Philosophy 6: Logic in Practice

Los Angeles Pierce College

Department of History, Philosophy, & Sociology

 

 

 

 

 

Lecture Notes

 

 

 

 

 

 

Lecture Notes for "Chapter Seven" of Porter's The Voice of Reason

 

 

 

 

 

 

        

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

 

 

 

 

 

 

 

 

 

 

 

 

        

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

 

 

 

 

 

 

 

 

 

 

 

 

        

E.G. of the Difference        

 

"Television presents a continuous display of violence in graphically explicit and extreme forms.  It also depicts sexuality not as a physical expression of internal love but in its most lewd forms and obscene manifestations.  We must conclude, therefore, that television contributes to the moral corruption of individuals exposed to it." 

 

Claim/Conclusion:  "television contributes to the moral corruption of individuals exposed to it." 

 

Warrant/Premise:  "Television presents a continuous display of violence in graphically explicit and extreme forms." 

 

Warrant/Premise:  Television "also depicts sexuality not as a physical expression of internal love but in its most lewd forms and obscene manifestations." 

 

 

 

 

 

 

 

 

 

 

 

 

        

Judging Arguments  

 

Analyzing arguments into their parts facilitates our judging those arguments

        

Soundness "the logic is not sound," "if the conclusion does not strictly follow from the premises"

 

 

 

 

 

 

 

 

 

 

 

 

        

Testing the E.G.         

 

"Has the writer shown that television does corrupt society?" 

 

"Doesn't TV refine and educate people in some of its programming?" 

 

"Has a causal link been shown between the depiction of gross sexuality and the deterioration of morals?" 

 

"Does TV promote violence in our culture or merely reflect it?" 

 

"And when can we say that sex is lewd and obscene?" 

        

 

 

 

 

 

 

 

 

 

 

 

 

Good Advice      

 

"In writing an essay, we should summarize our argument in the introduction and articulate the structure so the reader is prepared for our exposition." 

 

"Then we can develop the argument in the body of our essay, clearly indicating what we are arguing for and why we are arguing it." 

        

 

 

 

 

 

 

 

 

 

 

 

 

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"

        

 

 

 

 

 

 

 

 

 

 

 

 

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

        

 

 

 

 

 

 

 

 

 

 

 

 

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. 

 

 

 

 

 

 

 

 

 

 

 

 

        

Logical Forms of Statements E.G.       

 

(A) All unicorns are gauche creatures. 

 

(E) No unicorn is a gauche creature.

        

(I) Some unicorns are gauche creatures. 

        

(O) Some unicorns are not gauche creatures. 

        

 

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." 

 

 

 

 

 

 

 

 

 

 

 

 

        

Paraphrasing E.G.s   

 

"Cats have a quiet tread (flannel-footed)."        

translates to

"All cats are creatures with a quiet tread (flannel-footed)." 

 

 

"Several houses were damaged by the hurricane."     

translates to

"Some houses are structures damaged by the hurricane." 

 

 

"All men are not preoccupied with sports."        

translates to

"Some men are people preoccupied with sports." 

 

 

"No one need fear justice who is innocent of any crime."     

translates to

"No person who is innocent of any crime is a person who need fear justice." 

        

 

 

 

 

 

 

 

 

 

 

 

 

Implications     

 

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

        

 

 

 

 

 

 

 

 

 

 

 

 

Conversions     

 

Some statements' subjects and predicates are interchangeable

 

(A)     All unicorns are gauche creatures. 

 

does not convert to      

 

(A)     All gauche creatures are unicorns. 

                          

*

 

(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.

 

does not convert to      

 

(O)    Some gauche creatures are not unicorns. 

 

        

 

 

 

 

 

 

 

 

 

 

 

 

Trying it Out     

 

I. 1

 

I. 2

 

I. 3

 

IV. 2

 

IV. 3

 

V. 2

 

V. 3

 

VI. 1

 

VI. 2

 

 

 

 

 

 

 

 

 

 

 

 

        

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." 

 

 

 

 

 

 

 

 

 

 

 

 

        

Major Premise  

 

"The major premise consists of the chief reason for the conclusion"

 

"it is the premise that contains the term in the predicate of the conclusion." 

 

 

 

 

 

 

 

 

 

 

 

 

        

Minor Premise  

 

"The minor premise supports the conclusion in an auxiliary way" 

 

"it contains the term that appears in the subject of the conclusion." 

 

 

 

 

 

 

 

 

 

 

 

 

        

Syllogism E.G.  

 

Major Premise:     All single-horned creatures are special. 

Minor Premise:     All narwhals are single-horned creatures. 

Conclusion:          Narwhals are special. 

          

 

 

 

 

 

 

 

 

 

 

 

 

 

Enthymemes    

 

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

 

 

 

 

 

 

 

 

 

 

 

 

 

        

First Order Enthymeme     

 

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

 

 

 

 

 

 

 

 

 

 

 

 

        

First Order Enthymeme E.G.      

 

Major: 

Minor:  All narwhals are single-horned creatures.

Conclusion:  Narwhals are special.

 

 

 

 

 

 

 

 

 

 

 

 

        

Second Order Enthymeme         

 

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

 

 

 

 

 

 

 

 

 

 

 

 

        

Second Order Enthymeme E.G.  

 

Major:  All single-horned creatures are special.

Minor: 

Conclusion:  Narwhals are special.

 

 

 

 

 

 

 

 

 

 

 

 

        

Third Order Enthymeme    

 

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

 

 

 

 

 

 

 

 

 

 

 

 

        

Third Order Enthymeme E.G.     

 

Major:  All single-horned creatures are special.

Minor:  All narwhals are single-horned creatures.

Conclusion: 

 

 

 

 

 

 

 

 

 

 

 

 

        

Validity     

 

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

 

 

 

 

 

 

 

 

 

 

 

 

 

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

 

 

 

 

 

 

 

 

 

 

 

 

        

Invalid     

 

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

 

 

 

 

 

 

 

 

 

 

 

 

        

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. 

 

 

 

 

 

 

 

 

 

 

 

 

        

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." 

        

 

 

 

 

 

 

 

 

 

 

 

 

Trying it Out     

 

I. 3

 

II. 2

 

II. 3

 

IV. 4

 

IV. 6