CPHL214: Critical Thinking

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CPHL214Critical Thinking

• Making Sense of Arguments

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Argument Evaluation

• When an argument shows that its conclusion is
  worthy of acceptance, we say that the argument is
  good.
• When an argument fails to do so, we say that the
  argument is bad.

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Two Forms of Arguments

• Deductive Argument
• An argument intended to provide logically
  certain support for its conclusion.
• B. Inductive Argument
• An argument intended to provide merely probable
  support for its conclusion.

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A. Deductive Arguments

• A deductive argument is intended to provide
  absolute logical support for its conclusion.
• Final, definitive, undeniable support!
• When deductive arguments succeed, they guarantee
  their conclusion.

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• Examples
• All jocks must harass nerds.
• Homer is a jock.
• So, Homer must harass nerds.
• Im taller than Aimee.
• Aimee is taller than Melissa.
• So, Im taller than Melissa.
• If you were at the party, you definitely would
  have noticed Mya.
• You said you WERE at the party.
• So, you must have noticed Mya!

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• 2. A deductive argument that succeeds in
  providing conclusive support for its conclusion
  is said to be valid.
• Valid doesnt mean true!

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• Valid means the argument has good logical
  structure.
• A valid argument is such that if its premises are
  true, its conclusion must be true.
• Valid deductive arguments are truth-preserving.
• If the argument is valid, then if the premises
  are true, the conclusion has to be true, too.

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• 3. If a deductive argument fails at providing
  conclusive support for its conclusion, then its
  called invalid.
• 4. A deductively valid argument with true
  premises is said to be sound.

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• So, in order to be called sound a deductive
  argument has to have both of these qualities
• (i) deductively valid
• (ii) all premises true

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• Two questions when evaluating arguments
• I. Are the premises true?
• Do those premises lead to this
• conclusion?
• These are separate issues!
• You can have false premises that still support
  the conclusion given.
• You can have true premises that dont support the
  conclusion given.

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• (i)False premises that still support the
  conclusion given
• Pigs have wings.
• Any animal with wings can fly.
• So, pigs can fly.
• Each Ryerson student has won a Nobel Prize.
• Saul Bellow is a Ryerson student.
• Thus Saul Bellow has won a Nobel Prize.

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• (ii)True premises that dont support the
  conclusion given
• Gasoline is poison.
• Bleach is poison.
• So, gasoline is bleach.
• Ottawa is the capital of Canada.
• Washington is the capital of the U.S.
• Therefore snakes are reptiles.

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B. Inductive Arguments

• An inductive argument is intended to provide
  probable support for its conclusion - not
  certainty.
• Most Canadians like hockey.
• Andy is Canadian.
• So Andy probably likes hockey.

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• Im 67, which is taller than most people.
• So, Im likely taller than the next person I
  meet.
• In Holland, health care expenditures have
  decreased since the legalization of euthanasia.
• Canada is economically and politically similar
  to Holland.
• Thus if Canada were to legalize euthanasia, it
  would enjoy decreased healthcare expenditures.

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• An inductive argument that succeeds in providing
  probable support for its conclusion is said to be
  strong.
• A strong argument is such that if its premises
  are true, its conclusion is probably true.
• Ask yourself how much evidence do THESE premises
  provide for THIS conclusion?
• But dont ask yet whether the premises or
  conclusion are TRUE.

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• An inductively strong argument with true
  premises is said to be cogent.
• Thus to be called cogent, an inductive
  argument must have both of these qualities
• (i) inductively strong
• (ii) all premises true

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The Principle of Charity

• The Principle of Charity is a principle of
• interpretation that calls for us to give the
• benefit of doubt to a speaker / writer.
• We should assume (unless given clear
• indications otherwise) that they are basically
• reasonable, and interpret their words
• accordingly.

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• We should follow the P of C when reconstructing
  an authors arguments. This includes, among
  other things
• (i) Filling in implicit premises or conclusions
• Only members of the EU can leave the airport
  without a visa so Uncle Jack will have to hang
  around the airport during his stopover.

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• (ii) Avoiding excessive literalism and unfair
  word twisting
• Q107 is the worst radio station ever. You know
  I love classic rock, but they have a very
  limited playlist these days. You can only hear
  Purple Haze so many times.
• Uncharitable Interpretation?

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• Drugs are probably the greatest problem for
  the American underclass these days. Theyre
  cheap, readily available and very effective,
  unfortunately.
• Uncharitable Interpretation?

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Filling in Implicit Statements

• Sometimes authors leave out one or more premises
  and / or conclusions.
• Why?
• By mistake
• They think its too obvious to need saying
• Theyre hiding something
• Thus you need to be able to fill in these
  implicit assertions.

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Examples

• Hidden premise
• Argument Youre a student. So you must be short
  of cash.
• Hidden premise
• Hidden conclusion
• Argument The last piece of cake is gone! There
  are only two of us here, and I didnt take it.
• Hidden conclusion

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• Look, we know hes lied in the past. Theres no
  way we should trust him in the future!
• Hidden Assertion

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Eliminating Excess Verbiage

• One major task in reconstructing arguments is
  eliminating those parts of the text in question
  that are not, strictly speaking, part of the
  argument.
• Any part of the text that serves as neither a
  premise nor a conclusion in the argument can be
  eliminated.

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• Its about time they tore down the Gardiner,
  dont you think? I remember fondly the
  excitement in Toronto when it was built we took
  a drive into the city on the day it opened, and
  my mom made me wear my Sunday best. But there
  are more environmentally friendly ways of getting
  people in and out of the city, namely public
  transportation. And it is an eyesore and
  expensive to maintain. Public transportation is
  the way to go, if we want to build a better
  Toronto of the future.

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• P1. Public transportation, namely GO and the
  TTC, are better than the Gardiner for getting in
  and out of Toronto.
• P2. The Gardiner is an eyesore.
• P3. The Gardiner is expensive to maintain.
• _________________
• C. We should tear down the Gardiner.

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Argument Patterns

• The form of an argument is distinct from the
  content of the argument.
• That is, the shape or structure of the argument
  one thing what its about (its subject matter)
  is a separate issue.

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• Here are two very abstract argument forms
• Premise 1.
• So, conclusion.
• Premise 1.
• Premise 2.
• Therefore, conclusion.

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Or

• Premise 1.
• Premise 2.
• Therefore, (sub)conclusion 1.
• Therefore, further (main) conclusion 2!

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A more specific argument form

• If p, then q
• p
• Therefore, q
• Maybe p stands for Rahul likes South Park.
• Maybe q stands for Rahul likes Family Guy.
• Whatever p and q stand for in this argument, it
  is valid! It is not always sound, however.

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Arguments of this pattern are

• deductive and conditional.
• Theyre called conditional because they contain
  at least one conditional statement.
• A conditional statement is any ifthen
  statement.

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• In any conditional statement
• The first (if) part is called the antecedent.
• The second (then) part is called the consequent.

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• The antecedent is circled
• If you come over, then Ill leave!
• If you need my help, then just ask me.
• If you want to do well, then study hard.

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• Trickier examples
• If you work hard and are lucky, then youll do
  well in life.
• Ill help, if you ask.
• If you come over, Ill leave!
• Touch my carIll kick your butt!
• You can vote only if youre eighteen or older.

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• A conditional statement doesnt say that either
  the antecedent or the consequent is true.
• It just says If the antecedent is true, then
  the consequent is true, too.
• If I was a rockstar, then I would be living the
  good life right now.
• This of course does not imply that I in fact am
  a rockstar, nor does it imply that I am living
  the good life right now.

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Four ValidArgument Forms

• 1. Affirming the Antecedent (Modus Ponens)
• If p, then q
• p
• Therefore, q

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• Examples
• P1. If Spot barks, a burglar is in the house.
• P2. Spot is barking.
• C. Therefore, a burglar is in the house.
• P1. If youre a Martian, youve got blue
• blood.
• P2. Youre a Martian.
• C. So, youve got blue blood.

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• 2. Denying the Consequent (Modus Tollens)
• If p, then q
• Not q
• Therefore not p

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• P1. If it rains, the sidewalk gets wet.
• P2. But the sidewalks not wet.
• C. So, it must not have rained.
• P1. If you work in a bar, youre over 19.
• P2. Youre not over 19.
• C. So, you must not work in a bar.

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• 3. Hypothetical Syllogism
• If p, then q.
• If q, then r.
• Therefore, if p, then r.

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• Examples
• P1. If Guy steals the money, then he will go to
  jail.
• P2. If Guy goes to jail, then his family will
  suffer.
• Therefore, if Guy steals the money, then his
  family will
• suffer.
• P1. If Man is 5 then the Devil is 6.
• P2. If the Devil is 6 then God is 7.
• C. If Man is 5 then God is 7.

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• 4. Disjunctive Syllogism
• Either p or q
• Not p
• Therefore q
• OR
• Either p or q
• Not q
• Therefore p

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• A disjunction is any statement of the form
• Either p or q
• Sometimes we call them Either / or statements.
• p and q are called disjuncts.
• A disjunction asserts that at least one of the
  disjuncts is true.

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• Examples
• P1. She could only have seen that movie at Cannes
  or Venice.
• P2. I know she didnt see it at Venice.
• _______________________________________
• She must have seen it at Cannes.
• P1. The hard drive is fried or your power supply
  doesnt have enough juice.
• P2. Your power supply is in fact fine.
• ________________________________________
• C. The hard drive must be fried.

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• Three Invalid Argument Forms
• 1. Affirming a Disjunct
• Either p or q
• p
• Therefore not q
• Example
• P1. She could only have seen that movie at Cannes
  or Venice.
• P2. I know she did see it at Cannes.
• ______________________________
• C. She didnt see it at Venice.

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• 2. Denying the Antecedent
• If p, then q
• Not p
• . Not q
• Example
• (1) If Einstein invented the computer, then hes
  a genius.
• (2) Einstein did not invent the computer.
• _____________________________________
• Therefore,
• (3) Hes not a genius.

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• 3. Affirming the Consequent
• If p, then q
• q
• . p
• Example
• (1) If Einstein invented the computer, then hes
  a genius.
• (2) Einstein is a genius.
• _____________________________________
• Therefore,
• (3) Einstein invented the computer.

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Diagramming Arguments

• A diagram is simply a two-dimensional
  representation of an argument using numbers and
  arrows.
• We make them to clarify an arguments basic
  logical structure.

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• Since youre not having a good time, we should
  leave.
• First, each statement should be assigned a
  unique number
• (1) Youre not having a good time.
• (2) We should leave.

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• Second, premises should be connected by an arrow
  to the conclusions that they are intended to
  support
• (1) Youre not having a good time.
• (2) We should leave.
• Diagrams always flow downward on the page, with
  conclusions below the premises that support them.

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• Multiple premises can support a conclusion in one
  of two ways separately, or together.
• (a) Independent premises each lend some support
  to the conclusion, on their own.
• Dependent premises must be combined in order to
  support the conclusion.

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Independent Premises

• I am a philosopher. And, I watch Star Trek.
  Therefore, Im a geek.
• (1) I am a philosopher.
• (2) I watch Star Trek.
• (3) Im a geek.

The diagram illustrates that premises 1 and 2
each lead to conclusion 3.
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Dependent Premises

• I am taller than you. You are taller than
  Rahul. So I must be taller than Rahul.
• (1) I am taller than you.
• (2) You are taller than Rahul.
• (3) I must be taller than Rahul.

The line joining 1 and 2 shows that they two must
go together in order to support 3.
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Arguments with Independent and Dependent
Premises

• (1)I am a philosopher. (2)All philosophers are
  geeks. And, (3)I watch Star Trek. Therefore,
  (4)Im a geek.
• The first 2 premises are dependent premises,
  working together.
• The third premise stands alone in support of
  the conclusion.

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Arguments with Subarguments

• A subargument is an argument within an argument
• Lying is wrong, and you told a lie. So, youve
  done something wrong. All wrongdoers deserve to
  be punished. So, you deserve to be punished.
• (1)Lying is wrong, and (2)you told a lie. So,
  (3)youve done something wrong. (4)All wrongdoers
  deserve to be punished. So, (5)you deserve to be
  punished.

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• Heres the subargument
• (1)Lying is wrong, and (2)you told a lie. So,
  (3)youve done something wrong.

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• Heres the main argument
• (3)Youve done something wrong. (4)All
  wrongdoers deserve to be punished. So, (5)you
  deserve to be punished.

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• Here they are put together
• Statement 3 is a subconclusion both the
  conclusion of a subargument, and a premise of the
  main argument.

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• Youre a student. So, youre probably broke. So,
  you likely dont have money for beer.

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• (1)Youre a student. So, (2)youre probably
  broke. So, (3)you likely dont have money for
  beer.

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2
3
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A final example

• (1)I am taller than Rahul. (2)Rahul is taller
  than Francois. (3)Francois is taller than Mike.
  And (4)Mike is taller than you. So (5)I must be
  taller than you.

This argument has four premises working jointly
(together) to support the conclusion.