Text of Ling 21: Language and Thinking Lecture 4: Basic Logical Concepts
Ling 21: Language and Thinking Lecture 4: Basic Logical Concepts
ROAD MAP After a brief side journey into language and the brain, including: The physiology of the brain; The brain and language disorders; and Sign language and the brain, We now return to some basic logical concepts
Previously on Language & Thinking, We... Defined critical thinking; Identified traits of a critical thinker; Identified some of the barriers to critical thinking; and Defined and analyzed arguments in terms of their component parts (Premises & conclusions).
This chapter is EXTREMELY IMPORTANT because... It forms the foundation of EVERYTHING else that is to follow in this course. If you dont read and understand this chapter, you will not do well in this course. So, read the chapter, actively participate in the class and ASK QUESTIONS if you dont think you get it!
BASIC LOGICAL CONCEPTS Task: To distinguish good arguments from bad Two questions: Are the premises true? Do the premises provide good reasons to accept the conclusion?
TWO ARGUMENT TYPES Deductive arguments (try to) PROVE their conclusions Inductive arguments (try to) show that their conclusions are PLAUSIBLE or LIKELY
DEDUCTIVE ARGUMENTS Some pigs have wings. All winged things sing. Therefore, some pigs sing. Everyone has one and only one biological mother. Full sisters have the same biological mother. No one is her own biological mother. Therefore, there is no one whose biological mother is also her sister. EXERCISE: Solve the mysteries, CT pages 54-55.
INDUCTIVE ARGUMENTS Every ruby discovered thus far has been red. So, probably all rubies are red. Polls show that 87% of 5-year-olds believe in the tooth fairy. Marta is 5 years old. Marta probably believed in the tooth fairy. Chemically, potassium chloride is very similar to ordinary table salt (sodium chloride). Therefore, potassium chloride tastes like table salt.
THE DIFFERENCE Key: deductive / inductive If the premises are true the conclusion is necessarily / probably true. The premises provide conclusive / good evidence for the conclusion. It is impossible / unlikely for the premises to be true and the conclusion to be false. It is logically inconsistent / consistent to assert the premises but deny the conclusion.
FOUR TESTS Four tests allow us to identify deductive / inductive arguments The indicator word test The strict necessity test The common pattern test The principle of charity test
INDICATOR WORD TEST DeductionInduction CertainlyProbably DefinitelyLikely AbsolutelyPlausible ConclusivelyReasonable This entails thatThe odds are that
CAUTION! -Arguments may not contain any indicator words. Pleasure is not the same thing as happiness. The occasional self-destructive behavior of the rich and famous confirms this too vividly. (Tom Morris) -Arguers may use indicator words incorrectly. (People very often overstate their cases.) -In these cases, other tests must be used to determine whether an argument is deductive or inductive.
The Strict Necessity Test An arguments conclusion either follows with strict logical necessity from its premises or it does not. If an arguments conclusion does follow with strict logical necessity from its premises, the argument should always be treated as deductive. if an arguments conclusion does not follow with strict logical necessity from its premises, the argument should normally be treated as inductive.
The Strict Necessity Test Examples: Alan is a father. Therefore Alan is a male. Jill is a six-year-old. Therefore, Jill cannot run a mile in one minute flat.
COMMON PATTERN TEST Modus ponens (affirming the antecedent) If A then B. A. Therefore B. (A = antecedent; B = consequent) This is a very common pattern of deductive reasoning.
Common Pattern Test Example (modus ponens) If we are in Paris, then we are in France. -------A----------- --------B----------- We are in Paris. --------A--------- Therefore, we are in France. ---------B-----------
PRINCIPLE OF CHARITY TEST When interpreting an unclear argument, always give the speaker / writer the benefit of the doubt. Fosters good will and mutual understanding in an argument. Promotes the discovery of truth by insisting that we confront arguments that we ourselves admit to be the strongest and most plausible versions of those arguments.
Exceptions to the Strict Necessity Test An argument in which the conclusion does not follow necessarily from the premises should be treated as deductive if either: 1.The language or context make clear that the arguer intended to offer a logically conclusive argument, but the argument is in fact not logically conclusive; 2.The argument has a pattern of reasoning that is characteristically deductive, and nothing else about the argument indicated clearly that the argument is meant to be inductive.
Exceptions to the Strict Necessity Test Examples 1.Magellans ships sailed around the world. It necessarily follows, therefore, that the earth is a sphere. (The arguer intended to offer a logically conclusive argument, so it should be treated as deductive.) 2.If Im Bill Gates, then Im mortal. Im not Bill Gates. Therefore, Im not mortal. (The argument has a pattern of reasoning characteristic of deductive arguments, so should be treated as deductive.)
SUMMARY: How to distinguish deductive from inductive arguments If the conclusion follows necessarily from the premises = deductive If the conclusion does not follow necessarily from the premises = inductive, unless Language indicates it is deductive Argument has deductive pattern of reasoning If the argument has a pattern of reasoning that is characteristically deductive = deductive, unless Clear evidence indicates it is intended to be inductive If the argument has a pattern of reasoning that is characteristically inductive = inductive unless Clear evidence indicates it is intended to be deductive If the argument contains an indicator word If still in doubt: Principle of Charity
5 COMMON DEDUCTIVE PATTERNS Hypothetical syllogism Categorical syllogism Argument by elimination Argument based on mathematics Argument from definition
HYPOTHETICAL SYLLOGISM A syllogism is a three-line argument with two premises, one of which is a conditional. Modes ponens is a syllogism. Other syllogisms are: Chain arguments Modus tollens (denying the consequent) Denying the antecedent Affirming the consequent
CHAIN ARGUMENT If A then B. If B then C. Therefore if A then C. If you are blue in the face then you are lying. If you are lying then you cant be my friend. Therefore if you are blue in the face then you cant be my friend.
MODUS TOLLENS If A then B. Not B. Therefore not A. If were in Sacramento, were in California. Were not in California. Therefore, were not in Sacramento. If you love me, youll come with me to Tibet. You will not come with me to Tibet. Therefore you do not love me.
DENYING THE ANTECEDENT*** If A then B. Not A. Therefore not B. *If Tiger Woods won this years Masters then hes a great athlete. Tiger Woods didnt win this years Masters. Therefore, Tiger Woods is not a great athlete. *If Jack comes to the party, Jill will leave. Jack did not come to the party. Therefore Jill did not leave. ***Denying the antecedent is a fallacious deductive pattern
AFFIRMING THE CONSEQUENT*** If A then B. B. Therefore A. *If we are on Neptune then we are in the solar system. We are in the solar system. Therefore we are on Neptune. ***Affirming the consequent is a fallacious deductive pattern Exercise: Identify the argument pattern (ex. 3.2, p. 65)
MODUS PONENS (affirming the antecedent): If A then B. A. Therefore B. CHAIN: If A then B. If B then C. Therefore if A then C. MODUS TOLLENS: If A then B. Not B. Therefore not A. *DENYING THE ANTECEDENT: If A then B. Not A. Therefore not B. *AFFIRMING THE CONSEQUENT: If A then B. B. Therefore A.
PRINCIPLE OF CHARITY Attribute an arguer the strongest argument possible. Andy told me he ate at JBs yesterday. But JBs was destroyed by a fire a month ago. It is certain therefore that Andy is either lying or mistaken. Caution The Principle of Charity is a principle of argument interpretation, not a principle of argument repair.
CATEGORICAL SYLLOGISM A three-line argument in which each statement begins with one of the words all, some, or no. Some pigs have wings All winged things sing. Therefore some pigs sing.
ARGUMENT BY ELIMINATION Rules out various logical possibilities until only a single possibility remains. Either Dutch or Jack or Celia committed the murder. If D or J committed the murder then the weapon was a rope. The weapon was not a rope. Therefore neither D nor J committed the murder. Therefore C committed the murder.