*Critical ThinkingLECTURE 3Basic Logical Concepts

Lecture Notes 2008 McGraw Hill Higher Education

ArgumentIn critical thinking, an argument is a claim defended with reasons. The purpose of the argument is an attempt to convince someone (or even yourself) of something. Refer to Bassham p30

ArgumentPremisesConclusionSUPPORTshow effort inCONVINCINGpeople

Premise IndicatorsSinceBecausefor/for one thingfor the reason thatfollows frominasmuch asas shown by

given thatseeing thatowing toseeing thatas/as indicated byassuming thatconsidering that

Conclusion Indicatorsthereforehencethus/ergosofollows thatconsequentlywhich entails thatwhich proves that

which implies thatnecessarilymust be the case thatwhich means thatdemonstrates thatwe can conclude thatas a result

Evaluating Arguments: distinguishing good arguments from bad ones:In evaluating any argument, one should always ask two key questions:Are the premises true?Do the premises provide good reasons to accept the conclusion?

*A Valid ArgumentAn argument is valid if there is no possible way for its premises to be true and its conclusion false (at the same time). The conclusion, therefore, must follow from the premise(s).VALID ARGUMENT TRUE PREMISE TRUE CONCLUSION

*A Valid ArgumentFor example:Every student in this class has paid up the class subscription (true). Ah Meng is a student of this class (true). So Ah Meng has paid up his class subscription.(true)

*Definition of a Valid argumentA valid argument is a deductive argument in which the conclusion claimed follows necessarily from the premises that is, a deductive argument in which it is impossible for the premise to be true and the conclusion to be false at the same time.

*Examples of Valid/deductive argumentsIf Lassie barks, then Simon will wake up. Lassi barked. Simon woke up. This is a valid argument. It is impossible for the premises to be true and the conclusion false.

*An argument is valid when it is impossible for the premises to be true and the conclusion to be false (at the same time). An argument that is not valid is called invalid.A Valid Argument

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Consider this exampleAll dogs bark. Ralph is a dog. Therefore, Ralph barks.

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All dogs bark. Ralph is a dog. Therefore, Ralph barks.VALID

*All dogs bark.Ralph is a dog.

Therefore, Ralph barks.Lets take a deeper look at this argument:

*All dogs barkRalph is a dog

Therefore, Ralph barksLets take a deeper look at this argument:

*All dogs bark.Ralph is a dog.

Therefore, Ralph barks. If this is true And if this is true Then Ralph must be able to bark. There is no possible way it could be a false statement if the two premises are true.Lets look again at why its a valid argument:

*All dogs barkRalph is a dog

Therefore, Ralph barks If this is true And if this is true Then Ralph must be able to bark. There is no possible way it could be a false statement if the two premises are trueBut, what if the premises are not true?Sometimes dogs undergo surgery to remove theirlarynx (vocal cords). After this sort of operation theycannot bark.

This could be false

*All dogs bark. If this is trueBut, what if the premises are not true?

This could be falseIf this is the case ... then we would say that one of the premises is not true and we would REJECT the argument for that reason. Ralph is a dog

Therefore, Ralph barksRalph could bea dog which hashad its larynxremoved.

*All dogs bark If this is trueBut, what if the premises are not true?

This could be falseIf this is the case ...But, the important thing to remember is that the argument would STILL be VALID!Ralph is a dog

Therefore, Ralph barks

*All dogs bark.WHY would it still be a VALID argument?

If this is the case ...But, the important thing to remember is thatthe argument would STILL be VALID!Ralph is a dog

Therefore, Ralph barksIts still valid because the same rule applies:An argument is valid when theconclusion cannot be falseIFthe premises are true.

Therefore, even though this premise could turn out to be false, we are only interested - for the purposes of determining validity - in what would happen IF itwere true!

*Its still valid because the same rule applies:An argument is valid when theconclusion cannot be falseIFthe premises are true.

Therefore, even though this premise could turn out to be false, we are only interested - for the purposes of determining validity - in what would happen IF itwere true!All dogs barkWHY would it still be a VALID argument?

Remember our definition of a valid argument:

An argument is valid when it is impossible for theconclusion to be false if the premises are true.Therefore, Ralph barks.Ralph is a dog.

*Valid ArgumentValid arguments: The validity of an argument has nothing to do with the truth of its premises. If the premises would guarantee the conclusion, if the premises were true, then the argument is valid.

*Valid Argument but false premise and false conclusionValid argument: All squares are circles.All circles are triangles. Therefore, all squares are triangles.

Remember, a valid argument does not mean it is a good argument. An argument can be a good argument and be invalid and could be a bad argument but be valid (because it has false premises like the one above).

*However, Dr Mathew teaches philosophy. All philosophy professors are bald. So Dr Mathew is bald.

The argument is valid. There is no possible way the premises could be true and the conclusion false at the same time.

But it is a bad argument because the second premise is false.

*Invalid ArgumentConclusion that does not follow from the premise:Dr Matthew teaches Philosophy. So Dr Matthew is old.There is no connection. Premise does not support conclusion.

So what do you know of an invalid argument?1. If it does not follow from the premises.All dogs are animals. InvalidLassie is an animal.Therefore, Lassie is a dog. All humans are mortal. ValidSocrates is human.Therefore, Socrates is mortal.

Invalid argumentsAll pears are vegetables (false premise)All fruits are vegetables (false premise)Therefore, all pears are fruits (true conclusion)

All dogs are cats (false premise)All cats are whales (false premise)Therefore all whales are dogs (false conclusion)

*Invalid ArgumentsIf Im a monkeys uncle, then Im a primate(true premise)

Im not a monkeys uncle (true premise)So, Im not a primate (false conclusion)

*Deductive and Inductive Arguments

What are Deductive and Inductive arguments?

Deductive and Inductive Arguments

Traditionally, arguments have been divided into two types: deductive and inductive arguments. All arguments claim to provide support that is, evidence or reasons for their conclusions. But arguments differ in the amount of support they claim to provide.

DefinitionsDeductive arguments Try to prove their conclusions with rigorous, inescapable logic/premise(s).Inductive arguments Try to show that their conclusions are plausible or likely given the premise(s).Refer to Bassham p52

*Deductive & Inductive Arguments DeductiveAll humans are mortal.Socrates is human.Therefore, Socrates is mortal. InductiveEvery ruby so far discovered has been red.So, probably all rubies are red.

*Key differences between Deductive and Inductive Arguments(1)Deductive arguments claim thatIt is impossible for all the premises to be true and the conclusion false.It is unlikely for the premises to be true and the conclusion false.It is logically inconsistent to accept the premises and deny the conclusion If you accept the premises, you must accept the conclusion.INCONSISTENT - CONTRADICTORY/ CONFLICTING.

*Example of Deductive Argument`All oaks are trees.All trees are plants.So, all oaks are plants.

*Key differences between Deductive and Inductive Arguments(2)Inductive arguments claim that..If the premises are true, then the conclusion is probably true.The conclusion follows probably from the premises.The premises provide good (but not conclusive) evidence for the truth of the conclusion.It is unlikely for the premises to be true and the conclusion false.Although it is logically consistent to assert the premises and deny the conclusion, the conclusion is probably true if the premises are true.

*Example of Inductive ArgumentMost college students own a laptop.Swee Leng is a college student.So, Swee Leng probably owns a laptop.

DEDUCTIVE OR INDUCTIVE? 1. All men are mortal. (premise) 2. Socrates was a man. (premise) 3. Socrates was mortal. (conclusion)*

*Key differences between Deductive and Inductive Arguments(3)

Deductive arguments claim thatInductive arguments claim thatIf the premises are true, then the conclusion must be true.If the premises are true, then the conclusion is probably true.The conclusion follows necessarily from the premises.The conclusion follows probably from the premises.The premises provide conclusive evidence for the truth of the conclusion.The premises provide good (but not conclusive) evidence for the truth of the conclusion.It is impossible for all the premises to be true and the conclusion false.It is unlikely for the premises to be true and the conclusion false.It is logically inconsistent to assert the premises and deny the conclusion, if you accept the premises, you must accept the conclusion.Although it is logically consistent to assert the premises and deny the conclusion, the conclusion is probably true if the premises are true.

*Distinguishing deductive from Inductive Arguments(1)Indicator Words: Deductive: certainly, definitely, this entails that, conclusivelyInductive: probably, likely, one would expect, odds are, reasonable to assumeLike before, indicators are not perfect. They are not always present, and they can sometimes be misleading. (e.g., The speaker may say it certainly follows but be exaggerating, knowing that it only probably follows.)

*Distinguishing Deductive from Inductive Arguments (2)

The Strict Necessity Test: If it makes a good (valid) deductive argument, assume it is. If it does not, assume it is not. An arguments conclusion follows with strict logical necessity from its premises or it does not.

*Telling the difference between Deductive and Inductive Arguments (3)The Common Pattern Test: There are many common patterns that valid arguments use.For example: If P then Q. P. Therefore Q.This is called Modus Ponens If an argument follows one of these patterns, it is deductive.

*Distinguishing deductive from inductive argumentsDetermine whether the following arguments are deductive or inductive.The sign says it is 10 miles to the Kinta river. Therefore, it is approximately 10 miles to Kinta river. If Bigfoot is human, then Bigfoot has a heart. Bigfoot is not human So, Bigfoot does not have a heart.Simba is a lion. Necessarily, therefore, Simba must have four legs.4. All mosquitoes are insects. All insects are animals. So, all mosquitoes are animals.

*Common Patterns of Deductive ReasoningHypothetical SyllogismCategorical SyllogismArgument by EliminationArgument Based on Mathematics Argument from Definition

*Common Patterns of Deductive ReasoningHypothetical Syllogism: three line argument that contains at least one conditional. (if- then)1If A then B. A. Therefore B. (Modus Ponens)2 If P then Q.If Q then R. Therefore if P then R. (chain argument) If A then B. Not B. Therefore not A. (Modus Tollens)

*Example-Modus ponensIf we are in the Kuala Lumpur (A), we are in Malaysia (B).We are in Kuala Lumpur (A)So we are in Malaysia. (B)

Modus tollensConsider an example:If an intruder is detected by the alarm, the alarm goes off. The alarm does not go off. Therefore, no intruder is detected*

*Hypothetical SyllogismIf A (antecedent) then B (consequent). A. Therefore B. (One conditional premise, a second premise that asserts as true the antecedent and a conclusion that asserts[emphasizes/affirms/stresses] as true the consequent)

*Hypothetical SyllogismInvalid versions (that are still deductive):If A then B. Not A. Therefore not B. (denying the antecedent) If I am a female then I am a person. I am not a female. Therefore I am not a person. If A then B. B. Therefore A. (affirming the consequent). If were on Neptune then we are in the solar system. We are in the solar system. Therefore, were on Neptune. These are still called deductive because usually people think they are valid when they put them forward.

Hypothetical syllogism is a valid argument of the following form:

P Q. Q R. Therefore, P R. In other words, this kind of argument states that if one implies another, and that other implies a third, then the first implies the third.*

An example of hypothetical syllogism: If I do not wake up, then I cannot go to work. If I cannot go to work, then I will not get paid. Therefore, if I do not wake up, then I will not get paid.

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*Common Patterns of Deductive ReasoningCategorical Syllogism: a three-lined argument in which each statement begins with the word all, some or no. Example Forms: All as are bs. All bs are cs. Therefore, all as are cs. Some as are bs. All bs are cs. Therefore some as are cs.Example: All oaks are treesAll trees are plants. So all oaks are plants.

*Common Patterns of Deductive ReasoningArgument by Elimination: seeks to logically rule out various possibilities until only a single possibility remains. Example forms: A or B. Not B. Therefore A. P or Q. if A then not P. A. Therefore Q.Example: Either Joe walked to the library or he drove. But Joe didnt drive to the library. Therefore, Joe walked to the library.

*Common Patterns of Deductive ReasoningArguments based on Mathematics: argument in which the conclusion depends largely or entirely on some mathematical calculation or measurement. Example forms: There are four as and two bs. Therefore there are six things all together. Example: Eight is greater than four. 8>4Four is greater than two. 4>2Therefore, eight is greater than two. 8>2

*Common Patterns of Deductive ReasoningArguments from definition: an argument in which the conclusion is presented as being true in virtue of the definition of some key word or phrase. Examples:Bob is a bachelor. Therefore Bob is unmarried.Janelle is a cardiologist. Therefore, Janelle is a doctor.

Activity:1.Solve the following mini-mysteries using your deductive reasoning power.Either Moriarty was the murderer or Stapleton was the murderer.If Stapleton was the murderer, then traces of phosphorus should have been found on the body.No traces of phosphorus were found on the body.Whodunnit?(Who did it?)

2.Solve the following mini-mysteries using your deductive reasoning powerThe murder did not occur in the library.If Adler was the murderer, then the weapon was a revolver.Either Hope was the murderer, or Adler was the murderer.If Hope was the murderer, then the murder took place in the library.Whodunnit? With what weapon?

3.Solve the following mini-mysteries using your deductive reasoning powerThe murder was not committed on the moor.If Windi was the murderer, then the weapon was a rope.Either Windi was the murderer, or Carl was the murderer.If the weapon was a rope, then the murder was committed on the lowlands.If Carl was the murderer, then the weapon was a crowbar.If the weapon was a crowbar, then the murder was committed on the moor.Whodunnit?(Who did it?) With what weapon? Where was the murder committed?

*Summarizing Deductive ValidityA valid deductive argument is an argument in which it is impossible for all the premises to be true and the conclusion false. In other words: If the premises are true, the conclusion must be true.The conclusion follows necessarily from the premises. The premises provide logically conclusive grounds for the truth of the premises.The truth of the premises would guarantee the truth of the conclusion. It is logically inconsistent to assert all the premises but deny the conclusion. It is impossible for the premises to be true and the conclusion to be false.

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