Online research in philosophy

Book Information Travels in Four Dimensions: The Enigmas of Space and Time. Travels in Four Dimensions: The Enigmas of Space and Time Robin Le Poidevin , Oxford : Clarendon Press , 2003 , xvii + 275 , £14.99 ( cloth ); £8.99 ( paper ) By Robin Le Poidevin. Clarendon Press. Oxford. Pp. xvii + 275. £14.99 (cloth:); £8.99 (paper:).

D. Scott in his paper [5] on the mathematical models for the Church-Curry -calculus proved the following theorem.A topological space X. is an absolute extensor for the category of all topological spaces iff a contraction of X. is a topological space of Scott's open sets in a continuous lattice.

modality , understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language L by interpreting L in dynamic topological systems, i.e. ordered pairs X, f , where X is a topological space and f is a..

Time and being.--Summary of a seminar on the lecture "Time and being."--The end of philosophy and the task of thinking.--My way to phenomenology.

The possibility of time travel, as permitted in General Relativity, is responsible for constraining physical fields beyond what laws of nature would otherwise require. In the special case where time travel is limited to a single object returning to the past and interacting with itself, consistency constraints can be avoided if the dynamics is continuous and the object's state space satisfies a certain topological requirement: that all null-homotopic mappings from the state-space to itself have some fixed point. Where consistency constraints do exist, no new physics is needed to enforce them. One needs only to accept certain global topological constraints as laws, something that is reasonable in any case.

THE AUTHOR DISCUSSES SIMULTANEITY, ABSOLUTE SPACE AND TIME, THE NUMBER OF POSSIBLE DIMENSIONS, CAUSALITY, RIVAL SCIENTIFIC THEORIES OF THE SPATIO-TEMPORAL PROPERTIES OF THE UNIVERSE AND THE MEANING OF SPATIO-TEMPORAL TERMS IN ORDINARY AND SCIENTIFIC LANGUAGE. (BP, EDITED).

Space and time are the most fundamental features of our experience of the world, and yet they are also the most perplexing. Does time really flow, or is that simply an illusion? Did time have a beginning? What does it mean to say that time has a direction? Does space have boundaries, or is it infinite? Is change really possible? Could space and time exist in the absence of any objects or events? What, in the end, are space and time? Do they really exist, or are they simply the constructions of our minds? Robin Le Poidevin provides a clear, witty, and stimulating introduction to these deep questions and many other mind-boggling puzzles and paradoxes. He gives a vivid sense of the difficulties raised by our ordinary ideas about space and time, but he also gives us the basis to think about these problems independently, avoiding large amounts of jargon and technicality. His book is an invitation to think philosophically rather than a sustained argument for particular conclusions, but Le Poidevin does advance and defend a number of controversial views. He argues, for example, that time does not actually flow, that it is possible for space and time to be both finite and yet be without boundaries, and that causation is the key to an understanding of one of the deepest mysteries of time: its direction. Drawing on a variety of vivid examples from science, history, and literature, Travels in Four Dimensions brings to life some of the most profound questions imaginable.

We investigate computational properties of propositional logics for dynamical systems. First, we consider logics for dynamic topological systems (W.f), fi, where W is a topological space and f a homeomorphism on W. The logics come with ‘modal’ operators interpreted by the topological closure and interior, and temporal operators interpreted along the orbits {w, f(w), f2 (w), ˙˙˙} of points w ε W. We show that for various classes of topological spaces the resulting logics are not recursively enumerable (and so not recursively axiomatisable). This gives a ‘negative’ solution to a conjecture of Kremer and Mints. Second, we consider logics for dynamical systems (W, f), where W is a metric space and f and isometric function. The operators for topological interior/closure are replaced by distance operators of the form ‘everywhere/somewhere in the ball of radius a, ‘for a ε Q +. In contrast to the topological case, the resulting logic turns out to be decidable, but not in time bounded by any elementary function.

Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and can be understood as a topological modality. Topological dynamics studies the asymptotic properties of continuous maps on topological spaces. Let a dynamic topological system be a topological space X together wError: Corrupted memory profileError: read ICCBased color space profile errorith a continuous function f . f can be thought of in temporal terms, moving the points of the topological space from one moment to the next. Dynamic topological logics are the logics of dynamic topological systems, just as S4 is the logic of topological spaces. Dynamic topological logics are defined for a trimodal language with an S4-ish topological modality (interior), and two temporal modalities, (next) and ∗ (henceforth), both interpreted using the continuous function..