Kirjahaku

Colin Howson offers a solution to one of the central, unsolved problems of Western philosophy, the problem of induction. In the mid-eighteenth century David Hume argued that successful prediction tells us nothing about the truth of the predicting theory. No matter how many experimental tests a hypothesis passes, nothing can be legitimately inferred about its truth or probable truth. But physical theory routinely predicts the values of observable magnitudes to many places of decimals and within very small ranges of error. The chance of this sort of predictive success without a true theory seems so remote that the possibility should be dismissed. This suggests that Hume's argument must be wrong; but there is still no consensus on where exactly the flaw in the argument lies. Howson argues that there is no flaw, and examines the implications of this disturbing conclusion for the relation between science and its empirical base.

Colin Howson offers a solution to one of the central, unsolved problems of Western philosophy, the problem of induction. In the mid-eighteenth century David Hume argued that successful prediction tells us nothing about the truth of the predicting theory. No matter how many experimental tests a hypothesis passes, nothing can be legitimately inferred about its truth or probable truth. But physical theory routinely predicts the values of observable magnitudes to many small places of decimals and within very small ranges of error. The chance of this sort of predictive success without a true theory seems so remote that the possibility should be dismissed. This suggests that Hume's argument must be wrong; but there is still no consensus on where exactly this flaw lies. Howson argues that there is no flaw, and examines the implications of this disturbing conclusion for relation between science and its empirical base.

Logic With Trees is a new and original introduction to modern formal logic. Unlike most texts, it also contains discussions on more philosophical issues such as truth, conditionals and modal logic. It presents the formal material with clarity, preferring informal explanations and arguments to intimidatingly rigorous development. Worked examples and excercises enable the readers to check their progress. Logic With Trees equips students with * a complete and clear account of the truth-tree system for first order logic * the importance of logic and its relevance to many different disciplines * the skills to grasp sophisticated formal reasoning techniques necessary to explore complex metalogic * the ability to contest claims that `ordinary' reasoning is well represented by formal first order logic The issues covered include a thorough discussion of truth-functional and full first order logic, using the truth-tree or semantic tableau approach. Completeness and Soundness proofs are given for both truth-functional and first order trees. Much use is made of induction, which is presented in a clear and consistent manner. There is also discussion of alternative deductive systems, an introduction to transfinite numbers and categoricity, the Lowenhein-Skolem theories and the celebrated findings of Godel and Church. The book concludes with an account of Kripke's attempted solution of the liar paradox and a discussion of the weakness of truth-functional account of conditionals. Particularly useful to those who favour critical accounts of formal reasoning, it will be of interest to students of philosophy at first level and beyond and also students of mathematics and computer science.

Logic With Trees is a new and original introduction to modern formal logic. Unlike most texts, it also contains discussions on more philosophical issues such as truth, conditionals and modal logic. It presents the formal material with clarity, preferring informal explanations and arguments to intimidatingly rigorous development. Worked examples and excercises enable the readers to check their progress. Logic With Trees equips students with * a complete and clear account of the truth-tree system for first order logic * the importance of logic and its relevance to many different disciplines * the skills to grasp sophisticated formal reasoning techniques necessary to explore complex metalogic * the ability to contest claims that `ordinary' reasoning is well represented by formal first order logic The issues covered include a thorough discussion of truth-functional and full first order logic, using the truth-tree or semantic tableau approach. Completeness and Soundness proofs are given for both truth-functional and first order trees. Much use is made of induction, which is presented in a clear and consistent manner. There is also discussion of alternative deductive systems, an introduction to transfinite numbers and categoricity, the Lowenhein-Skolem theories and the celebrated findings of Godel and Church. The book concludes with an account of Kripke's attempted solution of the liar paradox and a discussion of the weakness of truth-functional account of conditionals. Particularly useful to those who favour critical accounts of formal reasoning, it will be of interest to students of philosophy at first level and beyond and also students of mathematics and computer science.

The growth of science and a correspondingly scientific way of looking at evidence have for the last three centuries slowly been gaining ground over religious explanations of the cosmos and mankind's place in it. However, not only is secularism now under renewed attack from religious fundamentalism, but it has also been widely claimed that the scientific evidence itself points strongly to a universe deliberately fine-tuned for life to evolve in it. In addition, certain aspects of human life, like consciousness and the ability to recognise the existence of universal moral standards, seem completely resistant to evolutionary explanation. In this book Colin Howson analyses in detail the evidence which is claimed to support belief in God's existence and argues that the claim is not well-founded. Moreover, there is very compelling evidence that an all-powerful, all-knowing God not only does not exist but cannot exist, a conclusion both surprising and provocative.