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 three 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, and  shall introduce interpretations to show failure of provability based on sentential form. In the second, we shall extend the method of interpretations to show failure of provability based on predicate form and 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.

Text: 

Merrie Bergmann, James Moor, and Jack Nelson, The Logic Book Fifth Edition (NewYork: The McGraw-Hill Companies Inc., 2009) $120.63 hardcopy/$66.50 as e-text online or downloadable for 180 days. The hardcopy has been ordered at both the Hunter College Bookstore and at Shakespeare's. The e-text is available by going to www.coursesmart.com. Click on for Students and follow prompts