Evaluating Deductive
Reasoning

Determine whether the argument’s
form (or structure) is valid or invalid.

Decide if the premises are true or
false.

A sound argument has both a valid
form and true premises.

An unsound argument has either an
invalid form, a false premise, or both.
Deduction and
Induction


In deductive reasoning,
the premises provide
conclusive support for
the truth of the
conclusion .
Any student who has
completed 12 or more
units with a GPA of 3.0
or higher is eligible to
join Alpha Gamma
Sigma. Gina has
completed 24 units and
her GPA is 3.2.
Therefore, Gina is
eligible to join Alpha
Gamma Sigma.

In inductive reasoning,
the premises provide
probabilistic support for
the conclusion.

Pace courses meet on
Saturdays. Since
Michelle drove off
Saturday with her book
bag, she is probably
taking a PACE course .
Signal Words

Words like must,
certainly, and

likely, it is
reasonable to
conclude, it is
plausible that,
necessarily
frequently signal
deductive
reasoning.

No Muslims eat
pork. Since Tariq
loves ham, he
must not be a
Muslim.
Words or phrases
like probably,
usually signal
inductive
reasoning.

Rose reads
her Bible at
work, so she
is probably a
believer.
Inductive or
Deductive?

A profession of certainty in matters of
religion is always a sign of religious
illiteracy. Since McArthur professes to
be certain about the truth of his religious
beliefs, we can infer that he is illiterate
about religion.

People who think we are living in the
“last days” of the universe are usually
not environmentalists. Since Hal
believes we are living in the “last days,”
it is safe to conclude that he is not an
environmentalist.

The Pope insists that Catholicism is the
only religion that is fully correct. Thus,
the Pope is not a pluralist.
Deductive Validity

A deductive
argument is valid
when it is
impossible for the
conclusion to be
false, if we
presume that the
premises are true.

All nuns are
pious. Helen is a
nun.
\ Helen is pious.
P
N
H
Deductive Arguments

Information content of the conclusion
is contained in the premises.

All artists are bohemians.
All bohemians are creative.

\ All artists are creative.

All A are B
All B are C
\ All A are C
Different content, same
form

All panthers are
predators.

All predators are
carnivores.

\ All panthers
are carnivores.

All A’s are B’s

All B’s are C’s

\ All A’s are C’s
Sound=Valid form +
true prem.s

All LAMC students are stressed people.

All stressed people are addicted to either, alcohol,
tobacco, chocolate, caffeine, exercise, or religion.

\ All LAMC students are addicted to either
alcohol, tobacco, chocolate, caffeine, exercise, or
religion.
Unsound?
What’s the missing
Premise?

All psychics are
pseudoscientists.

That’s why all
psychics are
unreliable.
What am I
wearing,
psychic
friend?
What Conclusion Follows?
What’s in
that
sandwich?
Logicians
Do it
Deductively

All Adventists are
vegetarians.

All vegetarians
are guiltless
eaters.

\?
Formal Fallacies

All Mormons are supernaturalists.

All Christians are supernaturalists.

\ All Mormons are Christians.
Valid or invalid?

All A’s are B’s

All C’s are B’s

\ A’s are C’s
Refutation by formal
analogy

All nuns are people

All priests are people

\ All nuns are priests

Same form, but obviously true
premises and false conclusion shows
that the form is invalid.
All A is B
All C is B
All A is C
Categorical Logic

A syllogism is an
argument having
two premises and
a conclusion.

There are four
types of
categorical
assertions.

A categorical
syllogism is made
up of assertions
about class
membership.

A: Universal
affirmative: All
Muslims are
monotheists.

E: Universal
Negative: No
Nuns are Priests.
Particular Categorical
Assertions

I: Particular
affirmative: Some
novelists are
alcoholics.

O: Particular
negative: Some
Hindus are not
vegetarians.

Overlapping circles can
represent these
assertions.
Some kittens are
playful.