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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.
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".
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.
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