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# Exam 1 Study Guide 4482

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This 8 page Study Guide was uploaded by Carly Ott on Friday February 13, 2015. The Study Guide belongs to 4482 at Washington State University taught by Nathaniel Nicol in Winter2015. Since its upload, it has received 136 views.

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Date Created: 02/13/15

Exam 1 Study Guide Deductive and Inductive Arguments comes to one conclusion general 9 particular better argument generalization strength of argument hangs on sample size particular 9 general Ex This frog is green and so is this one so all frogs are green Deductive Argument Forms all or nothing kind of argument 1 Argument based on math 0 Generally deductive one exception is some statistics 0 Ex Pythagorean formula holds for all right triangles 2 Argument from definition 0 A bachelor is an unmarried man etc 3 Categoricalsyllogism 0 Go by the standard form I 2 premises one conclusion categorical statements throughout I All P and Q premise All Q are X premise So all P are X conclusion 4 Hypothetical syllogism o Syllogism with a conditional 5 Disjunctive syllogism o Syllogism with a disjunction 0 Either S or D premise Not S premise Therefore it s D conclusion Inductive Argument Forms argument can ALWAYS be stronger or weaker 1 Prediction 0 Ex weather forecast 2 Argument from analogy o Similarity of cases is crucial 3 Generalization 0 From sample to whole This frog is green and so is this one so all frogs are green 4 Argument from authority 0 From testimony hearsay 5 Argument based on signs 0 Ex Slippery road ahead sign 6 Casual inference 0 But then post hoc ergo o Deductive arguments validinvalid and soundunsound o Soundunsound has to do with the truth of the premises All the premises must be true and the conclusion must be true 0 Inductive arguments strongweak and cogentuncogent o Cogentuncogent has to do with the truth ofthe premises All the premises must be true and the conclusion must be true Counter Example Method There are 3 steps to the method 1 Extract the form of the argument 2 Construct a substitution instance having true premises but a false conclusion 3 This proves that the argument is invalid 0 To sum the steps up you extract the form of the argument and substitute other words that could prove the form of the argument false showing the argument is invalid because it would have true premises but a false conclusion 0 Looking for true premises yet a false conclusion Terms to know 0 the part of a sentence containing a verb and stating something about the subject ex went home in John went home 0 a person or thing that is being discussed described or dealt with o areare not 0 all no some 0 universal or particular 0 affirmative or negative Categorical Propositions 1 A all S are P universal affirmative o S subject term P predicate term 2 g no S are P universal negative 3 1 some S are P particular affirmative 0 Some there exists at least one 4 9 some S are not P particular negative 0 Remember for universals you cannot say all 5 are not P You must say no 5 are P ConversionI ObversionI and Contraposition 0 these notes were given to us by the professor so for full notes they are on his website 1 Conversion 0 The method here is simply to switch the subject and the predicate o E and I will give you the same truth value w Converse Truth Value E NoAareB NoBareA same SomeAare B Some BareA same A All A are B All B are A undetermined 0 Some A are not B Some B are not A undetermined 2 Obversion o The method here is in two steps 1 change the quality of a given proposition affirmative to negative and vice versa do not change the quantity universal or pa rticular and 2 replace the predicate with its complement The argument from a given statement to its obverse is always valid w Obverse Truth Value A All Aare B NoAare nonB same E NoAare B AllAare nonB same I Some A are B Some A are not nonB same 0 SomeAare not B SomeAare nonB same 3 Contraposition o The method here is also two steps 1 switch the subject and the predicate and 2 replace both the subject and the predicate with their term complements o A and 0 will give you the same truth value w Contrapositive Truth Value A All A are B All nonA are nonB same 0 some A are not B Some nonB are not nonA same E No A are B Non nonB are nonA undetermined Some A are B Some nonB are nonA undetermined o For contraposition and conversion the 2nOI and 3rd vowels in their name will give you the same truth values And Obversion will always give you the same truth value 0 Contraposition A and O 0 Conversion E and Standard Forms 10 0 these notes are from the professor s website as well 1 Terms without Nouns 0 change adjective only to plural noun or pronoun o quotviolets are purple to quotall violets are purple flowers 2 Nonstandard Verbs 0 work the copula in E 0 quotall ducks swim to quotall ducks are animals that swim Singular Propositions 0 use a universal and a parameter 0 quotSocrates is mortal to quotAll people identical to S are people who are mortal Adverbs and Pronouns o where when who what lang after Wword goes into the subject term 0 quotnowhere on Earth are there any borogroves to quotno places on earth are places there are borogroves 0 quotwhenever he goes to a Cubs game he cheers to quotall times he goes to a Cubs game are times he cheers Unexpressed Quantifiers o guided by most probable meaning 0 quota tiger roa red to quotSome tigers are animals that roared o quotelephants have a trunk to quotall elephants are trunked animals 0 quotpigs cannot fly to quotall pigs are nonflyers 0 quotbirds sat on the fence to quotsome birds are fencesitters Nonstandard Quantifiers 0 notice especially few 0 usually just some but sometimes this and quotsomenot o quotA few clowns are funny to quotSome clowns are funny people 0 quotFew Cubs players are in the Hall of Fame to quotSome Cubs players are in the Hall of Fame and some Cubs players are not in the Hall of Fame Conditional Statements 0 use universals if antecedent and consequent about the same thing 0 ifgoes in the subject only ifin the predicate Exclusive Propositions 0 after only none but none except and noexcept this language goes in the predicate 0 quotonly moviestars can park there to quotall people who can park there are movie stars quotthe only 0 after the only goes in the subject term 0 quotThe only animals in this 200 are from Asia to quotall animals in this 200 are from Asia 0 quotPhilosophy majors are the only ones who will be hired to quotall those who will be hired are philosophy majors 10 Exceptive Propositions 0 all exceptbut S are P into pairs of conjoined categorical statements 0 quotall except students are invited to quotno students are invited people and all nonstudents are invited people Premises Indicators Since As indicated by Because For In that May be inferred from As Given that Seeing that For the reason that In as much as Owing to Conclusion Indicators Therefore Wherefore Thus Consequently We may infer Accordineg We may conclude that It must be that For this reason So Entails that Hence It follows that VENN DIAGRAMS FOR CATEGORICAL SYLLOGISMS 39 Only diagram the premises No shading or Xing is made for the conclusion 39 Universal before particular If the argument contains one universal premise and one particular premise the universal should be entered rst in the diagram 39 Focus on twd circles at a time When entering the information contained in a premise concentrate on the circles corresponding to the two terms in that statement 39 Universals shade the same area as on 2circle diagram When shading an area one must be careful to shade all of the area in question Astatements Estatements lstatements 0statements BOOLEAN DIAGRAMS Shade all sections of the subject of the statement that are outside the predicate of the statement including the sub section inside the 31quotl circle Shade all sections of the subject of the statement that are inside the predicate of the statement including the subsection inside the 3rd circle Place an 39X in the section of the subject of the statement that is inside the predicate of the statement If both subsections of this overlap are unshaded then put the 39X on the line between the two subsections Place an X in the section of the subject of the statement that is outside the predicate of the statement if both subsections are unshaded then put the X on the line between the two sub sections BOOLEAN TEST FOR VALIDITY Is the information of the conclusion ALREADY contained within the diagram of the premises If quotyesquot then the syllogism is valid If quotnoquot then the syllogism is invalid What would the diagram of the premises have to look like for the conclusion to be included in it Conclusion Type Diagram includes conclusion if and only if A All W are Y All parts of W that are NOT inside Y are shaded E No W are Y All parts of W that ARE inside Y are shaded There is an quotxquot that is both entirely inside W and 1 some w are Y entirely inside Y There is an x that is both entirely inside W and 01 some w are at Y entirely outside Y FOR THE ARISTOTELIAN STANDPOINT l Boolean test rst If the syllogism is Booleanvalid then stop The syllogism is unconditionally valid ie valid from both the Boolean and the Aristotelian standpoints 2 Circled X in any circle with only one open subsection If i the syllogism is a invalid from the Boolean standpoint and ii has two universal premises and a particular conclusion see whether there is a circle that is completely shaded except for one open area Ifdtere is enter a circled X in that area 3 Conditionally valid If the conclusion is included in the diagram of the premises when you use the circled x then the argument is conditionally valid ie invalid from the Boolean standpoint but valid from the Aristotelian standpoint on the condition that the circled X represents something that really exists 4 Existential fallacy check If the syllogism is conditionally valid determine if the circled X represents something that really exists If it does then the syllogism is valid from the Aristotelian standpoint The syllogistic form is unconditionally valid ie every argument of this form is valid on both the Boolean and Aristotelian interpretations is the syllogism valid on the Boolean test A N0 l Does it have two universal premises and a particular conclusion YES have 3 of their four parts shaded Are there any category circles that YES i l Is there a circledX in an area that would make the conclusion true if there were such objects YES i A N0 The syllogistic FORM is conditionally valid on the I Aristotelian interpretation Jr A Do a new diagram and add a circledx in any category circle that has 3 of its four parts shaded A N0 Are there in fact members of the category that generated the circledX YES A N0 The syllogism is valid on the Aristotelian interpretation N0 J The syllogisti cform is invalid on the Aristolelian interpretation ie the syllogism is not formally valid v The syllogism is invalid

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