Course Goals:  The course consists of four units. The goal of each unit is for students to master the meaning of certain key logical concepts and the techniques for showing whether or not those concepts hold in a given case. Unit 1, after presenting intuitive definitions of such logical concepts as logical truth, consistency, and validity, presents definitions of the truth-functional explications of these concepts. We shall present a symbolization technique to make manifest the truth-functional structure of a statement, and the truth-table technique for showing in particular whether statements are truth-functionally true, sets of statements truth-functionally consistent, arguments truth-functionally valid. The goal at the end of the unit is for students to be able to state the meaning of core logical concepts and their truth-functional explications, show the truth-functional structure of statements through symbolization, and correctly construct and properly interpret truth-tables.

Unit 2, building on Unit 1, introduces the truth-tree technique for showing whether or not the truth-functional properties hold in given cases, a technique far more efficient in general than truth-tables. The goal of the unit is for students to be able to correctly construct and properly interpret truth-trees, in addition to knowing the meaning of associated terminology. 

Unit 3 presents a deeper account of logical structure, quantificational structure, by adding predicates, constants, and quantifiers to our elements for showing truth-functional structure. We shall extend our symbolization technique to display the quantificational structure of statements, and present quantificational explications of the core logical concepts. The goal of the unit is to enable students to display symbolically the quantificational structure of a statement, to understand both basic terminology connected with this structural analysis and the definitions of quantificational explications of core logical concepts, and to determine, given certain specified conditions, the truth or falsity of statements analyzed at this level. 

Unit 4 extends the truth-tree technique to determine whether or not the quantificational explications of the core logical concepts hold in a given case. The goal is to enable students to construct and interpret truth trees properly, and to understand the vocabulary which characterizes them. We shall cover Chapters One through Four, Seven (omitting most of §7.8 and all of §7.9), and Nine (omitting §9.4 and §9.5) in the Bergmann, Moore, Nelson text. Handouts containing additional material will be distributed in connection with Chapter 7. 

Related Outcomes: This is an introductory course in formal deductive logic. Students completing the course should have developed a much sharper understanding of when the premises of an argument deductively entail its conclusion, when a set of statements is logically contradictory, and when a given statement is necessarily true. 

Text: 

Merrie Bergmann, James Moor, and Jack Nelson, The Logic Book Fifth Edition (NewYork: The McGraw-Hill Companies Inc., 2009) $120.63 hardcopy ISBN: 978-0-07-353563-0. The book is also available as an e-text for $66.50 180 day online or downloadable. The hardcopy has been ordered at both the Hunter College Bookstore and at Shakespeare's. The e-text may be obtained by going to www.coursesmart.com. Click on for Students and follow prompts