1. 1

2. 2 Day 1Intro Day 2Chapter 1 Day 3Chapter 2 Day 4Chapter 3 Day 5Chapter 4 Day 6Chapter 4 Day 7Chapter 4 Day 8EXAM #1 40% of Exam 1 60% of Exam 1 warm-up

3. 3

4. 4 science of reasoning Logic is the science of reasoning, which is to say: the academic discipline that investigates reasoning.

5. 5 reasoning is inferring (deducing) to infer is to draw conclusions (output) from premises (input).

6. 6 words/ideas related to ‘draw’ both words mean to pull an often used cognate of ‘draw’ is ‘draft’ (‘draught’)

7. 7

8. 8 You see smoke, (input) and you infer (deduce) that there is fire. (output) You count 19 in a group, (input) which originally had 20,(input) and you infer (deduce) that someone is missing.(output)

9. 9 arguments Logic evaluates reasoning in terms of arguments.

10. 10 ar·gu·ment (är “ gy … -m … nt) n. 1.a. A discussion in which disagreement is expressed; a debate. b. A quarrel; a dispute. c. Archaic. A reason or matter for dispute or contention: “sheath'd their swords for lack of argument” (Shakespeare). 2.a. A course of reasoning aimed at demonstrating truth or falsehood: presented a careful argument for extraterrestrial life. b. A fact or statement put forth as proof or evidence; a reason: The current low mortgage rates are an argument for buying a house now. 3.a. A summary or short statement of the plot or subject of a literary work. b. A topic; a subject: “You and love are still my argument” (Shakespeare). 4. Logic. The minor premise in a syllogism. 5. Mathematics. a. The independent variable of a function. b. The amplitude of a complex number. 6. Computer Science. A value used to evaluate a procedure or subroutine. [Middle English, from Old French, from Latin arg ¿ mentum, from arguere, to make clear. See ARGUE.] [American Heritage Dictionary]

11. 11 argument an argument is a collection of statements, one of which is designated as the conclusion, and the remainder of which are designated as the premises.

12. 12 statement A statement is a declarative sentence, i.e., a sentence that is capable of being true or false. Kinds of sentence  declarative  interrogative  imperative  exclamatory  performative Example the window is shut is the window shut? shut the window $%&@!!!! I hereby …

13. 13 there is smoke(premise) therefore, there is fire (conclusion) there are 19 persons currently(premise 1) there were 20 persons originally (premise 2) therefore, someone is missing(conclusion)

14. 14 1.are all the premises true? 2.does the conclusion follow from the premises? 1.do the premises rest on the facts? 2.does the conclusion rest on the premises? Alternatively,

15. 15

16. 16 it is both factually correct and valid. sound its conclusion follows from its premises valid all its premises are truefactually correct if and only ifan argument is

17. 17 therefore McHale is taller than Bird Parish is taller than McHale Parish is taller than Bird

18. 18

19. 19 Example 1 YESsound? YESvalid? YESfactually correct? T / Parish is taller than Bird T McHale is taller than Bird T Parish is taller than McHale

20. 20 Example 2 NOsound? YESvalid? NOfactually correct? F / Bird is taller than Parish F McHale is taller than Parish F Bird is taller than McHale

21. 21 Example 3 NOsound? NOvalid? YESfactually correct? T / McHale is taller than Bird T Parish is taller than Bird T Parish is taller than McHale

22. 22 Example 4 NOsound? NOvalid? NOfactually correct? F / Bird is taller than Parish F McHale is taller than Bird F McHale is taller than Parish

23. 23 Whether an argument is valid or invalid is determined entirely by its form. validity is a function of form

24. 24 If an argument is valid, then every argument with the same form is also valid. If an argument is invalid, then every argument with the same form is also invalid.

25. 25 In order to show that an argument is invalid, counterexample it is sufficient to find a counterexample to it.

26. 26 Consider an argument; call it . counterexample Then a counterexample to  is (by definition) any argument  * with the following properties: same form 1.  * has the same form as  ; true premises 2.  * has all true premises; false conclusion 3.  * has a false conclusion.

27. 27 Argument is taller than Parish is taller than McHale is taller than Parish is taller than Bird is taller than / McHale is taller than Bird T T T T T F Form is taller than is taller than is taller than X is taller than Y X is taller than Z / Y is taller than Z Counterexample is tallerthan The Library is taller than PeeWee Herman is taller than The Library is taller than Arnold Swarzenegger is taller than / PeeWee H. is taller than Arnold S.

28. 28

29. 29 Argument allare all UMass students are high school graduates someare some high school graduates are athletes someare / some UMass students are athletes T T T T T F allare someare someare Form all X are Y some Y are Z / some X are Z Counterexample allare all UMass students are high school graduates someare some high school graduates are U.S. senators someare / some UMass students are U.S. senators

30. 30