P250 | 16847 | Kaplan

“Does this conclusion follow from those premises?" This seems to be a question that calls upon us to exercise our imaginative powers. To determine the answer, our only option seems to be to try to imagine circumstances under which the premises come out true and the conclusion comes out false: if (and only if) we find no such circumstance imaginable, should we conclude that the answer is "Yes". But what a risky procedure this is! After all, the mere fact that we haven't been able to imagine a circumstance under which the premises come out true and the conclusion comes out false does not mean that there is no such circumstance. How can we know that we haven't simply overlooked the crucial circumstance? The central aim of this course is to show that there is a better, and very different, way to go about answering the question. We will see that a significant portion of English discourse exhibits a structure that enables it to be translated into a purely symbolic language. And we will see that, once premises and conclusion are translated into a purely symbolic language, the question "Does this conclusion follow from these premises?" can be decisively answered by a technique which involves nothing more than the manipulation of symbols according to precise rules.