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This is
Introductory Logic
PHI 120
Get a syllabus online,if you don't already have onehttp://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 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!
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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
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 QSince not PQ follows
Either P or QNot QSo 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., BarbaraAll 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
errors in reasoning other than false premises.
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• Valid Argument Valid Form
• Invalid Argument Invalid Form
Form of BarbaraAll A are BAll B are C--------------All A are C
Form of Modus Ponens (->E)If A, then BA--------------B
Form of Undistributed MiddleAll A are BAll C are B--------------All C are A
Form of Denying the AntecedentIf A, then Bnot 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 statementsTo say an argument is true, makes no sense!
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TRUTHGood 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
Validityversus
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.
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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