critical thinking 03 consistency

A Standard of Critical Thinking

Consistency

Review

Principle of Sufficient Principle of Sufficient Reason: for or any claim, Reason: for or any claim, give reason why it is give reason why it is true, or not.true, or not.

Principle of Charity: for Principle of Charity: for any claim, give it the any claim, give it the strongest possible strongest possible interpretation.interpretation.

Philosophy: the attempt to Philosophy: the attempt to answer, critically, the answer, critically, the epistemological, epistemological, metaphysical, and ethical metaphysical, and ethical questions.questions.

An Issue Question: is a An Issue Question: is a yes-or-no question, and is yes-or-no question, and is the way to formulate the way to formulate questions for the disputed questions for the disputed question method (question method (quaestioquaestio disputatadisputata).).

A virtue is an excellence, A virtue is an excellence, a mean between two a mean between two extremes called vices.extremes called vices.

the question

Reasons supporting the yes answer or

refuting the no answer.

Reasons supporting the no answer or refuting the yes

answer.

Which side has the better

reasons?

The Disputed Question Method

Review

Ambiguous: A term with Ambiguous: A term with more than one meaning.more than one meaning.

Truth: when a claim Truth: when a claim matches what is.matches what is.

Vague: A term with an Vague: A term with an unclear extension.unclear extension.

Claims are candidates Claims are candidates for truths, such as for truths, such as beliefs stated in beliefs stated in language.language.

answer.

reasons?

Does the thing designated by the subject have the property expressed by the predicate?

Review

answer.

reasons?

Do the things designated by the nouns stand in the relation expressed by the verb.

Review

Reviewto pursue the truth of a claim, avoid matters of taste, fill in the indices, and spell out the ceteris paribus.

to evaluate the truth of a claim determine whether the things designated by the nouns stand in the relation expressed by the verb.

to evaluate the truth of a claim determine whether the thing designated by the subject has the property expressed by the predicate

Review

to define a term give it one clear meaning.

to determine the truth of a claim determine whether the things designated by the nouns are in the extension of the verb.

to determine the truth of a claim determine whether the thing designated by the subject is in the extension of the predicate.

answer.

reasons?

Are the things designated by the nouns are in the extension of the verb?

Review

Descriptive definitions Descriptive definitions which describe or which describe or designate how a term is designate how a term is actually used.actually used.

Normative definitions Normative definitions which prescribe or which prescribe or stipulate how a term stipulate how a term ought to be used.ought to be used.

Descriptive claims which Descriptive claims which describe or designate describe or designate how things actually are.how things actually are.

Normative claims Normative claims which prescribe or which prescribe or stipulate how things stipulate how things ought to be.ought to be.

Law of Assumption—Law of Assumption—assume anything at any assume anything at any time.time.

Reviewdefine key terms—key terms are terms needed for the claim to be evaluated as true or false, they are terms whose properties or relations need to be specified or whose extensions need to be clarified.

define technical terms—technical terms are terms needed for critical thinking, such as truth, charity, and reason.

And Terms Indicative of Logical Structure

Logically Complex Truths

A Logically Simple Truth

The man is The man is cheating.cheating.

1 True

2 False

1 True

2 False

—He’s hiding cards

1 True

2 False —He’s doing magic

1 True

2 False

Two logical possibilities

Given that we’ve filled

in the indices,

made the ceteris paribus

explicit, and defined key

terms.

1 True

2 False

Also called States of Affairs or Possible Worlds

The man is The man is cheating.cheating. State DescriptionsState Descriptions

1 True The man is cheating.

2 FalseThe man is not

cheating.

Logical possibilities

How we describe logical

possibilities

Negation: Logical Complexity

1 True

2 False

The man is not The man is not cheating.cheating.

1 False

2 True

1 True

2 False

The man is not The man is not cheating.cheating.

1 False

2 True

it “flips” the truth value

Logical negation, often Logical negation, often expressed in English by expressed in English by ‘‘nonott ’’, is true when the , is true when the component claim is false, component claim is false, false when the component false when the component claim is true. It is claim is true. It is symbolized by symbolized by ‘‘~~ ’’ and has and has the logical form ~P.the logical form ~P.

1 True

2 False

1 False

2 True

~ “flips” the truth valueThe Logical Form of Negation: ~P, -P,

double negation

Any even number of negations cancel each other out.

No! They do not!

indicators for negations

a. notb. It is not the case that…c. n’t (the contraction)

- negations are often suppressed in common opposites such as on and off.

Fabricate a Truth

Test this out:Test this out:Take a true claim and make it false. Take a true claim and make it false. Then take a false claim and make it Then take a false claim and make it true.true.What happens when you add not to What happens when you add not to a true claim? What happens when a true claim? What happens when you add another not?you add another not?

Derek is leaping.Derek is leaping.

1 True

2 False

Two logical possibilities

Combining Logically Simple Truths

Derek is Derek is leaping.leaping.

Hansel is Hansel is leaping.leaping.

1 True True

2 True False

1 True True

2 True False

3 False True

1 True True

2 True False

3 False True

4 False False

1 True True

2 True False

3 False True

4 False False

Four possibilities

1 True True

2 True False

3 False True

4 False False

Four states of affairs

(states) or possible worlds

to calculate the number of possible worlds

raise two to the power of the number of claims being evaluated

Hansel is Hansel is leaping.leaping. State DescriptionsState Descriptions

1 True True Derek and Hansel are leaping

2 True FalseDerek leaps but Hansel

doesn't

3 False TrueHansel leaps but Derek

doesn’t

4 False FalseNeither Derek nor Hansel

Four State Descriptions

Logical Possibilities

Place your bet

HereHere’’s the bet:s the bet:In the next slide both Derek In the next slide both Derek and Hansel will be leaping.and Hansel will be leaping.

Which way would you bet, and Which way would you bet, and why?why?

Who wins the bet?

Derek is leaping.Derek is leaping. ANANDD

1 True ? True2 True False3 False True4 False False

In state #1 where both Derek and Hansel are leaping?

Who wins the bet?

1 TrueTrue

2 True False3 False True4 False False

In state #1 where both Derek and Hansel are leaping?

The complex claim is true when all the component claims are true, as they are in state

Who wins the bet?

1 TrueTrue

2 True ? False3 False True4 False False

The complex claim is true when all the component claims are true, as they are in state

How about case #2 where Derek is leaping but Hansel is not?

Who wins the bet?

1 TrueTrue

2 TrueFals

eFalse

3 False ? True4 False False

The complex claim is false when one or the other component claims are false…

…as they are in state #2…

Who wins the bet?

1 TrueTrue

2 TrueFals

eFalse

3 FalseFals

4 False False

The complex claim is false when one or the other component claims are false…

…or as they are in state #3, what about state #4?

Who wins the bet?

1 TrueTrue

2 TrueFals

eFalse

3 FalseFals

4 FalseFals

eFalse

The complex claim is false when both component claims are false.

As they are in state #4.

Logical conjunction, often Logical conjunction, often expressed in English by expressed in English by ‘‘andand’’, is true when the , is true when the component claims it joins component claims it joins are true, otherwise it is are true, otherwise it is false. It is symbolized by false. It is symbolized by ‘‘&& ’’. It. It’’s logical form is P & s logical form is P & Q.Q.

Logical Form of Conjunctions

P AND QP & QP • QP Q⋀

PP && QQ

1 TrueTrue

2 TrueFals

eFalse

3 FalseFals

4 FalseFals

eFalse

to prove a conjunction false

Prove that one of the component claims is false.

indicators for conjunctions

a. andb. butc. yetd. not both (includes

negation)

Putting conjunction and negation together

Contradictions

A Necessity of Logic

Let’s define ‘this square’ as the thing depicted below at x-position 303 px and y-position 318 px and of the dimensions

242 px by 242 px.

this square

Next let’s define ‘white’ as the color depicted below of the RGB values Red = 255, Green = 254, Blue = 235.

Contradictions

Now pay attention to your mental processes as we make the following claim:

Contradictions

>>This square is white and this square is >>This square is white and this square is not white.<<not white.<<

Contradictions

What was your reaction?What was your reaction?

Contradictions

Eleven is a prime number and

eleven is not a prime number.

Jacqui thinks black is more alluring than pink and

she doesn’t.

The music is loud and the music is quiet.*

Jupiter is bigger than Mars and it is not bigger than Mars.

The Constitution of the United States was adopted on September 17, 1787 and

The Constitution of the United States was adopted on July 4, 1776.*

Romeo and Juliette is a tragedy and it is not a tragedy.*

New York is and isn’t the largest city in the US.*

Hockey is better than basketball but it is not better than basketball.*

Putting Negation and Conjunction Together

Same-sex schools are optimal and same-sex schools are less than optimal.

Drinking milk is healthy and unhealthy.*

The jellyfish has tentacles—not!The child looks at the jellyfish and looks away from it*.

Which claim is not a contradiction?

Contradictions

The square is The square is whitewhite &&

The square is not The square is not whitewhite

1 True ? False

2 False ? True

The Logic of a Contradiction

Given that conjunctions are true when all component claims are true, what is the truth value of this

conjunction?

Contradictions

The square is The square is whitewhite &&

The square is not The square is not whitewhite

1 TrueFals

eFalse

2 FalseFals

The Logical Form of a Contradiction: P & ~P

Contradictions are false in all possible worlds.

Contradictions

PP && ~P~P

1 TrueFals

eFalse

2 FalseFals

The Logical Form of a Contradiction: P & ~P

Contradictions are false in all possible worlds.

Contradiction, a special Contradiction, a special form of conjunction in form of conjunction in which a claim and its which a claim and its negation are joined—they negation are joined—they are always false. The logical are always false. The logical form of a contradiction is P form of a contradiction is P & ~P.& ~P.

Contradictions

~~ (P(P && ~P)~P)

1 TrueFals

eFalse

2 FalseFals

The Logical Form of the Principle of Noncontradiction

The Principle of Noncontradiction is true in all possible worlds.

An Emergent Property

Neither hydrogen nor oxygen are wet at room temperature—wetness emerges as a property when they are properly combined. In a similar manner, being false in all possible worlds emerges when a claim and its negation are properly conjoined.

Contradiction

~(P & ~P)

The Principle of Noncontradiction

The Principle of The Principle of Noncontradiction, states Noncontradiction, states that no thing can, at the that no thing can, at the same time and in the same same time and in the same manner, both have and not manner, both have and not have the same property.have the same property.

The Principle of The Principle of Noncontradiction, (Noncontradiction, (specialspecial) ) no claim, adequately no claim, adequately defined, can be both true defined, can be both true and not true.and not true.

The Principle of The Principle of Noncontradiction, Noncontradiction, nono claim, claim, adequately defined, can be adequately defined, can be both true and not trueboth true and not true..

The Principle of The Principle of Noncontradiction Noncontradiction ~~((T & ~ T & ~ TT))

Consider…

Matters of Taste or Matters of Taste or OpinionOpinion

Matters of ConventionMatters of Convention

Matters of FactMatters of Fact

Matters of NecessityMatters of Necessity

Four Types of Truth

∏∏ == 3.141592...3.141592...

11 ++ 11 22==

π needs to be exact for a circle to be round

simple arithmetic is the way things are

PP && PP~~ (( ))Noncontradiction is needed for critical thinking

Consistency

A set of claims free from contradictions

The jellyfish has tentacles.

The child looks at the jellyfish.

Drinking milk is healthy.

Same-sex schools are optimal.

Eleven is a prime number.

The music is loud.Jupiter is bigger than

The Constitution of the United States was adopted on September 17, 1787

Romeo and Juliette is a tragedy.

New York is the largest city in the US.

Hockey is better than basketball.

Jacqui thinks black is more alluring than pink.

Consistency

A set of claims free from contradictions

The child looks at the jellyfish.

Drinking milk is healthy.

Same-sex schools are optimal.

Eleven is a prime number.

The jellyfish has tentacles—not.

The music is loud.Jupiter is bigger than

The Constitution of the United States was adopted on September 17, 1787

Romeo and Juliette is a tragedy.

New York is the largest city in the US.

Hockey is better than basketball.

Which claim causes the inconsistency?

Jacqui thinks black is more alluring than pink.

The Standard of The Standard of Consistency—accept only Consistency—accept only those beliefs which are those beliefs which are consistent with each other consistent with each other and any accessible and any accessible evidence.evidence.

Using the Principle of Noncontradiction to test

definitions.

Counterexamples

Line of Reasoning

An explanation showing that the

definition should be true of a specific example (thing or

event).

Another explanation showing that the

definition is not true of the same example.

Reject the original

definitionOriginal definition.

A Method for Reasoning with Contradictions

Proof by Counterexample

Another Line of Reasoning

Counterexamples

Testing Definitions for ConsistencyDefinition: ‘father’ means the female parent

You know the definition is wrong, but how can you prove it?

Extensions

Terms have extensions

being a vowel

True Definitions

The Subject and Predicate Have Identical Extensions

being divisible by two without a

remainder

144 57

being an even number

Even numbers are divisible by two without remainder

False Definitions

The Subject and Predicate Do Not Have Identical Extensions

being vowelsbeing a, e, i, o, and u

a, e, i, o, and u are the only vowels

Counterexamples

Definition: Definition: ‘‘fatherfather’’ means the female means the female parentparent

fatherfather the female parentthe female parentList of fathers: List of female parents:Adam, Joseph,

Martin,Muhammad

Michelle, Mary, Hillary, Sarah

Testing Definitions for Consistency

Generate lists of things that fall under the term being defined and the property used to define it — they should

be identical—stop when you show they are not.

False Definitions

being a female parent

being a father

a, e, i, o, and u are the only vowels

Joseph Hillar

yMartinMuhamma

Sarah Mar

Michelle

These lists are not identical, in fact, they have no overlap at all, no members in common.

Counterexamples

So: So: ‘‘fatherfather’’ does not meandoes not mean the female the female parentparent

fatherfather the female parentthe female parent

List of fathers: ≠List of female

parents:Adam, Joseph,

Martin,Muhammad

≠Michelle, Mary, Hillary, Sarah

By this definition

Hillary should be the father, because she is

a female parent.

Hillary is not the father but the mother, which is defined as the

female parent.

Reject: father

means the female parent

Father means the female parent

Applied

By all other sources

Counterexamples

Testing Definitions for ConsistencyReject: ‘father’ means the female parent

Proof: by this definition, Hillary is a father because she is the female parent, but she’s not a father according to many other sources (dictionaries and encyclopedias) which define the female parent as the mother. This is a contradiction, and I reject the definition in favor of general usage.

Counterexamples

Testing Definitions for ConsistencyReject: ‘father’ means the female parent

Alternate Proof: by this definition, Martin is not a father because he is not the female parent, but according to biology texts he is a father, because he is the sperm donor to the offspring. This definition is inconsistent with biological terminology—so I reject the definition.

Counterexamples

Testing Complex Definitions for ConsistencyDefinition: Mammals have fur, mammary glands, and

give live birth

Using the Principle of Noncontradiction, prove that this

claim is false.

Counterexamples

Testing Complex Definitions for Consistency

Break the definition into a series of claims which isolate each property, to prepare to test each. Then take the

one you will test.

Definition: Mammals have fur, mammary glands, and give live birth

Mammals have furMammals have mammary glands

Mammals give live birth

Counterexamples

Definition: Mammals give live birthDefinition: Mammals give live birth

mammalmammal giving live birthgiving live birth

List of mammals: list of things which give live

cats, dogs, humans, platypuses

cats, dogs, humans

Generate lists of things that fall under the term being defined and the property used to define it — stop when

you determine that they are not identical.

False Definitions

giving live birthbeing a mammal

humans

platypuses

These do have significant overlap, but they are not identical.

Counterexamples

So: Some mammals So: Some mammals do not givedo not give give live birth give live birth

mammalmammal giving live birthgiving live birth

List of mammals: ≠list of things which give live

cats, dogs, humans, platypuses

≠ cats, dogs, humans

By this definition

Platypuses should give live birth, as they have

fur and mammary glands.

Platypuses lay eggs and so do not give live

birth.

Reject: mammals give live

birth.

Applied

By research

Counterexamples

Testing Definitions for ConsistencyReject: ‘mammals’ means gives live birth

Proof: by this definition, Platypuses should give live birth, as they have fur and mammary glands, but research has discovered that Platypuses lay eggs and so do not give live birth. This definition contradicts the evidence, and I would revise the definition to be: mammals have fur and mammary glands.

Counterexamples

Alternate Proof: by this definition, Platypuses must not be mammals as they lay eggs rather than give live birth. But they are mammals insofar as they have fur and mammary glands. This definition is inconsistent with the rest of the taxonomical systems, and I would revise the definition to be: mammals have fur and mammary glands.

Reject: ‘mammals’ means gives live birth

to evaluate by counterexample

Isolate the subject and predicate, generate lists of things that fall under each, stopping when you determine that they are not identical.

proof by counterexample

Choose an item that is not on both lists, explain how the definition says it should be, then explain why it is not, indicate the inconsistency, and reject or revise the definition.

Using the Principle of Noncontradiction to test claims.

Reductio ad absurdam

Line of Reasoning

An explanation showing how the thing

designated by the subject has the

property expressed by the predicate.

Another explanation showing how the thing

designated by the subject does not have the property expressed

by the predicate.

Reject the original claim.

Original claim.

A formal extension of reasoning with contradictions

Claim: The jellyfish has no tentacles.

You know the claim is wrong, but how can

you prove it?

Testing Claims for Truth

Evidence:

the jellyfish

has tentacles

True Claims

The Subject has the Property Expressed by Predicate.

The jellyfish has tentacles

False Claims

Evidence:

the jellyfish

has no tentacles

The Subject is Inconsistent with the Property Expressed by Predicate.

The jellyfish has no tentacles

Claim: The jellyfish has no tentacles.

Testing Claims for Truth

Evidence:

the jellyfish

has tentacles

Line of Reasoning

The claim is that the jellyfish under

observation ought to have no tentacles.

But observation shows that the jellyfish in question has many

tentacles.

Reject the original claim.

The jellyfish has no tentacles.

A formal extension of reasoning with contradictions

Testing claims for ConsistencyReject: the jellyfish has no tentacles

Proof: The claim is that the jellyfish under observation ought to have no tentacles, perhaps due to predation. But cursory examination shows that the jellyfish has many tentacles which appear healthy. As the claim contradicts observation I reject it.

The Parts of a Reductio

The jellyfish under observation ought to have no tentacles, perhaps due to predation. But cursory examination shows that the jellyfish has many tentacles which appear healthy. As the claim contradicts observation I reject it.

The Parts of a Reductio

7. I reject it

4. by cursory examination

5. the jellyfish has many tentacles

2. due to predation

1. The jellyfish under observation ought to have no tentacles

6. the jellyfish has tentacles and the jellyfish has no tentacles

3. the jellyfish has no tentacles

1.claim2.reasons3.conclusion4.other reasons5.other conclusion

6.contradiction7.rejection

The Logical Form of a Reductio

Reductio ad absurdam, Indirect Proof, Proof by

Counterexample1.claim2.reasons3.conclusion4.other reasons5.other conclusion6.contradiction

7.rejection

Line of Reasoning

2. reasons3. conclusion

4. other reasons5. other conclusion

6. P & ~P

1. Claim

Reductio ad absurdamIndirect Proof, Proof by

Counterexample

7. Rejection

Some Cases

The Case of Sara ScatterleighSara woke in a hurried blur. Her alarm did not go

off. Her heart pounded as she got out of bed, dragged a comb across her head, found her way downstairs and drank a cup, looking up she noticed she was late. She grabbed her coat and grabbed her pack, out the door in seconds flat—her chemistry class started ten minutes ago! And this teacher always took role.Sara approached her class with apprehension, open the door and march in like she’s not late? Or try to steal in. Still out of breath from the jog to class, Sara opens the doors and marches right into the large lecture hall, only she doesn’t recognize a single soul. The teacher pauses his lecture to regard her, but it is not her chemistry teacher! Confused, Sara retreats into the hall and looks at the room number on the wall, it is the right room, she should be late, her chemistry class meets on Tuesdays and Thursdays. With a look of vacant frustration Sara draws out her phone to double check the time, and only then notices the day, Monday.

The Case of Mrs. RileyMost jurors were initially swayed by the Prosecutor’s claim that the accused were guilty. This was based on the testimony of Mrs. Riley, who positively identified the accused at the scene of the crime at the time the crime was committed. After all, Mrs. Riley seemed like an honest woman with no bias against the accused. Further, she testified that saw them from 100 feet away and was wearing her eye glasses—because of this everyone assumed that she could see 100 feet. However, on cross examination, the defense attorney, Vinny, conducted an impromptu eye test by holding up two fingers from a mere 50 feet away while she had her glasses on. Mrs. Riley failed this test, thinking she saw four fingers instead of two. So Mrs. Riley could not see 100 feet, because she could not see even 50 feet. As this is a contradiction the accused were found to be innocent.

The Case of Longfellow Deeds

In the case of one Longfellow Deeds it was claimed that Mr. Deeds was not legally competent to manage his own affairs. An attorney argued that Mr. Deeds suffered from what was then called bipolar disorder (we now call it manic depression). To show that Mr. Deeds was abnormal the attorney called many witnesses, who claimed Mr. Deeds was ‘pixelated’, ‘crazy’, ‘cracked’, and ‘nuts’. Examples of his abnormality included playing the tuba and running around naked in the park. However by giving the proper context Mr. Deeds made it plain that playing the tuba was as normal as doodling, filling in the ‘o’ s on a printed page, or having a nervous tick. Also, he ran around naked because he was drunk for the very first time—and behaving oddly when you are drunk is fairly normal. Because Mr. Deeds provided convincing counterexamples to the claims that his behavior was abnormal the judge declared him legally competent to manage his own affairs

The Case of the Reluctant Rubbernecker

A woman had just presented her paper to her local senator on the negative effects traffic oscillation due to rubbernecking—in short rubbernecking contributes to traffic jams. Her claim was that if everyone knew that rubbernecking caused up to 60% of the delays due to common accidents, they would do the right thing and there would be fewer rubberneckers. She recommended a public service advertising campaign, contending that once people knew the cause of such delays they would not rubberneck. The presentation was a success and she convinced the senator to back her plan. But as she drove home she noticed traffic slowing to a crawl, then saw the cause—a horrific accident. The woman felt the impulse to gawk, to be a rubbernecker. But she kept her mind firmly on the fact that she knew rubbernecking to be wrong and refused to contribute to a longer delay. She fought the impulse but, in the end, she gave in to her impulse, slowed down to gawk, and became another rubbernecker. Despite her knowledge and her best effort at self-control, she knew her thesis was flawed.

Reductio: An Example in Neuroscience

While Studying the actions of motor cells in monkeys (called motor cells because they are the first in the sequence that controls the muscles that move the body) Vittorio Gallese was moving around the lab during a lull in the day’s experiment. A monkey was sitting quietly, waiting for her next assignment, when Vittorio reached for something (perhaps ice cream) and heard a burst from the computer connected to the electrodes in the monkey’s brain. It might have sounded like static but to the ear of a neuroscientist meant the motor cells were firing. Vittorio thought the reaction was strange—the monkey was sitting quietly, not grasping anything, yet this neuron affiliated with grasping fired. No one could imagine that motor cells could fire merely at the perception of someone else’s actions. In light of the theory at the time this made no sense. Cells in the brain that send signals to other cells that are connected to muscles have no business firing when the monkey is completely still, hands in lap, watching somebody else’s actions. And yet they did.

The Case of the Mysterious Disease

In 1955 a mysterious illness infected nearly 300 of the staff of the Royal Free Hospital, forcing it to close. Some tests showed their muscles did not twitch or quiver uncontrollably, their reflexes were normal, and their nervous systems were normal. This led a few researchers to claim that it was merely mass hysteria and the patients were otherwise healthy. However, numerous studies showed that the group gave no indications of mass hysteria and that they exhibited a pattern of symptoms including severe exhaustion, memory loss, confusion, painful lymph nodes, muscle pain, and unusual headaches. These researchers claim that the disease was unnamed but real and that the patients were sick. Since then, the balance of evidence showed that the disease was real and it was subsequently named myalgic encephalomyelitis (ME) or chronic fatigue syndrome (CFS).

The Case of the Composite Soul

Against the claim that the soul is simple, Plato tells of Leontius, the son of Aglaion, who saw some corpses lying at the executioners feet. Leontius had a strong urge to indulge his morbid intrigue and gawk at the dead, but he forced himself to show respect by not indulging his morbid intrigue so he turned himself away. For a while he fought the urge and covered his face. But desire overcame him and he ran to the corpses and looked, then rebuked himself for this indignant act.

The Case of Renegade Mercury

Newton’s theory was remarkable in that it described force correctly in terms of acceleration and mass, explained gravity, and correctly predicted the course of the planets. Newton’s theory was right. Except for Mercury. Observation showed Newton’s theory did not accurately predict the orbit of Mercury. So the theory was wrong. Some even postulated another planet, Vulcan, to make the theory correspond with observation. But there was no planet Vulcan, it wasn’t until Einstein that a theory was discovered that could account for Mercury’s orbit.

Some Relevant Fallacies

Fallacies

A Problem Reductio: Law’s Not Fair

Some claim our legal system is fair. They point out that our legal system, when it functions properly, gives out impartial sentences and so it fair. However, our legal system is abstract, and so is without color, and can’t be pale, so it is not fair (look up fair, it means having a light complexion). But this means our legal system is fair and unfair, which is a contradiction. So I reject that our legal system is fair.

Line of Reasoning

Our legal system, when it functions properly, gives out impartial sentences and so it fair.

Our legal system is abstract, and so is without color, and can’t be pale, so it is not fair.

Our legal system is fair and unfair

Our legal system is fair.

What is the problem?

A Problem Reductio

Reject: our legal system is fair

Our legal system, when it functions properly, gives out impartial sentences and so it fair.

Our legal system is abstract, and so is without color, and can’t be pale, so it is not fair.

Equivocation

A Problem Reductio

The problem is that the argument uses the word fair in two different ways

—fair is ambiguous, it has more than one

meaning. One meaning has to do with being

impartial, the other has to do with having a pale

color. Using a word ambiguously in an

argument is the fallacy of equivocation.

Equivocation, to use a term Equivocation, to use a term ambiguously or vaguely in ambiguously or vaguely in an argument—it is a fallacy.an argument—it is a fallacy.

A Problem Reductio: Too Big to Fail

During a recent financial crisis many made the claim that some banks were too big to fail and needed to be bailed out with public funds to avoid catastrophe. But banks did fail, both large banks and small ones. Thus the claim is inconsistent with the evidence. And so it must be false that some banks were too big to fail.

to avoid equivocation

Define key terms by giving them one (to disambiguate) clear (to avoid vagueness) meaning.

Line of Reasoning

Some banks were too big to fail and needed to be bailed out with public funds.

Banks did fail, both large banks and small ones.

The claim is inconsistent

Our legal system is fair.

A Problem Reductio

Reject: some banks are too big to fail.

Some banks were too big to fail and needed to be bailed out with public funds.

Banks did fail, both large banks and small ones.

Equivocation

A Problem Reductio

The problem is that the argument switches

between a prescriptive/normative

claim (banks ought not be allowed to fail as they are too big and might cause a

catastrophe) and descriptive claim (the

observation that even big banks did fail). This is

another form of the fallacy of equivocation.

to avoid equivocation

Use the Principle of Charity to settle on the best interpretation, whether normative or descriptive.

A Problem Reductio: Too Big to Fail

Socrates claimed that women could be leaders of the ideal city state. He noted that women possess the same capacities in terms of leadership that men do. His pupils, however, noted that men and women have very different capacities and that only a fool would confuse women with men—they are different! Because this line of reasoning leads to the absurd conclusion that men and women are the same and not, his pupils laughed at the notion that women could be leaders.

Line of Reasoning

Women possess the same capacities in terms of leadership that men do.

Only a fool would confuse women with men—they are different with different capacities!

Men and women are the same and not.

Women can be leaders.

A Problem Reductio

Reject: women can be leaders.

Women possess the same capacities in terms of leadership that men do.

Only a fool would confuse women with men—they are different with different capacities!

Reductio ad ridiculim

A Problem Reductio

The problem is that the argument confuses

ridicule with reason. This is an example of a

reductio ad ridiculum—a fallacy. This example is based off an argument

given in Plato’s Republic—an argument which

Plato is careful to refute.

Reductio ad ridiculum, Reductio ad ridiculum, appealing to ridicule appealing to ridicule (making fun of an opposing (making fun of an opposing view) rather than providing view) rather than providing reasons against it—it is a reasons against it—it is a fallacy.fallacy.

to avoid reductio ad ridiculums

Use the Principle of Sufficient Reason and attempt to provide reasons for each claim.

SoundnessSoundness

Assignment

How do you prove a conditional false?

What does ‘if’ mean?

What is the difference between validity and

soundness?

critical thinking 03 consistency

review truth

true claim

false claim

truth valuethe man

component claim

better reasons

logical complexitythe

simple truththe man

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