This book is a philosophical study of the relations between hearing and thinking about music. The central problem it addresses is as follows: how is it possible to talk about what a listener perceives in terms that the listener does not recognize? By applying the concepts and techniques of analytic philosophy the author explores the ways in which musical hearing may be described as nonconceptual, and how such mental representation contrasts with conceptual thought. The author is both philosopher and musicologist (...) and uniquely combines the perspectives of both disciplines. Exploring the philosophical questions of mental representation in the relatively neglected, nonverbal domain of music, this study is a major contribution to the philosophical understanding of music perception and cognitive theory. (shrink)

What is the difference between a performance of Beethoven's Fifth Symphony and the symphony itself? What does it mean for musicians to be faithful to the works they perform? To answer this question, Goehr combines philosophical and historical methods of enquiry. She describes how the concept of a musical work emerged as late as 1800, and how it subsequently defined the norms, expectations, and behavior characteristic of classical musical practice. Out of the historical thesis, Goehr draws philosophical conclusions about the (...) normative functions of concepts and ideals. She also addresses current debates amongst conductors, early-music performers, and avant-gardists. (shrink)

A survey of the field of hypercomputation, including discussion of a variety of objections.

This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges.

Chasing Reality deals with the controversies over the reality of the external world. Distinguished philosopher Mario Bunge offers an extended defence of realism, a critique of various forms of contemporary anti-realism, and a sketch of his own version of realism, namely hylorealism. Bunge examines the main varieties of antirealism - Berkeley's, Hume's, and Kant's; positivism, phenomenology, and constructivism - and argues that all of these in fact hinder scientific research. Bunge's realist contention is that genuine explanations in the sciences appeal (...) to causal laws and mechanisms that are not directly observable, rather than simply to empirical generalisations. Genuine science, in his view, is objective even when it deals with subjective phenomena such as feelings of fear. This work defends a realist view of universals, kinds, possibilities, and dispositions, while rejecting contemporary accounts of these that are couched in terms of modal logic and 'possible worlds.'. (shrink)

Some have thought that the process of the expansion of the universe can be used to define an absolute ‘cosmic time’ which then serves as the absolute time required by tensed theories of time. Indeed, this is the very reason why many tense theorists are happy to concede that special relativity is incompatible with the tense thesis, because they think that general relativity, which trumps special relativity, and on which modern cosmology rests, supplies the means of defining temporal becoming using (...) cosmic time. I argue that cosmic time is not up to the task, and that these tense theorists should rethink their strategy in dealing with the theories of relativity. Introduction The Mellor-Rees argument against tense theories Can expansion combat such wrinkles? Event and creation horizons Bursting the balloon. (shrink)

A comprehensive model for describing various forms of developments in science is defined in precise, set-theoretic terms, and in the spirit of the structuralist approach in the philosophy of science. The model emends previous accounts in centering on single systems in a homogenous way, eliminating notions which essentially refer to sets of systems. This is achieved by eliminating the distinction between theoretical and non-theoretical terms as a primitive, and by introducing the notion of intended links. The force of the model (...) is demonstrated by formally incorporating many of the important, precise meta-theoretic concepts occurring in the literature. (shrink)

1.1 Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Tangent Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (...) . . . . . . . . . . . 7 1.3 Vector Fields, Integral Curves, and Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 Tensors and Tensor Fields on Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.5 The Action of Smooth Maps on Tensor Fields . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.6 Lie Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.7 Derivative Operators and Geodesics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 1.8 Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 1.9 Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 1.10 Hypersurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 1.11 Volume Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96.. (shrink)

Focusing on spacetime singularities, Earman engages with a host of foundational issues at the intersection of science and philosophy, ranging from the big bang to the possibility of time travel.

A controversial scientific vision predicts a time in which humans and machines will merge and create a new form of non-biological intelligence, explaining how the occurrence will solve such issues as pollution, hunger, and aging.

Keine ausführliche Beschreibung für "Die geistige Situation der Zeit" verfügbar.

We address the question of whether it is possible to operate a time machine by manipulating matter and energy so as to manufacture closed timelike curves. This question has received a great deal of attention in the physics literature, with attempts to prove no- go theorems based on classical general relativity and various hybrid theories serving as steps along the way towards quantum gravity. Despite the effort put into these no-go theorems, there is no widely accepted definition of a time (...) machine. We explain the conundrum that must be faced in providing a satisfactory definition and propose a resolution. Roughly, we require that all extensions of the time machine region contain closed timelike curves; the actions of the time machine operator are then sufficiently "potent" to guarantee that closed timelike curves appear. We then review no-go theorems based on classical general relativity, semi-classical quantum gravity, quantum field theory on curved spacetime, and Euclidean quantum gravity. Our verdict on the question of our title is that no result of sufficient generality to underwrite a confident "yes" has been proven. Our review of the no-go results does, however, highlight several foundational problems at the intersection of general relativity and quantum physics that lend substance to the search for an answer. (shrink)

Special relativity is said to prohibit faster-than-light (superluminal) signaling, yet controversy regularly arises as to whether this or that physical phenomenon violates the prohibition. I argue that the controversy is a result of a lack of clarity as to what it means to ‘signal’, and I propose a criterion. I show that according to this criterion, superluminal signaling is not prohibited by special relativity.

It has been argued that neural networks and other forms of analog computation may transcend the limits of Turing-machine computation; proofs have been offered on both sides, subject to differing assumptions. In this article I argue that the important comparisons between the two models of computation are not so much mathematical as epistemological. The Turing-machine model makes assumptions about information representation and processing that are badly matched to the realities of natural computation (information representation and processing in or inspired by (...) natural systems). This points to the need for new models of computation addressing issues orthogonal to those that have occupied the traditional theory of computation. (shrink)

überall einen richtigen Gebrauch der reinen Vernunft giebt, in welchem Fall es auch einen Canon derselben geben muß, so wird dieser nicht den speculativen, sondernden pr.ntischen Vernunftgebrauch betreffen, den wir also iezt ...

Originally published in 1949. This meticulously researched book presents a comprehensive outline and discussion of Aristotle’s mathematics with the author's translations of the greek. To Aristotle, mathematics was one of the three theoretical sciences, the others being theology and the philosophy of nature. Arranged thematically, this book considers his thinking in relation to the other sciences and looks into such specifics as squaring of the circle, syllogism, parallels, incommensurability of the diagonal, angles, universal proof, gnomons, infinity, agelessness of the universe, (...) surface of water, meteorology, metaphysics and mechanics such as levers, rudders, wedges, wheels and inertia. The last few short chapters address ‘problems’ that Aristotle posed but couldn’t answer, related ethics issues and a summary of some short treatises that only briefly touch on mathematics. (shrink)

Einleitung.--Zur Vorgeschichte der griechischen Philosophie: kosmogonische Dichtung und Prosa.--Die altionischen Naturphilosophen.--Pythagoras und die älteren Pythagoreer.--Xenophanes von Kolophon.--Herakleitos von Ephesos.--Die Elaten.--Empedokles.--Anaxagoras.--Leukippos.--Eklektiker und Epigonen.--Das Zeitalter der griechischen Aufklärung: Die Sophistik, Demokrit, die jüngeren Pythagoreer.

Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.

Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.

Aesthetics and Music is a rich and interesting study. Hamilton's approach is innovative. He interleaves chapters on the history of philosophical thought about music with more theoretical discussions of music, sound, rhythm and improvisation, but does not cover the work–performance relation, depiction or expression. He draws on an atypically broad range of examples, including avant-garde, medieval, non-Western and jazz. The assumptions are humanist: ‘I wish to argue for an aesthetic conception of music as an art … according to which music (...) is a human activity grounded in the body and bodily movement and interfused with human life’.The historical chapters are valuable and not without analysis and criticism. Hamilton shows how the ancient Greek theorists were more interested in music's mathematical properties as reflecting the underlying harmony of relations between cosmic bodies than in the practice of musicians. While they equated the value of art with its contribution to an education for citizenship and while their concept of the arts differed …. (shrink)

The goal of this article is to show that the structuralist approachprovides a powerful framework for the analysis of certain holistic phenomena in empirical theories.We focus on two aspects of holism. The first refers to the involvement of comprehensive complexes of hypothesesin the theoretical treatment of systems regarded in isolation. By contrast, the second refers to thecorrelation between the theoretical descriptions of different systems. It is demonstrated how these two aspectscan be analysed by making use of the structuralist notion of (...) theory-nets, and how they are reflected by a refinedversion of the Ramsey sentence. Furthermore, it is argued that there exists a tight correlation between theoccurrence of these two holistic phenomena, a specific form of underdetermination of terms which occur in thefundamental principles of an empirical theory, and the shaping of the theory's protective belt. After having dealtwith these questions in abstracto, the relevance of these considerations for a better understanding of the dynamicsof empirical theories is demonstrated in a concrete case study. It refers to the role holistic phenomenaplayed in the investigation of the anomalous advance of Mercury's perihelion and in the various attempts to eliminate this anomaly. (shrink)

In his bestselling work of popular science, Sir Roger Penrose takes us on a fascinating roller-coaster ride through the basic principles of physics, cosmology, mathematics, and philosophy to show that human thinking can never be emulated by a machine.

This paper is an enquiry into the logical, metaphysical, and physical possibility of time travel understood in the sense of the existence of closed worldlines that can be traced out by physical objects. We argue that none of the purported paradoxes rule out time travel either on grounds of logic or metaphysics. More relevantly, modern spacetime theories such as general relativity seem to permit models that feature closed worldlines. We discuss, in the context of Gödel's infamous argument for the ideality (...) of time based on his eponymous spacetime, what this apparent physical possibility of time travel means. Furthermore, we review the recent literature on so-called time machines, i.e., of devices that produce closed worldlines where none would have existed otherwise. Finally, we investigate what the implications of the quantum behaviour of matter for the possibility of time travel might be and explicate in what sense time travel might be possible according to leading contenders for full quantum theories of gravity such as string theory and loop quantum gravity. (shrink)

Aristotelian, or non-Platonist, realism holds that mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative or structural aspects of things, such as ratios, or patterns, or complexity, or numerosity, or symmetry. Let us start with an example, as Aristotelians always prefer, an example that introduces the essential themes of the Aristotelian view of mathematics. A typical mathematical truth is (...) that there are six different pairs in four objects: Figure 1. There are 6 different pairs in 4 objects The objects may be of any kind, physical, mental or abstract. The mathematical statement does not refer to any properties of the objects, but only to patterning of the parts in the complex of the four objects. If that seems to us less a solid truth about the real world than the causation of flu by viruses, that may be simply due to our blindness about relations, or tendency to regard them as somehow less real than things and properties. But relations (for example, relations of equality between parts of a structure) are as real as colours or causes. (shrink)

This volume is the first systematic presentation of the work of Albert Einstein, comprising fourteen essays by leading historians and philosophers of science that introduce readers to his work. Following an introduction that places Einstein's work in the context of his life and times, the book opens with essays on the papers of Einstein's 'miracle year', 1905, covering Brownian motion, light quanta, and special relativity, as well as his contributions to early quantum theory and the opposition to his light quantum (...) hypothesis. Further essays relate Einstein's path to the general theory of relativity (1915) and the beginnings of two fields it spawned, relativistic cosmology and gravitational waves. Essays on Einstein's later years examine his unified field theory program and his critique of quantum mechanics. The closing essays explore the relation between Einstein's work and twentieth-century philosophy, as well as his political writings. (shrink)

Key words: the continuum, structuralism, conceptual structuralism, basic structural conceptions, Euclidean geometry, Hilbertian geometry, the real number system, settheoretical conceptions, phenomenological conceptions, foundational conceptions, physical conceptions.