Introduction to Logic

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 persuasion Logic: 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

Definitions Statement: 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 • OJ Simpson intentionally killed Nicole Brown. • It is wrong to intentionally kill people. • Therefore what OJ did was wrong. Premise Premise Conclusion

Canonical Argument Form • Premise 1 • Premise 2 • Premise 3 • Conclusion

The Study of Argument Formal Logic The 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. Informal Logic The study of arguments in the real world. It is like a field science. At LCCC, this is covered in Critical Thinking.

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 argument Look to see if some statements support others. 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 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. He deserves a spot in the Hall of Fame Example taken from Cathal Woods, Introduction to Reasoning.

Example 2 Is 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 2 Is 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 2 1. Professors delight in boasting of their inventions, Before the thirteenth century we have no record by any such self-styled inventor.” 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 4 Is 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 4 • 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. • Whoever wishes to avoid being a criminal must profess to agree with Christ’s teaching but must avoid saying what that teaching was.

Another Definition Inference: The connection between statements in an argument. Argument glue. • Premise • Premise • Conclusion This motion is inference

Valid An argument is valid if it is impossible for the premises to be true and the conclusion false. Sound An argument is sound if it valid and has true premises.

A Valid Argument All people are mortal Socrates is a person. Socrates is mortal

Another Valid Argument All people are carrots Socrates is a person. Socrates is carrot

An invalid argument All people are mortal Socrates is a mortal All 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.

Strong An argument is strong if the premises would make the conclusion more likely if they were true. Cogent An argument is cogent if it is strong and the premises are true.

Deductive An argument is deductive if it aims at validity Inductive An 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?

He was both running and sitting still at the same time. • The colorless object was bright green. • The circle had sharp corners. Contradiction A contradiction is a statement that cannot possibly be true because of its basic logic.

All bachelors are unmarried men. • An invisible object can’t be seen. • All triangles have three sides. Tautology A tautology is a statement that must be true because of its basic logic.

It is raining right now. • I am a bachelor • This triangle is green Contingent Statement A statement that can be either true or false, depending on the way the world is apart from the sentence.

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

Logically equivalent statements effectively say the same thing.

Consistent statements A 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.

Introduction to Logic