When is a statement—theorem—provable from a set of assumptions—axioms, postulates, definitions? That is the central question of this course, stated broadly. As we shall develop, provability or derivability is a matter of the logical form of the assumptions and statements involved. We may distinguish sentential from predicate form. We may also distinguish techniques enabling us to show that a statement is provable given a set of assumptions from techniques letting us show that a statement is not provable from those assumptions.

We shall present these techniques in four units. In the first, we shall study a formal technique—sentential derivation—for showing the provability  of statements from assumptions based on their sentential form. In the second, we shall introduce interpretations to show failure of provability based first on sentential and then on predicate form. In the third, we shall extend  our derivation technique to show provability based on predicate form. In the last, we shall extend the interpretation and derivation techniques to statements involving further formal features including identity and operation symbols.

There will be a 50 minute examination after each unit of the course, the last occurring during the final examination period. Homework will ordinarily be due weekly and checked for currency. For those registering for the course as PHILO 275, the prerequisite is PHILO 171. For those registering for the course as MATH 275, the prerequisite is MATH156.

The text is Merrie Bergmann, James Moor, and Jack Nelson, The Logic Book Fifth Edition (New York: McGraw Hill Companies, Inc., 2009). $105.00 hardcopy/$52.94 as etext. Although the official text for the course is the Fifth Edition, to allow students to purchase the text used or to use a copy of the Fourth Edition already purchased, we shall indicate the corresponding page numbers in the Fourth Edition for reading assignments and the corresponding exercise numbers for homework assignments.