What makes a Good Argument?

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Two Characteristics of Good Arguments

• 1. The premises are true

• 2. The argument has proper form

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True Premises

• The premises are true when what they say about the world is accurate

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Proper Form

There is a relationship or connection between the premises and conclusion that make you believe the conclusion is true

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Deductive Argument

You go from a general principle to a specific example

It gives necessity

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(1) All men are mortal (2) Socrates is a man Therefore (3) Socrates is mortal

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If all the members of the class of things called MEN have a particular characteristic called MORTALITY

And Socrates is a member of that class called

MEN Then Socrates MUST have that characteristic

called MORTALITY

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Why? Because we have established a necessary /

logical connection between the premises and the conclusion

Such that if the premises are true then the conclusion

must be true

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Examples

(1) All men are mortal (1) All A has B (2) Socrates is a man (2) C is A There: Therefore (3) Socrates is mortal (3) C has B

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Valid Deductive Argument

• The conclusion follows necessarily from the premises

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Example

(1) All men have brown hair (2) Socrates is a man Therefore (3) Socrates has brown hair Is this Valid? YES!

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Proper Form Test

Book says that if we assume the premises are true

This will help us determine if the argument passes the proper form test

This true only for Valid Deductive Arguments

Not true for Sound Deductive Argument

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Sound Deductive Argument

• Valid argument with true premises

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(1) All roses are plants (1) All A’s are B’s (2) All roses have thorns (2) All A’s are C’s Therefore Therefore (3) All plants have thorns (3) All B’s are C’s

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Improper Form

If all the members of the class of things called ROSES have the characteristic of being PLANTS

And if all the members of the class of things called ROSES have the characteristic of having THORNS

Then is it necessary that all plants have thorns?

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No! Why?

Because the premises only establish a necessary connection between

Roses and Plants Roses and Thorns

But not between Plants and Thorns

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Proper Form

Must establish a necessary connection between the premises and the conclusion

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Exercises 2.1

• Break up into groups

• A 1-10

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2.1A #1

(1) Oxygen is an element essential for life on Earth as we know it,

Therefore, (2) If oxygen were to vanish from the Earth’s

atmosphere, life as we know it would cease.

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2.1A #1

I. Passes both tests.

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2.1A #2

(1) All birds can fly. (2) Penguins are birds. Therefore, (3) Penguins can fly.

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2.1A #2

Premise 1 is false, so argument does not pass TP test. If both premises were true, the conclusion

would follow, so the argument does pass the PF test.

It’s a valid argument.

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2.1A #3

(1) All cars are blue. (2) All pigs have wings. Therefore, (3) All buses have three wheels.

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2.1A #3

Fails both tests. Premises are false and irrelevant to conclusion.

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2.1A #4

(1) Elephants are mammals. (2) Dogs are mammals. Therefore, (3) Elephants are dogs.

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2.1A #4

Passes TP test This is an invalid deductive argument so it fails

the PF test.

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(1) Elephants are mammals. (1) E = M (2) Dogs are mammals. (2) D = M Therefore, (3) Elephants are dogs. (3) E = D

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2.1A #5

(l) Many types of plastic can be recycled. (2) Many types of glass can be recycled. Therefore, (3) Many types of paper can be recycled.

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2.1A #5

Argument passes TP test because both premises are true.

But it does not pass the PF Inductive argument because of “many” not “all”

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2.1A #6

(1) Julia Roberts is either a man or a woman. (2) Julia Roberts is a man. Therefore (3) Julia Roberts isn’t a woman.

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2.1A #6

Fails the TP test because premise 2 is false. Passes the PF Test Disjunctive syllogism

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2.1A #7

(1) Everyone likes pizza. (2) Everyone who likes pizza buys it regularly. Therefore, (3) Pizza sales will rise over the next six months

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2.1A #7

Don’t know about TP (empirical question) Fails PF because if everyone was already buying

pizza regularly. Why should sales increase? Wouldn’t they stay the same?

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2.1A #8

(1) If you drop wood into water, it floats unless it’s held underwater by a heavy object.

(2)Trees are made of wood. Therefore, (3) When trees fall into water, they float unless

they’re held underwater by a heavy object.

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2.1A #8

Passes both tests.

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2.1A #9

(1) The discovery of antibiotics increased life expectancy.

(2) Antibiotics have no effect on viruses, Therefore, (3) There must be some causes of reduced life

expectancy besides viruses.

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2.1A #9

The argument passes the TP test, but the argument does not pass PF test, as stated.

Hidden Premises? (viruses reduce life expectancy)

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2.1A #10

(1) All cars have three wheels. (2) Everything with three wheels is blue Therefore, (3) All cars are blue.

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2.1A #10

The argument fails the TP test because both premises are false.

IF they were true, they would prove the conclusion, so this argument passes the PF test.

It is a valid (unsound) deductive argument.

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Audience

• The audience of the argument is the group that the person making the argument wants to convince

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Exercises 2.2

• Do as class

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The Problem of Ignorance

• The problem of ignorance is that we don’t know everything

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Proper Form

• If the premises were true, they would provide support for the conclusion

• It expresses a relationship between the premises and the conclusion

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Logical Relationships

• In proper form arguments

• We are looking for logical relationships

• Based upon the premises

• What can we determine about the conclusion?

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(1) All men are mortal (2) Socrates is a man Therefore (3) Socrates is mortal (TP and PF: Sound) Relationship: If all members of the class of men have a

certain characteristic: mortality Then all the members of that class MUST also

have that characteristic: mortality

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Valid, but not Sound

(1) All men have brown hair (2) Socrates is a man Therefore (3) Socrates has brown hair (FP and PF: Valid) Conclusion follows necessarily from the

premises, but premises are NOT TRUE

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Groups (Fails PT Test)

(1) All G1 are G2 (1) All roses are plants (2) All G1 are G3 (2) All rose have thorns Therefore (3) All G2 are G3 Therefore (3) All plants have thorns

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Exercise 2.4

• Break up into groups

• A1-5

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2.4A #1

(1) All dogs are mammals (2) All mammals are things with hair Therefore, (3) All dogs are things with hair Form B

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2.4A #2

(1) If that’s a car, then I’m a donkey. (2) I’m a donkey. Therefore, (3) That’s a car.

Form D Invalid Modus Ponens

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2.4A #3

(1) All children are humans. (2) All humans are mammals Therefore, (3) All children are mammals. Form B Sound Deductive 51

2.4A #4

(1) All men are humans (2) All men are under eighteen years of age Therefore, (3) All women are under eighteen years of age Other Form Not Valid 52

2.4A #5

(1) If you throw a match on that gas, it will burn.

(2) You will throw a match on that gas. Therefore (3) It will burn Form C Valid Modus Ponens

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Deductive Arguments

• Claim that the truth of the premises show that the conclusion must be true

• Go from a general principle to a specific example

• Gives necessity

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Valid and Sound Deductive Arguments

• Valid = Conclusion follows necessarily from the premises

• Sound = Validity + true premises

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If, Then Statements

If A (antecedent), then B (consequent)

A ) B

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Modus Ponens (MP)

Affirm the Antecedent (1) If A, then B (2) We have A Therefore (3) We can affirm B

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Correct Form Example Affirm the Antecedent

(1) If Mary is a mother (A), then she must be a woman (B)

(2) Mary is a mother (A)

(3) Therefore, she must be a woman (B)

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Incorrect Form Example: Affirm the Consequent

(1) If Mary is a mother (A), then she must be a woman (B)

(2) Mary is a woman (B) (3) Therefore, she must be a mother (A)

You must learn the FORM

• 1. If it rains tomorrow (A), then I will bring my umbrella (B)

• 2. I brought my umbrella (B) • 3. Therefore what?

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Correct Form

• 1. If it rains tomorrow (A), then I will bring my umbrella (B)

• 2. It rained (A) • 3. Therefore?

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Modus Tollens (MT)

Deny the Consequent (1) If A, then B (2) We do not have B Therefore (3) We do not have A

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Correct Form Example Deny the Consequent

(1) If Mary is a mother (A), then she must be a woman (B)

(2) Mary is not a woman (-B)

(3) Therefore, she must not be a mother (-A)

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Incorrect Form Example Deny the Antecedent

(1) If Mary is a mother (A), then she must be a woman (B)

(2) Mary is a not mother (-A) (3) Therefore, she must not be a woman (-B)

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Disjunctive Syllogism (DS)

Deny the Disjunct Either A or B Either A or B Not A Not B Therefore B Therefore A

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Reductio ad Absurdem (RAA)

Reduce to an absurdity Reduce to a contradiction

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Example A = Absolute Truth SA = Statement that are Absolutely True (1) You have said there are no absolute truth [-A] (2) But if there is no absolute truth, then no one ever makes a

statement that is absolutely true [-A ) -SA] (3) But you have claimed to state an absolute truth [SA] (4) Therefore, your statement that there is no absolute truth is

not true because it leads to a logical contradiction [-SA and SA]

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Inductive Arguments

From Specific Examples to General Principle

Gives Probability

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Example

(1) There are trees on Island 1 (2) There are trees on Island 2 (3) There are trees on Island 3 ________________________ (4) All Islands have trees

Weak vs. Strong Inductive Arguments

The more examples / evidence, the stronger

the argument 1,000,000,000 Islands have trees Therefore all Island have trees

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GM Example

• Why use induction?

• Sometimes we have to

• Defective rate of cars!

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GM Example

• Why use induction?

• Sometimes we have to

• Defective rate of cars!

Strong and Weak Inductive Arguments

• Strong Inductive Arguments have many examples (Cogent)

• Weak Inductive Arguments have few examples

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Exercise 2.5

• Break up into groups

• A 1-10

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2.5A #1

(1) If that is a cow, then I am a goat (2) It is a cow Therefore (3) I am a goat Deductive and Valid Modus Ponens

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2.5A #2 (1)I called Joi and she said she was at the

library Therefore, (2) She is probably at the library Inductive

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2.5A #3

(1) The syllabus says that you need to cite three sources

(2) You only cite one source Therefore, (3) You won’t get the grade you want.

Deductive and valid.

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2.5A #4

(1) Francis had pepperoni and mushroom Therefore, (2) Francis had pepperoni on her pizza Deductive and valid.

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2.5A #5

Not an argument

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2.5A #6

(1) Bret is either in class or in the rec center (2) Bret is not in class Therefore, (3) Bret is in the rec center Deductive and valid. Disjunctive Syllogism

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2.5A #7

Not an argument. Instructions.

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2.5A #8

(1) My son started talking when he was two Therefore, (2) All children start speaking at two Inductive and weak because the author only has one case.

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2.5A #9

(1) All human beings are mortal (2) Socrates was a human being Therefore, (3) Socrates was mortal Deductive and sound

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2.5A #10

Not an argument. There are two statements here that would

make good premises, but no conclusion is drawn.

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Quick Review

• Proper Form Inductive • Deductive Weak / Strong • Valid Cogent • Sound • Modus Ponens • Modus Tollens • Disjunctive Syllogism

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