Presentation on theme: "CHAPTER 7 SYLLOGISMS IN ORDINARY LANGUAGE. OBJECTIVES 1.Identify the 3 ways an argument in ordinary language deviates from standard form 2.Reduce the."— Presentation transcript:
OBJECTIVES 1.Identify the 3 ways an argument in ordinary language deviates from standard form 2.Reduce the number of terms in a syllogism to 3 terms 3.Translate categorical propositions into standard form 4.Use a parameter to conduct uniform translation 5.Identify three types of enthymemes 6.Construct a sorites to test the validity of an argument 7.Identify disjunctive and hypothetical syllogisms 8.Describe three methods of responding to a dilemma
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.
SYLLOGISTIC ARGUMENTS First Deviation Order of the premises and conclusion not the same as standard-form argumentOrder of the premises and conclusion not the same as standard-form argument Second Deviation Premises appear to have more than 3 termsPremises appear to have more than 3 terms Third Deviation Component propositions may not be standard form propositionsComponent propositions may not be standard form propositions
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 –No wealthy persons are vagrants –All lawyers are wealthy persons –Therefore, no lawyers are vagrants
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 –All mammals are warm-blooded animals –No lizards are warm blooded animals –Therefore no lizards are mammals –Exercises
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".
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
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: –All mammals are warm-blooded animals –No snakes are warm-blooded animals –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.
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
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 meanSome animals are mean No automobiles are available for leaseNo automobiles are available for lease All our students are handsomeAll our students are handsome Mary is always lateMary 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.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: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 meanSome animals are ‘things that are mean.’ – Class is now things that are mean No automobiles are ‘things available for lease.’No automobiles are ‘things available for lease.’ All our students are ‘handsome persons.’All our students are ‘handsome persons.’ Mary is a ‘person who is always late.’Mary is a ‘person who is always late.’
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
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.
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.
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
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
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
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
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
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".
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
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
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
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
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.
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.
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
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
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
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)
Disjunctive and Hypothetical Syllogisms Hypothetical Syllogism –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.
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
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)
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.
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
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
Disjunctive and Hypothetical Syllogisms Principal Kinds of Syllogisms Categorical Syllogisms Disjunctive Syllogisms Hypothetical Syllogisms PureMixed 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
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
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:
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
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)
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!