Ebook: An Introduction to Mathematical Logic

This text was developed for a course at the upper-sophomore or junior level within the mathematics curriculum. It is intended as a course in logic useful to the student of mathematics rather than as a beginning course for a prospective specialist in philosophy. I have no doubt that the sophisticated reader will find sins of omission and commission in this presentation-no text is entirely satisfactory to-anyone, its author included. Most of the sins, I hope, will have resulted from deliberate choices of what I considered the lesser evil in the light of the aims of the text. One notable example is the omission of any discussion of language levels or of the distinction between use and mention of a symbol. In some places quotation marks are used to emphasize that a symbol is mentioned, but consistency in that usage was abandoned after the first draft, because it frequently turned out to have a distracting influence instead of a clarifying one.

With the exception of a few dispensable examples from the elementary calculus, a background in high school mathematics is all that is actually drawn upon. With a reasonably capable class, the whole text can be covered in a standard three semester-hour course. The plan of the book is described in § 1-7 (to thwart the student who habitually skips prefaces), and the reader might do well to turn to it at this point.