Presentation on theme: "SYLLOGISMS IN ORDINARY LANGUAGE"— Presentation transcript:
1 SYLLOGISMS IN ORDINARY LANGUAGE CHAPTER 7SYLLOGISMS IN ORDINARY LANGUAGE
2 OBJECTIVESIdentify the 3 ways an argument in ordinary language deviates from standard formReduce the number of terms in a syllogism to 3 termsTranslate categorical propositions into standard formUse a parameter to conduct uniform translationIdentify three types of enthymemesConstruct a sorites to test the validity of an argumentIdentify disjunctive and hypothetical syllogismsDescribe 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 syllogismReduction to standard form results in a standard-form translation.
4 SYLLOGISTIC ARGUMENTS First DeviationOrder of the premises and conclusion not the same as standard-form argumentSecond DeviationPremises appear to have more than 3 termsThird DeviationComponent propositions may not be standard form propositions
5 Reducing the Number of Terms to Three Eliminate SynonymsNo wealthy persons are vagrantsAll lawyers are rich peopleTherefore no attorneys are trampsSix terms can be reduced to threeAll lawyers are wealthy personsTherefore, no lawyers are vagrants
6 Reducing the Number of Terms to Three Eliminate Class ComplementsAll mammals are warm-blooded animalsNo lizards are warm-blooded animalsTherefore all lizards are non-mammalsUse Immediate InferencesNo lizards are warm blooded animalsTherefore no lizards are mammalsExercises
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 PropositionsAsserts that a specific individual belongs to a particular classUnit classOne-member class whose only member is that object itself“All S is P”IssuesExistential 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 animalsNo snakes are warm-blooded animalsTherefore, all snakes are non-mammalsIf 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 mammalsWe 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 predicatesSome flowers are beautifulReplace the adjective with a term designating the class of all objects that possess that attributeSome 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 meanNo automobiles are available for leaseAll our students are handsomeMary is always lateThe 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 meanNo 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 recognitionCreate a class and use the standard form of to beAll 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 attentionSome people drink lemonadeThese 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 propositionsAssert that the predicate applies only to the subject namedOnly citizens can voteReversing the subject and the predicate, and replace the only with allAll those who can vote are citizens
17 Translating Categorical Propositions into Standard Form Categorical propositions that contain no words at all to indicate quantityExamine the contentDogs are carnivores becomes All dogs are carnivoresChildren 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 translatedNothing is both round and squareNo round objects are square objects
19 Translating Categorical Propositions into Standard Form Exceptive PropositionsMakes two assertions: that all members of some class, except for members of one of its subclasses, are members of some other classAll but employees are eligibleAll non-employees are eligibleNo employees are eligibleTranslate into an explicit conjunction of two standard form categorical propositionsAll 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 formThe poor always you have with youUse ‘times’ as the parameter (temporal)All times are the times when you have the poor with youInserting 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 parameterAll places where soiled paper plates are scattered are places where careless people have picnickedThis place is a place where soiled paper plates are scatteredTherefore, this place is a place where careless people have picnickedExcercises
22 EnthymemesAn argument is enthymematic if it is incompletely stated depending on additional information for completion.An argument that contains an unstated propositionJones is a native-born AmericanTherefore, Jones is a citizenMissing a premise that is though to be understoodAll native-born Americans are citizensFirst-order enthymemeThe proposition that is taken for granted is the major premise
23 Enthymemes Second-order enthymemes Proposition taken for granted is the minor premiseAll students are opposed to the new regulationsTherefore, all sophomores are opposed to the new regulationsMissing minor premiseAll sophomores are atudents
24 Enthymemes Third – order enthymeme Proposition taken for granted is the conclusionNo true Christian is vain, but some churchgoers are vain.Infer the conclusionTherefore, some churchgoers are not true ChristiansExercises
25 SoritesSometimes 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 undemocraticAll undemocratic governments are unstableAll unstable governments are cruelAll cruel governments are objects of hateTherefore, all dictatorships are objects of hateThe 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 SoritesSorites, 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 SoritesIn 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 PropositionContains two component propositionsEither she was driven by stupidity or arroganceDisjunctsShe was driven by stupidityShe was driven by arrogance
29 Disjunctive and Hypothetical Syllogisms Disjunctive syllogismDisjunction in one premiseDenial or contradictory of one of its two disjuncts in other premiseValidly infer that the other disjunct is trueEither Mrs. Smith is my next door neighbor or Mrs. Robinson is my next door neighbor.Mrs. Robinson is not my next door neighborTherefore, Mrs. Smith is my next door neighborDisjunctive syllogism:Either A or B Not A Therefore, BInvalid disjunctive syllogism:Either A or B A Therefore, not B
30 Disjunctive and Hypothetical Syllogisms Hypothetical PropositionIf the first native is a politician, then the first native liesContains 2 propositionsAntecedent follows ifConsequent follows thenConditional proposition: if (some antecedent) then (some consequent)
31 Disjunctive and Hypothetical Syllogisms Contains at least one conditional proposition as a premisePure hypothetical syllogismAll 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 syllogismOne premise is conditional, the other is notModus Ponens (valid) – to affirmCategorical premise affirms the antecedent of the conditional premise, the conclusion affirms its consequentIf the second native told the truth, then only one native is a politician.The second native told the truthTherefore, only one native is a politician
33 Disjunctive and Hypothetical Syllogisms Fallacy of affirming the consequentCategorical premise affirms the consequent of the conditional premise rather than the antecedentIf Bacon wrote Hamlet, then Bacon was a great writerBacon was a great writerTherefore, Bacon wrote Hamlet(Any great writer could have written Hamlet)
34 Disjunctive and Hypothetical Syllogisms Mixed hypothetical syylogismModus tollens (valid) - to denyCategorical premise denies the consequent of the conditional premise and the conclusion denies its antecedentIf the one-eyed professor saw two red hats, then he could tell the color of the hat on his own headThe one- eyed professor could not tell the color of the hat on his own headTherefore, the one-eyed professor did not see two red hats.
35 Disjunctive and Hypothetical Syllogisms Fallacy of denying the antecedentCategorical premise denies the antecedent of the conditional premise, rather than the consequentIf John embezzled the bank funds, then John is guilty of a felony.John did not embezzle the bank fundsTherefore, John is not guilty of a felony(John could have committed another felony)Exercises
36 Disjunctive and Hypothetical Syllogisms pure hypothetical syllogismmixed hypothetical syllogismmodus ponens ponere = to affirmfallacy of affirming the consequentmodus tollens tollere = to denyfallacy of denying the antecedentif A then B if B then C QED if A then Cif A then B A QED Binvalid: if A then B B QED Aif A then B not B QED not Ainvalid: if A then B not A QED not B
37 Disjunctive and Hypothetical Syllogisms Principal Kinds of SyllogismsCategorical SyllogismsDisjunctive SyllogismsHypothetical SyllogismsPureMixedAll 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 trueIf P is true then Q is true If Q is true then R is true QED If P is true then R is trueIf P is true then Q is true P is true QED Q is true
38 The DilemmaThe Dilemma – claims that a choice must be made between two alternatives, both of which are usually badSimple dilemmaConclusion is a single categorical propositionIf 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 dilemmaThere are 3 solutions:
40 The Dilemma First, escaping between the horns Reject the disjunctive premiseIf 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 conjunctionIf students are fond of learning, they need no stimulusEven 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 politicsIf 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 hatedCounterdilemmaIf 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!