Logic: An Introduction to Elementary Logic

Logic is about consistency – but not about all types of consistency. For example, if a man supports Arsenal one day and Spurs the next, the he is fickle but not necessarily illogical. The type of consistency which concerns logicians is not loyalty or justice or sincerity; it is compatibility of beliefs. Logic, therefore, involves studying the situations in which a sentence is true or valid, and subsequently the rules which determine the validity or otherwise of a given argument.

From this starting point and assuming no previous knowledge of logic, Dr Hodges takes the reader through a whole gamut of logical expressions, symbols and notations in a simple and lively way. Many examples are given to illustrate the connections between truth and sentence-structure, and the emphasis throughout is on English, as opposed to artificial formal languages. The treatment of truth and consistency leads smoothly to tableau proofs, and readers who are more mathematically adventurous will find optional sections introducing context-free grammars, propositional calculus up to the Interpolation Theorem, and the logic of probability.