Philosophy
6: Logic in Practice
Los Angeles Pierce College
Department of History, Philosophy, & Sociology
Lecture Notes
Lecture Notes for
"Chapter Eight" of Porter's The
Voice of Reason
Deductive Formal Arguments
"In deductive
thinking we reason from a broad claim to some specific conclusion that can be
drawn from it"
"We 'deduce' a
particular from a general statement"
Sub-classifications of Deductive Formal Arguments
"Deductive thinking
has three patters ... categorical, hypothetical, and disjunctive."
Using Categorical Arguments
Categorical claims aren't
just broad, but universal
Middle Term
A term is called a
"middle term" "because it appears twice in the premises."
Discerning Soundness
"Usually we can tell
offhand if an argument is correct, but that is not always the case. When we are uncertain whether a
conclusion does follow from the premises we have to use strict procedures to
test the validity of the reasoning."
Watch the Steps
Affirmative v. Negative
First,
determine whether the premises and conclusion individually have the
sub-attribute of being affirmative or negative.
Universal v. Particular
Second,
determine whether the premises and conclusion individually have the
sub-attribute of being universal or particular
The Logical Forms
All unicorns are creatures
that addle.
A All S is P Universal
affirmative
No unicorns are creatures
that addle.
E No S is P Universal negative
Some unicorns are
creatures that addle.
I Some S is P Particular affirmative
Some unicorns are not
creatures that addle.
O Some S is
not P Particular
negative
Distribution
A term is distributed if
it covers every member of the class
Third,
determine whether or not the terms are distributed.
Distribution for
A: All
S is P E.G.: All parrots are birds
For the subject term,
parrots, "we are referring to every single parrot, so the subject term is
distributed"
For the predicate term,
birds, "we are not talking about all birds, so the predicate term is not
distributed," or undistributed
Distribution for
E: No
S is P E.G: No wars are profitable
The subject term, war,
"is distributed because the claim is that, of the entire category of wars,
non is profitable"
The predicate term,
profitable, "is also distributed because no member of the class of profitable
things is also a war"
Distribution for
I:
Some S is P E.G.: Some diseases are tropical
The subject term,
diseases, is undistributed as only "some diseases are referred to"
The predicate term,
tropical, is undistributed as "tropical" "does not refer to all
things in the tropics but only a portion of them"
Distribution for
O:
Some S is not P E.G.: Some New Englanders are not friendly
The subject term, New
Englanders, is undistributed as we are not referring to all of the members of
the category of New Englanders
The predicate term,
friendly, is distributed, "[f]or the claim is that some New Englanders are
excluded from the entire class of friendly people"
Rules of Validity for Categorical Deductive
Arguments
1) "At least one of
the premises must be affirmative"
2) "If a premise is
negative then the conclusion must also be negative, and if the conclusion is
negative then a premise must be negative"
3) "The middle term
must be distributed at least once"
4) "Any term
distributed in the conclusion must also be distributed in a premise"
Steps to Analyzing Categorical Deductive Arguments
1) "Separate the
conclusion form the premises"
2) "Paraphrase the
sentences into standard form"
3) "Arrange the
statements into a categorical syllogism, completing any enthymemes"
4) "Judge the
validity of the syllogism in terms of the four rules, using the factors of
affirmative or negative and distribution"
5) "Determine whether
the premises and conclusion are true and the argument sound"
Hypotheticals
The If/Then Form
"A hypothetical
argument has an 'if/then' pattern."
"We say that,
provided one thing is true, then another thing would follow."
The Parts of Hypotheticals
Antecedent
Consequent
Valid Hypotheticals
Affirming the antecedent
Denying the consequent
Valid Hypothetical / Affirming the Antecedent
When the minor premise
affirms the antecedent of the major premise, the conclusion follows necessarily
E.G. Valid Hypothetical / Affirming
the Antecedent
If a horse has a single
horn, then it is a unicorn
The horse named Charlie
has a single horn
Charlie is a unicorn
Valid Hypothetical / Denying the Consequent
When the minor premise
denies the consequent of the major premise, the conclusion follows necessarily
E.G. Valid Hypothetical / Denying
the Consequent
If a horse has a single
horn, then it is a unicorn
Tonto's horse, Scout, is
not a unicorn
Scout is not a horse with
a single horn
Steps for Judging Hypothetical Arguments
1) "Arrange the
statements into hypothetical form"
2) "Judge the
argument's validity in terms of the rules"
3) "Determine whether
the premises and conclusion are true, and the argument sound"
Disjunctives
Either/Or Alternatives
True Disjunctives / One Disjunct
"One of the disjuncts has to be true, so if we know one of the alternatives
to be false, we can declare the other to be true and produce a valid
argument."
"It does not matter
which disjunct we eliminate; the one remaining must
be true."
E.G. True Disjunctives / One
Disjunct
Either Charlie is a
narwhal or a unicorn
Charlie is not a narwhal
So, Charlie is a unicorn
Rules for Disjunctive Validity
"In a valid
disjunctive argument we deny one of the disjuncts and
affirm the other."
"An invalid
disjunctive argument is one which we affirm one of the disjuncts
and deny the other."
Qualification to Rules for
Disjunctive Validity
"One qualification
should be mentioned. In some types
of disjuncts we do eliminate one part by affirming
the other."
E.G. Qualification to Rules
for Disjunctive Validity
Either Charlie is in
Candy-Mountain or he is On Big Rock Candy Mountain
Charlie is in
Candy-Mountain
So, Charlie is not on Big
Rock Candy Mountain
Disjunctive Safety
"To be on the safe
side, we should follow the rule of denying one disjunct
and affirming the other."
"That applies to all
valid disjunctive arguments, so if we operate this way we are sure of being
correct."
Invalid Disjunctive Argument / Both Disjuncts True
"Since both [disjuncts] might be true, one disjunct
is not eliminated when we affirm the other."
E.G. Invalid Disjunctive Argument / Both Disjuncts True
Either Charlie is a
unicorn or a magical creature
Charlie is a unicorn
So, Charlie is not a
magical creature
False Disjuncts / False
Dilemmas / False Aporias
"Although some issues
can be neatly divided into either/or alternatives, many others are more complex
than that."
"We should be careful
not to pose 'false disjuncts' that make it appear as
though only two choices are possible when the options are much wider than
that."
Steps for Judging Disjunctive Arguments
1) "Arrange the
statements into disjunctive form"
2) "Judge the
argument's validity in terms of the rules"
3) "Determine whether
the premises and conclusions are true, and the argument sound"