• 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:Major premise: All pitchers hold water• Minor premise:Minor premise: Tom Glavin is a pitcher• Conclusion: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:major premise: All cats have 9 lives

minor premise:minor premise: “Whiskers” is a cat

conclusion: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 validvalid if its structure conforms to the rules of formal logic.• An argument is soundsound 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 Example of a valid, but unsound argumentunsound argumentmajor premise:major premise: All cats are pinkminor premise:minor premise: Felix is a catconclusion: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 Example of a valid and sound argumentsound argumentmajor premise:major premise: Anthrax is not a communicable diseaseminor premise:minor premise: Communicable diseases pose the greatest threat to public healthconclusion: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 syllogismsyllogism is a common form of deductive reasoning.

There are different types of syllogismscategoricalcategorical (universal premises)hypotheticalhypothetical (if-then premises)disjunctivedisjunctive (either-or premises)

All follow the basic form:major premiseminor premiseconclusion

Example of a valid categorical syllogism:

major premise:major premise: All Christians believe Jesus is the son of God.minor premise:minor premise: Biff is a Christian.conclusion: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:Major premise: If Biff likes Babbs, then he’ll ask her to the prom.

Minor premise:Minor premise: Biff likes Babbs,

Conclusion:Conclusion: Therefore, he’ll ask her to the prom.

Example of a valid disjunctive syllogism:

Major premise:Major premise: Either Babbs will get her navel pierced, or she’ll get a tongue stud.Minor premise:Minor premise: Babbs didn’t get her navel pierced.Conclusion:Conclusion: Therefore, Babbs got a tongue stud.

Major premise:Major premise: Any creature with six legs is an insect.Minor premise:Minor premise: . Dr. Gass has six legs.Conclusion:Conclusion: Therefore, Dr. Gass is an insect.

What kind of syllogism is this? (categorical, hypothetical, or disjunctive)

Are the premises true?Is the conclusion valid?Is the argument sound (true premises and a

valid conclusion)

Answer: Valid, but unsound

• 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 tried heroin has tried marijuana

Naomi hasn’t tried heroin

Therefore, Naomi hasn’t tried marijuana

A. affirming the consequent

B. denying the antecedent

C. undistributed middle term

D. valid syllogismAnswer: 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 syllogismAnswer: Affirming the Consequent

If A, then B

B

Therefore, A