Logic and Critical Thinking (GT
Logic and Critical Thinking (GT PHIL 110
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This 41 page Class Notes was uploaded by Isai Ondricka on Tuesday September 22, 2015. The Class Notes belongs to PHIL 110 at Colorado State University taught by Linda Rollin in Fall. Since its upload, it has received 64 views. For similar materials see /class/210338/phil-110-colorado-state-university in PHIL-Philosophy at Colorado State University.
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Date Created: 09/22/15
1 March Figure 1 Figure 2 Figure 3 Figure 4 All fish are animals that live in water All trout are fish All trout are animals that live in water AAA 1 Diagram the premises See if what remains matches the conclusion 3 February Subject term amp predicate term They have to be nouns or noun phrases No superheroes are bad people Quality Negative Quantity Universal Quantifier No Subject Superheroes Predicate Bad people Copula Are 11 letters in the subject term but the subject is made up of Batman Superman KickAss ampc The predicate term is 2 words but the predicate itself is the actual people Some dolphins are not intelligent Not in standard form llNot intelligent is not a noun noun phrase Fix it 9Some dolphins are not intelligent creatures Some whales are black Fix it 9Some whales are black objects Some marathon competitors are from Kenya Fix it 9Some marathon competitors are Kenyans No college student is stupid Fix it 9 No college student is a stupid person All professors who come to office hours are helpful to their students Fix it 9A professors who come to office hours are people who are helpful to their students Some jellyfish are deadly Fix it some jellyfish are deadly creatures All boys are very mean and deceiving Fix it 9A boys are very mean and deceiving people Fix the verb No candles can be left while still lit Fix it 9 No candles are objects that can be left while still lit All men lie Fix it 9A men are people who lie No cows are sheep E Subject Cows Predicate Sheep Quality Negative Quantity Universal All doctors have a PhD Truth value False Fix it 9 All doctors are people who have PhDs Juicy oranges rule All oranges are juicy All orange are juicy fruits things foods Don t use oranges All oranges are juicy oranges Don t repeat the entire subject when supplying the missing noun All California oranges are juicy All California oranges are juicy oranges Okay Modify Fix nonstandard missing quantifier Every student is happy All students are happy people There are elephants that are pink Some elephants are pink creatures Turkeys are stupid All turkeys are stupid creatures Turkeys are on sale at Safeway Some turkeys are items on sale at Safeway All Americans are not rich SF 9 Some Americans are not rich OR No Americans are rich people There isn t a form llall S are not P Nate s mistake Singular propositions About one person place thing Jessica is a graduate student All people identical to Jessica are graduate students Here identical means one amp the same as Ben is not a physics major No people identical to Ben are physics majors 25 January With an inductive argument even if it s really good new evidence can come up and change the truth value Deductive arguments are 100 Absolute Valid Invalid Sound All dogs are green Fido is a dog Therefore Fido is green If the premises are true the conclusion has to be true Deductive arguments only The premises guarantee the conclusion Guarantee if the premises were true the conclusion would have to be true Impossible for the conclusion to be false All beers are beverages Coors is a beverage Therefore Coors is a beer Only deductive Valid Premises are true Valid Form AIIAareB XisanA Therefore X is a B Invalid Form All Care D Y is a D Therefore Y is a C 15 February Immediate nferences 3 meanings of inference Argument Conclusion ofan argument nferential intent of an argument No dogs are cats Therefore no cats are dogs The P and C are logically equivalent This argument is valid If the premise is true the conclusion must be true Same truth value The C is the converse of the P This is a valid converse Some birds are fish Therefore some fish are birds What inference occurred between the premise and conclusion Converse Valid Because the truth value is the same if P is true C must be true Some dogs are not poodles Therefore some poodles are not dogs Not valid P is true but C is false Venn diagrams are different Invalid illicit converse Some birds are not dogs Therefore some dogs are not birds Illicit converse O proposition All 0 propositions have illicit converses Immediate inferences Converse Obverse Contra positive Complement of a term Dogs nondogs Cats noncats Mammals nonmammals Dedicated students 9 nondedicated students Nondogs 9 Dogs No D are nonM All D are M Obve rse Change quality and complement the P Obverses are always equivalent Some birds are not nonrobins Some birds are robins No students are nonresidents All students are residents Contrapositive All nonmammals are noncats All cats are mammals Switch S amp P complement both 20 January are a T Denver is the F The is F sentence is written in red Come over here Propositions Clint Eastwood is the best actor in Hollywood Proposition Abortion is wrong Proposition This sentence is false George Washington had scrambled eggs for breakfast on Dec 24 Proposition A proposition can be used as true false Truth value 9 it is either true or false Deductive vs inductive arguments Deductive 1 or more premises supposed to support a conclusion Conclusion follows absolutely from the premises Conclusion follows absolutely More precise f premises are true the conclusion has to be true Inductive 1 or more premise supposed to support the conclusion Premises give support Conclusion is probable Example of deductive argument All cats are purple Garfield is a cat So Garfield is purple Two kinds of quotgoodquot Valid If the premises are true then the conclusion must be true Sound Cat argument is valid 8 February Distribution A term is distributed in a proposition if the proposition gives information about every member of the category named by the term All dogs are mammals Dogs is distributed in this A proposition This A proposition distributes the term dogs Mammals is undistributed in this A proposition A S are P S is distributed P is undistributed No S are P S is distributed P is distributed Some S are P S is undistributed P is undistributed Some S are not P S is undistributed P is distributed Negatives distributed predicate Universals distributed subject 10 February No birds are elephants No overlap between birds and elephants All dogs are mammals Dog circle inside mammal circle Euler s circles Venn diagrams Shaded areas in a Venn diagram deletes the area there is nothing in there The exterior of the Venn diagram holds everything in the universe besides the S P Putting an X in part of a Venn diagram shows where at least one thing is Logically equivalent Same diagram No college students are people under 10 No people under 10 are college students They have the same meaning They describe the same state of affairs Converse Switch S amp P Keep everything else the same Write the converse of llNo dogs are catsquot No cats are dogs All skinny people are world class eaters All world class eaters are skinny people Not logically equivalent If two propositions are logically equivalent they have the same truth value 8 March Syllogistic Rules Terms can t change meaning Fallacy of four terms State and explain difference Both premises are universal and conclusion is particular Existential fallacy If the argument is in standard form Two negative premises Fallacy of exclusive premises If there is one negative premise the conclusion must be negative Fallacy of drawing an affirmative conclusion from a negative premise Aka fallacy of aff con from negprem These are the ones that are easier to spot Distribution review All S are P No Sare Some S are P Some S are notE The other rules depend on distribution The middle term has to be distributed in at least one premise Fallacy of undistributed middle If any term in the conclusion is disturbed it must have been distributed in its premise Illicit process of the major term illicit major Illicit process of the minor term illicit minor 27 January When writing arguments in standard mode C at bottom below premises Omit indicator words Propositions must be complete sentences Quiz Tuesday Write out premises and conclusion in standard order Basic definitions T F Definitions of validity Deductive arguments Valid Sound Not sound Invalid Unsound Studying in this class Deductive arguments How to tell if they re valid or invalid Putting them in a usable form 3 May Final Look over course outline Wednesday 11 May 24 Appeal to ignorance Premise says we don t know anything Conclusion says something based on that No one has ever been able to prove that ghosts don t exist Therefore ghosts do exist Fallacy of the slippery slope The domino fallacy quotDon t take the first step then all these things will happen DISASTERquot Use llfirst step tell what it is Tell what the series of steps and final outcome are Identify where evidence is missing Fallacy of complex question Have you stopped beating your wife Argument is all in one question State hidden question amp answer Begging the question Ex To use textbooks with profane and obscene language in them is immoral because it is not right for our students to read vulgar disrespectful and ugly words Premise and conclusion pretty much the same Does not give real evidence Circular argument Ambiguity Equivocation word changes meaning What changed meaning Give meanings Say conclusion shouldn t be drawn Amphiboly change in meaning caused by grammatical defect A phrase is used in a way that you can t tell what s being modified When a pronoun changes meaning Fallacy of accent Different conclusions depending on what word is emphasized 7 April Disjunctive syllogisms eitheror Hypothetical syllogisms ifthen Simple propositions My dog is brown Symbolize p Oppositedenialcontradictory My dog is not brown Symbolize p llnot p John doesn t run fast Symbolize quotqquot John does run fast 1 Disjunctive proposition two simple propositions joined by quotorquot Either Fido ran away or Fido got hit by a car Two simple propositions disjuncts Two kinds of or Inclusive or includes possibility of both being true Exclusive or excludes it one or the other It will be inclusive or in this class Take first disjunct p second q So p or q Orv In a disjunctive syllogism one premise is disjunctive other two are simple Fido ran away or Fido got hit by a car Fido didn t run away Fido got hit by a car Symbolize P V c NP c This form is valid disjunctive syllogism Because we use inclusive or both can be true Hypothetical proposition ifthen If you put your hand in fire then you will get burned It s impossible to put your hand in the fire and not get burned First simple proposition antecedent Second simple proposition consequent Symbolize If p then q p q quotif p then qquot Hypothetical syllogisms Pure 3 hypothetical propositions If you study hard you get all A s If you get all A s you get a scholarship If you study hard you get a scholarship Symbolize Label the conclusion first using p and r 1 February Categorical logic propositional logicAristotelian logic 2 premises amp 1 conclusion All propositions discuss how categories fit together 4 ways 2 categories can fit together 4 Categorical Propositions All students are hard workers A No students are hard workers E Some students are hard workers I Some students are not hard workers 0 Some at least one First category is the subject Second category is the predicate Quantifier all no some gives amounts Copula joiner verb 2 amp 4 are negative 1 amp 3 are affirmative 1 amp 2 are universal 3 amp 4 are particular Every categorical proposition has a quantity and a quality Quantity universal or particular Quality negative or affirmative 19 April Appeal to pity Use quotsympathyquot in the explanation Appeal to authority Because someone said so 24 February Syllogism a deductive argument with 2 premises and a conclusion Categorical syllogism 3 categorical propositions containing exactly 3 terms each of which occurs in exactly 2 of the propositions Example Some fourlegged creatures are gnus All gnus are herbivores Some fourlegged creatures are herbivores Middle term is in both premises but not in the conclusion Major term is predicate of conclusion Minor term is subject of conclusion Major premise contains the major term Minor premise contains the minor term Categorical syllogism standard form Each proposition must be in standard form Terms must match exactly Terms must be used in the same sense Major premise 9 minor premise 9 conclusion Figure 1 Figure 2 Figure 3 Figure 4 12 April Mixed hypothetical syllogisms Contain 1 ifthen Modus ponens p q P Therefore q Fallacy of affirming the consequent p q 0l Therefore p Modus tollens p q c Therefore Np Fallacy of denying the antecedent p q P Therefore q 24 March Special words Only Only A are B 9 All B are A The term immediately following only becomes the predicate of an A proposition quotThe only The term immediately following llthe only becomes the subject of an A proposition Wherever All places Where Same as wherever Whenever All times Today All times identical to today IfThen 17 February All apples are red objects Contradictory Some A are not R To form the contradictory of any proposition change the quantity and quality Universal 9 particular Affirmation 9 negative And vice versa Diagrams have shading where the other has an X Propositions and their contradictaries have opposite truth values Ways of stating the quot y of the U 39 r r 39 39 llAll dogs are good pets It is not true that It is false that The contradictory of It is not the case that The negation of The denial of All dogs are good pets not In standard form some dogs are not good pets 5 May Categorical propositions SubjectpredicateAEIOquantityquaitydistributed C IL I quotI r I I 1 Y Truefalseundetermined Contradictory Change quality amp quantity Simplify statements to get rid of non s 22 February Exa m 4 pages Quiz 1 Quiz 2 questions on newest material practice quiz In traditional Aristotelian logic there were fewer undetermineds arguments All S are P T Uses converses obverses contraries Some P are S T contradictories our way propositions say Makes existential assumption eXIstence Existential fallacy All premises are universal no El Conclusion is particular EI Boolean never commits EF 21 April Ad hominem to the person Abusive saying something mean Attack personally Circumstantial saying something special but not mean Eg Of course she ll vote for the teacher benefits she s a teacher 29 March Enthymeme A usually deductive argument with a part missing but understood Completing the enthymeme Filling in the part that s missing The result should be a valid argument Missinghiddenimpliedtacit premise or conclusion 28 April False cause Post hoc ergo propter hoe One thing happened then something else did Therefore the first caused the second 26 April Exam 3 Thursday DisjampHypSyll Fallacies Long Force pity ad hominem authority Short answer Identification Ad populum to the people Appealing to tradition family sense of group Flattery Making people feel guilty ampc Peer pressure Fallacy of accidentmisuse of a principle Use a general rule as a premise Apply to a specific case where the case is an exception to the rule Use llgeneral rulequot and llspecific casequot tell what they are Use quotexceptionquot tell why Converse accidenthasty generalization Jumping to conclusions Making a generalization from a specific case There is not enough evidence or the cases are exceptional 18 January An argument is a chunk of reasoning Someone s claim or belief along with their reasons Logic is the study of the methods and principles we use to decide whether something is good or bad reasoning Either I ll major in French or Spanish but there aren t many jobs for people who speak French so I ll major in Spanish Writing arguments in standard form Premise 1 Either I ll major in French or Spanish Premise 2 There aren t many jobs for a Frenchspeaker Conclusion I ll major in Spanish Premises Reasons Conclusion Thing that s being supported by the premises We need to see if the premises support the conclusion Are the premises true You shouldn t buy that Silverado Because it s purple and asked my friend and he said purple is a stupid color Prem 1 The Silverado is purple Prem 2 Purple is a stupid color Con You shouldn t buy the Silverado 3 March Syllogistic Rules Terms can t change meaning If they do 9 fallacy of four terms Tell which term changed meaning and give the two meanings Any standard form categorical syllogism with 2 negative premises is invalid Fallacy of exclusive premises 14 April Informal fallacies Fallacies of relevance Makes a statement that is irrelevant to the argument Appeal to Force Does not give a good reason to do something Threatens The minister said llGoing to church every Sunday is an important spiritual activity because if you don t you ll burn in hellquot Always has a twopart conclusion Action amp ideaprinciple Go to church every Sunday amp going to church is an important spiritual activity Explanation should include Who commits the fallacy What fallacy These two apply to any fallacy explanation What action is being urged Who is being quotconvincedquot What is the threat Quote amp explain as needed What s wrong No relevant evidence for ideaprinciple
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