Introduction to Logic

Class 1: What is Logic?

What is Logic?Definition of Logic:

“Logic is the study of virtue in argument, where an argument is considered virtuous if it helps us get to the truth”

A Contrast:Rhetoric: The study of effective persuasionLogic: The study of legitimate persuasion

An argument in logic is not just two people contradicting and

insulting each other.

For more of what an argument is not: http://www.youtube.com/watch?v=kQFKtI6gn9Y

DefinitionsStatement: A unit of language that can be

true or false.Argument: A connected series of

statements designed to convince an audience of another sentence.

Conclusion: the statements that an argument tries to convince an audience of.

Premises: the statement that an argument uses to support the conclusion.

For the purposes of this course, these words will be used interchangeably:

• Sentence• Statement• Assertion• Proposition

They don’t really meant the same thing, but we won’t worry about the difference.

Example

1. OJ Simpson intentionally killed Nicole Brown.

2. It is wrong to intentionally kill people.

3. Therefore what OJ did was wrong.

Premise

Premise

Conclusion

Canonical Argument Form

1.Premise 12.Premise 23.Premise 34.Conclusion

The Study of Argument

Informal LogicThe study of arguments in the real world. It is like a field science. At LCCC, this is covered in Critical Thinking.

Formal LogicThe study of arguments in artificial conditions, including especially invented languages. It is like a laboratory science. At LCCC this is studied in Introduction to Logic.

An ob/ob mouse and a normal mouse

Via wikipedia, http://en.wikipedia.org/wiki/File:Fatmouse.jpg#file/ . Licensed under Creative Commons.

A normal argument and a formal argument.

“Mortality rates for women undergoing early abortions, where the procedure is legal, appear to be as low as or lower than the rates for normal childbirth. Consequently, any interest of the State in protecting the woman from an inherently hazardous procedure, except when it would be equally dangerous for her to forgo it, has largely disappeared.” Harry Blackmun, Roe v. Wade

Formal Language

• Formal logic replaces the ordinary language of argument with a symbolic language.

• This language is meant to be free of all ambiguity and vagueness.

• The language is meant to wear its logical structure on its face.

• Our formal languages: SL and QL.

How to tell an argument1. Look to see if some statements support

others. 2. Look for premises and conclusions

Premise indicator words: because, as, for, since, given that, for the reason that.

Conclusion indicator words: Therefore, thus, hence, so consequently, it follows that, in conclusion, as a result, then, must, accordingly, this implies that, this entails that, we may infer that,

Example 1

Is this an argument?Cal Ripken has provided years of valuable

service to the Orioles. He has appeared in 19 All-Star games. He was a World Series champion in 1983. His number has been retired by the Orioles. Therefore, he deserves a spot in the Hall of Fame

Example taken from Cathal Woods, Introduction to Reasoning.

Example 1

Is this an argument?Cal Ripken has provided years of valuable

service to the Orioles. He has appeared in 19 All-Star games. He was a World Series champion in 1983. His number has been retired by the Orioles. Therefore, he deserves a spot in the Hall of Fame

Example taken from Cathal Woods, Introduction to Reasoning.

Example 1

1. Cal Ripken has provided years of valuable service to the Orioles.

2. He has appeared in 19 All-Star games. 3. He was a World Series champion in 1983. 4. His number has been retired by the Orioles. 5. He deserves a spot in the Hall of Fame

Example taken from Cathal Woods, Introduction to Reasoning.

Example 2Is this an argument?“We can suspect that the inventor [of eyeglasses]

was not an academic, for professors delight in boasting of their inventions, and before the thirteenth century we have no record by any such self-styled inventor.” —D.J. Boostin, The Discoverers

Example from Salmon, Marilee (1995) Introduction to Logic and Critical Thinking 3rd edition Fort Worth, TX: Harcourt Brace

Example 2Is this an argument?“We can suspect that the inventor [of eyeglasses]

was not an academic, for professors delight in boasting of their inventions, and before the thirteenth century we have no record by any such self-styled inventor.” —D.J. Boostin, The Discoverers

Example 21. Professors delight in boasting of their

inventions, 2. Before the thirteenth century we have no

record by any such self-styled inventor.” 3. The inventor [of eyeglasses] was not an

academic.

Example 3

Is this an argument?“President Clinton today made a parting appeal to

Indians for eased tensions in their region and stronger ties with America as he looked toward a brief and diplomatically dicey stop in Pakistan. ‘Friends don't have to agree on every issue,’ he told business leaders in a domed room of the Bombay stock market. ‘They just have to have an honest relationship about it.’” New York Times March 24, 2000.

Example 3

Not an argument, just reporting events.

Example 4Is this an argument?“In England under the blasphemy laws it is illegal to

express disbelief in the Christian religion. It is also illegal to teach what Christ taught on the subject of non-resistance. Therefore, whoever wishes to avoid being a criminal must profess to agree with Christ’s teaching but must avoid saying what that teaching was.”

—Bertrand Russell, Skeptical Essays (1928)

Example 4Is this an argument?“In England under the blasphemy laws it is illegal to

express disbelief in the Christian religion. It is also illegal to teach what Christ taught on the subject of non-resistance. Therefore, whoever wishes to avoid being a criminal must profess to agree with Christ’s teaching but must avoid saying what that teaching was.”

—Bertrand Russell, Skeptical Essays (1928)

Example 41. In England under the blasphemy laws it is

illegal to express disbelief in the Christian religion

2. It is also illegal to teach what Christ taught on the subject of non-resistance.

3. Whoever wishes to avoid being a criminal must profess to agree with Christ’s teaching but must avoid saying what that teaching was.

• Premise• Premise• Conclusion

This motion is inference

Another Definition

Inference: The connection between statements in an argument. Argument glue.

ValidAn argument is valid if it is impossible for the premises to be true and the conclusion false.

SoundAn argument is sound if it valid and has true premises.

A Valid Argument

All people are mortalSocrates is a person. Socrates is mortal

Another Valid Argument

All people are carrotsSocrates is a person. Socrates is carrot

An invalid argument

All people are mortalSocrates is a mortalAll people are Socrates

A Valid Argument

If George Washington were beheaded, he would be dead.

George Washington was beheaded. Therefore George Washington is dead.

An Invalid Argument

If George Washington were beheaded, he would be dead.

George Washington is dead. Therefore George Washington was beheaded.

StrongAn argument is strong if the premises would make the conclusion more likely if they were true.

CogentAn argument is cogent if it is strong and the premises are true.

DeductiveAn argument is deductive if it aims at validity

InductiveAn argument is inductive if it aims at strength

Suppose a five year old child asked you what a contradiction was. How would you explain it?

ContradictionA contradiction is a statement that cannot possibly be true because of its basic logic.

• He was both running and sitting still at the same time.

• The colorless object was bright green.• The circle had sharp corners.

TautologyA tautology is a statement that must be true because of its basic logic.

• All bachelors are unmarried men.• An invisible object can’t be seen.• All triangles have three sides.

Contingent StatementA statement that can be either true or false, depending on the way the world is apart from the sentence.

• It is raining right now.• I am a bachelor• This triangle is green

Logically equivalent statementsTwo statements are logically equivalent if they both have to be true, or both have to be false, because of their basic logic.

It is raining Water is falling from the sky

Bob is a bachelor Bob is an unmarried man

Peter Parker loves Mary Jane Watson

Spider-man loves Mary Jane Watson

Logically equivalent statements effectively say the same thing.

Consistent statementsA set of statements is consistent if it is logically possible for them all to be true.

These sentences are consistent• This shape is a triangle• This shape is red • If something is a red, then it must have three

sides

These sentences are consistent• This shape is a triangle• This shape is red • If something is red, then it must have four

sides.