Ratio's Distinctive Thinking: Credit Unions & Brand Consistency
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Transcript of 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
yes:
no:
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
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.
yes:
no:
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?
Does the thing designated by the subject have the property expressed by the predicate?
The Disputed Question Method
Review
yes:
no:
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?
Do the things designated by the nouns stand in the relation expressed by the verb.
The Disputed Question Method
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.
yes:
no:
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?
Are the things designated by the nouns are in the extension of the verb?
The Disputed Question Method
Review
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
A Logically Simple Truth
The man is The man is cheating.cheating.
1 True
2 False
—He’s hiding cards
A Logically Simple Truth
The man is The man is cheating.cheating.
1 True
2 False —He’s doing magic
A Logically Simple Truth
The man is The man is cheating.cheating.
1 True
2 False
Two logical possibilities
Given that we’ve filled
in the indices,
made the ceteris paribus
explicit, and defined key
terms.
A Logically Simple Truth
The man is The man is cheating.cheating.
1 True
2 False
Also called States of Affairs or Possible Worlds
A Logically Simple Truth
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
The man is The man is cheating.cheating.
1 True
2 False
The man is not The man is not cheating.cheating.
1 False
2 True
The man is The man is cheating.cheating.
1 True
2 False
The man is not The man is not cheating.cheating.
1 False
2 True
it “flips” the truth value
Negation: Logical Complexity
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.
PP
1 True
2 False
~P~P
1 False
2 True
~ “flips” the truth valueThe Logical Form of Negation: ~P, -P,
¬ P
Negation: Logical Complexity
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?
A Logically Simple Truth
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
3
4
Logically Complex Truths
Derek is Derek is leaping.leaping.
Hansel is Hansel is leaping.leaping.
1 True True
2 True False
3
4
Logically Complex Truths
Derek is Derek is leaping.leaping.
Hansel is Hansel is leaping.leaping.
1 True True
2 True False
3 False True
4
Logically Complex Truths
Derek is Derek is leaping.leaping.
Hansel is Hansel is leaping.leaping.
1 True True
2 True False
3 False True
4 False False
Logically Complex Truths
Derek is Derek is leaping.leaping.
Hansel is Hansel is leaping.leaping.
1 True True
2 True False
3 False True
4 False False
Four possibilities
Logically Complex Truths
Derek is Derek is leaping.leaping.
Hansel is Hansel is leaping.leaping.
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
2n
Logically Complex Truths
Derek is Derek is leaping.leaping.
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
leaps
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?
Logical Possibilities
Who wins the bet?
Derek is leaping.Derek is leaping. ANANDD
Hansel is Hansel is leaping.leaping.
1 True ? True2 True False3 False True4 False False
In state #1 where both Derek and Hansel are leaping?
Logical Possibilities
Who wins the bet?
Derek is leaping.Derek is leaping. ANANDD
Hansel is Hansel is leaping.leaping.
1 TrueTrue
True
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
#1.
Logical Possibilities
Who wins the bet?
Derek is leaping.Derek is leaping. ANANDD
Hansel is Hansel is leaping.leaping.
1 TrueTrue
True
2 True ? False3 False True4 False False
The complex claim is true when all the component claims are true, as they are in state
#1.
How about case #2 where Derek is leaping but Hansel is not?
Logical Possibilities
Who wins the bet?
Derek is leaping.Derek is leaping. ANANDD
Hansel is Hansel is leaping.leaping.
1 TrueTrue
True
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…
Logical Possibilities
Who wins the bet?
Derek is leaping.Derek is leaping. ANANDD
Hansel is Hansel is leaping.leaping.
1 TrueTrue
True
2 TrueFals
eFalse
3 FalseFals
eTrue
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?
Logical Possibilities
Who wins the bet?
Derek is leaping.Derek is leaping. ANANDD
Hansel is Hansel is leaping.leaping.
1 TrueTrue
True
2 TrueFals
eFalse
3 FalseFals
eTrue
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
True
2 TrueFals
eFalse
3 FalseFals
eTrue
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
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.
white
Contradictions
A Necessity of Logic
Now pay attention to your mental processes as we make the following claim:
Contradictions
A Necessity of Logic
Now pay attention to your mental processes as we make the following claim:
Contradictions
A Necessity of Logic
Now pay attention to your mental processes as we make the following claim:
>>This square is white and this square is >>This square is white and this square is not white.<<not white.<<
Contradictions
A Necessity of Logic
What was your reaction?What was your reaction?
Contradictions
A Necessity of Logic
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
eTrue
The Logical Form of a Contradiction: P & ~P
Contradictions are false in all possible worlds.
Contradictions
PP && ~P~P
1 TrueFals
eFalse
2 FalseFals
eTrue
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
eTrue
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 jellyfish has tentacles.
The music is loud.Jupiter is bigger than
Mars.
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 jellyfish has tentacles.
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
Mars.
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
A
BC
D
E
F G
H
I
J
K
LM
NO
PQ
R
S
TU
V
W
X
YY Z
being a vowel
True Definitions
The Subject and Predicate Have Identical Extensions
being divisible by two without a
remainder
22
9
11
32 2
7
21
13
66
3
14
144 57
7
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
A
B
C
D
E
FG
H
I
J
K
LM
NO
PQ
R
STU
V
W
X
YY
Z
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
The Subject and Predicate Do Not Have Identical Extensions
being a female parent
being a father
a, e, i, o, and u are the only vowels
Adam
Joseph Hillar
yMartinMuhamma
d
Sarah Mar
y
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
Testing Definitions for Consistency
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
Proof by Counterexample
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
birth
cats, dogs, humans, platypuses
cats, dogs, humans
Testing Complex Definitions for Consistency
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
The Subject and Predicate Do Not Have Identical Extensions
giving live birthbeing a mammal
Mammals give live birth
cats
dogs
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
birth
cats, dogs, humans, platypuses
≠ cats, dogs, humans
Testing Complex Definitions for Consistency
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.
Mammals give live birth
Applied
Proof by Counterexample
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
Testing Definitions for Consistency
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
Reductio ad absurdam
Another Line of Reasoning
Reductio ad absurdam
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
Reductio ad absurdam
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
Reductio ad absurdam
Another Line of Reasoning
Reductio ad absurdam
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
Reductio ad absurdam
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 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 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 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 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
Reductio ad absurdam
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
Reductio ad absurdam
Another Line of Reasoning
7. Rejection
Some Cases
Reductio ad absurdam
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
Another Line of Reasoning
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.
What is the problem?
A Problem Reductio
Another Line of Reasoning
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.
What is the problem?
A Problem Reductio
Another Line of Reasoning
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?