### 3 Basic Types of Reasoning

```2 Basic Types of Reasoning
Deductive
 Inductive

Deductive Reasoning
Attempts to provide sufficient (or
conclusive) evidence for the conclusion
 Deductive reasoning can be recognized by
the structure of the argument and
sometimes by the conclusion offered

Inductive Reasoning
Attempts to make the conclusion probable
or likely—evidence is not intended to be
conclusive
 Typically recognized by probabilistic
claims in either or both of the premises
and conclusions
 Includes statistical and demographic
reasoning, predictions, analogies and
explanations

Some Examples
Either Bob or Joe was going to win the
award. Bob didn’t win, so Joe must have.
 I think Wayne committed the murder. He
bloody glove was found on the scene, and
he has no alibi.
 I’m sure Alice knows how to swim. After
all, most people know how to swim.

More Examples
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If you stop smoking, you’ll live longer. Current
research shows that on average, non-smokers
live 5.5 years longer than smokers.
If we stick with our current quarterback, our team
probably won’t get any better. He’s had a few
years now, and we haven’t improved yet.
Perhaps it’s time for someone new.
Since 2 x 2=4, and 22 is the same as 2 x 2, then
22=4.
Judging Validity
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A deductive argument is judged on 2 criteria:
validity and soundness
An argument is valid if the truth of the premises
would guarantee the truth of the conclusion
An argument is invalid if the conclusion could be
false even if all the premises are true
N.B.: This judgment is purely formal—it has
nothing to do with the truth of either premises or
conclusions
Some Examples
Either the kitchen is on fire, or my pot
roast is burning. I can see the kitchen’s
not on fire, so my pot roast must be
burning.
 All CEOs are wealthy. Martin is wealthy,
so he must be a CEO.
 Only Democrats would vote for Hilary
Clinton. Wade is a Democrat, so he must
have voted for Hilary.

More Examples
Deceptive advertising is no different from
lying. Since lying is wrong, so too is
 Republicans support tax cuts for the
wealthy. George is a Republican, so he
must support tax cuts for the wealthy.
 Republicans support tax cuts for the
wealthy. John supports tax cuts for the
wealthy, so he must be a Republican.

Argument Forms
There are some argument form that are
always valid
They are: Modus Ponens, Modus Tollens,
Categorical Syllogism, Disjunctive
Syllogism, Hypothetical Syllogism and
Constructive Dilemma
Argument Forms Continued
There are two argument structures that are
always invalid.
They are: Affirming the Consequent and
Denying the Antecedent
Soundness and Unsoundness
A deductive argument is sound is (1) it is
valid, and (2) its premises are true.
 A deductive argument is unsound if either
(1) it is invalid, or (2) it is valid, but at least
one premise is false
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Some Examples
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All men are mortal. Socrates is a man, therefore
Socrates is mortal.
Either the moon is made or green cheese, or I’m
the Pope. Unfortunately, the moon IS made of
green cheese, so I’m sadly not the Pope.
If the General Manager was retained, our team’s
losing ways were bound to continue. Since I see
we aren’t winning yet, we must have retained the
General manager.
Only rock stars and athletes are wealthy. Since
Ellen is pretty wealthy, she must be either a rock
star or an athlete.
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