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Author:   Michael Gabbay
Publisher:   Broadview Press Ltd
Imprint:   Broadview Press Ltd
Edition:   illustrated Edition
Dimensions:   Width: 15.20cm , Height: 1.10cm , Length: 22.90cm
Weight:   0.370kg
ISBN:  

9781551114057

ISBN 10:   1551114054
Pages:   224
Publication Date:   04 September 2002
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   Available To Order  
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Table of Contents

1. Arguments and Validity Validity and Arguments A little argument A theory of validity Examples of valid and invalid arguments Valid arguments Invalid arguments Validity and the structure of an argument Validity is independent of meaning Determining validity by changing to an easier meaning Other forms of argument Modus Ponens and friends More valid arguments Conclusions Exercises 2. Truth Functionality Embedded sentences Basic and simple sentences found in larger sentences Truth values Propositions Truth values of complex sentences Truth functional sentences Non-truth functional sentences Different words, same truth function Same word, different truth functions A problem for truth functionality Exercises   3. Formalisation of Truth Functions Formalising truth functions Formalising and, not and or Formalising sentences Truth Tables How to read truth tables Negation Conjunction Disjunction Material equivalence The formalisation of material equivalence Material equivalence in sentences Exercises 4. Truth Tables and Tautologies Tautologies and how to find them Truth tables with more than two letters How to write the exclusive “or” Exercises 5. Material Implication and Validity Material implication in theory The truth conditions of material implication The truth table for material implication Counterfactuals, a problem for the truth tables Material implication does not imply any causality Only if Material implication in practice More interesting tautologies DeMorgan’s Laws Some jolly big truth tables Truth tables for analysing arguments Exercises   6. The Tableaux Method Indirect Proof: a preliminary The way of the tableau for tautologies The rules of the tableau Exercises The way of the tableau for validity Exercises   7. Propositional Logic: The Interesting Bits What is so interesting? Only three truth functions are necessary Only two truth functions are necessary Only one truth function is necessary Sheffer stroke Another sufficient truth function The big problem with propositional logic Natural language is more than a few sentences Exercises   8. Where Sheffer Can Put His Stroke Everyone will have a stroke, eventually A shelf shuffling game An interesting property of truth tables Back to the shelf game What’s the connection? Sheffer stroke What we have just been doing   9. Syllogisms and Venn Diagrams The Syllogism The Greek’s theory The modern theory Formalising syllogisms Venn diagrams What to do with your Venn diagrams Some intuition for Venn diagrams Venn diagrams for validity Three circle Venn diagrams Venn and Aristotle Problems with Venn diagrams Complicated arguments can be difficult to draw Venn diagrams cannot do truth functions Exercises   10. Predicate Logic: On Natural Language Names and Predicates Formalisation of sentences Exercises Quantifiers and Variables An important and helpful convention Sentences with multiple Quantifiers Syllogisms in predicate logic Buckets of eggs Exercises   11. The Tableaux and Identity A BIG warning The extra rules Choice of variables Exercises Arguments in predicate logic The standard arguments Arguments with multiple qualifiers Exercises Identity Identity and more new rules Identity for sentences of quantity There is at least There are at most There are exactly Exercises Will it ever end? A. The complete tableaux rules B. Famous Truth Tables C. A brief summary of Classical Logic References Index

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Author Information

Michael Gabbay teaches in the department of Philosophy at Kings College, the University of London.

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