Essays on Aristotle's Sea-Battle, Lazy Argument, Argument Reaper, Diodorus' Master Argument -/- The book is devoted to the ancient logical theories, reconstruction of their semantic proprieties and possibilities of their interpretation by modern logical tools. The Ancient arguments are frequently misunderstood in modern interpretations since authors usually have tendency to ignore their historical proprieties and theoretical background what usually leads to a quite inappropriate picture of the argument’s original form and mission. Author’s primary intention was to draw attention to the (...) complexity of some historical arguments and to the theoretical context in which arguments were created, circulated, developed, and finally tuned. Four well-known ancient arguments – with a common central subject related to the future contingencies problem – are reconstructed from available historical sources: “The Sea Battle”, which is drawn from Aristotle’s treatise De Interpretatione; two arguments, usually ascribed to the Stoics, “The Lazy Argument” and “The Reaper”; “The Master Argument” of the Megarian philosopher Diodorus. Arguments are linguistically and semantically detaily analyzed, formally presented by reflecting some relevant corresponding hypotheses based on physical or logical theories of their ancient authors, and finally covered by appropriate logical tools familiar to a modern reader. Two appendices are added at the closing part of the book. One covering some assumptions relevant for understanding of rival streams in ancient theories of meaning related to the nature of names and naming; the other is devoted to the ancient understanding of logical proposition and attempts to find an adequate Latin translation of the Greek delicate philosophical term “ἀξίωμα”. (shrink)

Many authors have noted that there are types of English modal sentences cannot be formalized in the language of basic first-order modal logic. Some widely discussed examples include “There could have been things other than there actually are” and “Everyone who is actually rich could have been poor.” In response to this lack of expressive power, many authors have discussed extensions of first-order modal logic with two-dimensional operators. But claims about the relative expressive power of these extensions are often justified (...) only by example rather than by rigorous proof. In this paper, we provide proofs of many of these claims and present a more complete picture of the expressive landscape for such languages. (shrink)

A “conceptual spaces” approach is used to formalize Aristotle’s main intuitions about time and change, and other ideas about temporal points of view. That approach has been used in earlier studies about points of view. Properties of entities are represented by locations in multidimensional conceptual spaces; and concepts of entities are identified with subsets or regions of conceptual spaces. The dimensions of the spaces, called “determinables”, are qualities in a very general sense. A temporal element is introduced by adding a (...) time variable to state functions that map entities into conceptual spaces. That way, states may have some permanency or stability around time instances. Following Aristotle’s intuitions, changes and events will not be necessarily instant phenomena, instead they could be processual and interval dependent. Change is defined relatively to the interval during which the change is taking place. Time intervals themselves are taken to represent points of view. To have a point of view is to look at the world as it is in the selected interval. Many important concepts are relativized to intervals, for instance change, events, identity, ontology, potentiality, etc. The definition of points of view as intervals allows to compare points of view in relation to all these concepts. The conceptual space approach has an immediate semantic and structural character, but it is tempting to develop also logics to describe them. A formal language is introduced to show how this could be done. (shrink)

This article deals with the semantics of “double-access” sentences. They are defined as English sentences which have a past tense morpheme in the matrix clause and a present tense morpheme in a subordinate clause in the immediate scope of the matrix past tense. They receive a very peculiar interpretation, which we will refer to as a “double-access interpretation.” The episode described in the embedded clause makes reference to two times: the time referred to by the matrix predicate and the utterance (...) time of the whole sentence. Previous studies on this construction are largely descriptive and do not attempt to analyze it formally, with one important exception. Abusch (1991) addresses the problems connected with the construction and proposes that double-access interpretations involvede re attitudes about intervals. Her proposal contains an important insight and provides one possible account of the double-access construction. My proposal was independently developed at approximately the same time as Abusch's and offers an alternative explanation for the phenomena. I consider a series of hypotheses and conclude that double-access readings involvede re attitude reports about state individuals. This account is couched in an eventuality-based framework and employs the techniques proposed by Cresswell and von Stechow (1982). In order to yield the desired reading, the tense must first adjoin to the complement S, then to the matrix S, leaving two traces in the process. (shrink)

This book is a synthesis of more than three decades of research into the concept of time and its semiotic nature. If traditional philosophy – and philosophy of time should be no exception – in the shadow of advancing biology can be said to have reached an impasse, one important reason for this, in harmony with Wittgenstein’s vision, appears to have been its lack of appropriate tools for explicating language. The present theory of time proceeds, accordingly, from the exploration of (...) temporal expressions in language as an evolutionary fact. It derives in a hypothetical, coherent feedback process of hierarchically ordered distinctions the semantics of time from its biologically dictated perceptual and cognitive-pragmatic origins. The corresponding abductive-regulative model is anchored in the assumption of biological rhythmization as the very foundation of perception and mental/physical action. Understood to originate in space and spatial perspective, time reveals itself as an instrument for temporal perspective on motion (events and situations) in a process of analysis, i.e., discontinuation of chaos made divisible and continuous by the rhythmical screen. Whereas traditional philosophy of time paid attention almost exclusively to the temporal category of tense, the biopragmatic model sees strong evidence in the perspectival nature of time for ascribing the decisive, and probably universal, role in temporal analysis to the linguistic category of aspect. Aspect may, according to the present findings, be assumed to partake already of change-of-state and cause-effect analysis without which man’s adaptation to new situations – and precondition for survival – would be inconceivable. The proposed model of space/time cognition, inspired by Hegelian dialectics, Heidegger-Gadamer’s hermeneutic circle and Peircean logic, makes Kantian a priori superfluous and liberates time from its enigmatic appearance. For the first time in temporal studies it thus appears possible to derive hypothetically linguistic expressions of time all the way from pretemporal, homogeneous continuity effected by biological rhythmization, via pretemporal metonymic (Gestalt), chunk-wise partitioning – as a general precondition for the perception and, based on primary metaphorization, the cognition of things, space and motion – to temporal analysis/discontinuation proper, primarily by aspectual perspective, and the subsequent synthesized, heterogeneous continuity of temporally ordered events. The conception of time, so disastrous for modern temporal logic, i.e., as moving object assigned extension, divisible continuity (‛linearity’) and direction, can be shown to have emerged as a result of secondary metaphorization. (shrink)