Reasoning

Effectively

Six criteria for evaluating philosophical claims and theories:

Conceptual clarity = define your terms!Consistency = any contradictions?

Logical inconsistencySelf-referential inconsistency

Rational coherence = how do the parts “hang together”?Comprehensiveness = does a philosophy account for a wide range of

phenomena?Compatibility = does a part of your philosophy fly in the face of well-

established facts and theories?Compelling = warranted?!

Montreal is about 200 km from Ottawa, while Toronto is 400 km from Ottawa. Toronto is closer to

Ottawa than Montreal. Logical inconsistency

There are no truths.

Self-referential inconsistency

John is taller than Jake, and Jake is taller than Fred, while Fred is taller

than John.

Logical inconsistency

This sentence is not true.

Self-referential inconsistency

A. It is always morally wrong to take the life of another human being. B. It is morally permissible to execute serious criminals.

Logical inconsistency

The Goal of PhilosophyExcerpt from page 45

Logic =the study of methods for evaluating arguments and reasoning.

Some Key Terms:A set of statements in which one or more of the statements attempt to provide reasons or evidence for the truth of another statement =ARGUMENT

A statement in an argument that serves to provide evidence for the truth of a claim =PREMISE (OR REASON)

The statement in an argument that the premises are claimed to support or imply =CONCLUSION

List several premise indicators:SinceBecauseFor/for one thingFor the reason

thatFollows fromInasmuch as

As shown byGiven thatSeeing thatOwing toSeeing thatAs/as indicated byAssuming thatConsidering that

List several conclusion indicators:

ThereforeHenceThus/ergoSoFollows thatConsequentlyWhich entails thatAccordingly

Which proves thatWhich implies thatNecessarilyMust be the case

thatWhich means thatDemonstrates thatWe can conclude

thatAs a result

A ____ argument is one in which it is claimed that the conclusion necessarily follows from the

premises. Deductive

An argument in which it is claimed that the premises make the conclusion highly probable:

_____Inductive argument

A form of reasoning that tries to show that a particular theory is superior to all its

competitors and that it is therefore likely to be true: ___

Abductive argument (inference to the best explanation)

Deductive ArgumentsFirst, is the argument valid or invalid?The significance of validity…

If valid, is the argument sound?

Example:1. If all events are caused, then we

are not free. 2. All events are caused. Therefore: We are not free.

Valid?Sound?

Some key terms:Two simpler statements that are connected with the words if and then =CONDITIONAL STATEMENT

The first part of a conditional statement (the if clause) = ANTECEDENT

The second part of a conditional statement ( the then clause) =CONSEQUENT

Example:If I study for the Chapter 1 test on Monday, then I’ll earn a good grade.

A conditional statement claims that the truth of the antecedent is a

sufficient condition for the truth of the consequent (page A2)

More key terms:Sufficient condition = statement A is a sufficient condition

for statement B if the truth of A guarantees the truth of BExample: Being pregnant (A) is a sufficient condition for being

female (B).Necessary condition: statement A is a necessary condition

for statement B if the truth of B requires the truth of AExample: Being a female (A) is a necessary condition for being

pregnant (B). [However, being a female is not a sufficient condition for being

pregnant.]

Sufficient Conditions (X guarantees Y)Earning a total of 900 points (90%) in this Honors Philosophy

class is a sufficient condition for earning a final grade of H-. If you have 900 points for the course, then it must follow that you will have a final grade of H-. [not necessary as 920 points would too]

Pouring a gallon of freezing water on my sleeping student is sufficient to wake him up. If I pour the gallon of freezing water on him then it’s guaranteed that he will wake up. [not necessary as a punch to the jaw would do it as well]

Rain pouring from the sky is a sufficient condition for the ground to be wet. [not necessary, as the sprinkler could be on]

Necessary Conditions (If we don’t have X, we won’t have Y)

Having gasoline in my car (I have a gasoline engine) is a necessary condition for my car to start. Without gasoline (x) my car (y) will not start. Of course, having gasoline in the car does not guarantee that my car will start. There are many other conditions needed for my car to start.

Having oxygen in the earth’s atmosphere is a necessary condition for human life. Certainly, having oxygen will not guarantee human life. There are many other conditions needed for human life other than oxygen in the atmosphere.

Being 18 years of age is a necessary condition for being able to buy cigarettes legally in Ohio. Of course, being 18 does not guarantee that a person will buy cigarettes. There are many other conditions that lead to a person buying cigarettes than being 18 years of age.

Is sunlight a necessary or sufficient condition for the

roses to bloom?Sunlight is a necessary condition for the roses to bloom, since without sunlight it would be impossible for the roses to bloom.  It is not a sufficient condition, though, because sunlight alone does not guarantee that the roses will bloom.

Is earning a final grade of C a necessary or sufficient condition for

passing the course?Earning a final grade of C is a sufficient condition for

passing this course because earning a C guarantees passing it.  It is not a necessary condition because there are other ways to pass the course other than earning final grade of C.

Is being a male a necessary or sufficient condition for being a

father?Being a male is  a necessary condition for being a

father since it is impossible to be a father without being a male.  Being a male is not a sufficient condition, however, since being a male does not guarantee that a male will be a father.

Is having the flu virus a necessary or sufficient condition for being

sick?Having a flu virus is sufficient for being sick, but

not necessary since there are other ways to be sick besides having a flu virus.

Is being composed of H2O a necessary or sufficient condition for

being water?Both! Something must be H2O to be water,

and if it is nothing but H2O that is sufficient to make it water.

Well-Known Valid Deductive Argument Forms

Modus Ponens

(Affirming the

Antecedent)

Modus Tollens

(Denying the Consequent)

Hypothetical Syllogism

Disjunctive Syllogism

1. If P, then Q. 2. P. 3. Therefore:

Q.

1. If P, then Q. 2. Not-Q.3. Therefore:

not-P.

1. If P, then Q. 2. If Q, then R.3. Therefore: if

P, then R.

1. Either P or Q.

2. Not-P. 3. Therefore:

Q.

Modus Ponens (Affirming the Antecedent)1. If P, then Q. 2. P. 3. Therefore: Q.

1. If Spot is a dog, then Spot is a mammal

2. Spot is a dog.3. Therefore, Spot is a

mammal.

Philosophical Example of Modus Ponens

1. If the universe shows evidence of design, then there is a God.

2. The universe shows evidence of design.

3. Therefore, there is a God.

Modus Tollens (Denying the Consequent)

1. If P, then Q. 2. Not-Q. 3. Therefore: not-

P.

1. If John is eligible for the award, then he is a junior.

2. John is not a junior.

3. Therefore, John is not eligible for the

award.

Philosophical Examples of Modus Tollens1. If we are morally

responsible for our actions, then we

have freedom of the will. 2. We do not have

freedom of the will. 3. Therefore, we are

not morally responsible for our actions.

1. If God exists, there

would be no unnecessary evil

in the world. 2. There is

unnecessary evil in the world.

3. Therefore, God does not exist.

FallacyA fallacy is an argument form that is logically defective because the premises provide little or no support for the conclusion.

Fallacy of Denying the Antecedent1. If P, then Q. 2. Not-P. 3. Therefore: not-

Q.

1. If Jones is a mother, then Jones is a

parent.2. Jones is not a

mother.3. Therefore,

Jones is not a parent.

Philosophical Example of the Fallacy of Denying the Antecedent

1. If Thomas Aquinas’s arguments for God are valid, then there is a God.

2. Thomas Aquinas’s arguments for God are not valid.

3. Therefore, there is not a God.

Fallacy of Affirming the Consequent1. If P, then Q. 2. Q. 3. Therefore: P.

1. If George Washington was assassinated, then he is dead.

2. George Washington is dead.

3. Therefore, George Washington was assassinated.

Philosophical Example of Affirming the Consequent

1. If morality is completely subjective, then people will differ in their moral beliefs.

2. People do differ in their moral beliefs. 3. Therefore, morality is completely subjective. (There

are no objective truths about what is morally right or wrong.)

Another Example1. If medical science is completely subjective, then

people will differ in their medical beliefs. 2. People do differ in their medical beliefs.

(Some people believe that sacrificing twin babies will cure the community of a plague; on the other hand, our society doesn’t believe this.)

3. Therefore, medical science is completely subjective. (There are no objective truths about what will or won’t cure disease—a false conclusion.)

SyllogismA syllogism is a deductive argument with two premises and a conclusion.

Hypothetical Syllogism1. If P, then Q. 2. If Q, then R. 3. Therefore: if

P, then R.

1. If I learn logic, then I will write better essays.

2. If I write better essays, then I will get better grades.

3. Therefore, if I learn logic, then I will get better grades.

Philosophical Example of a Valid Hypothetical Syllogism

1. If the methods of science give us only information about physical reality, then science cannot tell us whether a nonphysical reality exists.

2. If science cannot tell us whether a nonphysical reality exists, then science cannot tell us whether we have a soul.

3. Therefore, if the methods of science give us only information about physical reality, then science

cannot tell us whether we have a soul.

Disjunctive StatementA disjunctive statement asserts that at least one of two alternatives is true. It typically is expressed as an either-or statement.

Disjunctive Syllogism1. Either P or Q. 2. Not-P. 3. Therefore: Q.

1. Either the bulb is burnt out or it is not receiving electricity.

2. The bulb is not burnt out.

3. Therefore, the bulb is not receiving electricity.

Philosophical Example of a Disjunctive Syllogism

1. Either the universe contains in itself a sufficient reason for its existence or it was caused to exist.

2. The universe does not contain in itself a sufficient reason for its existence.

3. Therefore, the universe was caused to exist.

Fallacy of Affirming the Disjunct

1. Either P or Q. 2. P. 3. Therefore: not-

Q.

1. Either the bulb is burnt out or it is not receiving

electricity.2. The bulb is burnt

out.3. Therefore, the bulb

is receiving electricity.

Philosophical Example of the Fallacy of Affirming the Disjunct

1. Either reason is the source of moral principles or divine revelation is.

2. Reason is the source of moral principles. 3. Therefore, divine revelation is not the source of moral principles.

Valid/Argument Form?Either I left my wallet on my dresser or I must have lost it

The wallet is not on my dresserTherefore, I have lost it.

Valid/Disjunctive syllogism

Valid/Argument Form?

1. If Queen Elizabeth is an American citizen, then she is a human being.

2. Queen Elizabeth is not an American citizen.Therefore, Queen Elizabeth is not a human being.

Invalid/Denying the Antecedent

Valid/Argument Form?If I have prepared thoroughly, I will do well.I have prepared thoroughly.Therefore, I will do well.

Valid/Modus Ponens (Affirming the Antecedent)

Valid/Argument Form?

1. If Bill Gates owns Fort Knox, then he is rich.2. Bill Gates is rich. Therefore, Bill Gates owns Fort Knox.

Invalid/Affirming the Consequent

Valid/Argument Form?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.

Valid/Hypothetical Syllogism

Valid/Argument Form?

1. If red, then black.2. If black, then yellow.Therefore: if yellow, then red.

Invalid Hypothetical Syllogism

Valid/Argument Form?If Janice is a really good friend, then she will remember my birthday.

She did not remember my birthday.Therefore, Janice is not a really good friend.

Valid/Modus Tollens (Denying the Consequent)

Valid/Argument Form?1. Either Max is a cat or Max is a mammal. 2. Max is a cat. Therefore, Max is not a mammal.

Invalid/Affirming the Disjunct

Inductive ArgumentsRemember, if the premises are true, then it is highly

probably that the conclusion is true

Important Inductive Argument FormsEnumerative Inductive

ArgumentArgument by Analogy Inference to the Best

Explanation

1. All observed A are B.Therefore: all A are probably

B.

1. A is like B.2. B has property C.Therefore: A has property C.

1. A2. The best explanation for

A is B.Therefore: B

1. All cars that I have observed have been red.

Therefore: Probably all cars everywhere are red.

1. Taking this philosophy class is similar to taking an English class.

2. I always get low grades in my English classes.

Therefore: I conclude that I will also get a low grade in this philosophy class.

1. I have heard strange noises late at night in my room.

2. The best explanation for these strange noises is that they are caused by ghosts.

Therefore: Ghosts probably exist.

Strong vs. Cogent ArgumentsA strong argument is an

inductive argument in which true premises would make the conclusion highly probable

A cogent argument is a strong inductive argument with true premises

Informal Fallacies

A type of bad reasoning that can be detected only by examining the content of the argument

America: love it or leave it

False Dilemma

You may argue that God doesn't exist, but you are just following a fad

Ad Hominem (Abusive)

Fred said that he is smarter than Jill, but he didn't prove it, so it must be false.

Appeal to Ignorance

Bill and Jill are arguing about cleaning out their closets: Jill: “We should clean out the closets. They are getting a bit messy.” Bill: “Why, we just went through those closets last year. Do we have to clean them out everyday?” Jill: “I never said anything about cleaning them out every day. You just want to keep all your junk forever, which is just ridiculous.”

Straw Man

Fred, the Australian, stole my wallet. Thus, all Australians are thieves

Hasty Generalization

The brick wall is six feet tall. Thus, the bricks in the wall are six feet tall.

Division (Whole to Part)

Since scientists cannot prove that global warming will occur, it probably won't.

Appeal to Ignorance

Each brick is three inches high, thus, the brick wall is three inches high.

Composition (Part to Whole)

A plane is a carpenter’s tool, and the Boeing 737 is a plane, hence the Boeing 737 is a carpenter's tool .

Equivocation

Either I keep smoking, or I’ll get fat. I don’t want to get fat, so I better keep smoking.

False Dichotomy

Germany is a militant country. Thus, each German is militant.

Division (Whole to Part)

We should discount what Prime Minister Brown says about taxation because he won't be hurt by the increase.

Ad Hominem (Circumstantial)

Since I’m not lying, it follows that I’m telling the truth.

Begging the Question

Child: “Can we get a dog?”Parent: “No.”Child: “It would protect us.”Parent: “Still, no.”Child: “Why do you want to leave us and our house unprotected?”

Straw Man

Money makes people arrogant False Cause

The book I have written is loved by everyone who reads it.

Wishful Thinking

People are like dogs. They respond best to clear discipline.

False Analogy

Every person is either wholly good or wholly evil

False Dilemma (False Dichotomy)

Because the brain is capable of consciousness, each neural cell in the brain must be capable of consciousness.

Division (Whole to Part)

Since you cannot prove that ghosts do not exist, they must exist.

Appeal to Ignorance

Government is like business, so just as business must be sensitive primarily to the bottom line, so also must government.

False Analogy

Each part of the show, from the special effects to the acting is a masterpiece. So, the whole show is a masterpiece.

Composition (Part to Whole)

So Kim argues that “El Taquito is the best Mexican restaurant in town. They make their own tortillas, they only use the freshest ingredients, and everything I've had there has been delicious.”

Art replies: “Kim is Japanese, and so we can ignore his opinion on Mexican food.”

Ad Hominem (Abusive)

Drinking fresh water will keep you well.

False Cause

We know that God exists, since the Bible says God exists. What the Bible says must be true, since God wrote it and God never lies.

Begging the Question

Minorities get paid less than “whites” in America. Therefore, the black CEO of a multi-billion dollar company gets paid less than the white janitor who cleans his office.

Division (Whole to Part)

In my philosophy class we have been examining some of the obstacles to discovering truth. Therefore I conclude that it is impossible to ever discover truth.

Hasty Generalization