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Please turn off all cell phones! Presentation: "Good Arguments" This is Introductory Logic PHI 120 Get a syllabus online, if you don't already have one http://sweb.uky.edu/~rsand1/phi120/ 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 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! Good Arguments The Criteria A Good Argument (p.25) (A) Given the premises, the conclusion follows with either deductive validity or inductive strength. and (B) The premises are true.” A Good Argument (A) Inferential connection – Deductive validity or – Inductive strength Either or, but not both (B) True premise(s) – Empirical statements vs. – Non-empirical statements Good Arguments (A) Inferential Connection ─ the way the conclusion follows from premises ─ Inferential Connection: 2 Kinds “the way the conclusion follows” A. Validity: Deductive arguments – Necessary connection between premises and conclusion • Inferential Connection is one of certainty B. Strength: Inductive Arguments – Unnecessary or contingent connection • Inferential connection is one of probability Inferential Connection: 2 Kinds A. Validity: Deductive arguments – Necessary connection between premises and conclusion • Inferential Connection is one of certainty There are 80 women and 20Arguments men in this room. I am B. Strength: Inductive going to pick a person at random. So I would likely –select Unnecessary a woman. or contingent connection • Inferential connection is one of probability Inferential Connection B. Inductive Arguments: conclusion follows with some degree of probability Three sorts: – Generalizations – Causal arguments – Analogies Inferential Connection B. 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 Inferential Connection: 2 Kinds A. Validity: Deductive arguments you are connection a man or a woman. Sincepremises you are not a –Either Necessary between and man, it follows that you are a woman. conclusion integer is either even or odd. The integer 2 –AnConclusion follows with certainty is not odd. So it is even. Either P or Q Since not P Q follows Either P or Q Not Q So P Logical Form Deductive Arguments Logical Form • Valid form, e.g., Barbara All A are B All B are C -------------All A are C All cats are carnivores. All carnivores are predators. -------------------------------------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 Logical Form • Other valid forms: Modus Ponens (or "->E rule") If A, then B A -------------B If a person is a man, then he cannot give birth. The person is a man. ---------------------------------------------------------------Thus he cannot give birth. The conclusion is necessarily true, given the premises. Logical Form • Other valid forms: Modus Tollens If A, then B not B -------------not A If a person is a man, then he cannot give birth. This person can give birth, though. ---------------------------------------------------------------Hence she is not a man. The conclusion is necessarily true, given the premises. Logical Form • Other valid forms: Disjunctive Syllogism (or "vE rule") Either A or B not A -------------B An integer is either even or odd. The integer 3 is not even. -------------------------------------Therefore the integer 3 is odd. The conclusion is necessarily true, given the premises. Logical Form errors in reasoning other • Formal Fallacies than false premises. – No necessary connection between premises and conclusion Fallacy of “Undistributed Middle” All A are B All C are B -------------All C are A All cats are carnivores. All dogs are carnivores. -------------------------------------All dogs are cats. Not a Valid Argument Logical Form • Valid Argument Valid Form Form of Barbara All A are B All B are C -------------All A are C Form of Modus Ponens (->E) If A, then B A -------------B • Invalid Argument Invalid Form Form of Undistributed Middle All A are B All C are B -------------All C are A Form of Denying the Antecedent If A, then B not A -------------not B Good Arguments (B) True premise(s) 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) STOP! Validity and Strength concern arguments Truth and Falsity concern statements Good Arguments TRUTH Statements (p.40) 1. empirical statements ─ truth verifiable in principle by experience • assertions of statistical probability – • statements of historical fact – • “45% of Kentuckians over 50 years of age smoke or ingest tobacco” “Caesar crossed the Rubicon in 49 B.C.” statements of observation – “The far side of the moon never receives direct light from the sun.” Statements (p.40) 2. non-empirical statements ─ truth in principle not verifiable by experience • mathematical formulas – • Statements of identity – • “25 times 5 equals 100” “A rose is a rose.” Definitions – “A foot is the measure of twelve inches.” Sound Deductive Arguments Study This Concept At Home Validity versus Soundness 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? Validity versus Soundness arguments are valid, • PropertiesAllofsound deductive arguments but not all valid arguments are sound. – Valid Argument: An argument whose conclusion follows necessarily from given premises – Sound Argument: A valid argument whose premises are all true. • Validity ≠ soundness Summary • Good arguments have two criteria 1. The manner by which the conclusion follows from given premises • Deductively valid – Sound Argument = valid + all true premises • Invalid – Inductively strong – Inductively weak 2. True premise(s) • Empirical vs. non-empirical statements • Truth vs. Validity/Strength – Arguments are neither true nor false 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