1. Introduction

        The study of logic has, for over 2000 years, engaged the  interest of both those who wish to gain practical  advantage from a knowledge of the principles of  reasoning and those who pursue the subject for its own  sake. The practical benefits of this study are undeniable.  Those with an interest in increasing, organizing, or using  knowledge have turned to logic­from the early Greek  philosophers to the men from many fields who together  developed modern computer science on the basis of their  knowledge of formal logic. Moreover, logic, as it  develops, becomes an increasingly important and  intriguing theoretical discipline. By no means a static  ëbody of knowledgeí that exists to be learned and  used, logic is a viable and creative field. Its study is an  arena for creative human endeavor. The goal of logic is  stable, but means for attaining that goal are being  expanded and new ones formulated.

        The study of logic provides a means of facilitating the  attempt to develop well-argued positions and to evaluate  critically the positions espoused by others. The material  that follows is not designed to give the reader mastery of  the techniques of formal logic. Rather, it is aimed at  facilitating communication­at enabling the reader to  understand some of the uses of logic which he or she will  come across, in the classroom or in the literature, when  beginning the study of a contemporary analytical  approach to philosophical problems.

        The goal of logic, which we said above was a stable one,  is the preservation of truth. Before continuing a  discussion of this goal, it will be helpful to distinguish  conclusive from inconclusive reasoning. Conclusive  reasoning guarantees that the goal of logic has been  reached. That is, it guarantees that in the process of  reasoning there has not been a passage from what is true  to what is false. The study of conclusive reasoning is  usually called deductive logic~ Some reasoning, though  good, is inconclusive because the information contained  in the conclusion goes beyond that contained in the  grounds for the conclusion. For example:

        (1) Each of the twenty cows inoculated with  Smithís vaccine promptly died.

         (2) (Therefore) Smithís vaccine is fatal to all  cows.

Here it is possible that the grounds stated in (1) are true  while the conclusion drawn in (2) is false; the truth of (1)  does not guarantee the truth of (2).

        The study of good reasoning of this sort has usually been  included in what is called inductive logic. While the  preservation of truth may not be guaranteed in inductive  reasoning, this goal remains an important principle in the  evaluation of inductive reasoning and of principles of  inductive logic. The analysis of inductive arguments is  complex indeed and goes far beyond the scope of our  present concerns. In our subsequent discussion we shall  restrict our attention to conclusive reasoning,

        In distinguishing between conclusive and inconclusive  reasoning, we utilized the idea of passage from grounds  to conclusions. We may consider logic to be an analysis of  the structure of reasoning. Although we do not maintain  that all reasoning need be linguistic, it is convenient for  the purposes at hand to give a linguistic formulation of  these ideas of grounds, passage, and conclusion. Let us  think then of a single instance of reasoning as an  argument. An argument is a set of declarative  sentences, one of which is claimed to follow from the  others and is identified as the conclusion. The  remaining sentences, which are offered as grounds for the  conclusion, are called premises.

        The most basic mark of quality for an argument is  validity. An argument is valid when it is not possible  for all its premises to be true while the conclusion is  false. Obviously such arguments guarantee the  preservation of truth in that one cannot start from  premises, all of which are true, and yet end with a  conclusion which is false. Notice, however, that the  preservation of truth does not require that all truths  explicit in the premises have been preserved. Typically  the conclusion of a valid argument will not contain all the  information that is guaranteed by the grounds.

        As a goal, the preservation of truth is a kind of quality  control on reasoning But even strict adherence to that  goal will not alone guarantee that the conclusions which  are the products of our reasoning are true. For even  flawless reasoning can lead to a false conclusion if it  begins from grounds which include a false pftmise. For  this reason it is useful to notice a distinction between  arguments that exhibit good reasoning and arguments that  not only exhibit good reasoning but also start with true  premises. Arguments of the former kind we have called  valid; arguments of the latter kind we will call sound.  That is, an argument is sound if and only if it is a valid  argument having no false premise. We can thus challenge  the soundness of an argument either by challenging its  validity or by challenging the truth of one or more of its  premises

         Usually we want our arguments to be not only valid but  also sound, since when we know that an argument is  sound we know that its conclusion is true. But arguments  which are valid though not sound may also be useful.  For example we can, wben certain conditions are met,  use an argument which is valid but not sound to show  that a particular sentence is false. Suppose we know both  that an argument is valid and that its conclusion is false.  We know then that at least one of its premises is false.  For if all the premises of a valid argument are true, its  conclusion is true. Now suppose also that we know, of  all its premises but one, that they are true. Then it must  be that one premise which is false.

        If it is more often the soundness of an argument than  merely its validity that we seek, why can we not think of  the goal of logic as extended beyond analysis of the  structure of reasoning and arguments to evaluation of  grounds or premises? To do so would be to include  within the subject of logic not only the structure of  reasoning but also absolutely everything else that can  find its way into the premises of our reasoning! Against  this prospect of the whole of human knowledge as the  proper purview of logic, a guarantee of the preservation  of truth is a modest aim indeed. But it is not a trivial one;  pursuit of this goal is of value throughout the quest for  knowledge.