one focuses on the features of global objects, such as possible worlds or models of a theory, whereas the other’s concern is the possible behaviour of individual objects. It then gives an outline of an individuals-based analysis of the determinism of theories. Finally, a general relativistic spacetime with non-isometric extensions is described and used to illustrate a conflict between the two approaches: this spacetime is indeterministic by the first approach but deterministic by the (...) second approach. (shrink)

We investigate the concepts of past, present, and future that build upon a modal distinction between a settled past and an open future. The concepts are defined in terms of a pre-causal ordering that is determined by the qualitative differences between alternative possible histories. We look what an event’s past, present, and future look like in the so-called Minkowskian Branching Structures, one in which histories are isomorphic to Minkowski space-time.