Logic in School Program

1. Logic in School Program Creighton University Director: Dr. Jinmei Yuan (jinmei@creighton.edu)Student Teachers: Mark Holmberg Andrew Trapp Jason Bodewitz Elizabeth Epsen http://www.youtube.com/watch?v=xrShK-NVMIU

2. Overview Meet every week • There will be quizzes (about every 2 weeks at the beginning of class), some homework assignments, tests, and in-class handouts/exercises • The quizzes could be unannounced • We will tell you the test dates in advance

3. Overview Part II • Typical schedule each day: • Journal exercise • Go over questions from homework/previous class lesson (if any) • Lesson • Example problems / questions • Assign homework problems / readings

4. Class Notes • Please raise your hand if you have a question or wish to answer one of ours • We want to encourage everyone to get involved in class, so even if you’re not sure of an answer for instance, still feel free to try to answer – we are all learning together 

5. Lesson 1: Basic ConceptsArguments, Premises, and Conclusions • Logic: the organized body of knowledge, or science, that evaluates arguments • Aim: to develop system of methods to use as criteria for evaluating arguments of others and for constructing our own; to determine good arguments from bad arguments • Syllogistic logic: developed by Aristotle (384-322 B.C.); a kind of logic in which the fundamental elements are terms, and arguments are evaluated as good or bad depending on how the terms are arranged in the argument • Modal logic: also by Aristotle, but includes concepts such as possibility, necessity, belief, and doubt

6. Arguments • Argument: a group of statements, one or more of which (premises) are claimed to provide support for, or reasons to believe, one of the others (conclusions) • Good argument: premises support the conclusion • Bad argument: premises do not support conclusion (even if they claim to)

7. Arguments • Made up of statements • Statement: a sentence that is either true (T) or false (⊥) • Melatonin helps relieve jet lag. (T) • No wives ever cheat on their husbands. (⊥) • Truth values (of a statement) • Many sentences, unlike statements, cannot be said to be T or ⊥ • Questions (Where is Tom?) • Proposals (Let’s go to a movie.) • Suggestions (I suggest you get contact lenses.) • Commands (Turn off the TV.) • Exclamations (Wow!)

8. Statements • Premises • Statements that set forth the reasons or evidence • Conclusions • Statements that the evidence is claimed to support or imply (claimed to follow from the premises)

9. Example of an Argument • Good Argument: • All film stars are celebrities. (Premise 1) • Halle Berry is a film star. (Premise 2) • Therefore, Halle Berry is a celebrity. (Conclusion) • Bad Argument: • Some film stars are men. • Cameron Diaz is a film star. • Therefore, Cameron Diaz is a man.

10. Conclusion Indicators • Therefore • Wherefore • Thus • Consequently • We may infer • Accordingly • We may conclude • It must be that • For this reason • So • Entails that • Hence • It follows that • Implies that • As a result

11. Premise Indicators • Since • As indicated by • Because • For • In that • May be inferred from • As • Given that • Seeing that • For the reason that • Inasmuch as • Owing to • Example: Expectant mothers should never use recreational drugs, since the use of these drugs can jeopardize the development of the fetus.

12. Indicators • Sometimes there are no indicators: • (Also, some passages that contain arguments contain statements that are neither premises nor conclusions) • The space program deserves increased expenditures in the years ahead. Not only does the national defense depend upon it, but the program will more than pay for itself in terms of technological spinoffs. Furthermore, at current funding levels the program cannot fulfill its anticipated potential.

13. Argument Reconstruction • Break up compound statements • Always list premises first, then conclusions:P1: The national defense is dependent upon the space program.P2: The space program will more than pay for itself in terms of technological spinoffs.P3: At current funding levels the space program cannot fulfill its anticipated potential.C: The space program deserves increased expenditures in the years ahead.

14. Inference & Proposition • Inference: the reasoning process expressed by an argument • “Inference=Argument” • Proposition: the meaning or information content of a statement • “Proposition=Statement”

15. Homework • Problems: Exercise 1.1 • Pages 7-9, Numbers 1-21 • Try these on your own; we will review some next class • Reading: Chapter 8 (Symbolic Logic) • Pages 299-309