Margarita Vázquez

This book seeks to arrive at a better understanding of the relationships between the objective and subjective aspects of time. It discusses the existence of fluent time, a controversial concept in many areas, from philosophy to physics. Fluent time is understood as directional time with a past, a present and a future. We experience fluent time in our lives and we adopt a temporal perspective in our ways of knowing and acting. Nevertheless, the existence of fluent time has been debated for both philosophical and scientific reasons, thus creating a rift between the subjective and objective aspects of time. Starting from the basic notion of points of view, or perspectives, this book explores the relationships between objective or external time, as it has been conceptualized by science, and subjective or internal time, which is involved in our lived experiences. It establishes a general framework encompassing the nature, structure and mode of existence of points of view, in which the objective and subjective aspects of time can be integrated. The book mainly addresses researchers and postgraduates in philosophy and logic. Additionally, it offers inspiration for physicists and computer scientists involved in the modeling and simulation of complex behaviors for which the representation of internal time should be considered together with the notion of objective, external time.

There are very few analyses of the structure of points of view. However, we can identify two general approaches. One of them assumes as a paradigm the structure of propositional attitudes. Here, points of view are understood as having an internal structure similar to the one we can find in propositional attitudes. The other approach is based on the notions of location and access. Here, the internal structure of points of view is not directly addressed. The features that are emphasised are related with the role that points of view are intended to have. Points of view would be ways of having access to the world, and to ourselves, from certain emplacements. The paper has three parts. In the first one, we present these two approaches and some interesting developments inside each one of them. In the second one, we examine more closely the relationships between the two approaches. In the third part of the paper, we defend the non-reducible relational nature and modal character of points of view obtaining some conclusions.

Time has a highly unstable place between the objective and the subjective. On the one side, there are very well known philosophical arguments trying to show that time has only a subjective reality, even that it is merely a subjective epiphenomenon. On the other side, we are compelled to take points of view as non dispensable elements of reality, at least of a reality capable of containing beings like us. And points of view offer a world of temporal entities existing in an objective way. Moreover, points of view themselves appear to be temporal entities among other temporal entities. We analyse both aspects of time. Our main focus will be McTaggart’s arguments against the reality of a fluent time, what he called temporal series of kind A. We will distinguish three very different arguments in McTaggart works. We analyse them in detail. And we reject their conclusive character. Our final target is to maintain that there is a room for fluent time in what is internal to points of view but external to the subjects adopting those points of view.

We propose an analysis of the notion of model as crucially related to the notion of point of view. A model in this sense would always suggest a certain way of looking at a real system, a certain way of thinking about it and a certain way of acting upon it. We focus on System Dynamics as a paradigmatic case with respect to many of the features and problems we can find in the field of modelling and simulation. We analyse in detail some of those features. All of them would be present in many other cases of construction and use of models. Furthermore, they would support the thesis that a model can be fruitfully understood as offering a point of view capable of improving our own points of view over a certain system. The point of view offered by the model could include both non-conceptual and conceptual contents, it would have a complex structure and behaviour, and it would have direct consequences on the decisions made by the subjects adopting that point of view

There are very few analyses of the structure of points of view. However, we can identify two general approaches. One of them assumes as a paradigm the structure of propositional attitudes. Here, points of view are understood as having an internal structure similar to the one we can find in propositional attitudes. The other approach is based on the notions of location and access. Here, the internal structure of points of view is not directly addressed. The features that are emphasised are related with the role that points of view are intended to have. Points of view would be ways of having access to the world, and to ourselves, from certain emplacements. The paper has three parts. In the first one, we present these two approaches and some interesting developments inside each one of them. In the second one, we examine more closely the relationships between the two approaches. In the third part of the paper, we defend the non-reducible relational nature and modal character of points of view obtaining some conclusions.

Nuestro principal objetivo en este trabajo es el de analizar si es posible construir sistemas lógicos temporales-epistémicos lo suficientemente satisfactorios. Sin embargo, las principales dificultades para lograr este propósito provienen del hecho de tener que combinar una perspectiva temporal absoluta con una perspectiva epistémica relativa a cada agente; es decir, por un lado, los instantes de tiempo vienen determinados desde el punto de vista de un observador situado fuera del mundo, y, por otro lado, las alternativas epistémicas de cada agente son relativas a dicho agente. Pensamos que algunas de estas dificultades podrían ser superadas con la ayuda de las lógicas híbridas, puesto que este tipo de lógicas simplifica la combinación de sistemas temporales y epistémicos, y así podemos evitar tener que construir modelos excesivamente complicados. Our main goal in this paper is to analyse if it is possible to build some suitable Temporal-Epistemic Systems. However, the main difficulties in order to aim this goal come from the fact of having to combine an absolute temporal perspective with a relative epistemic perspective; that is, on one hand, temporal points are determined from the point of view of an observer placed outside the world, and, on the other hand, the epistemic alternatives of each agent are relative to that agent. We think that some of these difficulties could be solved with the help of hybrid logics, because this kind of logics simplifies the combination of temporal and epistemic systems, and so we can avoid building highly complicated models

In this paper, I analyze the "surprise exam paradox". I think that the paradox can be avoided and I am going to focus on three points: 1) A conflict arises between reasoning and the confidence in the person that makes the original statement. If we examine the situation by reasoning we conclude that the statement is not going to come true, because we trust the person that states it. However, if it is not possible to happen, it happens, and the person told the truth; 2) There is a disjunction among the days of the week: “or it is the first day or it is the second day or … it is the last day” (or Monday or Tuesday or Wednesday or Thursday or Friday). If I still have not been given the exam by Friday, the only possible conclusion is that the exam will be given on Friday. On Thursday, however, thesituation is completely different; 3) It seems that this paradox is a case of contingent futures, which branching time logics usually solve. The truth-value of the sentences is only relative to the branch that takes place in the end.

Prior's approach to time has been neglected by semanticists for several reasons. The main one, we believe, is the inability of Priorean tense logic to refer to times. The second one, is the inability to account for some important features of natural language such as temporal anaphora and the role of temporal constructions in discourse. Priorean tense logic has, however, one important advantage over other accounts: the internal perspective of time (due to its modal nature). This paper examines extensions of Priorean tense logic in which reference to times is possible, focusing on the so-called hybrid temporal logic. We will outline some of its main features and analyze some of its philosophical implications.

Prior's approach to time has been neglected by semanticists for several reasons. The main one, we believe, is the inability of Priorean tense logic to refer to times. The second one, is the inability to account for some important features of natural language such as temporal anaphora and the role of temporal constructions in discourse. Priorean tense logic has, however, one important advantage over other accounts: the internal perspective of time (due to its modal nature). This paper examines extensions of Priorean tense logic in which reference to times is possible, focusing on the so-called hybrid temporal logic. We will outline some of its main features and analyze some of its philosophical implications. © 2013 Elsevier B.V., All rights reserved.

This paper analyzes the temporal structures that are appropriate to study the notion of point of view. For understanding time, the image of a cable is used, instead of the classical one of a tree. It is examined how to understand time in this way and how to formalize it. A logical approach to the notion of point of view is also shown. When we analyze the points of view and their structure, it seems clear that we must take into account the time t in which a point of view is attributed to a subject. A two-dimensional temporal logic which combines a modal dimension for possibilities and a temporal one for the flow of time, offers a clear view of the temporary location of a point of view. In this logic, we have histories, thanks to the temporal dimension, and evaluation is in two indices, time and history. These stories can be seen as different scenarios, providing a clear advantage when applying to the analysis of the notion of point of view. The conclusion is that, in order to give a proper approach for the notion of point of view, all these aspects should be combined.

In this paper I analyze the temporal structures that are appropriate to study the notion of point of view. When we analyze the points of view and their structure, it seems clear that we must take into account the time t in which a point of view is attributed to a subject. A two-dimensional temporal logic which combines a modal dimension for possibilities and a temporal one for the flow of time, offers a clear view of the temporary location of a point of view. In this logic, we have histories, thanks to the temporal dimension, and evaluation is in two indices, time and history. These stories can be seen as different scenarios, providing a clear advantage when applying to the analysis of the notion of point of view. The conclusion is that, in order to give a proper approach for the notion of point of view, all these aspects should be combined.