What is a logical argument?
What is deductive reasoning?
Fundamentals of Academic WritingLogical relations• Deductive logic– Claims to provide conclusive support for the truthof a conclusion• Inductive logic– Arguments support a conclusion, but do not claim
to show that it is necessarily trueDeductive logic• Categorical propositions– Deductive arguments are either valid or invalid.
– Premises are either true or not true.
– If the argument is valid and the premises are true,
then the conclusion is true.

Deductive logic• Categorical propositions– All S is P.
– No S is P.
– Some S is P.
– Some S is not P.

• Quantity: Some or All• Quality: Positive or Negative (no, not)

Deductive logic• Categorical propositions– All dogs are mammals.
– No dogs are fish.
– Some mammals are carnivores.
– Some mammals are not carnivores.

• The truth of a proposition is determined by its“fit” with the world.
– “Some mammals are carnivores” is true if and only
if there are some mammals that eat meat.

Deductive logic• Categorical propositions– “Physicians licensed to practice in Japan must pass theNational Medical Licensing Board Exam.”– All licensed physicians in Japan are people whopassed the Licensing Board Exam.
– All S is P.

Exercise• Create one or more categorical statements ofthe following types. Compare your statementswith your group members’.
– All S is P.
– No S is P. (= All S is not-P.)– Some S is P.
– Some S is not P.

Syllogisms• Syllogism: A conclusion inferred from twopremises
All Cretans are liars.
All liars are dishonest.
∴ All Cretans are dishonest.

Syllogisms
All Cretans are liars.
All liars are dishonest.
∴ All Cretans are dishonest.
– Major term: Predicate (“is P”) of the conclusion– Minor term: Subject (e.g. “All S”) of the conclusion– Middle term: Term in both premises that is not inthe conclusion

Syllogisms
All Cretans are liars.
All liars are dishonest.
∴ All Cretans are dishonest.
• Major term
• Minor term
• Middle term
• ∴ “Ergo”, Latin for “therefore”

Syllogisms
All enzymes are proteins.
All proteins are organic compounds.
∴ All enzymes are organic compounds.

Syllogisms
Some plankton is algae.
All algae consume CO2.
Therefore, some plankton consume CO2.
“Plankton helps reduce levels of CO2, since the algae inplankton consume CO2 from the environment.”Deductive logic• If the argument is valid and the premises aretrue, then the conclusion is true.
– Valid: The argument (relation of the premises)
necessarily entails the conclusion.
– True: The premises accurately reflect the world.

• Deductive logic is used to prove that theconclusion must be true (if the premises aretrue).

Deductive logic• If the argument is valid and the premises aretrue, then the conclusion is true.
– Valid (but not true)

Humans are animals.
All animals live under water.
Therefore, humans live under water.

Deductive logic• If the argument is valid and the premises aretrue, then the conclusion is true.
– True (but not valid)

Humans are animals.
Some animals live under water.
Therefore, humans sometimes live under water.

Deductive logic• If the argument is valid and the premises aretrue, then the conclusion is true.
Humans are animals.
All animals breathe.
Therefore, humans breathe.
• Deductive logic is used to prove that theconclusion must be true (if the premises aretrue).

Exercise• Work with your group members. Try to create
one or more valid (preferably true) syllogisms.
All S are M.
Carbon atoms are atoms.
All M are P.
All atoms have mass.
∴ All S are P. Therefore, carbon atoms have mass
(No S are M; Some S are M; Some S are not M; etc.)

Deductive logic• There are other deductive arguments, butsyllogism is probably the most commonly usedin most types of academic writing.
• Let’s look at how to turn a syllogism into an
academic paper.

Logic in writing

PremiseOur business has a reputation for poor service.
Businesses with a reputation for poor service have few
customers.
PremiseTherefore, our business has few customers.
Conclusion– If the argument is valid and the premises are true,
then the conclusion is true.

Logic in writing Valid

Our business has a reputation for poor service.
Businesses with a reputation for poor service have few
customers.
Therefore, our business has few customers.
– If the argument is valid and the premises are true,
then the conclusion is true.

Logic in writing• The paper will need one section showing that
“Our business has a bad reputation” is true.
• The next section will show “Businesses withbad reputations have few customers” is true.
• The conclusion section needs to show how thetrue premises and the valid argument prove
the author’s conclusion. (It will probably also
recommend changing the reputation.)

Logic in reading• When you read, ask yourself:– What is the conclusion?
– What is the argument? (In other words, what
premises lead to the conclusion?)– Is the argument valid?
– Are the premises true?

Logic in reading“I do not believe that we can have any freedom in thephilosophical sense, for we act not only under external
compulsion but also by inner necessity.”– Albert EinsteinLogic in reading“I do not believe that we can have any freedom in thephilosophical sense, for we act not only under external
compulsion but also by inner necessity.”– Albert Einstein• What is the conclusion?
– People are not free. (All people are not free.)Logic in reading“I do not believe that we can have any freedom in thephilosophical sense, for we act not only under external
compulsion but also by inner necessity.”– Albert Einstein• What are the premises?
– People act under compulsion and necessity.
– (The other premise is not stated, but implied.)Things acting under compulsion are not free.

Logic in reading• Is the logic valid?
– All people are under compulsion and necessity.
– All things under compulsion and necessity are notfree.
– Therefore, all people are not free.
 Valid

Logic in reading“I do not believe that we can have any freedom in thephilosophical sense, for we act not only under external
compulsion but also by inner necessity.”– Albert Einstein• Are the premises true?
– I’m not sure. It’s more a matter of “belief” than“fit with the world”.

Logic in reading“To those who scare peace-loving people with phantoms
of lost liberty, my message is this: Your tactics only aid
terrorists, for they erode our national unity.”– John Ashcroft (US politician)Logic in reading“To those who scare peace-loving people with phantoms
of lost liberty, my message is this: Your tactics only aid
terrorists, for they erode our national unity.”– John Ashcroft (US politician)• What is the conclusion?
– People who ‘scare with phantoms of lost liberty’
aid terrorists.
(All people who argue for liberty are aids toterrorists.)

Logic in reading“To those who scare peace-loving people with phantoms
of lost liberty, my message is this: Your tactics only aid
terrorists, for they erode our national unity.”– John Ashcroft (US politician)• What are the premises?
– People who argue for liberty ‘erode our nationalunity’ (disagree with the US government).
– Terrorists disagree with the US government.

Logic in reading
All P is M.
Q is M.
• Is the argument valid?
∴ All Pwith
is Q.the– All people who argue for liberty disagree
US government.
– Terrorists disagree with the US government.
– Therefore, all people who argue for liberty areaids to terrorists.

Logic in reading• Is the argument valid?
– All rabbits run fast.
– Usain Bolt runs fast.
– Therefore, Usain Bolt is a rabbit.

 Not valid

All P is M.
Q is M.
∴ All P is Q.

Logical relations• Deductive logic– Claims to provide conclusive support for the truthof a conclusion• Inductive logic– Arguments support a conclusion, but do not claim
to show that it is necessarily true