Philosophy 6: Logic in Practice 

Los Angeles Pierce College 

Department of History, Philosophy, & Sociology 

 

 

  

  

 

 

 

Final Review

 

 

 

 

 

 

 

 

 

 

The Structure of an Argument

Premises supporting conclusions

 

Warrants supporting claims

 

 

 

 

Indicator Words

Differentiating premises from conclusions, and warrants from claims can sometimes be tricky

 

Indicator words make such differentiations easier

"we can find help by looking for 'indicator words' that point to the conclusion or to the premises." 

 

"These words can almost always be relied upon as signals, telling us which statements are which in the argument." 

 

 

 

Premise/Warrant

Indicator Words

since

 

inasmuch as

 

because

 

for the reasons that

for

 

in view of the fact

whereas

 

as evidenced by

 

 

 

Conclusion/Claim

Indicator Words

consequently

 

we can conclude that

 

therefore

 

it follows that

thus

 

we may infer that

so

 

this means that

hence

 

it leads us to believe that

accordingly

 

this bears our the point that

 

 

 

Judging Arguments

Analyzing arguments into their parts facilitates our judging those arguments

"Having separated the two, we can then decide whether the case has been made for the conclusion." 

 

"Whether or not we agree with the position we must first identify the logic of the argument to test its soundness." 

 

 

 

Logical

Translations

/

Paraphrasing

Formalizing statements facilitates our testing for soundness

 

"The process of casting sentences that we find in a text into one of these four forms is technically called paraphrasing"

"the sentences that comprise [premises or conclusions, etc.] must be cast in a certain mold in order to be handled logically." 

 

"in formal reasoning the statements that contain our premises and conclusions have to be rendered in a strict form so that we know exactly what is being claimed." 

 

 

 

Quality

/

Affirmative

or

Negative

"in this process of paraphrasing we designate the affirmative or negative quality of a statement principally by using words 'no' or 'not.'" 

 

 

 

 

Quantity

/

All of a Class

or

Part of a Class

"We indicate quantity, meaning whether we are referring to the entire class or only a portion of it, by using the words 'all' or 'some.'" 

 

And something to memorize: all entails some, but some does not entail all

 

 

 

 

Copula

/

Is

or

Are

"In addition, we must render the subject and the predicate as classes of objects with the verb 'is' or 'are' as the copula joining two halves." 

 

 

 

 

Target

Forms

The target in paraphrasing is to render statements into one of our different logical forms

"every written statement can be translated into one of these four forms." 

 

 

 

Logical Forms

of

Statements

(A)

 

All X is Y. 

 

(E)

 

No X is Y.

(I)

 

Some X is Y. 

(O)

 

Some X is not Y. 

 

 

 

The Trick

"the main trick is to translate sentences into statements covering all or some, none or not, and to use language that designates categories or classes of objects." 

 

 

 

 

Implications

Once rendered into logical form, it becomes easier to see what does and does not follow

 

 

 

 

(A)

If (A) is true

All unicorns are gauche creatures.

 

If (A) is false

 

 

(E) is false

No unicorns are gauche creatures. 

 

(E) is undetermined

_

If (A) is true, then (E) is false: if all unicorns are gauche, then, easily, we can't say that none are. 

 

If (A) is false, then (E) is undetermined: if it is false that all unicorns are gauche, that doesn't mean that there could be at least one gauche one lurking out thereÐbut, it could also be the case that there are in fact no gauche unicorns.

 

 

(I) is true

Some unicorns are gauche creatures.

 

(I) is undetermined

If (A) is true, then (I) is true: if all unicorns are gauche, then surely some are. 

 

If (A) is false, then (I) is undetermined: if it is false that all unicorns are gauche, that doesn't mean that there could be at least one gauche one lurking out thereÐbut, it could also be the case that there are in fact no gauche unicorns. 

 

 

(O) is false

Some unicorns are not gauche creatures.

 

(O) is true

_

If (A) is true, then (O) is false: if all unicorns are gauche, then it can't be the case that there are still, at the same time, some that are not gauche. 

 

If (A) is false, then (O) is true: if it is false that all unicorns are gauche, then of course there are some that are not gauche creatures.  

 

 

 

 

 

(E)

If (E) is true

No unicorns are gauche creatures. 

 

If (E) is false

 

 

(A) is false

All Unicorns are gauche creatures.

 

(A) is undetermined

If (E) is true, then (A) is false: if no unicorns are gauche, then the exact opposite cannot be true too. 

 

If (E) is false, then (A) is undetermined: if it is not the case that there are no gauche unicorns, then it could be the case that there are some gauche unicorns, but it could also be the case that all unicorns are gauche. 

 

 

(I) is false

Some unicorns are gauche creatures.

 

(I) is true

_

If (E) is true, then (I) is false: if no unicorns are gauche, then, then some unicorns can't be gauche. 

 

If (E) is false, then (I) is true: if it is not the case that there are no gauche unicorns, then surely there are some gauche unicorns. 

 

 

(O) is true

Some unicorns are not gauche creatures.

 

(O) is undetermined

_

If (E) is true, then (O) is true: if no unicorns are gauche, then surely some are. 

 

If (E) is false, then (O) is undetermined: if it is not the case that there are no gauche unicorns, then it could be the case that all unicorns are gauche but it could also be the case that there are some gauche unicorns. 

 

 

 

 

 

(I)

If (I) is true

Some unicorns are gauche creatures.

 

If (I) is false

 

 

(A) is undetermined 

All Unicorns are gauche creatures.

 

(A) is false

_

If (I) is true, then (A) is undetermined: if it is true that there are some gauche unicorns, then it could be the case that all unicorns are gauche too, but it could also be the case that not all unicorns are gauche. 

 

If (I) is false, then (A) is false: if it is false that there are some gauche unicorns, then it can't be the case that all unicorns are gauche. 

 

 

(E) is false

No unicorns are gauche creatures. 

 

(E) is true

_

If (I) is true, then (E) is false: if it is true that there are some gauche unicorns, then it can't be the case that there are no gauche unicorns. 

 

If (I) is false, then (E) is true: if it is false that there are some gauche unicorns, then it is true to day that there are no gauche unicorns. 

 

 

(O) is undetermined

Some unicorns are not gauche creatures.

 

(O) is true

_

If (I) is true, then (O) is undetermined: if it is true that there are some gauche unicorns, then it could be the case that not all unicorns are gauche, but it could also the case that all unicorns are gauche too. 

 

If (I) is false, then (O) is true: if it is false that there are some gauche unicorns, then it would be true to say that some unicorns are not gauche. 

 

 

 

 

 

(O)

If (O) is true

Some unicorns are not gauche creatures.

 

If (O) is false

 

 

(A) is false

All Unicorns are gauche creatures.

 

(A) is true

 

_

If (O) is true, (A) is false: just because some unicorns are not gauche does not mean that all unicorns are not gauche.

 

If (O) is false, (A) is true: if it is false that there are some unicorns that are not gauche, then it all unicorns are gauche.  Consider the opposite, if all unicorns are gauche, then it could not be the case that some unicorns are, at the same time, not gauche. 

 

 

(E) is undetermined

No unicorns are gauche creatures. 

 

(E) is false

 

_

If (O) is true, (E) is undetermined:  if some unicorns are not gauche, then it could be that, in fact, there are no unicorns are gauche, but it could also be the case that there are some gauche unicorns. 

 

If (O) is false, (E) is false: if it is false that some unicorns are not gauche creatures, then all unicorns are gauche, which means it would be false to claim that no unicorn is gauche. 

 

 

(I) is undetermined

Some unicorns are gauche creatures.

 

(I) is true

 

_

If (O) is true, then (I) is undetermined: if some unicorns are not gauche, then it could be the case that there are some gauche unicorns, but it could also be the case that there are no gauche unicorns at all. 

 

If (O) is false, then (I) is true: if it is false that some unicorns are not gauche creatures, then, of course, there are some gauche unicorns. 

 

 

 

Conversions

Some statements' subjects and predicates are interchangeable

 

 

 

(A)

All unicorns are gauche creatures. 

 

 

does not convert to

(A)

All gauche creatures are unicorns. 

_

What other creatures are gauche?  Are panthers gauche too? 

 

If any, then (A) can't be converted. 

 

 

 

 

 

 

(E)

No unicorns are gauche creatures.

 

 

does convert to

(E)

No gauche creatures are unicorns. 

 

 

 

 

 

 

 

 

(I)

Some unicorns are gauche creatures.

 

 

does convert to

(I)

Some gauche creatures are unicorns. 

 

 

 

 

 

 

 

 

(O)

Some unicorns are not gauche creatures.

_

This is a claim about the qualities of unicorns. 

 

does not convert to

(O)

Some gauche creatures are not unicorns. 

_

This is a claim about the qualities of other creatures. 

 

 

 

 

 

 

 

Syllogisms

"In a syllogism we lay out our train of reasoning in an explicit way, identifying the major premise of the argument, the minor premise and the conclusion." 

The "ordering of premises and conclusions in a logical structure is called a syllogismÐthe basic form of deductive logic." 

 

 

 

Enthymemes

Arguments "with an unstated premise or conclusion" are "incomplete arguments called enthymemes." 

 

"Sometimes enthymemes are used for purposes of deception when the missing section would reveal the argument as unsound"

 

"usually they occur because the premise or conclusion is too obvious to state." 

 

 

 

First Order

Enthymeme

"When an argument lacks the major premise it is called an enthymeme of the first order"

 

 

 

 

Second Order

Enthymeme

"one that lacks the minor premise is an enthymeme of the second order"

 

 

 

 

Third Order Enthymeme

"one missing the conclusion is an enthymeme of the third order"

 

 

 

 

Validity

"an argument is called valid if, given the premises, the conclusion is unavoidable." 

 

"Validity ... applies to the structure of an argument"

Validity does not apply to "the statements that make up [an argument's] content"

 

 

 

Invalid

"An argument ... where the conclusion fails to follow from the premises, is consider invalid." 

"the form of the argument is flawed so that the reasons that are given do not support the claim that is made." 

 

 

 

Truth

"Truth ... is a quality of statements, and we call a statement false if it fails to reflect reality." 

 

 

 

 

True & Invalid

All mammals are creatures that breathe. 

All narwhals are creatures that breathe. 

All narwhals are mammals. 

"If the conclusion to an argument is true by accident rather than by necessity, that is, true but not valid, then the argument is valueless because it cannot be proven." 

 

 

 

Valid & Untrue

All mammals are creatures that lay eggs. 

All cedars are mammals. 

All cedars are creatures that lay eggs. 

 

 

 

 

True & Valid

/

Sound

"a sound argument must be both valid and true, that is, valid in form and with premises and a conclusion that are true." 

 

 

 

 

 

 

 

 

 

Deductive

Formal

Arguments

Deductive Formal Arguments

 

"In deductive thinking we reason from a broad claim to some specific conclusion that can be drawn from it" 

 

"We 'deduce' a particular from a general statement"

"We begin with a blanket assertion, then show what would necessarily follow as a logical consequence." 

 

 

 

 

 

Sub-classifications of

Deductive

Formal

Arguments

"Deductive thinking has three patters ... categorical, hypothetical, and disjunctive." 

 

 

 

 

 

 

Inductive

Formal

Arguments

"In the inductive process we reason from specific instances to some generalization based upon those instances." 

 

"We begin with an examination of particular cases, then reach some general conclusionÐjust the reverse of deduction." 

 

 

 

 

 

Sub-classifications of

Inductive

Formal

Arguments

"Inductive reasoning has four types:  analogy, causation, generalization, and hypothesis"

 

 

 

 

 

 

Using Categorical

Arguments

Categorical claims aren't just broad, but universal

"When a deductive argument is not just broad based, but begins with a universal claim, it is referred to as categorical in nature." 

 

"The major premise is not surrounded by qualifications, exceptions, or alternatives but asserts that something is the case universally." 

 

 

 

 

 

E.G.

Categorical

Argument

All unicorns are creatures that have a single horn

Charlie is a unicorn

Therefore Charlie is a creature that has a single horn

 

 

 

 

 

 

Analyzing the

E.G.

Categorical

Argument

into Terms

"we can see that the statement consist of three terms as subject and predicate"

 

Term: unicorns

Term: creatures that have a single horn

Term: Charlie

"Learning this vocabulary is important for you to be able to refer to the basic parts of a categorical syllogism." 

 

 

 

 

 

Middle Term

A term is called a "middle term" "because it appears twice in the premises"

 

 

 

 

 

 

Discerning

Soundness

"Usually we can tell offhand if an argument is correct, but that is not always the case." 

 

"When we are uncertain whether a conclusion does follow from the premises we have to use strict procedures to test the validity of the reasoning." 

 

 

 

 

 

 

Attributing:

Affirmative

v.

Negative

/

Universal

v.

Particular

In discerning validity 

 

1st determine whether the premises and conclusion individually have the sub-attribute of being affirmative or negative

 

2nd determine whether the premises and conclusion individually have the sub-attribute of being universal or particular

"First, we must analyze the premises and the conclusion to comprise the syllogism to see whether they are affirmative or negative, and whether they refer to all or only some of a class, that is, whether they are universal or particular." 

 

 

 

 

 

Table for:

Affirmative

v.

Negative

/

Universal

v.

Particular

Sentence

 

Standard From

Attribute

 

All unicorns are creatures that addle

A

All S is P

Universal affirmative

No unicorns are creatures that addle

E

No S is P

Universal negative

Some unicorns are creatures that addle

I

Some S is P

Particular affirmative

Some unicorns are not creatures that addle

O

Some S is not P

Particular negative

 

 

 

 

Distribution

A term is distributed if it covers every member of the class

 

3rd determine whether or not the terms are distributed

"Following [the attribute analysis] we must then break the sentences down further to see whether the subject and predicate terms are distributed, that is, whether they cover every member of the class." 

 

"Some terms in the sentences that make up the syllogism refer to everything that comprises the group and some refer only to some of them." 

 

 

 

 

 

Distribution

Table

 

Standard From

Subject Term

Predicate Term

 

 

A

All S is P

Distributed

Undistributed

 

E

No S is P

Distributed

Distributed

 

I

Some S is P

Undistributed

Undistributed

 

O

Some S is not P

Undistributed

Distributed

 

 

 

 

 

Distribution for

A: All S is P

/

D U

E.G.:  All parrots are birds

 

For the subject term, parrots, "we are referring to every single parrot, so the subject term is distributed"

 

For the predicate term, birds, "we are not talking about all birds, so the predicate term is not distributed," or undistributed

 

 

 

 

 

 

Distribution for

E: No S is P

/

D D

E.G: No wars are profitable

 

The subject term, war, "is distributed because the claim is that, of the entire category of wars, non is profitable" 

 

The predicate term, profitable, "is also distributed because no member of the class of profitable things is also a war"

 

 

 

 

 

 

Distribution for

I: Some S is P

/

U U

E.G.:  Some diseases are tropical

 

The subject term, diseases, is undistributed as only "some diseases are referred to"

 

The predicate term, tropical, is undistributed as "tropical" "does not refer to all things in the tropics but only a portion of them"

 

 

 

 

 

 

Distribution for

O: Some S is not P

/

U D

E.G.:  Some New Englanders are not friendly

 

The subject term, New Englanders, is undistributed as we are not referring to all of the members of the category of New Englanders

 

The predicate term, friendly, is distributed, "[f]or the claim is that some New Englanders are excluded from the entire class of friendly people"

 

 

 

 

 

 

Rules of Validity for

Categorical Deductive Arguments

1) "At least one of the premises must be affirmative"

 

2) "If a premise is negative then the conclusion must also be negative, and if the conclusion is negative then a premise must be negative"

 

3) "The middle term must be distributed at least once"

 

4) "Any term distributed in the conclusion must also be distributed in a premise"

"Once we understand affirmative and negative and the concept of distribution, we can apply the rules governing the validity of deductive arguments of a categorical type." 

 

 

 

 

 

E.G.

Violation of Rule One

Violation of 1) "At least one of the premises must be affirmative"

 

"No Australians are poor swimmers"

"Some poor swimmers are not sailors"

"No sailors are Australians"

 

Why Invalid:  "no affirmative premises are present"

 

 

 

 

 

 

E.G.

Violation of Rule

Two

Violation of:  2) "If a premise is negative then the conclusion must also be negative, and if the conclusion is negative then a premise must be negative"

 

"No fish is a fattening food"

"All fattening food is tasty"

"Some fish is tasty"

 

Why Invalid:  "a negative premise is not followed by a negative conclusion"

 

 

 

 

 

 

E.G.

Violation of Rule

Three

Violation of:  3) "The middle term must be distributed at least once"

 

"All feminists are pro-choice"

"Some Communists are pro-choice"

"Some feminists are Communists" 

 

Why Invalid:  "the middle term 'pro-choice' is not distributed because it appears in the predicate of two A propositions" which means that it is not distributed

 

 

 

 

 

 

E.G.

Violation of Rule

Four

Violation of:  4) "Any term distributed in the conclusion must also be distributed in a premise"

 

"All stars are bright"

"No planets are stars"

"No planets are bright"

 

Why Invalid:  in the conclusion, "bright" is distributed, but "bright "occurs as the predicate of an A proposition" in the major premise which means that it is undistributed

 

 

 

 

 

 

Steps to Analyzing

Categorical Deductive Arguments

1) "Separate the conclusion form the premises"

 

2) "Paraphrase the sentences into standard form"

 

3) "Arrange the statements into a categorical syllogism, completing any enthymemes"

 

4) "Judge the validity of the syllogism in terms of the four rules, using the factors of affirmative or negative and distribution"

 

5) "Determine whether the premises and conclusion are true and the argument sound"

 

 

 

 

 

 

Trying it Out

/

E.G. of

Following the Steps to Analyzing

Categorical Deductive Arguments

I. 6

 

"Librarians tend to be shy, unlike cheerleaders, none of whom seems a shy type at all.  It is safe to assume, therefore, that no librarians become cheerleaders." 

 

 

 

 

 

 

Trying it Out

/

E.G. of

Following the Steps to Analyzing

Categorical Deductive Arguments

/

Step One

1) "Separate the conclusion form the premises"

 

From:  "Librarians tend to be shy, unlike cheerleaders, none of whom seems a shy type at all.  It is safe to assume, therefore, that no librarians become cheerleaders." 

 

To: 

 

"Librarians tend to be shy,"

 

"cheerleaders, none of whom seems a shy type at all"

 

"therefore, ... no librarians become cheerleaders"

 

 

 

 

 

 

Trying it Out

/

E.G. of

Following the Steps to Analyzing

Categorical Deductive Arguments

/

Step Two

2) "Paraphrase the sentences into standard form"

 

From:  "Librarians tend to be shy,"

 

To:  All librarians are people who are shy

 

From:  "cheerleaders, none of whom seems a shy type at all"

 

To:  No cheerleaders are people who are shy

(Not To:  All cheerleaders are not people who are shy)

 

From:  "therefore, ... no librarians become cheerleaders"

 

To:  No librarians are cheerleaders

 

 

 

 

 

 

Trying it Out

/

E.G. of

Following the Steps to Analyzing

Categorical Deductive Arguments

/

Step Three

3) "Arrange the statements into a categorical syllogism, completing any enthymemes"

 

All librarians are people who are shy

No cheerleaders are people who are shy

No librarians are cheerleaders

 

 

 

 

 

 

Trying it Out

/

E.G. of

Following the Steps to Analyzing

Categorical Deductive Arguments

/

Step Four

4) "Judge the validity of the syllogism in terms of the four rules, using the factors of affirmative or negative and distribution"

 

All librarians are people who are shy

Affirmative Universal

Subject Distributed

Predicate Undistributed

 

No cheerleaders are people who are shy

Universal Negative

Subject Distributed

Predicate Distributed

 

No librarians are cheerleaders

Universal Negative

Subject Distributed

Predicate Distributed

 

 

 

 

 

 

Trying it Out

/

E.G. of

Following the Steps to Analyzing

Categorical Deductive Arguments

/

Step Four

Rules

Recall the four rules: 

 

1) "At least one of the premises must be affirmative"

 

2) "If a premise is negative then the conclusion must also be negative, and if the conclusion is negative then a premise must be negative"

 

3) "The middle term must be distributed at least once"

 

4) "Any term distributed in the conclusion must also be distributed in a premise"

 

 

 

 

 

 

Trying it Out

/

E.G. of

Following the Steps to Analyzing

Categorical Deductive Arguments

/

Step Four

/

Rule One

1) "At least one of the premises must be affirmative"

 

All librarians are people who are shy

Affirmative Universal

Subject Distributed

Predicate Undistributed

 

No cheerleaders are people who are shy

Universal Negative

Subject Distributed

Predicate Distributed

 

No librarians are cheerleaders

Universal Negative

Subject Distributed

Predicate Distributed

 

Verdict:  Pass

 

 

 

 

 

 

Trying it Out

/

E.G. of

Following the Steps to Analyzing

Categorical Deductive Arguments

/

Step Four

/

Rule Two

2) "If a premise is negative then the conclusion must also be negative, and if the conclusion is negative then a premise must be negative"

 

All librarians are people who are shy

Affirmative Universal

Subject Distributed

Predicate Undistributed

 

No cheerleaders are people who are shy

Universal Negative

Subject Distributed

Predicate Distributed

 

No librarians are cheerleaders

Universal Negative

Subject Distributed

Predicate Distributed

 

Verdict:  Pass

 

 

 

 

 

 

Trying it Out

/

E.G. of

Following the Steps to Analyzing

Categorical Deductive Arguments

/

Step Four

/

Rule Three

3) "The middle term must be distributed at least once"

 

Recall, a term is called a "middle term" "because it appears twice in the premises"

 

All librarians are people who are shy

Affirmative Universal

Subject Distributed

Predicate Undistributed

 

No cheerleaders are people who are shy

Universal Negative

Subject Distributed

Predicate Distributed

 

No librarians are cheerleaders

Universal Negative

Subject Distributed

Predicate Distributed

 

Verdict:  Pass

 

 

 

 

 

 

Trying it Out

/

E.G. of

Following the Steps to Analyzing

Categorical Deductive Arguments

/

Step Four

/

Rule Four

4) "Any term distributed in the conclusion must also be distributed in a premise"

 

All librarians are people who are shy

Affirmative Universal

Subject Distributed

Predicate Undistributed

 

No cheerleaders are people who are shy

Universal Negative

Subject Distributed

Predicate Distributed

 

No librarians are cheerleaders

Universal Negative

Subject Distributed

Predicate Distributed

 

Verdict:  Pass

 

 

 

 

 

 

Trying it Out

/

E.G. of

Following the Steps to Analyzing

Categorical Deductive Arguments

/

Step Four

All librarians are people who are shy

No cheerleaders are people who are shy

No librarians are cheerleaders

 

Verdict:  Valid?  Invalid?

 

 

 

 

 

 

Trying it Out

/

E.G. of

Following the Steps to Analyzing

Categorical Deductive Arguments

/

Step Five

5) "Determine whether the premises and conclusion are true and the argument sound"

 

All librarians are people who are shy

True?  False? 

 

No cheerleaders are people who are shy

True?  False? 

 

No librarians are cheerleaders

True?  False?  [Why would we ask?]

 

Verdict:  Sound?  Unsound? 

 

 

 

 

 

 

 

 

 

 

Hypotheticals

The If/Then Form

"Hypothetical arguments are usually more obvious than categorical ones." 

 

"Rather than being embedded in some text, they appear on the surface, which makes them easier to evaluate and to build into an argument." 

 

 

 

 

"A hypothetical argument has an 'if/then' pattern." 

 

"We say that, provided one thing is true, then another thing would follow." 

 

 

"It is conditional in form rather than making some absolute claim." 

 

"An assumption is made at the start and the argument then carries out the implications of that assumption." 

 

 

 

The Parts of

Hypotheticals

Antecedent

 

Consequent

"The first part of the major premise, from 'if' to 'then,' is called the antecedent, and the second part, from 'then' the end of the sentence, is called the consequent." 

 

 

 

Valid

Hypotheticals

Affirming the antecedent

 

Denying the consequent

"the two valid forms of hypothetical thinking are affirming the antecedent and denying the consequent." 

 

 

 

Valid

Hypothetical

/

Affirming the Antecedent

When the minor premise affirms the antecedent of the major premise, the conclusion follows necessarily

"The argument is perfectly valid because, in the minor premise, we have affirmed the antecedent." 

 

 

 

E.G.

Valid

Hypothetical

/

Affirming the Antecedent

If a horse has a single horn, then it is a unicorn

The horse named Charlie has a single horn

Charlie is a unicorn

 

 

 

 

Valid

Hypothetical

/

Denying the Consequent

When the minor premise denies the consequent of the major premise, the conclusion follows necessarily

"Here we have denied the consequent, and although the reasoning might be more difficult to see, it is also correct." 

 

 

 

E.G.

Valid

Hypothetical

/

Denying the Consequent

If a horse has a single horn, then it is a unicorn

Tonto's horse, Scout, is not a unicorn

Scout is not a horse with a single horn

 

 

 

 

Invalid

Hypotheticals

Denying the antecedent

 

Affirming the consequent

 

 

 

 

Invalid

Hypothetical

/

Denying the Antecedent

When the minor premise denies the antecedent of the major premise, the conclusion does not follow

 

 

 

 

E.G.

Invalid

Hypothetical

/

Denying the Antecedent

If Charlie is a unicorn, then he can turn mosquitos into Skittles & Jelly Beans

Charlie is not a unicorn

So, Charlie can't turn mosquitos into Skittles & Jelly Beans

 

 

 

 

Invalid

Hypothetical

/

Affirming the Consequent

When the minor premise affirms the consequent of the major premise, the conclusion does not follow

 

 

 

 

E.G.

Invalid

Hypothetical

/

Affirming the Consequent

If Charlie is a unicorn, then he can turn mosquitos into Skittles and Jelly Beans

Charlie can turn mosquitos into Skittles and Jelly Beans

So, Charlie is a unicorn

 

 

 

 

Steps for

Judging

Hypothetical

Arguments

1) "Arrange the statements into hypothetical form" 

 

2) "Judge the argument's validity in terms of the rules"

 

3) "Determine whether the premises and conclusion are true, and the argument sound"

 

 

 

 

Disjunctives

Either/Or Alternatives

"In a disjunctive sentence two possibilities are presented, at least one of which is true (although both might be)." 

 

 

 

True

Disjunctives

/

One Disjunct

"One of the disjuncts has to be true, so if we know one of the alternatives to be false, we can declare the other to be true and produce a valid argument." 

 

"It does not matter which disjunct we eliminate; the one remaining must be true." 

 

 

 

 

E.G.

True

Disjunctives

/

One Disjunct

Either Charlie is a narwhal or a unicorn

Charlie is not a narwhal

So, Charlie is a unicorn

 

 

 

 

Rules for

Disjunctive Validity

"In a valid disjunctive argument we deny one of the disjuncts and affirm the other." 

 

"An invalid disjunctive argument is one which we affirm one of the disjuncts and deny the other." 

 

 

 

 

Qualification to

Rules for

Disjunctive Validity

"One qualification should be mentioned.  In some types of disjuncts we do eliminate one part by affirming the other." 

 

 

 

 

 

E.G.

Qualification to

Rules for

Disjunctive Validity

Either Charlie is in Candy-Mountain or he is On Big Rock Candy Mountain

Charlie is in Candy-Mountain

So, Charlie is not on Big Rock Candy Mountain

 

 

 

 

Disjunctive

Safety

"To be on the safe side, we should follow the rule of denying one disjunct and affirming the other." 

 

"That applies to all valid disjunctive arguments, so if we operate this way we are sure of being correct." 

 

 

 

 

Invalid

Disjunctive

Argument

/

Both Disjuncts True

"Since both [disjuncts] might be true, one disjunct is not eliminated when we affirm the other."

"in fact both [disjuncts] could be [true]." 

 

"That means we would not get a valid argument by affirming one part of the disjunct in the minor premise and denying the other in our conclusion." 

 

 

 

E.G.

Invalid

Disjunctive

Argument 

/

Both Disjuncts True

Either Charlie is a unicorn or a magical creature

Charlie is a unicorn

So, Charlie is not a magical creature

 

 

 

 

False Disjuncts

/

False Dilemmas

/

False

Aporias

"Although some issues can be neatly divided into either/or alternatives, many others are more complex than that." 

 

"We should be careful not to pose 'false disjuncts' that make it appear as though only two choices are possible when the options are much wider than that." 

"This is sometimes called binary thinkingÐseeing the world in terms of pairs of opposites.  Life usually is more subtle, nuanced, and shaded than offering a choice between black and white." 

 

 

 

Steps for

Judging

Disjunctive

Arguments

1) "Arrange the statements into disjunctive form"

 

2) "Judge the argument's validity in terms of the rules"

 

3) "Determine whether the premises and conclusions are true, and the argument sound"

 

 

 

 

 

 

 

 

Inductive

Formal

Arguments

"In the inductive process we reason from specific instances to some generalization based upon those instances." 

 

From particular cases to general conclusion

"We begin with an examination of particular cases, then reach some general conclusionÐjust the reverse of deduction." 

 

"we begin with particulars and derive a general conclusion that follows from them."

 

 

 

Inductive

Formal

Arguments

/

In a Sense,

Educated Guesses

"Induction hazards an educated guess based on strong but not absolute proof about some general conclusion that can be drawn from the evidence." 

"In inductive arguments, we extend the premises and make a claim beyond the cases that are given." 

 

 

 

 

 

Inductive

Formal

Arguments

/

Certitude

Inductive conclusions do not have certitude

Inductive arguments are "not nearly as reliable as [deductive arguments] because the conclusion is never certain." 

 

 

 

Inductive

Formal

Arguments

/

Certitude

/

E.G.

"even for the statement that the sun will shine every day, which is based on all recorded instances in the past but not on all possible instances." 

 

 

 

 

Inductive

Formal

Arguments

/

Probability

With inductive arguments, we seek

 

Not certainty, but a "high degree of probability"

"rather than striving for certainty we have to settle for a high degree of probability, and the task in induction is simply to increase the probability that our conclusion is correct." 

 

"Used properly, induction can lead to extremely reliable generalizations, as science has shown." 

 

 

 

Sub-classifications of

Inductive

Formal

Arguments

 

 

 

"Inductive reasoning has four types:  analogy, causation, generalization, and hypothesis"

Causation

 

 

Analogy

 

 

Generalization

 

 

Hypothesis

 

 

 

 

 

Causation

The Consequent and the Subsequent

 

 

 

 

Similarity

Causation ­ Similarity

 

Consider "the 'law of similarity,' whereby like is thought to produce like." 

 

Here we have "cases where on event is thought to be the cause of another just because it came first." 

 

 

 

 

False

Connection

Two unrelated events are illicitly assumed to connected

"A false connection has been established between two events such that we assume that the one event is responsible for the other when, in fact, they are unrelated."

 

"The mistake of the ["]pretechnological person["] is to assume a causal connection where there is only an unrelated series of events." 

 

"One piece of knowledge we do possess is that this decision cannot be made by observation but only by reasoning." 

 

Hume:  "we never see a cause." 

 

"we only perceive one event followed by another event, and we infer that there is a causal relationship." 

 

"After Hume, we can no longer identify a cause-effect connection by saying 'I can see it,' but only by claiming, 'I can prove it.'" 

 

 

 

Similarity

E.G.

Consider Pythagoras and beans

 

 

 

 

Connections

"Sometimes when we say that one event has produced another that claim is reasonable and correct." 

 

"Not all of the connection we accept are absurd, of course." 

 

"If we expect rain after seeing low, dark clouds, that is perfectly legitimate"

 

 

 

Distinguishing

Necessary

v.

Accidental

Sequences

"The problem, therefore, lies in recognizing genuine causal connections and distinguishing them from mere temporal succession."

 

Necessary Sequence

 

       ­

 

Accidental Sequence

 "That is, in our reasoning we need to separate a necessary train of happenings from an accidental one." 

 

 

 

 

 

Causes

"A causal event compels a further event to occur rather than simply preceding it." 

 

 

 

 

Subsequent

v.

Consequent

An Accidental Sequence has Merely Subsequent Steps

 

A Necessary Sequence has Consequent Steps

"Another way of putting the point is to say that some events are subsequent, meaning that they just happen to follow, while others are consequent; they occur because of the earlier event." 

 

 

 

Four Methods of

Establishing

Causal

Connections

Agreement

 

Difference

 

Agreement and Difference

 

Concomitant Variations

"The nineteenth-century English philosopher John Stuart Mill ... considerably refined the process of identifying causal connections." 

 

"Mill specified four 'methods' that can be used to recognize cause-effect chains: that of agreement, difference, agreement and difference, and concomitant variations." 

 

 

 

Method One

/

Method

of

Agreement

"If two or more instances of the phenomenon under investigation have only on e circumstance in common, the circumstance in which alone all the instances agree, is the cause (or effect) of the given phenomenon." 

 

 

 

 

Method One

/

Method

of

Agreement

/

E.G.

Prior Factor

Effect

 

Cabbage, Pickle, Parsnip

Sick

Carrot, Pickle, Turnip

Sick

Onion, Pickle, Garlic

Sick

Tomato, Pickle, Beet

Sick

So _________ is the cause

 

 

 

Method One

/

Method

of

Agreement

/

Limits

 

"That common denominator might be the cause, or it could be something wholly irrelevant and unconnected." 

 

 

"Although this method has been used to identify the cause of everything from crime and pollution to creativity and success, it suffers from a major defect: that there is very often more than one common factor." 

 

"The number of ways in which cases agree can be endless, so we never know which of the multiple, common, prior factors is the cause." 

 

"we do not know whether we can halt our inquiry once we have found some factor in common." 

 

"We are always left with nagging suspicion that if only we had pursued the matter a little further, tested more people, conducted our survey more thoroughly, then we would learn the actual cause." 

 

 

 

Method One

/

Method

of

Agreement

/

Limits E.G.

Charlie the unicorn drank a latte one evening, cafŽ con leche the next evening, and tea with milk the following evening.  In all three cases Charlie couldn't get to be before midnight, so being a logical unicorn he decided to eliminate the dairy products from his evening drink. 

 

 

 

 

Method Two

/

Method of Difference

"If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstances in common save for one, that one occurring only in the former; the circumstance in which alone the two instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon." 

 

 

 

 

Method Two

/

Method of Difference

/

E.G.

Prior Factor

Effect

 

Narwhal, Hot Dog, Steak

Not Sick

Steak, Sausage, Unicorn

Not Sick

Hot Dog, McNugget, Corndog

Sick

Roadkill, Ribs, Cutlet

Not Sick

So _________ is the cause

 

 

 

Method Two

/

Method of Difference

/

Limits

"just as the areas of agreement can be numerous, so can the differences."

 

"we can never be sure we have struck the significant difference, found the real culprit, the genuine cause behind the effect." 

"Although this approach seems more persuasive, the obvious problem with it is that, just as the areas of agreement can be numerous, so can the differences." 

 

"This being so, we can never be sure we have struck the significant difference, found the real culprit, the genuine cause behind the effect." 

 

 

 

Method Two

/

Method of Difference

/

Limits E.G.

The McNuggets may have been fine and the sick person may have gotten sick because they shook a sick person's hand

 

 

 

 

Method Three

/

Method of Agreement and Difference

"Here we judge as the cause that element which all preceding events have in common (agreement) after factoring out any common elements that did not result in the subsequent event (difference)." 

 

"We are then left with the common element present only in positive instances, and that is taken as the cause." 

 

 

 

 

Method Three

/

Method of Agreement and Difference

/

E.G.

Prior Factors

Effects

 

Durian, Blueberry, Apple

Sick

Durian, Raspberry, Apple

Sick

Durian, Orange, Pineapple

Not Sick

Durian, Peach, Pineapple

Not Sick

So _________ is the cause

 

 

 

Method Four

/

Method of Concomitant

Variations

"Here we try to establish causation by recognizing a correlation in the way one set of events varies in relation to another." 

 

"we see a correlation in degree and regularity between two events, such that we infer that the first must be causally related to the second."

This method "is usually employed when a continuous flow of events is involved and we often cannot control for the negative occurrences." 

 

 

 

Method Four

/

Method of Concomitant

Variations

/

E.G.

"For example, people have observed that the height of the tide depends upon the phases of the moon." 

 

"When the moon is full the tide is highest; a half-moon is followed by a medium tide; and a low tide seems to be related to a quarter or a crescent moon." 

 

"Because of the consistency and predictability of the relation, we can infer a cause-effect link: the larger the moon, the higher the tide." 

 

 

 

 

Necessary

&

Sufficient

Conditions

"a necessary condition is that without which something cannot occur." 

 

"The sufficient conditions are those that in the presence of which something must occur." 

"one basic way of proving causal connections is to ask whether the second event could have occurred without the first." 

 

"If it [the second condition] could not, the first event can be named as a cause." 

 

In technical terms this means identifying the first even as a necessary condition for the second." 

 

 

 

Necessary

&

Sufficient

Conditions

/

E.G.

"Salt cannot occur without the presence of sodium, but that is not enough.  One part chlorine is also necessary, and the two together they the (sic.) sufficient conditions for producing salt (NaCl)." 

 

 

 

 

Necessary

&

Sufficient

Conditions

/

Qualification

Not all conditions are causes

"sometimes conditions are not the same as causes." 

 

"When there is such a differentiation between conditions and causes, the conditions are usually the more passive circumstances while the causes consist of more active elements." 

 

 

 

Necessary

&

Sufficient

Conditions

/

Qualification

/

E.G.

Charlie has got to get to Candy Mountain so he bums some money off me so he can rent a car (he needs a convertible, for obvious reasons, so he can't borrow my car)

 

I loan Charlie fifty quid

 

Charlie gets into a car accident

 

Charlie, not the finest unicorn at logic, pins some of the blame on me since my loaning him fifty quid was one of the conditions the lead to him getting into an accident

 

I defend myself by pointing out to Charlie that ...

 

Not all conditions are causes

 

 

 

 

Causes

Proximate

&

Causes

Remote

Proximate Causes

 

     ­ 

 

Remote Causes

 

 

 

 

Proximate

Cause

"a proximate cause is that which immediately triggers an event."

 

A proximate cause "functions as the factor that precipitates some happening." 

 

 

 

 

Remote

Cause

"A remote cause, on the other hand, is the background cause that ultimately produces a certain effect; these causes are usually multiple." 

 

Remote causes "stretch backwards in time as links in the cause-effect chain, and contribute to the inevitable and final outcome." 

 

 

 

 

Proximate and Remote

Causes

/

E.G.

WWI

 

 

 

 

Difficulties

With Cause

"One lesson to be learned is that most events are the consequence of numerous causes, so try (sic.) to find the single cause or 'real' cause, whether proximate or remote, can be a futile exercise." 

 

"Some causes are certainly main ones and others peripheral, but rarely do we find one event that can be labeled as the cause." 

 

 

 

 

Some Problems in Determining Causation

Cause v. Effect

 

Causation v. Correlation

 

Logical v. Psychological

 

 

 

 

Difficulty in

Distinguishing

Cause from Effect

Cause and effect "vary in relation to each other, but the direction is hard to determine." 

 

 

 

 

Difficulty in

Distinguishing

Cause from Effect

/

E.G.

"it is hard to determine whether the times create great leaders or great leaders create the times"

 

"is seeing believing or believing seeing, that is, do our prior expectations make our perceptions selective?" 

 

 

 

 

Difficulty in

Distinguishing

Causation from Correlation

Can statistical correlations "be taken as causal correlations?" 

 

"a distinction does exist between correlation and causation." 

 

 

 

 

Difficulty in

Distinguishing

Causation from Correlation

/

E.G.

This is "the main point of debate with regard to cigarette smoking and cancer." 

 

"the Tobacco Institute has argued that the only evidence presented for the connection between smoking and cancer is the high statistical correlation between heavy smoking and incidence of cancer." 

 

"But, it is claimed, no causal proof has been established, and until such proof is forthcoming we cannot claim that smokers are more likely to contract cancer than nonsmokers." 

 

 

 

 

Difficulty in

Distinguishing

The Logical from the Psychological

This problem "has to do without tendency to attribute causation to events that are connected only periodically, not constantly." 

 

And "intermittent reinforcement is very powerfulÐmuch more powerful, in fact, than regular reinforcement." 

 

 

 

 

Difficulty in

Distinguishing

The Logical from the Psychological

/

E.G.

"from a psychological point of view the occasional win confirms the gambler in the belief.  The logical and the psychological are at odds in this situation, and obviously we should try to be governed by logic and not by whatever might be satisfying to think?" 

 

 

 

 

 

 

 

Similes

&

Metaphors

"Similes and metaphors are figures of speech that compare two things for their illuminating or evocative resemblance."

 

"similes and metaphors compare things that are essentially different except for some arresting similarity"

They are "poetic devices that draw together events, objects, or ideas, which are otherwise dissimilar, in a striking comparison." 

 

"similes and metaphors compare things that are essentially different except for some arresting similarity"

 

 

 

Similes

"Similes, from the Latin meaning 'likeness,' use the terms 'as' or 'like' to make the comparison explicit"

 

 

 

 

Metaphors

"metaphors, from the Greek meaning 'transfer,' dispense with the indicator terms and imply the connection by substituting the language of one for the other." 

 

"metaphors make their comparisons in a subtle way and even more effectively." 

 

"They are sometimes called the soul of poetry, and might even antedate logical thinking; early human beings could have grasped resemblances apart from discursive thought." 

 

 

 

Analogical

Arguments

"From the Greek ana logon, 'according to a ratio," analogies declare a relationship between two things, a parallel connection, usually between two ideas or a set of ideas." 

 

"analogical arguments compare things that are alike in all essential respects and are then claimed to be alike in some further respect." 

"Analogical arguments operate outside the realm of poetry in the sense that they do not attempt to be evocative but to prove a point." 

 

Freud:  "'Analogies decide nothing, that is true, but they can make one feel more at home." 

 

"Finding analogies does seem a very creative approach to reasoning, for when we do so we think horizontally rather than vertically.  That is, instead of operating sequentially, as in causation and deductive syllogisms ... we think in lateral terms, discovering unexpected but strong parallels between objects, events, or ideas." 

 

 

 

Analogical

Arguments

/

E.G.

/

Watchmaker

Watchmaker

"The English theologian William Paley ... presented one of the best known analogical arguments.  Paley tried to support the view of St. Thomas Aquinas that the world exhibits evidence of a purposeful design and therefore proves the existence of an intelligent designer, that is, god." 

 

"Paley did this by comparing the world to the mechanism of a watch.  If we were on a deserted island and found a watch ticking away in perfect order, we would have to assume that a watchmaker had produced the watch.  To maintain that the parts just came together by pure chance to form a functioning watch would be farfetched and strain credibility.  In the same way, when we come upon the world operating in an organized and structured fashion, we cannot assume that the orderliness is accidental.  We must conclude that a creator designed the world with the complex organization that it exhibits." 

 

 

 

Analogical

Arguments

/

E.G.

/

Copernicus

"It was analogical thinking that led Copernicus to conceive of a heliocentric rather than a geocentric solar system.  One day while Copernicus was drifting down a river in a boat, he experienced the illusion that the bank was moving while his boat remained still.  The idea suddenly struck him that it could also be an illusion that the sun moved around the earth while the earth remained stationary; perhaps it was the earth that revolved around the sun.  He verified his analogy by experimental device, and revolutionized our conception of the universe." 

 

 

 

 

Analogical

Arguments

/

Carefully 

"one of its basic weaknesses ... almost anything can be proven by carefully selecting the comparison." 

 

 

 

 

Analogical

Arguments

/

Carefully 

/

E.G.

Old age

 

Wine

 

v.

 

Condemned

"If we want to argue for the blessedness of old age we can compare it to the maturing of a fine wine or say that one achieves senior status in the community, acquires patience and wisdom, free from the tyranny of the passions." 

 

"But if we want to show the sadness of old age we can compare it to a house that is decrepit and crumbling, a pitiful ruin dimly reflecting its former dignity." 

 

 

 

Analogical

Arguments

/

Effectiveness

Follow the rules

"Just as there are rules for determining which causal arguments are most probable, there are criteria that can be used to test the strength of analogical arguments." 

 

 

 

Analogical

Arguments

/

Rule One

1) "The two cases must be alike in all essential respects, and the greater the similarities the more probable the argument." 

 

"we want to be sure that we have numerous characteristics that are alike in the cases compared." 

"the greater the resemblance between the things that are compared, the greater the probability that the argument is sound." 

 

"an argument in which the analogical arguments compare in many essential respects is more reliable than one in which only a few resemblances are evident." 

 

 

 

Analogical

Arguments

/

Rule One

/

E.G.

A herd of unicorns is composed of individual unicorns working to achieve a common goal, and just as teamwork is necessary for unicorns to achieve their common goals, it is likewise necessary for narwhals

 

A pod of narwhals is composed of individual narwhals working together to achieve a common goal

 

So, narwhals should evince teamwork

 

 

 

 

Analogical

Arguments

/

Rule Two

2) "The greater the number of cases compared, the stronger the probability of the conclusion." 

"the force of the analogy will increase in direct relation to the number of instances used as a base." 

 

 

 

Analogical

Arguments

/

Rule Two

/

E.G.

It is not just that one herd of unicorns (composed of individual unicorns working to achieve a common goal) evinces teamwork, thirteen different herds of unicorns have the same qualities. 

 

 

 

 

Analogical

Arguments

/

Rule Three

3) "The greater the dissimilarity of the cases used as the base of the analogy, the higher the probability of the conclusion." 

 

"we are concerned to diversify the cases themselves so that we are not using just one type as a foundation for the analogy." 

 

 

 

 

Analogical

Arguments

/

Rule Three

/

E.G.

And its not just the Californian Bearded Unicorns that have these qualities, it is also the Wooly Unicorns of Montana, the Frisky Unicorns of Kšln, and the Freckled Unicorns of Bielefeld that evince teamwork

 

If it could be shown that even horses have the same qualities, and thus teamwork, the analogy would be even stronger

 

 

 

 

Analogical

Arguments

/

Veracity

Probability, not certainty

"If all three rules are followed, the likelihood of the analogy being correct is increased considerably, although we can never be certain of our conclusion." 

 

"even after we take the precautions we never know whether the two cases do compare in that one additional respect that we are trying to prove." 

 

"Ultimately, that is always unknown, but we can reinforce what we do know and hope thereby to arrive at a reliable conclusion about something not directly provable." 

 

 

 

Analogical

Arguments

/

W/in One

Category

"In analogical reasoning we do not have to compare two very different objects, and when we compare objects in the same category the reliability of the analogy increases." 

"Analogies of this type are easier to make and verify, although they do not possess the provocative character or more remote connections." 

 

"What we gain in reliability we lose in charm." 

 

 

 

Analogical

Arguments

/

W/in One

Category

Unicorns should avoid entering Candy Mountain

 

Charlie the Unicorn lost his kidneys after being lured into Candy Mountain, and chances are, other unicorns will lose theirs if they too enter Candy Mountain

 

 

 

 

Analogical

Arguments

/

Reductio ad Absurdum

Objection

"drawing out the implications of an argument to the point where it appears ludicrous ... is called a reductio ad absurdum." 

 

"in criticizing an analogy, instead of challenging the resemblance one can accept it and then show how ridiculous it would be if carried to its logical conclusion." 

 

"In a sense, we are actually demonstrating that the analogy has many dissimilarities and is therefore an extremely weak argument." 

"the reductio ad absurdum should be carried to the point where the proposer is forced to withdraw the analogy altogether." 

 

 

 

 

 

Analogical

Arguments

/

Reductio ad Absurdum

Objection

/

E.G.

"The German philosopher Arthur Schopenhauer ... once said that books are like mirrors; if an ass looks in you cannot expect an angel to look out.  We could criticize this comparison by asking whether books also have a backing of sliver acetate, shatter when dropped, and reverse right and left." 

 

 

 

 

Analogical

Arguments

/

Reductio ad Absurdum

Objection

/

E.G. Critique

Is the textbook missing something? 

 

We're told that a good analogy shows similarity between essential properties. 

 

Consider this version: 

 

Bacon argued that without a good scientific method, knowledge is passed down through the ages the same way that stones travel down river.  What we is a rigorous scientific method so that bits of knowledge get passed down through the ages the same way that logs travel down a river.  But we could object (according to the textbook's logic) that bits of scientific knowledge are neither like stones or logs. 

 

What are the essential properties being analogized? 

 

 

 

 

Analogical

Arguments

/

Reductio ad Absurdum

Objection

/

Important Respects

Properties Trivial

 

v.

 

Properties Weighty 

 

Important Respects:  "No two things can be identical in all respects, or course, for then they would be the same thing, but they should be alike in all important respects." 

 

Crucial Points:  "In constructing an analogical argument, therefore, care must be taken that the parallels are especially close, touch at numerous crucial points." 

 

Essential Respects:  "The cases are not alike in all essential respects, which is the main requirement of a strong analogical argument." 

 

 

 

 

 

 

 

 

 

Generalizing

&

Describing

Generalizations can be used to justify a conclusion when those justifications are well founded. 

"A number of claims we make are generalizations that we think hold true." 

 

"we support our generalization with evidence, build a case to show our position is justified." 

 

 

 

Generalizing

In

General

We are generalizing animals

 

"knowledge would hardly be possible unless we made connections, saw similarities between things, and reached broad conclusions about them." 

"We generalize all the time"

 

"knowledge would hardly be possible unless we made connections, saw similarities between things, and reached broad conclusions about them." 

 

 

 

Abstraction

as a

Mode

of

Generalization

Individuals may have unique characteristics, but we can find common characteristics amongst them

 

And "sees similarities in the differences that allow a generalization to be made." 

 "Having abstracted the characteristics that [things] have in common, we form a generalization that holds true for all [such things]."

 

 

 

 

 

Stereotyping

Stereotyping happens when "each member of the group is treated as typical and assumed to possess all the group's features." 

"But isn't this stereotyping?  Only if each member of the group is treated as typical and assumed to possess all the group's features." 

 

 

 

 

 

Avoiding

Stereotyping

We are engaged in inductive generalizations, so remember, we are in the land of probabilities only

 

"Each person should be treated as an individual even though he or she will probably exhibit some characteristics of the group." 

 

 

 

 

Fair

Generalizations

To have a fair generalization is to have one that attains an appropriate level of probability

 

A fair generalization attains an appropriate level of probability when it is well founded

"Generalizing, then, is something unavoidable, the lessons we draw from experience, and since we must generalize the trick is to do it well." 

 

"As in all forms of induction, we want to reach a conclusion that is highly probable, which means one based on strong evidence." 

 

"We want to make sure we have a good foundation for our generalization and that our reasoning is solid." 

 

 

 

Generalizations

Inductive

­

Generalizations Descriptive

Before finding out how to have a well founded generalization, consider the distinction between

 

Generalized Descriptions

 

&

 

Inductive Generalizations

"Let's make a distinction, though, before we address the question of how to form reliable generalizations." 

 

"We need to differentiate between a generalized description and an inductive generalization." 

 

 

 

Generalized

Description

Here there is a "blanket statement based on information about every member of the group." 

"In a generalized description we make some blanket statement based on information about every member of the group." 

 

"We fell safe in making these broad statements because they cover every person and thing we've mentioned." 

 

 

 

Inductive

Generalizations

Here there is a claim "about the entire group on the basis of an examination of some of its members." 

"In inductive generalizations, by contrast, we make a statement about the entire group on the basis of an examination of some of its members." 

 

"We are not describing but inferring from some to all." 

 

 

 

Good

Generalizations

"The main problem in generalizing, therefore, is figuring out how to achieve reliability."

 

"What percentage of a group must be examined for us to feel secure about a generalization in our argument?" 

 

"Which members should we use as a representative cross section?" 

 

 

 

Using

a

Fair

Sample

"in building a generalization into our argument we must be sure it is based on a fair sample." 

 

"This means one of sufficient size and randomness to make the generalization" reasonable or well-founded. 

 

"It must also be properly stratified." 

 

 

 

 

Size

"the number of cases we examine should be large enough to represent the whole." 

 

Judgment here is needed as the subject matter will determine the acceptable size of the sample

 

A "way to determine whether the sample is sufficiently large is to see what the generalization is about." 

"It stands to reason that the number of cases we examine should be large enough to represent the whole." 

 

"One way to judge how many that should be is to look at what we are generalizing about." 

 

"For some things we will need a very large sample, for others only a few cases will be sufficient." 

 

 

 

Singular

E.G.

In some cases, we need a singular sample

 

"From the fact that we burn our hand in fire, we can conclude that fire burns." 

 

"Can we generalize from one instance?" 

 

"That depends on the case." 

 

"From the fact that we burn our hand in fire, we can conclude that fire burns." 

 

"Depending on the situation, it might be a general truth we can rely on and not an isolated instance." 

 

 

 

Small

E.G.

Hardness of diamonds

"If we were generalizing about the hardness of diamonds, for instance, two or three examples would be enough because every diamond will have the same properties." 

 

"If a few diamonds are found to be hard enough to score glass, then we know that any diamonds will score glass." 

 

"In this case, if you've seen one, you've seen them all." 

 

 

 

Large

E.G.

Hardness of wood

"if we are generalizing about the hardness of wood, we might have to examine hundreds of samples because wood is not uniform in hardness." 

 

"There are many types of wood from light balsa, to pine or walnut, to dense woods like ebony or oak (ebony is so heaving, in fact, that it sinks!)." 

 

"If we were writing a report, we would need to show that the research had been extensive.  Only then would people accept our generalization about the hardness of wood." 

 

 

 

Sufficient

Size

"The moral of the story is that if we want to generalize in our argument we need a large enough sample on which to base it"

 

 

 

 

Problems

w/

Sufficient

Size

"we may not always know the subject well enough to determine in advance whether a large or small sample is needed." 

"there is a problem with judging adequate size by looking at the subject of the generalization." 

 

 

 

 

 

Hands-On

Method

"In this method we increase the sample size until the results begin to repeat themselves." 

 

"Then we can stop, knowing we have examined enough cases." 

 

"A hands-on experiment ... is the most reliable method of determining whether our generalization is based on an adequate sample size." 

"In these situations we may be able to use another method to determine the ideal size of the sample." 

 

"Rather than speculating on the proper size based on the nature of the subject, we should use this method whenever possible." 

 

 

 

Randomness

Here we can thwart biased generalizations

 

"we must make sure that the sample studied represents the whole and does not bias our conclusion." 

 

"Unless our sample is random, our generalization will be distorted rather than fair." 

"In addition to achieving a fair sample in terms of size, we must also pay attention to the factor of randomness." 

 

"We want to avoid 'loading' the sample in favor of a particular result but give every member of the class an equal chance of being chosen." 

 

 

 

The Bias Danger

"we tend to perceive and remember what we are seeking, and to ignore counter instances." 

"our generalization shouldn't just perpetuate some biased viewpoint but try to get at the truth of things." 

 

"Bias can creep into our thinking in unconscious ways that are hard to detect." 

 

"Not only could we be biased because of the prejudices we bring to our investigation, but also because of more subtle psychological factors that block a clear understanding." 

 

"Whatever our generalization, we must be on a guard so that our psychological attitudes and prejudices do not warp the result." 

 

 

 

Stratification

"Here we want to include all strata or classes that could have an important effect on our generalization." 

 

"Every relevant group must be taken into account." 

"If we [leave] our [any relevant categories], the sample [will] not represent the whole and our generalization [will] not be sound." 

 

 

 

Reliability

With those three steps completed, our generalization becomes more reliable

"It is only after we feel comfortable that a generalization is reliable that we can use it in our argument." 

 

 

 

Steps

to

Fair

Generalization

Size

 

Randomness

 

Stratification

 

 

 

 

Steps

to

Fair

Generalization

/

Step One

/

Size

1) "Check for adequate size in terms of the nature of the subject matter." 

 

"In an experimental situation, take repeated samples until the results begin to repeat themselves." 

 

 

 

 

Steps

to

Fair

Generalization

/

Step Two 

/

Randomness

2) "Be sure the generalization is random and free from bias in the sampling, so that each of the relevant elements has an equal chance of being chosen." 

 

 

 

 

Steps

to

Fair

Generalization

/

Step Three 

/

Stratification

3) "Make certain the sample is stratified, which means that all relevant categories are included and none is excluded that would significantly affect the generalization." 

 

 

 

 

 

 

 

 

Hypotheses

in

Arguments

"A hypothesis can be defined as an explanatory principle accounting for known facts." 

 

"In hypothetical thinking we want to know why something is true, and we reason backward to find some explanation for the facts, one that makes sense of them."

 

"We use our imagination to find some reason why things are the way they are."  

 

 

 

 

Resonance

w/

Analogical

Arguments

Just as we go from the known to the unknown in analogical arguments, by employing an hypothesis, we go from known facts to an unknown explanation.  

 

"the facts are known but the explanation for the facts is missing." 

 

(See what I did there?) 

"Whatever theory we devise must be plausible and account for the phenomenon." 

 

 

 

Evaluating Hypotheses

"How ... do we separate the genuine hypothesis from the fictional one?" 

 

"What separates a reliable hypothesis from an unreliable one or, more precisely, what features must a sound hypothesis possess?" 

"Some hypotheses ... bear little relation to reality." 

 

 

 

 

 

Developing

an

Adequate Hypothesis

"We must pay attention to these five rules in order to develop sound hypotheses." 

 

1) Consistency

 

2) Plausibility

 

3) Comprehensiveness

 

4) Simplicity

 

5) Predictability

"By their very nature, hypotheses are highly speculative, sometimes little more than educated guesses, but if we operate with integrity we can present hypotheses that are reasonable and much more likely to be correct." 

 

 

 

Measuring the

Adequacy

of

Hypotheses

/

Consistency

"Consistency with other hypotheses we accept." 

 

"A new hypothesis should be congruent with the bulk of hypotheses that we believe to be true." 

 

"It should fit in with the body of explanations that from our outlook on life." 

 

 

 

 

Measuring the

Adequacy

of

Hypotheses

/

Consistency

/

Revolutions

"Sometimes, of course, a new hypothesis will force us to rethink a number of our basic assumptions and becomes a new paradigm." 

 

"Skepticism seems the proper response at the start, holding onto what we have believed until such a time as we receive overwhelming proof to the contrary." 

 

 

 

 

Measuring the

Adequacy

of

Hypotheses

/

Consistency

/

Revolutions

E.G.

"This happened when the Copernican theory was accepted over the Ptolemaic one, and people began to believe that the earth revolved around the sun rather than the sun around the earth." 

"such revolutions in philosophical thinking are relatively rare." 

 

 

 

Consistency

and Our

Expectations

"We should therefore demand consistency in any hypothesis we read about, and we should not except anyone to accept our novel hypothesis if it means that person must radically revise his or her beliefs." 

 

Really?

"If the hypothesis we want to accept is at variance with the bulk of hypotheses that others and we have adopted, then we should take the path of humility and accept the traditional ideas." 

 

 

 

 

Measuring the

Adequacy

of

Hypotheses

/

Plausibility

"any new hypothesis must be plausible according to common sense and traditional ideas." 

 

"Every event can be explained in any number of ways, so to determine which hypothesis should be accepted we must screen out the very unlikely ones." 

"Since we do have established explanations for a great deal of occurrences in the natural world, any new hypothesis must be plausible according to common sense and traditional ideas." 

 

 

 

 

 

 

"we want to begin our inquiry with the most credible explanation and end up endorsing the hypothesis that is the most plausible." 

"We certainly should never argue that if we can't explain something it must be due to the occult, because then we are committing the fallacy of ignorance." 

 

 

 

 

 

Measuring the

Adequacy

of

Hypotheses

/

Comprehensiveness

"Any hypothesis that we present should be the most complete explanation we can find." 

 

"Many hypotheses will provide a partial answer to the question we are investigating, but we want the most encompassing one that will not leave important parts unexplained." 

 

"the hypothesis is not just closer to the truth but to the whole truth." 

 

 

 

Measuring the

Adequacy

of

Hypotheses

/

Simplicity

Ockham's Razor / Principle of Parsimony

 

"It states that 'entities should not be multiplied beyond what is required,' that is, as simple explanation is preferable to a complicated one." 

 

"This principle is attributed to the fourteenth-century theologian William of Ockham, and it is also called Ockham's Razor or the Law of Parsimony." 

 

"In other words, it argues for economy in thinking, and claims simplicity is best in a hypothesis or any other theory." 

 

 

 

Measuring the

Adequacy

of

Hypotheses

/

Predictability

"given the conditions described in our hypothesis, we can expect certain results to follow." 

 

"if nothing can be predicted on the basis of our hypothesis, this counts against its soundness, and we should hesitate to use it in our argument." 

"If our hypothesis is sound, we should be able to predict events based on that assumption." 

 

 

 

 

 

 

 

 

 

 

 

 


 

Final Exam / Part One

 

Questions A through Z are worth 1 point each.

 

 

A) Write out the first rule of validity for categorical deductive arguments. 

 

B) Write out the second rule of validity for categorical deductive arguments.

 

C) Write out the third rule of validity for categorical deductive arguments.

 

D) Write out the fourth rule of validity for categorical deductive arguments.

 

E) Name one valid hypothetical. 

 

F) Name the other valid hypothetical. 

 

G) Write out the one rule for disjunctive validity. 

 

H) Write out the "agreement" method of establishing causal connections. 

 

I) Write out the "difference" method of establishing causal connections. 

 

J) Write out the "agreement and difference" method of establishing causal connections. 

 

K) Write out the "concomitant variations" method of establishing causal connections. 

 

L) Explain what a remote cause is. 

 

M) Explain what a proximate cause is. 

 

N) Explain the difference between subsequent and consequent.

 

O) Explain the difference between necessary and sufficient conditions. 

 

P) Write out the first "essential respects," or "multiply the similarities," rule of analogical arguments.

 

Q) Write out the second "greater number," or "multiply the instances," rule of analogical arguments.

 

R) Write out the third "greater dissimilarity," or "diversify the base," rule of analogical arguments.

 

S) Write out the first, "size" step to fair generalizations. 

 

T) Write out the second, "randomness" step to fair generalizations. 

 

U) Write out the third, "stratification" step to fair generalizations. 

 

V) Write out the first, "consistency" rule to having a good hypothesis. 

 

W) Write out the second, "plausibility" rule to having a good hypothesis. 

 

X) Write out the third, "comprehensiveness" rule to having a good hypothesis. 

 

Y) Write out the fourth, "simplicity" rule to having a good hypothesis. 

 

Z) Write out the fifth, "predictability" rule to having a good hypothesis. 

 

 

_