1. SYLLOGISMS IN ORDINARY LANGUAGE
CHAPTER 7
SYLLOGISMS IN ORDINARY LANGUAGE

2. OBJECTIVES
Identify the 3 ways an argument in ordinary language deviates from standard form
Reduce the number of terms in a syllogism to 3 terms
Translate categorical propositions into standard form
Use a parameter to conduct uniform translation
Identify three types of enthymemes
Construct a sorites to test the validity of an argument
Identify disjunctive and hypothetical syllogisms
Describe three methods of responding to a dilemma

3. SYLLOGISTIC ARGUMENTS
An argument that is a standard form categorical syllogism, or can be reformulated as a standard form categorical syllogism
Reduction to standard form results in a standard-form translation.

4. SYLLOGISTIC ARGUMENTS
First Deviation
Order of the premises and conclusion not the same as standard-form argument
Second Deviation
Premises appear to have more than 3 terms
Third Deviation
Component propositions may not be standard form propositions

5. Reducing the Number of Terms to Three
Eliminate Synonyms
No wealthy persons are vagrants
All lawyers are rich people
Therefore no attorneys are tramps
Six terms can be reduced to three
All lawyers are wealthy persons
Therefore, no lawyers are vagrants

6. Reducing the Number of Terms to Three
Eliminate Class Complements
All mammals are warm-blooded animals
No lizards are warm-blooded animals
Therefore all lizards are non-mammals
Use Immediate Inferences
No lizards are warm blooded animals
Therefore no lizards are mammals
Exercises

7. Translating Categorical Propositions into Standard Form
Singular Propositions "I play tennis" becomes "All (the class that contains just me) play tennis" and "Some (the class that contains just me) play tennis" - (The "All ... play tennis" lacks existential import).
Adjectives as Predicates "That serve was wicked" becomes "That serve was a wicked serve".
Copula Not a Form of "To Be" "That serve spins" becomes "That serve is a serve that spins".
Non-Standard Form Arrangement "Aces are all well-placed serves" becomes "All aces are well-placed serves".
Quantities not "All", "No", or "Some" "A student did well" becomes "Some student did well". "Not every S is P" becomes "Some S is not P" and "Not any S is P" becomes "No S is P".
Exclusive Propositions "Only S is P" or "None but S is P" become "All P is S".
No Quantity Specified "Fit men play tennis" becomes "Some tennis players are fit men".
Do Not Resemble Standard Form "A stroke is forehand or backhand" becomes "No backhand stroke is a forehand stroke".
Exceptive Propositions "All except employees may enter" becomes both "All non-employees may enter" and "No employees may enter".

8. Translating Categorical Propositions into Standard Form
Singular Propositions
Asserts that a specific individual belongs to a particular class
Unit class
One-member class whose only member is that object itself
“All S is P”
Issues
Existential Import (some is complicated)
Fallacy of the Undistributed Middle

9. Translating Categorical Propositions into Standard Form
Consider the following argument:
All mammals are warm-blooded animals
No snakes are warm-blooded animals
Therefore, all snakes are non-mammals
If we applied our general rules for syllogisms to the above argument, we would judge it to be invalid because (1) it contains four terms; and (2) it has an affirmative conclusion drawn from a negative premise. We can, however, modify it slightly without changing the substance of the argument and see that it is perfectly valid. Consider this change:
Therefore, no snakes are mammals
We have reduced the number of terms to three by simply obverting the conclusion: ‘All snakes are non-mammals” becomes “No snakes are mammals.” These 2 propositions are equivalent. The syllogism is now in standard-form and is known to be valid.

10. Translating Categorical Propositions into Standard Form
Categorical Propositions that have adjectives or adjectival phrases as predicates
Some flowers are beautiful
Replace the adjective with a term designating the class of all objects that possess that attribute
Some flowers are beauties

11. Translating Categorical Propositions into Standard Form
Many categorical propositions contain adjectives or adverbs as predicates instead of terms denoting a class of objects. For example:
Some animals are mean
No automobiles are available for lease
All our students are handsome
Mary is always late
The predicates in the above propositions convey attributes of the subject. Some animals are “mean.” No automobiles are ‘available for lease.” All our students are ‘handsome.’ Mary is ‘always late.’ Every attribute, however, determines a class, a group of things possessing that attribute.
We can always change the proposition to indicate a class of objects to which the attribute applies. While there are other ways of expressing these propositions, these examples should help you get the idea. Putting the above propositions into standard form:
Some animals are ‘things that are mean.’ – Class is now things that are mean
No automobiles are ‘things available for lease.’
All our students are ‘handsome persons.’
Mary is a ‘person who is always late.’

12. Translating Categorical Propositions into Standard Form
Categorical Propositions whose main verbs are other than the standard form of ‘to be.’
All people seek recognition
Create a class and use the standard form of to be
All people are seekers of recognition

13. Translating Categorical Propositions into Standard Form
The standard cupola for categorical propositions used in syllogisms is a form of the verb ‘to be’ (such as is, was, are, etc.) Consider these:
All children desire attention
Some people drink lemonade
These propositions are easily translated into standard form by regarding all of the proposition except the subject term and the quantifier as naming a class-defining attribute, and replace it by a standard cupola and a term designating the class determined by that class-defining attribute. The above would then become:
All children are desirers of attention.
Some people are drinkers of lemonade.
“Desirers of attention” has now become a class of people (or objects), those who desire attention. The standard cupola ‘are’ is inserted. ‘Drinkers of lemonade’ is now a class, those people who drink lemonade. The standard cupola ‘are’ is again inserted here.

14. Translating Categorical Propositions into Standard Form
Standard form ingredients are all present , but not arranged in standard form order.
Racehorses are all thoroughbreds.
Decide which term is the subject term and then rearrange the words to reflect a standard form categorical proposition.
All racehorses are thoroughbreds.

15. Translating Categorical Propositions into Standard Form
Categorical propositions whose quantities are indicated by words other than ‘all’, ‘no’, or ‘some.’
‘Every’ or ‘any’ are translated into ‘all’
‘A’ or ‘an’ may be all or ‘some’ depending on context of sentence
‘The’ may refer to a particular individual or all members of a class
‘not every’ and ‘not any’ will also depend on context

16. Translating Categorical Propositions into Standard Form
Exclusive propositions
Assert that the predicate applies only to the subject named
Only citizens can vote
Reversing the subject and the predicate, and replace the only with all
All those who can vote are citizens

17. Translating Categorical Propositions into Standard Form
Categorical propositions that contain no words at all to indicate quantity
Examine the content
Dogs are carnivores becomes All dogs are carnivores
Children are present becomes Some children are beings who are present

18. Translating Categorical Propositions into Standard Form
Propositions that do not resemble standard-form categorical propositions, but can be translated
Nothing is both round and square
No round objects are square objects

19. Translating Categorical Propositions into Standard Form
Exceptive Propositions
Makes two assertions: that all members of some class, except for members of one of its subclasses, are members of some other class
All but employees are eligible
All non-employees are eligible
No employees are eligible
Translate into an explicit conjunction of two standard form categorical propositions
All non-employees are eligible persons, and no employees are eligible persons.
Exercises

20. Uniform Translation Parameter
An auxiliary symbol that aids in reformulating an assertion into standard form
The poor always you have with you
Use ‘times’ as the parameter (temporal)
All times are the times when you have the poor with you
Inserting a parameter can eliminate excess terms: "The poor are always with us" becomes "All times are times when the poor are with us". "I always win when my serve is on" becomes "All matches that I play when my serve is on are matches that I win".

21. Uniform Translation Consider reducing by using a parameter
Soiled paper places are scattered only where careless people have picnicked.
There are soiled paper plates scattered about here.
Therefore, careless people must have been picnicking here.
Use ‘places’ as the parameter
All places where soiled paper plates are scattered are places where careless people have picnicked
This place is a place where soiled paper plates are scattered
Therefore, this place is a place where careless people have picnicked
Excercises

22. Enthymemes
An argument is enthymematic if it is incompletely stated depending on additional information for completion.
An argument that contains an unstated proposition
Jones is a native-born American
Therefore, Jones is a citizen
Missing a premise that is though to be understood
All native-born Americans are citizens
First-order enthymeme
The proposition that is taken for granted is the major premise

23. Enthymemes Second-order enthymemes
Proposition taken for granted is the minor premise
All students are opposed to the new regulations
Therefore, all sophomores are opposed to the new regulations
Missing minor premise
All sophomores are atudents

24. Enthymemes Third – order enthymeme
Proposition taken for granted is the conclusion
No true Christian is vain, but some churchgoers are vain.
Infer the conclusion
Therefore, some churchgoers are not true Christians
Exercises

25. Sorites
Sometimes a single categorical proposition will not suffice for drawing a desired conclusion from a group of premises. The evidence for a conclusion consists of more than two propositions. The inference is not a syllogism in such cases but a series of syllogisms. Consider the following:
All dictatorships are undemocratic
All undemocratic governments are unstable
All unstable governments are cruel
All cruel governments are objects of hate
Therefore, all dictatorships are objects of hate
The inference (stated in the conclusion) may be tested by means of the syllogistic rules. The argument is a chain of syllogisms in which the conclusion of one becomes the premise of another. In the above syllogism, however, the conclusions of all except the last one are unexpressed.
A sorite is a chain of syllogisms in which the conclusion of one is a premise in another, in which all the conclusions except the last one are unexpressed, and in which the premises are so arranged that any two successive ones contain a common term.

26. Sorites
Sorites, appear in 2 distinct types: the Aristotlean and the Goclenian. It is the arrangement of the propositions within the sorites which determine what type it is.
In the Aristotlean, the first premise contains the subject of the conclusion and the common term of two successive propositions appears first as a predicate and next as a subject. An example of an Aristotlean sorite:
A=B. Aristotle is a man.
B=C. All men are mammals.
C=D. All mammals are living beings.
D=E. All living beings are substances
_____
A=E. Therefore, Aristotle is a substance.

27. Sorites
In a Goclenian sorite, the arrangement is different. The first premise contains the predicate of the conclusion and the common term of two successive propositions appears first as a subject and next as a predicate. An example of a Goclenian sorite:
D=E. One who has no peace of mind is miserable.
C=D. One who lacks much has no peace of mind.
B=C. One who has many desired lacks much.
A=B. One who has many vices, has many desires.
____
A=E. Therefore, one who has many vices is miserable.
Exercises

28. Disjunctive and Hypothetical Syllogisms
Disjunctive Proposition
Contains two component propositions
Either she was driven by stupidity or arrogance
Disjuncts
She was driven by stupidity
She was driven by arrogance

29. Disjunctive and Hypothetical Syllogisms
Disjunctive syllogism
Disjunction in one premise
Denial or contradictory of one of its two disjuncts in other premise
Validly infer that the other disjunct is true
Either Mrs. Smith is my next door neighbor or Mrs. Robinson is my next door neighbor.
Mrs. Robinson is not my next door neighbor
Therefore, Mrs. Smith is my next door neighbor
Disjunctive syllogism:
Either A or B Not A Therefore, B
Invalid disjunctive syllogism:
Either A or B A Therefore, not B

30. Disjunctive and Hypothetical Syllogisms
Hypothetical Proposition
If the first native is a politician, then the first native lies
Contains 2 propositions
Antecedent follows if
Consequent follows then
Conditional proposition: if (some antecedent) then (some consequent)

31. Disjunctive and Hypothetical Syllogisms
Contains at least one conditional proposition as a premise
Pure hypothetical syllogism
All premises are conditional
(if p then l) If the first native is a politician, then he lies.
(if l then denies p) If he lies, then he denies being a politician
(therefore, if p then denies p). Therefore, if the first native is a politician, then he denies being a politician.

32. Disjunctive and Hypothetical Syllogisms
Mixed hypothetical syllogism
One premise is conditional, the other is not
Modus Ponens (valid) – to affirm
Categorical premise affirms the antecedent of the conditional premise, the conclusion affirms its consequent
If the second native told the truth, then only one native is a politician.
The second native told the truth
Therefore, only one native is a politician

33. Disjunctive and Hypothetical Syllogisms
Fallacy of affirming the consequent
Categorical premise affirms the consequent of the conditional premise rather than the antecedent
If Bacon wrote Hamlet, then Bacon was a great writer
Bacon was a great writer
Therefore, Bacon wrote Hamlet
(Any great writer could have written Hamlet)

34. Disjunctive and Hypothetical Syllogisms
Mixed hypothetical syylogism
Modus tollens (valid) - to deny
Categorical premise denies the consequent of the conditional premise and the conclusion denies its antecedent
If the one-eyed professor saw two red hats, then he could tell the color of the hat on his own head
The one- eyed professor could not tell the color of the hat on his own head
Therefore, the one-eyed professor did not see two red hats.

35. Disjunctive and Hypothetical Syllogisms
Fallacy of denying the antecedent
Categorical premise denies the antecedent of the conditional premise, rather than the consequent
If John embezzled the bank funds, then John is guilty of a felony.
John did not embezzle the bank funds
Therefore, John is not guilty of a felony
(John could have committed another felony)
Exercises

36. Disjunctive and Hypothetical Syllogisms
pure hypothetical syllogism
mixed hypothetical syllogism
modus ponens ponere = to affirm
fallacy of affirming the consequent
modus tollens tollere = to deny
fallacy of denying the antecedent
if A then B if B then C QED if A then C
if A then B A QED B
invalid: if A then B B QED A
if A then B not B QED not A
invalid: if A then B not A QED not B

37. Disjunctive and Hypothetical Syllogisms
Principal Kinds of Syllogisms
Categorical Syllogisms
Disjunctive Syllogisms
Hypothetical Syllogisms
Pure
Mixed
All M is P All S is M QED All S is P.
Either P or Q is true P is not true QED Q is true
If P is true then Q is true If Q is true then R is true QED If P is true then R is true
If P is true then Q is true P is true QED Q is true

38. The Dilemma
The Dilemma – claims that a choice must be made between two alternatives, both of which are usually bad
Simple dilemma
Conclusion is a single categorical proposition
If the blessed in heaven have no desires, they will be perfectly content; so they will be also if their desires are fully gratified; but either they have no desires, or they have them fully gratified; therefore they will be perfectly content

39. The Dilemma Complex dilemma – Conclusion is a disjunction
Every time we talked to higher level managers, they kept saying they didn’t know anything about the problems below them… Either the group at the top didn’t know, in which case they should have known, or they did know, in which case they were lying to us.
On this one is said to ‘be caught on the horns’ of the dilemma
There are 3 solutions:

40. The Dilemma First, escaping between the horns
Reject the disjunctive premise
If students are fond of learning, they need no stimulus, and if they dislike learning, no stimulus would be useless. But any student is either fond of learning or dislikes it. Therefore a stimulus is either needless or useless.
Introduce a third type of student: one who is indifferent to learning

41. The Dilemma Second, grasp the dilemma by the horns
Reject the premise that is a conjunction
If students are fond of learning, they need no stimulus
Even the students who are fond of learning may sometimes need stimulus (grades)

42. The Dilemma Third, rebut the dilemma by means of a counterdilemma
Dilemma to not enter politics
If you say what is just then men will hate you; and if you say what is unjust, the gods will hate you; but you must say either one or the other; therefore you will be hated
Counterdilemma
If I say what is just, the gods will love me; and if I say what is unjust, men will love me; I must say either one or the other. Therefore, I shall be loved!

43. End