Philosophy | Introductory symbolic logic
P250 | 19782 | Kaplan

Does this conclusion follow from those premises?" This seems to be a
question which 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.

Virginia Klenk, Understanding symbolic Logic,  (McGraw Hill) 4th ed .