TA Section: Th TBA
Course Description Logic is the study of valid demonstrative argumentation. A valid argument is one whose premises imply its conclusion. Implication is in turn a matter of argumentative structure. One statement implies another if the form of the two statements guarantees that if the first is true, then the second must also be true. Logic thus begins with an abstract analysis of language designed to expose the form of statements. We will undertake this analysis by learning to paraphrase English statements with sentences of a more perspicuous notation. Armed with our analysis, we will proceed to a rigorous definition of implication. We will then develop formal methods for ascertaining the implication of one statement by others, and reflect philosophically upon what we have thereby achieved.
Our course is split into two units. The first unit treats truth-functional logic, those aspects of logical structure which emerge out of reflection on English expressions such as “and,” “not,” “either …or,” and “if … then,” which are used to combine statements into compound statements. The second unit extends our results by examining the logical structure revealed by the behavior of such words as “every,” “each,” “all,” “some,” “none,” and “it”—words essential for the expression of generality.
Logic may sound like a dry subject. Indeed, it is a dry subject. After all, “and,” “not,” and “every” are dull words compared with those you examine in other courses, such as “atom,” “matrix,” “biotic,” “vascular,” “virus,” “inflation,” “democracy,” “heteronormative,” “patriarchy,” “justice,” and “god.” But our humble logical words occur in discourse on every subject matter whatsoever. Studying logic reveals a framework to which thought on any subject must conform on pain of incoherence. Our class will uncover the principles that underlie the aggregation of knowledge. Logic’s interest lies in its unique abstractness, and in the combination of that abstractness with mathematical rigor.
This will be a theoretical course, not a practical “how-to-think” course. However, the logical techniques we will study will give you an enhanced grasp of the logical structure of English sentences, and thinking about these techniques will afford an experience of abstract, rigorous thinking. These two benefits will contribute to your ability to critically analyze both your own reasoning and the reasoning of others.
Course Requirements Problem Sets – 50%
You will be assigned a problem set at the end of each Wednesday class. You must submit your solutions to these problems in class the following Monday. Late submissions will not be graded. Electronic submissions are not allowed. There will be no make-up problem sets. Your lowest problem set score will be dropped in determining this portion of your grade. You are encouraged to talk with each other about the problem sets, but the final written work that you turn in must be your own.
Midterm Exam – 20%
There will be a two-hour midterm exam on Wednesday July 17. Make-up midterm exams will be given only to students who provide an acceptable and documented reason for missing the exam.
Final Exam – 30%
There will be a cumulative three-hour final exam on Wednesday August 7. Make-up final exams will be given only to students who provide an acceptable and documented reason for missing the exam.
How to do well in this class Come to class prepared. Being prepared means that you have completed the assigned reading, thought carefully about it, and have begun to formulate questions concerning any issues which it raises. Give yourself time to complete the problem sets. If you run into difficulties, turn in what you have managed to finish, and make a note to carefully attend to the worked solutions provided in the next class. It will behoove you to practice with further problems until you are confident that you have understood your earlier mistake. Logic has a steep learning curve. The concepts which we will investigate in this class are initially straightforward, but do not be fooled: if you are not vigilant in keeping up with the assigned material you will quickly fall behind.
Plagiarism and Academic Integrity Any student who plagiarizes any assignment in this course will have their case referred to the Administrative Board of the Summer School, with the likely penalty of being required to withdraw. If you are unsure about what constitutes plagiarism, see me before you turn in any work. You can find Harvard Summer School’s policies on academic integrity here: http://www.summer.harvard.edu/exams-grades-policies/student-responsibilities#integ
Textbook Goldfarb, Warren. Deductive Logic (DL). Indianapolis: Hackett Publishing Co., 2003.
Class Reading Schedule 1. Monday June 24 Statements; Conjunction and Negation DL § 1-3
2. Wednesday June 26 Disjunction, Conditional, and Paraphrase DL § 4-8
3. Monday July 1 Interpretation and Validity DL § 9-11, 13
4. Wednesday July 3 Use and Mention; General Laws DL § 12, 14
5. Monday July 8 DNF and Expressive Adequacy DL § 15-16
6. Wednesday July 10 Truth-functional deductions (DL supplement §14a)
7. Monday July 15 Truth-functional deductions continued (DL supplement §14b)
8. Wednesday July 17 Conclusion of truth-functional deductions DL §18-20
MID-TERM EXAM 9. Monday July 22 Monadic Quantification Theory DL §21-24
10. Wednesday July 24 Polyadic Quantification Theory DL § 28-29
11. Monday July 29 Interpretation and Validity DL § 30-31
12. Wednesday July 31 Deduction and Identity DL §32-34, 41
13. Monday August 5 Names and Descriptions DL §42-44
14. Wednesday August 7 FINAL EXAM