Argumento e inferencia

Arguments and Inference


The Discipline of Logic

Human life is full of decisions, including significant choices about what to believe. Although everyone prefers to believe what is true, we often disagree with each other about what that is in particular instances. It may be that some of our most fundamental convictions in life are acquired by haphazard means rather than by the use ofreason, but we all recognize that our beliefs about ourselves and the world often hang together in important ways.


If I believe that whales are mammals and that all mammals are fish, then it would also make sense for me to believe that whales are fish. Even someone who (rightly!) disagreed with my understanding of biological taxonomy could appreciate the consistent, reasonable way in whichI used my mistaken beliefs as the foundation upon which to establish a new one. On the other hand, if I decide to believe that Hamlet was Danish because I believe that Hamlet was a character in a play by Shaw and that some Danes are Shavian characters, then even someone who shares my belief in the result could point out that I haven't actually provided good reasons for accepting its truth.In general, we can respect the directness of a path even when we don't accept the points at which it begins and ends. Thus, it is possible to distinguish correct reasoning from incorrect reasoning independently of our agreement on substantive matters. Logic is the discipline that studies this distinction—both by determining the conditions under which the truth of certain beliefs leads naturallyto the truth of some other belief, and by drawing attention to the ways in which we may be led to believe something without respect for its truth. This provides no guarantee that we will always arrive at the truth, since the beliefs with which we begin are sometimes in error. But following the principles of correct reasoning does ensure that no additional mistakes creep in during the course of ourprogress.


In this review of elementary logic, we'll undertake a broad survey of the major varieties of reasoning that have been examined by logicians of the Western philosophical tradition. We'll see how certain patterns of thinking do invariably lead from truth to truth while other patterns do not, and we'll develop the skills of using the former while avoiding the latter. It will behelpful to begin by defining some of the technical terms that describe human reasoning in general.


The Structure of Argument

Our fundamental unit of what may be asserted or denied is the proposition (or statement) that is typically expressed by a declarative sentence. Logicians of earlier centuries often identified propositions with the mental acts of affirming them, often calledjudgments, but we can evade some interesting but thorny philosophical issues by avoiding this locution.
Propositions are distinct from the sentences that convey them. "Smith loves Jones" expresses exactly the same proposition as "Jones is loved by Smith," while the sentence "Today is my birthday" can be used to convey many different propositions, depending upon who happens to utter it, and on whatday. But each proposition is either true or false. Sometimes, of course, we don't know which of these truth-values a particular proposition has ("There is life on the third moon of Jupiter" is presently an example), but we can be sure that it has one or the other.


The chief concern of logic is how the truth of some propositions is connected with the truth of another. Thus, we will usuallyconsider a group of related propositions. An argument is a set of two or more propositions related to each other in such a way that all but one of them (the premises) are supposed to provide support for the remaining one (the conclusion). The transition or movement from premises to conclusion, the logical connection between them, is the inference upon which the argument relies.
Notice that...