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Logic basic concepts and methods George W. Matthews Pennsylvania College of Technology Fall 2015

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Page 1: Logic

Logicbasic concepts and methods

George W. Matthews

Pennsylvania College of Technology

Fall 2015

Page 2: Logic

What is an argument?

Any series of statements in which one (theconclusion) is meant to follow from or besupported by, the others (the premises).

An attempt to show that one statement is true onthe basis of other statements.

A presentation of the evidence for a claim.

Not a verbal fight that has two (or more) sides.

Page 3: Logic

Statements

Sentences that say something about something.

Statements are either true or false.

examples

“The cat ate my homework.”

“Xena is the tenth planet.”

“It is never acceptable to killanother human being.”

Statements are distinguished from other kinds ofsentences like questions, commands, exclamationswhich are neither true nor false.

Page 4: Logic

Premise Indicators

Premises are given information that we are askedto accept as a basis for argument.

Premise indicators tell us which claims theargument starts from.

examples

Since . . .

Because of . . .

Assume for the sake ofargument that . . .

We all know that . . .

Page 5: Logic

Conclusion Indicators

Conclusions are the points being established by theargument.

Conclusion indicators tell us where the argument isgoing.

examples

Therefore . . .

Thus . . .

So we can see that . . .

It follows that . . .

Page 6: Logic

Identify Premises and Conclusion

We know for a fact that my client was not atthe scene of the crime. Furthermore, the chiefprosecution witness is a known perjurer. Thusmy client is not guilty.

in standard form

My client was not at the scene of the crime.The chief prosecution witness is a knownperjurer.

My client is not guilty.

Page 7: Logic

Identify Premises and Conclusion

We know for a fact that my client was not atthe scene of the crime. Furthermore, the chiefprosecution witness is a known perjurer. Thusmy client is not guilty.

in standard form

My client was not at the scene of the crime.The chief prosecution witness is a knownperjurer.

My client is not guilty.

Page 8: Logic

Identify Premises and Conclusion

Christopher Columbus was a criminal. This isbecause whoever steals land or gold, enslavespeople or kills innocent people is a criminal andhe did all of the these things.

in standard form

Whoever steals land or gold, enslaves people orkills innocent people is a criminal.Christopher Columbus did all of the thesethings.

Christopher Columbus was a criminal.

Page 9: Logic

Identify Premises and Conclusion

Christopher Columbus was a criminal. This isbecause whoever steals land or gold, enslavespeople or kills innocent people is a criminal andhe did all of the these things.

in standard form

Whoever steals land or gold, enslaves people orkills innocent people is a criminal.Christopher Columbus did all of the thesethings.

Christopher Columbus was a criminal.

Page 10: Logic

What makes a good argument?

The best, most persuasive arguments are bothvalid and sound.

definition: In a valid argument, if thepremises are true, the conclusion must be true.

definition: A sound argument is a validargument with premises that are really true.

Page 11: Logic

Valid or invalid?

All human beings are mortal.Socrates is a human being.Whoever is going to die worries about dyingoccasionally.

Socrates worries about dying occasionally.

This argument is in standard form.

If the premises are true must the conclusion alsobe true?

YES, this argument is VALID.

Page 12: Logic

Valid or invalid?

All human beings are mortal.Socrates is a human being.Whoever is going to die worries about dyingoccasionally.

Socrates worries about dying occasionally.

This argument is in standard form.

If the premises are true must the conclusion alsobe true?

YES, this argument is VALID.

Page 13: Logic

Valid or invalid?

All human beings are animals.Plato is an animal.

Plato is a human being.

If the premises are true must the conclusion alsobe true?

NO, this argument is INVALID.

Page 14: Logic

Valid or invalid?

All human beings are animals.Plato is an animal.

Plato is a human being.

If the premises are true must the conclusion alsobe true?

NO, this argument is INVALID.

Page 15: Logic

Valid or invalid?

If abortion is wrong it should be illegal.Abortion is wrong.

Abortion should be illegal.

Can the premises both be true and the conclusionbe false?

No. The only way for the conclusion to be false isif at least one of the premises were false, so thisargument is VALID.

But is it sound?

Page 16: Logic

Valid or invalid?

If abortion is wrong it should be illegal.Abortion is wrong.

Abortion should be illegal.

Can the premises both be true and the conclusionbe false?

No. The only way for the conclusion to be false isif at least one of the premises were false, so thisargument is VALID.

But is it sound?

Page 17: Logic

Valid or invalid?

If abortion is wrong it should be illegal.Abortion is wrong.

Abortion should be illegal.

Can the premises both be true and the conclusionbe false?

No. The only way for the conclusion to be false isif at least one of the premises were false, so thisargument is VALID.

But is it sound?

Page 18: Logic

Sound or unsound?

Poor people do not have much money.It costs a lot of money to buy first class airlinetickets.

So poor people do not fly first class except inunusual circumstances.

This argument is VALID.

To check if it is sound we need to know if thepremises are really true.

The first premise is true by definition and thesecond is true in fact.

Thus this argument is SOUND, the conclusion isreally true.

Page 19: Logic

Sound or unsound?

Poor people do not have much money.It costs a lot of money to buy first class airlinetickets.

So poor people do not fly first class except inunusual circumstances.

This argument is VALID.

To check if it is sound we need to know if thepremises are really true.

The first premise is true by definition and thesecond is true in fact.

Thus this argument is SOUND, the conclusion isreally true.

Page 20: Logic

Sound or unsound?

Poor people do not have much money.It costs a lot of money to buy first class airlinetickets.

So poor people do not fly first class except inunusual circumstances.

This argument is VALID.

To check if it is sound we need to know if thepremises are really true.

The first premise is true by definition and thesecond is true in fact.

Thus this argument is SOUND, the conclusion isreally true.

Page 21: Logic

Sound or unsound?

Poor people do not have much money.If you do not have something, you must notwant it.

So poor people are poor of their own free will,because they want to be poor.

Are both premises of this argument true?

The first premise is true by definition.

The second premise is false – so this argument isUNSOUND, even though it is VALID.

Page 22: Logic

Sound or unsound?

If abortion is wrong it should be illegal.Abortion is wrong.

Abortion should be illegal.

This is a valid argument, but are the premisesreally true?

The second premise needs more argument to backit up since it is not obviously true.

The first premise is false.

This argument is UNSOUND.

Page 23: Logic

Summary: analyzing arguments

identifyargument

invalid

DISCARD – conclusion does not follow

valid

unsound

DISCARD – premises false

sound

ACCEPT – conclusion is true

Page 24: Logic

Summary: analyzing arguments

identifyargument

invalid

DISCARD – conclusion does not follow

valid

unsound

DISCARD – premises false

sound

ACCEPT – conclusion is true

Page 25: Logic

Summary: analyzing arguments

identifyargument

invalid

DISCARD – conclusion does not follow

valid

unsound

DISCARD – premises false

sound

ACCEPT – conclusion is true

Page 26: Logic

Summary: analyzing arguments

identifyargument

invalid

DISCARD – conclusion does not follow

valid

unsound

DISCARD – premises false

sound

ACCEPT – conclusion is true

Page 27: Logic

Summary: analyzing arguments

identifyargument

invalid

DISCARD – conclusion does not follow

valid

unsound

DISCARD – premises false

sound

ACCEPT – conclusion is true

Page 28: Logic

Summary: analyzing arguments

identifyargument

invalid

DISCARD – conclusion does not follow

valid

unsound

DISCARD – premises false

sound

ACCEPT – conclusion is true


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