Abstract

The central contention of this thesis is that the relation that has been required to hold between an argument and its symbolisations is unnecessarily strong. If we are to use logic to determine the validity of arguments the usual requirements of equivalence, suggested by a translation view of symbolisation, between premises and their symbolisations and conclusions and their symbolisations can be weakened. By distinguishing between cases in which a valid argument shows the validity of another and cases in which an invalid argument shows the invalidity of another we can weaken the equivalence requirement to logical implication or its converse. For determining validity this can be thought of as the reduction view of symbolisation, for it is analogous to Aristotle's method of reduction of syllogisms. Chapter 1 introduces the concept of argument and determines the relation between the informal concept of validity that logic is being used to test for and the technical notions of model-theoretic, proof-theoretic and schematic validity. Chapter 2 examines the concept of form and its role in determining validity and invalidity. It is argued that while formal methods have an important role in determining validity they are severely limited in their application to determining invalidity and associated logical relations. Chapter 3 begins by arguing that the standard technique of symbolising and testing for validity is unreliable and then proposes weaker asymmetric sufficient conditions for determining the validity or invalidity of an argument from the validity or invalidity of its symbolisation. Chapter 4 shows how these conditions can be applied in restoring reliability to the technique of testing for validity. One application shows under what circumstances natural language conditionals can be reliably symbolised using the material conditional. Chapter 5 critically examines the arguments given in introductory logic texts to justify using logic to test validity. Since most of these books take for granted that an argument and its symbolisation should be equivalent, they need to argue a stronger case than is required by the conditions in Chapter 3. The last chapter, Chapter 6, examines the reliable use of logic-like formalisms in computer science in applications including deductive question-answering