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INTRO LOGIC

INTRO LOGIC. DAY 02. Schedule for Unit 1. warm-up. 40% of Exam 1. 60% of Exam 1. Chapter 1 Basic Concepts. What is logic?. Logic is the science of reasoning , which is to say: the academic discipline that investigates reasoning. What is reasoning?.

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INTRO LOGIC

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  1. INTRO LOGIC DAY 02

  2. Schedule for Unit 1 warm-up 40% of Exam 1 60% of Exam 1

  3. Chapter 1Basic Concepts

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

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

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

  7. Examples of Reasoning • 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)

  8. Basic Idea • Logic evaluates reasoning in terms of arguments.

  9. What is an argument? • 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]

  10. For purposes of logic… • 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.

  11. What is a 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 …

  12. Examples of Arguments • 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)

  13. 2 questions about an argument • 1. are all the premises true? • 2. does the conclusion follow fromthe premises? Alternatively, 1. do the premises rest onthe facts? 2. does the conclusion rest onthe premises?

  14. conclusion premises facts

  15. Definitions an argument is if and only if factually correct all its premises are true valid its conclusion follows from its premises sound it is both factually correctand valid.

  16. Example 1 Parish is taller than McHale McHale is taller than Bird therefore Parish is taller than Bird

  17. Example 1 Parish is taller than McHale T McHale is taller than Bird T / Parish is taller than Bird T factually correct? YES valid? YES sound? YES

  18. Example 2 Bird is taller than McHale F McHale is taller than Parish F / Bird is taller than Parish F factually correct? NO valid? YES sound? NO

  19. Example 3 Parish is taller than McHale T Parish is taller than Bird T / McHale is taller than Bird T factually correct? YES valid? NO sound? NO

  20. Example 4 McHale is taller than Parish F McHale is taller than Bird F / Bird is taller than Parish F factually correct? NO valid? NO sound? NO

  21. Fundamental Principle Of Logic • Whether an argument is valid or invalidis determined entirely by its form. validity is a function of form

  22. In other words… • If an argument is valid, • then every argument • with the same form • is alsovalid. If an argument is invalid, then every argument with the same form is alsoinvalid.

  23. Method Of Counterexamples • In order to show that an argument is invalid, • it is sufficient to find a counterexample to it.

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

  25. Example 1 • Argument • Parish is taller than McHale • Parish is taller than Bird • / McHale is taller than Bird T T T Form X is taller than Y X is taller than Z/ Y is taller than Z Counterexample The Library is tallerthan PeeWee Herman The Library is taller than Arnold Swarzenegger / PeeWee H. is taller than Arnold S. T T F

  26. Example 2 Argument all UMass students are high school graduates some high school graduates are athletes /some UMass students are athletes T T T Formall X are Ysome Y are Z/some X are Z Counterexample all UMass students are high school graduates some high school graduates are U.S. senators /some UMass students are U.S. senators T T F

  27. THE END

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