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 or probable truth of the predicting theory. Howson claims that Hume's argument is correct, and examines what follows about the relation between science and its empirical base.

This user-friendly, comprehensive course in probability and statistics as applied to physical and social science explains the probability calculus, distributions and densities, and the rivals of Beyesianism - the classical, logical, and subjective theories. Howson and Urbach clearly lay out the theory of classical inference, the Neyman-Pearson theory of significance tests, the classical theory of estimation, and regression analysis. The work is controversial, but gives a fair and accurate account of the anti-Bayesian views it criticizes. The authors examined the way scientists actually appeal to probability arguments, and explain the 'classical' approach to statistical inference, which they demonstrate to be full of flaws. They then present the Bayesian method, showing that it avoids the difficulties of the classical system. Finally, they reply to all the major criticisms levelled against the Bayesian method, especially the charge that it is "too subjective".

This introduction to modern formal logic also contains discussions on more philosophical issues, such as truth, conditionals and modal logic. It presents the formal material using informal explanations and arguments rather than rigorous development. Worked examples and exercises enable readers to check their progress. The aim is to equip 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 needed to grasp sophisticated formal reasoning techniques necessary to explore complex metalogic; and the ability to contest claims that "ordinary" reasoning is well represented by formal first order logic. The issues covered include 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.

Contents:
Introduction. Part 1: Truth-Functional Logic Chapter 1. The Basics 1. Deductively Valid Inference 2. Syntax: Connectives and the Principle of Composition 3. Semantics: Truth-Functionality 4. Negation and Conjunction 5. Disjunction 6. Truth-Functional Equivalence 7. The Conditional 8. Some Other Connectives, and the Biconditional Chapter 2. Truth Trees 1. Truth-Functionally Valid Inference 2. Conjugate Tree Diagrams 3. Truth Trees 4. Tautologies and Contradictions Chapter 3. Propositional Languages 1. Propositional Languages 2. Object Language and Metalanguage 3. Ancestral Trees 4. An Induction Principle 5. Multiple Conjunctions and Disjunctions 6. The Disjunctive Normal Form Theorem 7. Adequate Sets of Connectives 8. The Duality Principle 9. Conjunctive Normal Forms Chapter 4. Soundness and Completeness 1. The Standard Propositional Language 2. Truth Trees Again 3. Truth-Functional Consistency, Truth-Functionally Valid Inferences, and Trees 4. Soundness and Completeness Part 2: First Order Logic Chapter 5. Introduction 1. Some Non-Truth-Functional Inferences 2. Quantifiers and Variables 3. Relations 4. Formalising English Sentences Chapter 6. First Languages: Syntax and Two More Trees Rules 1. First Order Languages 2. Two More Tree Rules 3. Tree Proofs Chapter 7. First Order Languages: Semantics 1. Interpretations 2. Formulas and Truth 3. The Tree Rules Revisited 4. Consistency and Validity 5. Logical Truth and Logical Equivalence Chapter 8. Soundness and Completeness 1. Applying the Tree Rules 2. Branch Models 3. Soundness and Completeness Theorems 4. Compactness Chapter 9. Identity 1. Identity 2. Tree Rules For Identity 3. Some Arithmetic 4. Functions and Function Symbols 5. Working with Equations 6. Is Identity Part of Logic? Chapter 10. Alternative Deductive Systems for First Order Logic 1. Introduction 2. H 3 ND 4. Comparisons 5. Intuitionism Chapter 11. First Order Theories 1. First Order Theories 2. Infinite Cardinals 3. Lowenheim-Skolem Theorems 4. Second Order Languages 5. Completeness 6. The Liar Paradox Chapter 12. Beyond the Fringe 1. Counterfactual Conditions 2. Modal Propositional Logic 3. Indicative Conditionals and 4. Conclusion. List of Notation. Answers to Selected Exercises.

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.

First published in 1976, this is a volume of studies on the problems of theory-appraisal in the physical sciences - how and why important theories are developed, changed and are replaced, and by what criteria we judge one theory an advance on another. The volume is introduced by a classic paper of Imre Lakatos's, which sets out a theory for tackling these problems - the methodology of scientific research programmes. Five contributors then test this theory against particular and celebrated case-studies in the history of the physical sciences (particularly in the nineteenth century). The volume ends with a characteristically forceful and original critique of the whole enterprise by Paul Feyerabend. the book is a companion volume to Method and Appraisal in Economics. Both are natural sequels to Criticism and the Growth of Knowledge and attempt to work out in particular cases the implications of some of the theories presented in that book.

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.

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.

First published in 1976, this is a volume of studies on the problems of theory-appraisal in the physical sciences - how and why important theories are developed, changed and are replaced, and by what criteria we judge one theory an advance on another. The volume is introduced by a classic paper of Imre Lakatos's, which sets out a theory for tackling these problems - the methodology of scientific research programmes. Five contributors then test this theory against particular and celebrated case-studies in the history of the physical sciences (particularly in the nineteenth century). The volume ends with a characteristically forceful and original critique of the whole enterprise by Paul Feyerabend. the book is a companion volume to Method and Appraisal in Economics. Both are natural sequels to Criticism and the Growth of Knowledge and attempt to work out in particular cases the implications of some of the theories presented in that book.