• Definition: “reasoning from known
premises, or premises presumed to be
true, to a certain conclusion.”
• In contrast, most everyday arguments
involve inductive reasoning.
• reasoning from uncertain premises to
probabalistic conclusions
• “inference-making”
• Formal logic cannot
establish the truth of the
premises. The truth of the
premises must be
presumed, or taken as a
given.
• Some premises may be
proven or authenticated by
scientific testing, reference
to external sources, etc.
• Some premises may be
granted or stipulated by all
the parties to an argument
• Some premises may have
been established as the
conclusion of a previous
argument
• DNA testing and
paternity
• If a DNA sample is
collected and analyzed
properly and,
• If the DNA is an exact
match with the alleged
father,
• Then that person is the
father.
• There is no middle
ground. A deductive
argument can’t be
“sort of” valid.
• By contrast, everyday
arguments enjoy
degrees of probability-plausible, possible,
reasonable, believable,
etc.
• The fundamental property of a valid, deductive
argument is that IF the premises are true, THEN
the conclusion necessarily follows.
• The conclusion is said to be “entailed” in, or
contained in, the premises.
• If all pigs have curly tails
• And Nadine is a pig
• Then Nadine has a curly tail
• If the meanings of key terms are vague or
ambiguous, or change during the course of a
deductive argument, then no valid conclusion may
be reached.
• Major premise: All pitchers hold water
• Minor premise: Tom Glavin is a pitcher
• Conclusion: Therefore, Tom Glavin holds water
(the term “pitcher” has two different meanings in
this argument, so no valid conclusion can be
reached)
major premise: All cats have 9 lives
minor premise: “Whiskers” is a cat
conclusion: Therefore, Whiskers has 9 lives
(Note: it doesn’t matter whether cats really
have 9 lives; the argument is premised on
the assumption that they do.)
• An argument is valid if its structure conforms
to the rules of formal logic.
• An argument is sound if it is valid, and its
premises are true.
• Thus validity is a prerequisite for soundness,
but an argument needn’t be sound to be
valid.
• If sound, then valid too
• If valid, not necessarily sound
Example of a valid, but
unsound argument
major premise: All cats
are pink
minor premise: Felix is a
cat
conclusion: Therefore,
Felix is pink
(Cats aren’t pink, which
makes the first premise
untrue. Validity, however,
presumes the truth of the
premises.)
Example of a valid and sound
argument
major premise: Anthrax is not
a communicable disease
minor premise:
Communicable diseases
pose the greatest threat to
public health
conclusion: Therefore,
anthrax does not pose the
greatest threat to public
health
(The premises are true and
the conclusion is valid, that is,
it necessarily follows from the
premises)
The syllogism is a common form of deductive
reasoning.
There are different types of syllogisms
categorical (universal premises)
hypothetical (if-then premises)
disjunctive (either-or premises)
All follow the basic form:
major premise
minor premise
conclusion
Example of a valid categorical syllogism:
major premise: All Christians believe Jesus
is the son of God.
minor premise: Biff is a Christian.
conclusion: Biff believes Jesus is the son of
God.
(Note: validity isn’t affected by whether the
premises are true or not. Obviously, other religions
don’t accept Jesus as the son of God.)
Example of a valid hypothetical syllogism:
Major premise: If Biff likes Babbs, then he’ll
ask her to the prom.
Minor premise: Biff likes Babbs,
Conclusion: Therefore, he’ll ask her to the
prom.
Example of a valid disjunctive syllogism:
Major premise: Either Babbs will get her
navel pierced, or she’ll get a tongue stud.
Minor premise: Babbs didn’t get her navel
pierced.
Conclusion: Therefore, Babbs got a tongue
stud.
Major premise: Any creature with six legs is
an insect.
Minor premise: . Dr. Gass has six legs.
Conclusion: Therefore, Dr. Gass is an insect.
What kind of syllogism is this? (categorical,
hypothetical, or disjunctive)
Are the premises true?
Answer: Valid, but
Is the conclusion valid?
unsound
Is the argument sound (true premises
and a valid
conclusion)
• Affirming the consequent
• Invalid Example:
• If A, then B
•B
• Therefore, A
• Invalid Example:
• Students who plagiarize are expelled from
school
• Rex was expelled from school
• Rex must have plagiarized
• Denying the antecedent
• Invalid example:
• If A, then B
• Not A
• Therefore, not B
• Invalid example:
• If you exceed the speed limit, you’ll get a
ticket.
• I’m not exceeding the speed limit.
• Therefore, I won’t get a ticket.
• Undistributed middle term:
• Valid example:
• All A are B
• All B are C
• Therefore, all A are C
• Invalid example
• All A are B
• All C are B
• Therefore, all A are C
The middle term, B,
must serve as the
subject of one premise,
and the predicate of
another premise, but
cannot occur in the
conclusion
• Undistributed middle term:
• Invalid example:
• All humans need air to breathe
• All dogs need air to breathe
• Therefore, all humans need dogs
All rock stars want to
become movie
stars
Morton wants to
become a movie
star
Therefore, Morton
must be a rock star
A. affirming the
consequent
B. denying the
antecedent
C. undistributed
middle term
D. valid syllogism
Answer:
Undistributed Middle
Term
Anyone who has
lived in California for
more than a few
years has
experienced an
earthquake
Nadine has lived in
California for more
than a few years
Nadine has
experienced an
earthquake
A. affirming the
consequent
B. denying the
antecedent
C. undistributed
middle term
D. valid syllogism
Answer: Valid
Syllogism
Anyone who has
A. affirming the
tried heroin has
consequent
tried marijuana
B. denying the
Naomi hasn’t tried
antecedent
heroin
C. undistributed
Therefore, Naomi
middle term
hasn’t tried
D. valid syllogism
marijuana
Answer: Denying the Antecedent
If A, then B
Not A
Therefore, not B
All Christian
fundamentalists are
opposed to
abortion
Nadine is opposed to
abortion
Nadine is a Christian
fundamentalist
A. affirming the
consequent
B. denying the
antecedent
C. undistributed
middle term
D. valid syllogism
Answer: Affirming the Consequent
If A, then B
B
Therefore, A