Logic in School Program Creighton University Director: Dr. Jinmei Yuan Student Teachers: Mark Holmberg Andrew Trapp Jason Bodewitz Elizabeth Epsen

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 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

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

Class Notes Please raise your hand if you have a question or wish to answer one of ours 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 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

Lesson 1: Basic Concepts Arguments, Premises, and Conclusions Logic: the organized body of knowledge, or science, that evaluates arguments 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 ( 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 Syllogistic logic: developed by Aristotle ( 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 Modal logic: also by Aristotle, but includes concepts such as possibility, necessity, belief, and doubt

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) 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)

Arguments Made up of statements Made up of statements –Statement: a sentence that is either true (T) or false ( ⊥ ) Melatonin helps relieve jet lag. (T) Melatonin helps relieve jet lag. (T) No wives ever cheat on their husbands. ( ⊥ ) No wives ever cheat on their husbands. ( ⊥ ) Truth values (of a statement) Truth values (of a statement) Many sentences, unlike statements, cannot be said to be T or ⊥ 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!)

Statements 1. Premises Statements that set forth the reasons or evidenceStatements that set forth the reasons or evidence 2. Conclusions Statements that the evidence is claimed to support or imply (claimed to follow from the premises)Statements that the evidence is claimed to support or imply (claimed to follow from the premises)

Example of an Argument  Good Argument: 1. All film stars are celebrities. (Premise 1) 2. Halle Berry is a film star. (Premise 2) 3. Therefore, Halle Berry is a celebrity. (Conclusion) Bad Argument: Bad Argument: 1. Some film stars are men. 2. Cameron Diaz is a film star. 3. Therefore, Cameron Diaz is a man.

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

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

Indicators Sometimes there are no indicators: Sometimes there are no indicators: (Also, some passages that contain arguments contain statements that are neither premises nor conclusions) (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.

Argument Reconstruction Break up compound statements 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. 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.

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

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