This is Introductory Logic PHI 120

1. Presentation: "Good Arguments" Please turn off all cell phones! This isIntroductory LogicPHI 120 Get a syllabus online, if you don't already have one http://sweb.uky.edu/~rsand1/phi120/

2. Homework for Next Lecture • Allen/Hand, The Logic Primer(“a text of minimal chattiness”) • Pay special attention to: • Section 1.1, p. 1-2 • study definitions: argument, validity, soundness • Section 1.2: p. 3-5 • Study concepts: formal language, vocabulary, connectives (p. 4-5), metavariable • Section 1.3: read p. 10-15 • Exercise 1.3: 1-25

3. MW 10:00 am - 10:50 am CB 118 • 001 M 3:00 pm - 3:50 pm • 002 M 9:00 am - 9:50 am • 003 M 11:00 am - 11:50 am • 004 M 12:00 pm - 12:50 pm • 005 M 1:00 pm - 1:50 pm • 006 M 2:00 pm - 2:50 pm • 007 F 9:00 am - 9:50 am • 008 F 10:00 am - 10:50 am • 009 F 11:00 am - 11:50 am MW 1:00 pm - 1:50 pm BioSci 107 • 010 F 12:00 pm - 12:50 pm • 011 F 1:00 pm - 1:50 pm • 012 F 2:00 pm - 2:50 pm • 013 M 8:00 am - 8:50 am • 014 W 8:00 am - 8:50 am • 015 W 9:00 am - 9:50 am • 016 W 10:00 am - 10:50 am • 017 W 11:00 am - 11:50 am • 018 W 12:00 pm - 12:50 pm Memorize your section number!

4. Good Arguments The Criteria

5. A Good Argument (p.25) (A) Given the premises, the conclusion follows with either • deductive validityor • inductive strength. and (B) The premises are true.”

6. A Good Argument (A) Inferential connection • Deductive validity or • Inductive strength (B) True premise(s) • Empirical statementsvs. • Non-empirical statements Either or, but not both

7. Good Arguments (A) Inferential Connection─ the way the conclusion follows from premises─

8. Inferential Connection: 2 Kinds “the way the conclusion follows” • Validity: Deductive arguments • Necessary connection between premises and conclusion • Inferential Connection is one of certainty • Strength: Inductive Arguments • Unnecessary or contingent connection • Inferential connection is one of probability

9. Inferential Connection: 2 Kinds • Validity: Deductive arguments • Necessary connection between premises and conclusion • Inferential Connection is one of certainty • Strength: Inductive Arguments • Unnecessary or contingent connection • Inferential connection is one of probability There are 80 women and 20 men in this room. I am going to pick a person at random. So I would likely select a woman.

10. Inferential Connection • Inductive Arguments: conclusion follows with some degree of probability Three sorts: • Generalizations • Causal arguments • Analogies

11. Inferential Connection • Inductive Arguments: conclusion follows with some degree of probability Three sorts: • Generalizations • Causal arguments • Analogies • Conclusion • might be true • might be false • Inference • stronger • weaker

12. Inferential Connection: 2 Kinds • Validity:Deductive arguments • Necessary connection between premises and conclusion • Conclusion follows with certainty Either you are a man or a woman. Since you are not a man, it follows that you are a woman. An integer is either even or odd. The integer 2 is not odd. So it is even. EitherPorQ SincenotP Qfollows EitherPorQ NotQ So P

13. Logical Form Deductive Arguments

14. Logical Form • Valid form, e.g., Barbara All A are B All cats are carnivores. All B are C All carnivores are predators. -------------- -------------------------------------- All A are C All cats are predators. • This is a valid argument form. • There is a necessary connection between A and C • Hence, this is a deductively valid argument

15. Logical Form • Other valid forms: Modus Ponens (or "->E rule") If A, then B If a person is a man, then he cannot give birth. AThe person is a man. -------------- ---------------------------------------------------------------- B Thus he cannot give birth. The conclusion is necessarily true, given the premises.

16. Logical Form • Other valid forms: Modus Tollens If A, then B If a person is a man, then he cannot give birth. notBThis person can give birth, though. -------------- ---------------------------------------------------------------- notA Hence she is not a man. The conclusion is necessarily true, given the premises.

17. Logical Form • Other valid forms: Disjunctive Syllogism (or "vE rule") Either A or B An integer is either even or odd. notA The integer 3 is not even. -------------- -------------------------------------- B Therefore the integer 3 is odd. The conclusion is necessarily true, given the premises.

18. Logical Form errors in reasoning other than false premises. • Formal Fallacies • No necessary connection between premises and conclusion Fallacy of “Undistributed Middle” All A are B All cats are carnivores. All C are B All dogs are carnivores. -------------- -------------------------------------- All C are A All dogs are cats. Not a Valid Argument

19. Logical Form • Valid Argument Valid Form • Invalid Argument Invalid Form Form of Barbara All A are B All B are C -------------- All A are C Form of Undistributed Middle All A are B All C are B -------------- All C are A Form of Modus Ponens (->E) If A, then B A -------------- B Form of Denying the Antecedent If A, then B not A -------------- not B

20. Good Arguments (B) True premise(s)

21. A Good Argument • “One in which (A) given the premises, the conclusion follows from them either with deductive validity or inductive strength,and (B) the premises are true.” (p.25)

22. STOP! Validity and Strength concern arguments Truth and Falsity concern statements To say an argument is true, makes no sense!

23. Good Arguments Truth

24. Statements (p.40) • empirical statements─ truth verifiable in principle by experience • assertions of statistical probability • “45% of Kentuckians over 50 years of age smoke or ingest tobacco” • statements of historical fact • “Caesar crossed the Rubicon in 49 B.C.” • statements of observation • “The far side of the moon never receives direct light from the sun.”

25. Statements (p.40) • non-empirical statements─ truth in principle not verifiable by experience • mathematical formulas • “25 times 5 equals 100” • Statements of identity • “A rose is a rose.” • Definitions • “A foot is the measure of twelve inches.”

26. Sound Deductive Arguments Study This Concept At Home Validity versus Soundness

27. A Good Argument • “One in which (A) given the premises, the conclusion follows from them either with deductive validity or inductive strength, and(B) the premises are true.” (p.25) A good deductive argument is a sound argument. • question: what kind of statement is this? • Empirical? or • Non-empirical?

28. Validity versus Soundness All sound arguments are valid, but not all valid arguments are sound. • Properties of deductive arguments • Valid Argument: An argument whose conclusion follows necessarily from given premises • Sound Argument: A valid argument whose premises are all true. • Validity ≠ soundness

29. Summary • Good arguments have two criteria • The manner by which the conclusion follows from given premises • Deductively valid • Sound Argument = valid + all true premises • Invalid • Inductively strong • Inductively weak • True premise(s) • Empirical vs. non-empirical statements • Truth vs. Validity/Strength • Arguments are neither true nor false

30. Homework for Next Lecture • Allen/Hand, The Logic Primer(“a text of minimal chattiness”) • Pay special attention to: • Section 1.1, p. 1-2 • study definitions: argument, validity, soundness • Section 1.2: p. 3-5 • Study concepts: formal language, vocabulary, connectives (p. 4-5), metavariable • Section 1.3: read p. 10-15 • Exercise 1.3: 1-25