Critical Thinking 03 consistency

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Slides for the concepts of conjunction, negation, contradiction, the Principle of Noncontradiction, proof by counter-example, and reductio ad absurdams

Slides for the concepts of conjunction, negation, contradiction, the Principle of Noncontradiction, proof by counter-example, and reductio ad absurdams

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  • 1. Consistency A Standard of Critical Thinking
  • 2. Review Philosophy: the attempt to answer, critically, the epistemological, metaphysical, and ethical questions. An Issue Question: is a yes-orno question, and is the way to formulate questions for the disputed question method (quaestio disputata). Principle of Charity: for any claim, give it the strongest possible interpretation. Principle of Sufficient Reason: for or any claim, give reason why it is true, or not. A virtue is an excellence, a mean between two extremes called vices.
  • 3. Review The Disputed Question Method yes: Reasons supporting the yes answer or refuting the no answer. Which side has the better reasons? the question no: Reasons supporting the no answer or refuting the yes answer.
  • 4. Review Truth: when a claim matches what is. Ambiguous: A term with more than one meaning. Claims are candidates for truths, such as beliefs stated in language. Vague: A term with an unclear extension.
  • 5. Review The Disputed Question Method Reasons supporting the yes answer or refuting the no answer. yes: Does the thing designated by the subject have the property expressed by the predicate? no: Which side has the better reasons? Reasons supporting the no answer or refuting the yes answer.
  • 6. Review The Disputed Question Method Reasons supporting the yes answer or refuting the no answer. yes: Do the things designated by the nouns stand in the relation expressed by the verb. no: Which side has the better reasons? Reasons supporting the no answer or refuting the yes answer.
  • 7. Review to pursue the truth of a claim, avoid matters of taste, fill in the indices, and spell out the ceteris paribus. to evaluate the truth of a claim determine whether the thing designated by the subject has the property expressed by the predicate to evaluate the truth of a claim determine whether the things designated by the nouns stand in the relation expressed by the verb.
  • 8. Review to determine the truth of a claim determine whether the thing designated by the subject is in the extension of the predicate. to determine the truth of a claim determine whether the things designated by the nouns are in the extension of the verb. to define a term give it one clear meaning.
  • 9. Review The Disputed Question Method yes: Reasons supporting the yes answer or refuting the no answer. Are the things designated by the nouns are in the extension of the verb? no: Which side has the better reasons? Reasons supporting the no answer or refuting the yes answer.
  • 10. Review Normative definitions which prescribe or stipulate how a term ought to be used. Descriptive definitions which describe or designate how a term is actually used. Normative claims which prescribe or stipulate how things ought to be. Descriptive claims which describe or designate how things actually are. Law of Assumption— assume anything at any time.
  • 11. Review define key terms—key terms are terms needed for the claim to be evaluated as true or false, they are terms whose properties or relations need to be specified or whose extensions need to be clarified. define technical terms— technical terms are terms needed for critical thinking, such as truth, charity, and reason.
  • 12. Logically Complex Truths And Terms Indicative of Logical Structure
  • 13. A Logically Simple Truth The man is cheating. 1 True 2 False
  • 14. A Logically Simple Truth The man is cheating. 1 True 2 False —He’s hiding cards
  • 15. A Logically Simple Truth The man is cheating. 1 True 2 False —He’s doing magic
  • 16. A Logically Simple Truth Two logical possibilities The man is cheating. 1 True 2 False Given that we’ve filled in the indices, made the ceteris paribus explicit, and defined key terms.
  • 17. A Logically Simple Truth Also called States of Affairs or Possible Worlds The man is cheating. 1 True 2 False
  • 18. A Logically Simple Truth How we describe logical possibilities Logical possibilities The man is cheating. State Descriptions 1 True The man is cheating. 2 False The man is not cheating.
  • 19. Negation: Logical Complexity The man is cheating. The man is not cheating. 1 True 1 False 2 False 2 True
  • 20. Negation: Logical Complexity it “flips” the truth value The man is cheating. The man is not cheating. 1 True 1 False 2 False 2 True
  • 21. Logical negation, often expressed in English by ‘not’, is true when the component claim is false, false when the component claim is true. It is symbolized by ‘~’ and has the logical form ~P.
  • 22. Negation: Logical Complexity ~ “flips” the truth value The Logical Form of Negation: ~P, -P, ¬ P P ~P 1 True 1 False 2 False 2 True
  • 23. double negation Any even number of negations cancel each other out. No! They do not!
  • 24. indicators for negations - a. not b. It is not the case that… c. n’t (the contraction) negations are often suppressed in common opposites such as on and off.
  • 25. Fabricate a Truth Test this out: Take a true claim and make it false. Then take a false claim and make it true. What happens when you add not to a true claim? What happens when you add another not?
  • 26. A Logically Simple Truth Two logical possibilities Derek is leaping. 1 True 2 False
  • 27. Combining Logically Simple Truths Derek is leaping. 1 2 3 4 Hansel is leaping. True True
  • 28. Logically Complex Truths Derek is leaping. Hansel is leaping. 1 True True 2 True False 3 4
  • 29. Logically Complex Truths Derek is leaping. Hansel is leaping. 1 True True 2 True False 3 False True 4
  • 30. Logically Complex Truths Derek is leaping. Hansel is leaping. 1 True True 2 True False 3 False True 4 False False
  • 31. Logically Complex Truths Four possibilities Derek is leaping. Hansel is leaping. 1 True True 2 True False 3 False True 4 False False
  • 32. Logically Complex Truths Four states of affairs (states) or possible worlds Derek is leaping. Hansel is leaping. 1 True True 2 True False 3 False True 4 False False
  • 33. to calculate the number of possible worlds raise two to the power of the number of claims being evaluated 2 n
  • 34. Logically Complex Truths Four State Descriptions Derek is leaping. Hansel is leaping. State Descriptions 1 True True Derek and Hansel are leaping 2 True False Derek leaps but Hansel doesn't 3 False True Hansel leaps but Derek doesn’t 4 False False Neither Derek nor Hansel leaps
  • 35. Logical Possibilities Place your bet Here’s the bet: In the next slide both Derek and Hansel will be leaping. Which way would you bet, and why?
  • 36. Logical Possibilities Who wins the bet? In state #1 where both Derek and Hansel are leaping? Derek is leaping. AND Hansel is leaping. 1 True ? True 2 True False 3 False True 4 False False
  • 37. Logical Possibilities Who wins the bet? In state #1 where both Derek and Hansel are leaping? Derek is leaping. AND Hansel is leaping. 1 True True True 2 True False 3 False True 4 False False The complex claim is true when all the component claims are true, as they are in state #1.
  • 38. Logical Possibilities Who wins the bet? The complex claim is true when all the component claims are true, as they are in state #1. Derek is leaping. AND Hansel is leaping. 1 True True True 2 True ? False 3 False True 4 False False How about case #2 where Derek is leaping but Hansel is not?
  • 39. Logical Possibilities Who wins the bet? The complex claim is false when one or the other component claims are false… Derek is leaping. AND Hansel is leaping. 1 True True True 2 True False False 3 False ? True 4 False False …as they are in state #2…
  • 40. Logical Possibilities Who wins the bet? The complex claim is false when one or the other component claims are false… Derek is leaping. AND Hansel is leaping. 1 True True True 2 True False False 3 False False True 4 False False …or as they are in state #3, what about state #4?
  • 41. Logical Possibilities Who wins the bet? The complex claim is false when both component claims are false. Derek is leaping. AND Hansel is leaping. 1 True True True 2 True False False 3 False False True 4 False False False As they are in state #4.
  • 42. Logical conjunction, often expressed in English by ‘and’, is true when the component claims it joins are true, otherwise it is false. It is symbolized by ‘&’. It’s logical form is P & Q.
  • 43. Logical Form of Conjunctions P AND Q P&Q P•Q P⋀Q P & Q 1 True True True 2 True False False 3 False False True 4 False False False
  • 44. to prove a conjunction false Prove that one of the component claims is false.
  • 45. indicators for conjunctions a. b. c. d. and but yet not both (includes negation)
  • 46. Contradictions Putting conjunction and negation together
  • 47. Contradictions A Necessity of Logic Let’s define ‘this square’ as the thing depicted below at x-position 303 px and y-position 318 px and of the dimensions 242 px by 242 px. this square
  • 48. Contradictions A Necessity of Logic Next let’s define ‘white’ as the color depicted below of the RGB values Red = 255, Green = 254, Blue = 235. white
  • 49. Contradictions A Necessity of Logic Now pay attention to your mental processes as we make the following claim:
  • 50. Contradictions A Necessity of Logic Now pay attention to your mental processes as we make the following claim:
  • 51. Contradictions A Necessity of Logic Now pay attention to your mental processes as we make the following claim: >>This square is white and this square is not white.<<
  • 52. Contradictions A Necessity of Logic What was your reaction?
  • 53. Contradictions Putting Negation and Conjunction Together Which claim is not a contradiction? Hockey is better than basketball but it is not better than basketball.* Jupiter is bigger than Mars and it is not bigger than Mars. Drinking milk is healthy and unhealthy.* New York is and isn’t the largest city in the US.* Same-sex schools are optimal and same-sex schools are less than optimal. Eleven is a prime number and eleven is not a prime number. Romeo and Juliette is a tragedy and it is not a tragedy.* The child looks at the jellyfish and looks away from it*. The jellyfish has tentacles—not! The music is loud and the Jacqui thinks black is more alluring than pink and music is quiet.* she doesn’t. The Constitution of the United States was adopted on September 17, 1787 and The Constitution of the United States was adopted on July 4, 1776.*
  • 54. Contradictions The Logic of a Contradiction The square is white & The square is not white 1 True ? False 2 False ? True Given that conjunctions are true when all component claims are true, what is the truth value of this conjunction?
  • 55. Contradictions The Logical Form of a Contradiction: P & ~P The square is white & The square is not white 1 True False False 2 False False True Contradictions are false in all possible worlds.
  • 56. Contradictions The Logical Form of a Contradiction: P & ~P P & ~P 1 True False False 2 False False True Contradictions are false in all possible worlds.
  • 57. Contradiction, a special form of conjunction in which a claim and its negation are joined— they are always false. The logical form of a contradiction is P & ~P.
  • 58. Contradictions The Logical Form of the Principle of Noncontradiction ~ (P & ~P) 1 True False False 2 False False True The Principle of Noncontradiction is true in all possible worlds.
  • 59. Contradiction An Emergent Property Neither hydrogen nor oxygen are wet at room temperature—wetness emerges as a property when they are properly combined. In a similar manner, being false in all possible worlds emerges when a claim and its negation are properly conjoined.
  • 60. The Principle of Noncontradiction ~(P & ~P)
  • 61. The Principle of Noncontradiction, states that no thing can, at the same time and in the same manner, both have and not have the same property.
  • 62. The Principle of Noncontradiction, (special) no claim, adequately defined, can be both true and not true.
  • 63. The Principle of Noncontradiction, no claim, adequately defined, can be both true and not true. The Principle of Noncontradiction ~(T & ~ T)
  • 64. Consider… Four Types of Truth ∏ Matters of Taste or Opinion Matters of Convention Matters of Fact Matters of Necessity = 3.141592... π needs to be exact for a circle to be round + 1 = 1 2 simple arithmetic is the way things are ~ ( P & P ) Noncontradiction is needed for critical thinking
  • 65. Consistency A set of claims free from contradictions Romeo and Juliette is a tragedy. The jellyfish has tentacles. Eleven is a prime The music is loud. number. Drinking milk is healthy. Jupiter is bigger than Mars. Same-sex schools are optimal. Hockey is better than basketball. The jellyfish has tentacles. Jacqui thinks black is more alluring than pink. New York is the largest city in the US. The child looks at the jellyfish. The Constitution of the United States was adopted on September 17, 1787
  • 66. Consistency A set of claims free from contradictions Which claim causes the inconsistency? Romeo and Juliette is a tragedy. The jellyfish has tentacles. Eleven is a prime The music is loud. number. Drinking milk is healthy. Jupiter is bigger than Mars. Same-sex schools are optimal. Hockey is better than basketball. The jellyfish has tentacles—not. Jacqui thinks black is more alluring than pink. New York is the largest city in the US. The child looks at the jellyfish. The Constitution of the United States was adopted on September 17, 1787
  • 67. The Standard of Consistency— accept only those beliefs which are consistent with each other and any accessible evidence.
  • 68. Counterexamples Using the Principle of Noncontradiction to test definitions.
  • 69. Proof by Counterexample A Method for Reasoning with Contradictions Line of Reasoning An explanation showing that the definition should be true of a specific example (thing or event). Reject the original definition Original definition. Another Line of Reasoning Another explanation showing that the definition is not true of the same example.
  • 70. Counterexamples Testing Definitions for Consistency Definition: ‘father’ means the female parent You know the definition is wrong, but how can you prove it?
  • 71. Extensions Terms have extensions being a vowel M X N D C L Y V B F E A R Q O W P S I U H G K J Z T
  • 72. True Definitions The Subject and Predicate Have Identical Extensions Even numbers are divisible by two without remainder being divisible by two without a remainder being an even number 3 9 22 1 1 21 32 14 77 27 66 144 13 5
  • 73. False Definitions The Subject and Predicate Do Not Have Identical Extensions a, e, i, o, and u are the only vowels being a, e, i, o, and u being vowels B L M F V G C X N D E A O I U R Q K Y H P J Z T S W
  • 74. Counterexamples Testing Definitions for Consistency Definition: ‘father’ means the female parent father the female parent List of fathers: List of female parents: Adam, Joseph, Martin, Michelle, Mary, Hillary, Sarah Muhammad Generate lists of things that fall under the term being defined and the property used to define it — they should be identical— stop when you show they are not.
  • 75. False Definitions The Subject and Predicate Do Not Have Identical Extensions a, e, i, o, and u are the only vowels being a father Joseph Adam Martin Muhammad being a female parent Michelle Hillary Sarah Mary These lists are not identical, in fact, they have no overlap at all, no members in common.
  • 76. Counterexamples Testing Definitions for Consistency So: ‘father’ does not mean the female parent father List of fathers: Adam, Joseph, Martin, Muhammad the female parent ≠ List of female parents: ≠ Michelle, Mary, Hillary, Sarah
  • 77. Proof by Counterexample Applied By this definition Hillary should be the father, because she is a female parent. Father means the female parent By all other sources Reject: father means the female parent Hillary is not the father but the mother, which is defined as the female parent.
  • 78. Counterexamples Testing Definitions for Consistency Reject: ‘father’ means the female parent Proof: by this definition, Hillary is a father because she is the female parent, but she’s not a father according to many other sources (dictionaries and encyclopedias) which define the female parent as the mother. This is a contradiction, and I reject the definition in favor of general usage.
  • 79. Counterexamples Testing Definitions for Consistency Reject: ‘father’ means the female parent Alternate Proof: by this definition, Martin is not a father because he is not the female parent, but according to biology texts he is a father, because he is the sperm donor to the offspring. This definition is inconsistent with biological terminology—so I reject the definition.
  • 80. Counterexamples Testing Complex Definitions for Consistency Definition: Mammals have fur, mammary glands, and give live birth Using the Principle of Noncontradiction, prove that this claim is false.
  • 81. Counterexamples Testing Complex Definitions for Consistency Definition: Mammals have fur, mammary glands, and give live birth Mammals have fur Mammals have mammary glands Mammals give live birth Break the definition into a series of claims which isolate each property, to prepare to test each. Then take the one you will test.
  • 82. Counterexamples Testing Complex Definitions for Consistency Definition: Mammals give live birth mammal giving live birth List of mammals: list of things which give live birth cats, dogs, humans, platypuses cats, dogs, humans Generate lists of things that fall under the term being defined and the property used to define it — stop when you determine that they are not identical.
  • 83. False Definitions The Subject and Predicate Do Not Have Identical Extensions Mammals give live birth being a mammal giving live birth dogs platypuses cats humans These do have significant overlap, but they are not identical.
  • 84. Counterexamples Testing Complex Definitions for Consistency So: Some mammals do not give give live birth mammal giving live birth List of mammals: ≠ list of things which give live birth cats, dogs, humans, platypuses ≠ cats, dogs, humans
  • 85. Proof by Counterexample Applied By this definition Mammals give live birth By research Platypuses should give live birth, as they have fur and mammary glands. Reject: mammals give live birth. Platypuses lay eggs and so do not give live birth.
  • 86. Counterexamples Testing Definitions for Consistency Reject: ‘mammals’ means gives live birth Proof: by this definition, Platypuses should give live birth, as they have fur and mammary glands, but research has discovered that Platypuses lay eggs and so do not give live birth. This definition contradicts the evidence, and I would revise the definition to be: mammals have fur and mammary glands.
  • 87. Counterexamples Testing Definitions for Consistency Reject: ‘mammals’ means gives live birth Alternate Proof: by this definition, Platypuses must not be mammals as they lay eggs rather than give live birth. But they are mammals insofar as they have fur and mammary glands. This definition is inconsistent with the rest of the taxonomical systems, and I would revise the definition to be: mammals have fur and mammary glands.
  • 88. to evaluate by counterexample Isolate the subject and predicate, generate lists of things that fall under each, stopping when you determine that they are not identical.
  • 89. proof by counterexample Choose an item that is not on both lists, explain how the definition says it should be, then explain why it is not, indicate the inconsistency, and reject or revise the definition.
  • 90. Reductio ad absurdam Using the Principle of Noncontradiction to test claims.
  • 91. Reductio ad absurdam A formal extension of reasoning with contradictions Line of Reasoning Original claim. Another Line of Reasoning An explanation showing how the thing designated by the subject has the property expressed by the predicate. Reject the original claim. Another explanation showing how the thing designated by the subject does not have the property expressed by the predicate.
  • 92. Reductio ad absurdam Testing Claims for Truth Claim: The jellyfish has no tentacles. You know the claim is wrong, but how can you prove it?
  • 93. True Claims The Subject has the Property Expressed by Predicate. The jellyfish has tentacles Evidence: the jellyfish has tentacles
  • 94. False Claims The Subject is Inconsistent with the Property Expressed by Predicate. The jellyfish has no tentacles Evidence: the jellyfish has no tentacles
  • 95. Reductio ad absurdam Testing Claims for Truth Claim: The jellyfish has no tentacles. Evidence: the jellyfish has tentacles
  • 96. Reductio ad absurdam A formal extension of reasoning with contradictions Line of Reasoning The claim is that the jellyfish under observation ought to have no tentacles. The jellyfish has no tentacles. Another Line of Reasoning Reject the original claim. But observation shows that the jellyfish in question has many tentacles.
  • 97. Reductio ad absurdam Testing claims for Consistency Reject: the jellyfish has no tentacles Proof: The claim is that the jellyfish under observation ought to have no tentacles, perhaps due to predation. But cursory examination shows that the jellyfish has many tentacles which appear healthy. As the claim contradicts observation I reject it.
  • 98. Reductio ad absurdam The Parts of a Reductio The jellyfish under observation ought to have no tentacles, perhaps due to predation. But cursory examination shows that the jellyfish has many tentacles which appear healthy. As the claim contradicts observation I reject it.
  • 99. Reductio ad absurdam The Parts of a Reductio 1. The jellyfish under observation ought to have no tentacles 2. due to predation 3. the jellyfish has no tentacles 1.claim 2.reasons 3.conclusion 4.other reasons 5.other conclusion 6.contradiction 7.rejection 4. by cursory examination 5. the jellyfish has many tentacles 6. the jellyfish has tentacles and the jellyfish has no tentacles 7. I reject it
  • 100. The Logical Form of a Reductio Reductio ad absurdam, Indirect Proof, Proof by Counterexample 1.claim 2.reasons 3.conclusion 4.other reasons 5.other conclusion 6.contradiction 7.rejection
  • 101. Reductio ad absurdam Reductio ad absurdam Indirect Proof, Proof by Counterexample Line of Reasoning 1. Claim 2. reasons 3. conclusion 6. P & ~P Another Line 4. other reasons of Reasoning 5. other conclusion 7. Rejection
  • 102. Reductio ad absurdam Some Cases
  • 103. The Case of Sara Scatterleigh Sara woke in a hurried blur. Her alarm did not go off. Her heart pounded as she got out of bed, dragged a comb across her head, found her way downstairs and drank a cup, looking up she noticed she was late. She grabbed her coat and grabbed her pack, out the door in seconds flat—her chemistry class started ten minutes ago! And this teacher always took role. Sara approached her class with apprehension, open the door and march in like she’s not late? Or try to steal in. Still out of breath from the jog to class, Sara opens the doors and marches right into the large lecture hall, only she doesn’t recognize a single soul. The teacher pauses his lecture to regard her, but it is not her chemistry teacher! Confused, Sara retreats into the hall and looks at the room number on the wall, it is the right room, she should be late, her chemistry class meets on Tuesdays and Thursdays. With a look of vacant frustration Sara draws out her phone to double check the time, and only then notices the day, Monday.
  • 104. The Case of Mrs. Riley Most jurors were initially swayed by the Prosecutor’s claim that the accused were guilty. This was based on the testimony of Mrs. Riley, who positively identified the accused at the scene of the crime at the time the crime was committed. After all, Mrs. Riley seemed like an honest woman with no bias against the accused. Further, she testified that saw them from 100 feet away and was wearing her eye glasses— because of this everyone assumed that she could see 100 feet. However, on cross examination, the defense attorney, Vinny, conducted an impromptu eye test by holding up two fingers from a mere 50 feet away while she had her glasses on. Mrs. Riley failed this test, thinking she saw four fingers instead of two. So Mrs. Riley could not see 100 feet, because she could not see even 50 feet. As this is a contradiction the accused were found to be innocent.
  • 105. The Case of Longfellow Deeds In the case of one Longfellow Deeds it was claimed that Mr. Deeds was not legally competent to manage his own affairs. An attorney argued that Mr. Deeds suffered from what was then called bipolar disorder (we now call it manic depression). To show that Mr. Deeds was abnormal the attorney called many witnesses, who claimed Mr. Deeds was ‘pixelated’, ‘crazy’, ‘cracked’, and ‘nuts’. Examples of his abnormality included playing the tuba and running around naked in the park. However by giving the proper context Mr. Deeds made it plain that playing the tuba was as normal as doodling, filling in the ‘o’ s on a printed page, or having a nervous tick. Also, he ran around naked because he was drunk for the very first time—and behaving oddly when you are drunk is fairly normal. Because Mr. Deeds provided convincing counterexamples to the claims that his behavior was abnormal the judge declared him legally competent to manage his own affairs
  • 106. The Case of the Reluctant Rubbernecker A woman had just presented her paper to her local senator on the negative effects traffic oscillation due to rubbernecking—in short rubbernecking contributes to traffic jams. Her claim was that if everyone knew that rubbernecking caused up to 60% of the delays due to common accidents, they would do the right thing and there would be fewer rubberneckers. She recommended a public service advertising campaign, contending that once people knew the cause of such delays they would not rubberneck. The presentation was a success and she convinced the senator to back her plan. But as she drove home she noticed traffic slowing to a crawl, then saw the cause—a horrific accident. The woman felt the impulse to gawk, to be a rubbernecker. But she kept her mind firmly on the fact that she knew rubbernecking to be wrong and refused to contribute to a longer delay. She fought the impulse but, in the end, she gave in to her impulse, slowed down to gawk, and became another rubbernecker. Despite her knowledge and her best effort at self-control, she knew her thesis was flawed.
  • 107. Reductio: An Example in Neuroscience While Studying the actions of motor cells in monkeys (called motor cells because they are the first in the sequence that controls the muscles that move the body) Vittorio Gallese was moving around the lab during a lull in the day’s experiment. A monkey was sitting quietly, waiting for her next assignment, when Vittorio reached for something (perhaps ice cream) and heard a burst from the computer connected to the electrodes in the monkey’s brain. It might have sounded like static but to the ear of a neuroscientist meant the motor cells were firing. Vittorio thought the reaction was strange—the monkey was sitting quietly, not grasping anything, yet this neuron affiliated with grasping fired. No one could imagine that motor cells could fire merely at the perception of someone else’s actions. In light of the theory at the time this made no sense. Cells in the brain that send signals to other cells that are connected to muscles have no business firing when the monkey is completely still, hands in lap, watching somebody else’s actions. And yet they did.
  • 108. The Case of the Mysterious Disease In 1955 a mysterious illness infected nearly 300 of the staff of the Royal Free Hospital, forcing it to close. Some tests showed their muscles did not twitch or quiver uncontrollably, their reflexes were normal, and their nervous systems were normal. This led a few researchers to claim that it was merely mass hysteria and the patients were otherwise healthy. However, numerous studies showed that the group gave no indications of mass hysteria and that they exhibited a pattern of symptoms including severe exhaustion, memory loss, confusion, painful lymph nodes, muscle pain, and unusual headaches. These researchers claim that the disease was unnamed but real and that the patients were sick. Since then, the balance of evidence showed that the disease was real and it was subsequently named myalgic encephalomyelitis (ME) or chronic fatigue syndrome (CFS).
  • 109. The Case of the Composite Soul Against the claim that the soul is simple, Plato tells of Leontius, the son of Aglaion, who saw some corpses lying at the executioners feet. Leontius had a strong urge to indulge his morbid intrigue and gawk at the dead, but he forced himself to show respect by not indulging his morbid intrigue so he turned himself away. For a while he fought the urge and covered his face. But desire overcame him and he ran to the corpses and looked, then rebuked himself for this indignant act.
  • 110. The Case of Renegade Mercury Newton’s theory was remarkable in that it described force correctly in terms of acceleration and mass, explained gravity, and correctly predicted the course of the planets. Newton’s theory was right. Except for Mercury. Observation showed Newton’s theory did not accurately predict the orbit of Mercury. So the theory was wrong. Some even postulated another planet, Vulcan, to make the theory correspond with observation. But there was no planet Vulcan, it wasn’t until Einstein that a theory was discovered that could account for Mercury’s orbit.
  • 111. Fallacies Some Relevant Fallacies
  • 112. A Problem Reductio: Law’s Not Fair Some claim our legal system is fair. They point out that our legal system, when it functions properly, gives out impartial sentences and so it fair. However, our legal system is abstract, and so is without color, and can’t be pale, so it is not fair (look up fair, it means having a light complexion). But this means our legal system is fair and unfair, which is a contradiction. So I reject that our legal system is fair.
  • 113. A Problem Reductio What is the problem? Line of Reasoning Our legal system, when it functions properly, gives out impartial sentences and so it fair. Our legal system is Our legal system is fair. fair and unfair Our legal system is abstract, and so is Another Line without color, and of Reasoning can’t be pale, so it is not fair. Reject: our legal system is fair
  • 114. A Problem Reductio Equivocation Our legal system, when it functions properly, gives out impartial sentences and so it fair. Our legal system is abstract, and so is without color, and can’t be pale, so it is not fair. The problem is that the argument uses the word fair in two different ways—fair is ambiguous, it has more than one meaning. One meaning has to do with being impartial, the other has to do with having a pale color. Using a word ambiguously in an argument is the fallacy of equivocation.
  • 115. Equivocation, to use a term ambiguously or vaguely in an argument—it is a fallacy.
  • 116. A Problem Reductio: Too Big to Fail During a recent financial crisis many made the claim that some banks were too big to fail and needed to be bailed out with public funds to avoid catastrophe. But banks did fail, both large banks and small ones. Thus the claim is inconsistent with the evidence. And so it must be false that some banks were too big to fail.
  • 117. to avoid equivocation Define key terms by giving them one (to disambiguate) clear (to avoid vagueness) meaning.
  • 118. A Problem Reductio What is the problem? Line of Reasoning Some banks were too big to fail and needed to be bailed out with public funds. Our legal system is fair. The claim is inconsistent Banks did fail, both Another Line large banks and of Reasoning small ones. Reject: some banks are too big to fail.
  • 119. A Problem Reductio Equivocation Some banks were too big to fail and needed to be bailed out with public funds. Banks did fail, both large banks and small ones. The problem is that the argument switches between a prescriptive/normative claim (banks ought not be allowed to fail as they are too big and might cause a catastrophe) and descriptive claim (the observation that even big banks did fail). This is another form of the fallacy of equivocation.
  • 120. to avoid equivocation Use the Principle of Charity to settle on the best interpretation, whether normative or descriptive.
  • 121. A Problem Reductio: Too Big to Fail Socrates claimed that women could be leaders of the ideal city state. He noted that women possess the same capacities in terms of leadership that men do. His pupils, however, noted that men and women have very different capacities and that only a fool would confuse women with men—they are different! Because this line of reasoning leads to the absurd conclusion that men and women are the same and not, his pupils laughed at the notion that women could be leaders.
  • 122. A Problem Reductio What is the problem? Line of Reasoning Women possess the same capacities in terms of leadership that men do. Men and Reject: women are Women can be leaders. women can the same and be leaders. not. Only a fool would confuse women Another Line with men—they are of Reasoning different with different capacities!
  • 123. A Problem Reductio Reductio ad ridiculim Women possess the same capacities in terms of leadership that men do. Only a fool would confuse women with men—they are different with different capacities! The problem is that the argument confuses ridicule with reason. This is an example of a reductio ad ridiculum—a fallacy. This example is based off an argument given in Plato’s Republic—an argument which Plato is careful to refute.
  • 124. Reductio ad ridiculum, appealing to ridicule (making fun of an opposing view) rather than providing reasons against it—it is a fallacy.
  • 125. to avoid reductio ad ridiculums Use the Principle of Sufficient Reason and attempt to provide reasons for each claim.
  • 126. Assignment What is the difference between validity and soundness? Soundness How do you prove a conditional false? What does ‘if’ mean?