### Good Arguments

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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
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
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