Transcript Good Arguments
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Presentation: "Good Arguments"
Introductory Logic PHI 120
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Homework for Next Lecture
Allen/Hand ,
The Logic Primer
(“a text of minimal chattiness”)
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Pay special attention to:
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Section 1.1, p. 1-2
–
study definitions: argument, validity, soundness
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Section 1.2: p. 3-5
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Study concepts: formal language, vocabulary, connectives (p. 4-5), metavariable
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Section 1.3: read p. 10-15
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Exercise 1.3: 1-25
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MW 1:00 pm - 1:50 pm BioSci 107
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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
B. Strength: Inductive Arguments
– going to pick a person at random. So I would likely Unnecessary 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 • •
Conclusion
might be true might be false – Causal arguments – Analogies • •
Inference
stronger weaker
Inferential Connection: 2 Kinds
A. Validity: Deductive arguments
– Necessary connection between premises and – Conclusion 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 B If a person is a man , then he cannot give birth .
A 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 A If a person is a man , then he cannot give birth .
not B 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
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than false premises.
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 .
Not a Valid Argument
All C are A All dogs are cats .
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, (B) the premises are true.” (p.25) and
STOP!
Validity and Strength concern arguments Truth and Falsity concern statements
Good Arguments
TRUTH
Statements (p.40)
1. empirical statements
principle by experience ─ truth verifiable in • –
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.”
Statements (p.40)
2. non-empirical statements
not verifiable by experience ─ truth in principle • –
mathematical formulas
“25 times 5 equals 100” • –
Statements of identity
“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.
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question: what kind of statement is this?
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Empirical?
or
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Non-empirical?
Validity versus Soundness
• Properties of 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