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This volume brings together many of Terence Horgan's essays on paradoxes: Newcomb's problem, the Monty Hall problem, the two-envelope paradox, the sorites paradox, and the Sleeping Beauty problem. Newcomb's problem arises because the ordinary concept of practical rationality constitutively includes normative standards that can sometimes come into direct conflict with one another. The Monty Hall problem reveals that sometimes the higher-order fact of one's having reliably received pertinent new first-order information constitutes stronger pertinent new information than does the new first-order information itself. The two-envelope paradox reveals that epistemic-probability contexts are weakly hyper-intensional; that therefore, non-zero epistemic probabilities sometimes accrue to epistemic possibilities that are not metaphysical possibilities; that therefore, the available acts in a given decision problem sometimes can simultaneously possess several different kinds of non-standard expected utility that rank the acts incompatibly. The sorites paradox reveals that a certain kind of logical incoherence is inherent to vagueness, and that therefore, ontological vagueness is impossible. The Sleeping Beauty problem reveals that some questions of probability are properly answered using a generalized variant of standard conditionalization that is applicable to essentially indexical self-locational possibilities, and deploys "preliminary" probabilities of such possibilities that are not prior probabilities. The volume also includes three new essays: one on Newcomb's problem, one on the Sleeping Beauty problem, and an essay on epistemic probability that articulates and motivates a number of novel claims about epistemic probability that Horgan has come to espouse in the course of his writings on paradoxes. A common theme unifying these essays is that philosophically interesting paradoxes typically resist either easy solutions or solutions that are formally/mathematically highly technical. Another unifying theme is that such paradoxes often have deep-sometimes disturbing-philosophical morals.
The ancient semantic paradoxes were thought to undermine the rationalist metaphysics of Plato, and their modern relatives have been used by Russell and others to administer some severe logical and epistemological shocks. These are not just tricks or puzzles, but are intimately connected with some of the liveliest and most basic philosophical disputes about logical form, universals, reference and predication. Dr Cargile offers here an original and sustained treatment of this range of issues, and in fact presents an unfashionable defence of a platonistic ontology. He argues that the paradoxes arise not from mistakes in classical assumptions about truth or from an ontology that includes propositions and properties, but from mistakes in describing what propositions and properties are conveyed by particular linguistic expressions. The book should interest, and may well surprise, philosophers and others concerned with semantics and the foundations of logic.
These essays, deceptively simple in phrasing, address current and historic issues.
An entertaining introduction to logic and reasoning, packed with puzzles and thought experiments for the reader to try "Peter Cave takes us on an edifying tour through the world of paradoxes, and there is much to be learned, as well as much enjoyment to be had, in the process." -Adrian W. Moore, University of Oxford, UK "'This sentence is false' is a sentence printed on the cover of this book. A sentence is not a name. So what is the name of the book? This book (whatever its name) is full of intriguing philosophical puzzles ... Paradoxes may seem trivial at first glance, but further thought reveals them to be challenges to some of our most fundamental beliefs and preconceptions. Peter Cave entertainingly escorts the reader through a great variety of these fascinating puzzles, shining light that is fresh and bright." -Laurence Goldstein, University of Kent, UK "This is a truly wonderful book. The topic is tough, but Peter Cave brings it to life. He manages to give new insights on old topics, which is itself remarkable, and he also brings in plenty of less familiar topics ... All in all, it is a joy to see such cleverness and clarity of thought coexisting with such an easy (and light and amusing) writing style." -Professor Imre Leader, Cambridge University, UK Put your neurons through their paces with this lively and engaging introduction to paradoxes. From "Buridan's Ass" and the "Surprise Examination" to "The Liar" and "Sleeping Beauty," This Sentence is False introduces all the key philosophical paradoxes. This fascinating guide to logic and reasoning is packed with puzzles and thought experiments to actively engage the reader in critical thinking. As well as paradoxes that occur in our everyday lives, topics also include God, ethics, political philosophy, space, and time. This Sentence is False will put your mind to the test, challenge what you think you know, and lead you on a fascinating journey through logical reasoning.
Since antiquity, opposed concepts such as the One and the Many, the Finite and the Infinite, and the Absolute and the Relative, have been a driving force in philosophical, scientific, and mathematical thought. Yet they have also given rise to perplexing problems and conceptual paradoxes which continue to haunt scientists and philosophers. In Oppositions and Paradoxes, John L. Bell explains and investigates the paradoxes and puzzles that arise out of conceptual oppositions in physics and mathematics. In the process, Bell not only motivates abstract conceptual thinking about the paradoxes at issue, but he also offers a compelling introduction to central ideas in such otherwise-difficult topics as non-Euclidean geometry, relativity, and quantum physics. These paradoxes are often as fun as they are flabbergasting. Consider, for example, the famous Tristram Shandy paradox: an immortal man composing an autobiography so slowly as to require a year of writing to describe each day of his life — he would, if he had infinite time, presumably never complete the work, although no individual part of it would remain unwritten. Or think of an office mailbox labelled “mail for those with no mailbox”—if this is a person’s mailbox, how can they possibly have “no mailbox”? These and many other paradoxes straddle the boundary between physics and metaphysics, and demonstrate the hidden difficulty in many of our most basic concepts.
Paradoxes are more than just intellectual puzzles - they raise substantive philosophical issues and offer the promise of increased philosophical knowledge. In this introduction to paradox and paradoxes, Doris Olin shows how seductive paradoxes can be, why they confuse and confound, and why they continue to fascinate. Olin examines the nature of paradox, outlining a rigorous definition and providing a clear and incisive statement of what does and does not count as a resolution of a paradox. The view that a statement can be both true and false, that contradictions can be true, is seen to provide a challenge to the account of paradox resolution, and is explored. With this framework in place, the book then turns to an in-depth treatment of the Prediction Paradox, versions of the Preface/Fallibility Paradox, the Lottery Paradox, Newcomb's Problem, the Prisoner's Dilemma and the Sorites Paradox. Each of these paradoxes is shown to have considerable philosophical punch. Olin unpacks the central arguments in a clear and systematic fashion, offers original analyses and solutions, and exposes further unsettling implications for some of our most deep-seated principles and convictions.
Paradox Lost covers ten of philosophy’s most fascinating paradoxes, in which seemingly compelling reasoning leads to absurd conclusions. The following paradoxes are included: The Liar Paradox, in which a sentence says of itself that it is false. Is the sentence true or false? The Sorites Paradox, in which we imagine removing grains of sand one at a time from a heap of sand. Is there a particular grain whose removal converts the heap to a non-heap? The Puzzle of the Self-Torturer, in which a series of seemingly rational choices has us accepting a life of excruciating pain, in exchange for millions of dollars. Newcomb’s Problem, in which we seemingly maximize our expected profit by taking an unknown sum of money, rather than taking the same sum plus $1000. The Surprise Quiz Paradox, in which a professor finds that it is impossible to give a surprise quiz on any particular day of the week . . . but also that if this is so, then a surprise quiz can be given on any day. The Two Envelope Paradox, in which we are asked to choose between two indistinguishable envelopes, and it is seemingly shown that each envelope is preferable to the other. The Ravens Paradox, in which observing a purple shoe provides evidence that all ravens are black. The Shooting Room Paradox, in which a deadly game kills 90% of all who play, yet each individual’s survival turns on the flip of a fair coin. Each paradox is clearly described, common mistakes are explored, and a clear, logical solution offered. Paradox Lost will appeal to professional philosophers, students of philosophy, and all who love intellectual puzzles.
'This sentence is false'. Is it? If a hotel with an infinite number of rooms is fully occupied, can it still accommodate a new guest? How can we have emotional responses to fiction, when we know that the objects of our emotions do not exist?