Logic is the anatomy of thought (John Locke)
Logic takes care of itself; all we have to do is look and see how it
does it. (LW)
Deduction
Induction
Fallacies
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The basic aim of deductive reasoning is to start
with some assumption or premise and extract from
it a conclusion—a logical consequence—that is
concealed but implicit in it.
Thus:
1a. Nuclear power poses more risks of harm to the
environment than fossil fuels.
 1b. Fossil fuels pose fewer risks of harm to the
environment than nuclear power.

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We may infer 1b from 1a.
The premise, 1a, implies the conclusion, 1b.
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However, the inference does not depend upon the truth
of the premise.
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Another example:
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Given 2a: that President Truman was underrated by
his critics.
I can infer 2b: that his critics underrated President
Truman.
Both propositions are equivalent, because the
rules of English grammar permit us to shift the
subject/predicate phrases without changing
the conditions that make the proposition true.
Remember:
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Even if a proposition follows from another
proposition, they need not be true.

If we claim that:
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3a. The Gettysburg Address is longer than the
Declaration of Independence.
 We know that 3a is false, but we may validly deduce that:

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3b. The Declaration of Independence is shorter than
the Gettysburg Address.
However, the inference is valid, because
conclusion follows logically (viz., deductively)
from 3a.
Rule: Valid conclusions are not necessarily
true.
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Texas is larger than California. (1st Premise)
California is larger than Arizona. (2nd Premise)
Texas is larger than Arizona. (Conclusion)
Rule: The conclusion is derivable from the two
premises.
If the two premises are true,
 then the conclusion must be true.

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The concept of being larger than has a quality
called transivity (351).
For example:
If A > B
 If B > C
 Then A > C

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Therefore, it follows from the premises that:
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If Texas is larger than California.
If California is larger than Arizona.
Then Texas is larger than Arizona.
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The validity of deductive inference is a formal
property of argument (352).
This syllogism is valid:
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African American slaves were treated worse than
white indentured servants.
Indentured white servants were treated worse than
free white labor.
Therefore, African American slaves were treated
worse than free white labor.
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If A, then B.
A
Then, B.
So, based upon the previous syllogism:
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If a youth is an African American slave, he is
probably treated worse than a youth in indentured
service.
This youth is an African American slave.
Therefore, he is probably treated worse than if he
had been an indentured servant.
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Valid deductive arguments that can only be
true if they have meaning.
The form of this syllogism is valid, but the
syllogism is not true, because it has no
meaning.
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If the slithy toves, then the gyres gimble.
The slithy toves.
Therefore, the gyres gimble.

False or meaningless conclusions can be drawn
from false or meaningless assumptions.
The Met has the finest collection of abstract
impressionist paintings in the world.
 The finest collection of abstract impressionist
paintings includes dozens of canvasses by Winslow
Homer.
 Therefore, the Met has dozens of paintings by
Winslow Homer.

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The conclusion follows, but all of the
propositions may be false.
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If President Truman knew the Japanese were
about to surrender, then is was immoral for
him to order that the atom bombs be dropped
on Hiroshima and Nagasaki.
Truman knew the Japanese were about to
surrender.
Therefore, it was immoral of him to order
dropping those bombs.
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The second premise (Truman knew) may be
true on moral grounds, not historical grounds.
The first premise (If Truman knew, then he was
immoral to drop the bombs), implies a
principle of moral responsibility.
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The truth of the conclusion, therefore, relies on our
acceptance of a general rule of moral responsibility.
To the extent we accept the premises as true, then we
decide if the premises prove the conclusion.
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Either censorship of television shows is
overdue, or our society is indifferent to the
education of its youth.
Our society is not indifferent to the education
of its youth.
Therefore, censorship of television is overdue.
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Assert a disjunction with two or more disjuncts in
the major premise; then deny all but one in the minor
premise; and infer the validity of the remaining
disjunct as the conclusion.
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Dilemmas occur when a forced choice between
two or more equally unattractive alternatives.
If the U.S. bombs targets in Libya, innocent people
will be killed, and the Arab world will be angered.
 If the U.S. doesn’t bomb Libyan targets, then
terrorists won’t be punished, and the U.S. will lose
respect among other governments.
 Either the U.S. bombs Libyan targets or it doesn’t.
Therefore, unattractive consequences will follow: the
terrorists will be killed, or terrorists will go
unpunished.
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If the President bombs terror sites in an African
country, she will prevent a horrible genocide.
If the President bombs the terror sites, African
terrorists (who have a top-secret air-traffic
control device) will down all American planes
in flight—thereby killing thousands of
Americans.
Either the President will bomb the terror sites
or not. Unattractive consequences will follow:
genocide will be prevented or Americans will
die.
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If Sophie chooses one of her children to die in
the gas chambers of Auschwitz, she and the
other child will live.
She will suffer, no matter whom she chooses.
She will either choose her son or daughter. She
will suffer. One of them will die in a gas
chamber.
Were there any ways out of the dilemma?