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

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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

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MW 10:00 am - 10:50 amCB 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!

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Good Arguments The Criteria

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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.”

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

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

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Inferential Connection: 2 Kinds 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 “the way the conclusion follows”

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Inferential Connection: 2 Kinds 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 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.

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

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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 Conclusion might be true might be false Inference stronger weaker Inference stronger weaker

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Inferential Connection: 2 Kinds A.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. Either P or Q Since not P Q follows Either P or Q Since not P Q follows Either P or Q Not Q So P An integer is either even or odd. The integer 2 is not odd. So it is even.

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Logical Form Deductive Arguments

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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

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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. A The person is a man. -------------- ---------------------------------------------------------------- B Thus he cannot give birth. The conclusion is necessarily true, given the premises.

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

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

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Logical Form 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 Not a Valid Argument errors in reasoning other than false premises.

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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 Barbara All A are B All B are C -------------- All A are C Form of Modus Ponens (->E) If A, then B A -------------- B Form of Modus Ponens (->E) If A, then B A -------------- B Form of Undistributed Middle All A are B All C are B -------------- All C are A 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 Form of Denying the Antecedent If A, then B not A -------------- not B Logical Form

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Good Arguments (B) True premise(s)

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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)

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STOP! Validity and Strength concern arguments Truth and Falsity concern statements

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TRUTH Good Arguments

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Statements (p.40) 1.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.”

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Statements (p.40) 2.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.”

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

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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?

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Validity versus Soundness 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 All sound arguments are valid, but not all valid arguments are sound. All sound arguments are valid, but not all valid arguments are sound.

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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

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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

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