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Inductive/Deductive Reasoning. Mendocino College Critical Thinking class, Spring 2012

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  • Premises about the correlation of two things can indicate a causal relationship between them, but additional factors must be confirmed to establish the exact form of the causal relationship. Argument by cause attempts to establish a cause and effect relationship between two events. This is a form of reasoning that argues that the interactions of two or more incidents are not merely coincidental, but was actually related in some meaningful way.
  • Despite the inherent weakness in this argument, a person who is a legitimate expert is more likely to be right than wrong when making considered claims within her area of expertise. In a sense, the claim is being accepted because it is reasonable to believe that the expert has tested the claim and found it to be reliable. So, if the expert has found it to be reliable, then it is reasonable to accept it as being true. Thus, the listener is accepting a claim based on the testimony of the expert. Naturally, the main challenge is determining whether the person in question is a legitimate expert or not. Is the authority qualified to make a judgment? Is the authority trustworthy and honest? Is the authority experienced?
  • Argument by sign asserts that two or more things are so closely related that the presence or absence of one indicates the presence or absence of the other. This is in some ways a type of tightly linked cause and effect reasoning that has more certainty. Footprints are an indication that someone has walked by recently. The sun rising is a sign of the morning. Is the relationship strong? Is the relationship automatic? Is there an alternate cause? Is there an accumulation of signs pointing towards agreement? Are there contradictory signs present?
  • If it looks like a duck, swims like a duck, and quacks like a duck, then it probably is a duck. The process of analogical inference involves noting the shared properties of two or more things, and from this basis inferring that they also share some further property. An analogical argument is an argument in which one concludes that two things are alike in a certain respect because they are alike in other respects. So we can say, Obama is like superman, because he takes the same stance. Analogies can range from the very literal, such as drawing an analogy between humans and the rats used to test a new medicine, to the metaphorical, such as the blood and money example given above. Are there significant points of similarity or difference? Are the points of similarity crucial to the comparison? Are the differences irrelevant to the comparison? Is the analogy strengthened by quantity, or is there just one comparison? Is the analogy realistic, or is it hypothetical or fantastic?
  • Induction/Deduction

    1. 1. Constructing Arguments:Inductive &DeductiveReasoning
    2. 2. What is an Argument?
    3. 3. An argument is aform of thinkingin which certainstatements(reasons) areoffered insupport ofanotherstatement(conclusion).
    4. 4. Reasoning Thinking that uses statements of reason in support of conclusions.
    5. 5. Reason The faculty of reason (rationality) is a mental ability found in human beings and normally considered to be a definitive characteristic of human nature. It is closely associated with such human activities as language, science, art, mathematics, and philosophy. Reason is the way rational beings propose and consider explanations concerning cause and effect, true and false, and what is good or bad. The ways in which human beings reason through an argument are the subject of inquiries in the field of logic.
    6. 6.  Reasons—Statements that support another statement (known as the conclusion). Reasons justify a conclusion, or make it more probable. Conclusion—A statement that explains, asserts or predicts on the basis of statements known as reasons that are offered as evidence for it.
    7. 7. Inductive Reasoning
    8. 8. Inductive Reasoning: An argument form in which one reasons from premises that are known or assumed to be true to a conclusion that is supported by the premises but does not necessarily follow from them.The kind of thinking that is done to form general ideas basedon experience and observation.Inductive reasoning allows us to create generalizations aboutthings, such as people, places, events, the environment, etc.
    9. 9. Inductive Reasoning: The process of recognizing patterns or observing patterns and drawing a conclusion based on that pattern. Reasoning from a specific case or cases and deriving a general rule.
    10. 10. Inductive Reasoning: by example by cause by authority by sign by analogy
    11. 11. By Example Owls turning head We can induce from these examples that owls (or most or many owls) have the ability to turn their heads in a unique way.
    12. 12. By CauseArgument by causeattempts to establisha cause and effectrelationship betweentwo events. The linkbelow gives us acausal explanationfor the owl’s ability toturn its head.Owl head-turning explained—also an authority speaking on her area of expertise
    13. 13. By AuthorityA person who is alegitimate expert is morelikely to be right thanwrong when makingconsidered claims withinher area of expertise. Theclaim is being acceptedbecause it is reasonableto believe that the experthas tested the claim andfound it to be reliable. here’s an authority on wild cheetahs
    14. 14. By SignThis is in some ways atype of tightly linkedcause and effectreasoning that has morecertainty. Footprints arean indication thatsomeone has walked byrecently. The sun risingis a sign of the morning. Here’s Sherlock Holmes inferring many truths from a hat
    15. 15. By Analogy/Comparison if it quacks like a duck…
    16. 16. Inductive conclusions areestablished in four stages:• Observation: collect facts, without bias.• Analysis: classify the facts, identifying patterns of regularity.• Inference: From the patterns, infer generalizations about the relations between the facts.• Confirmation: Testing the inference through further observation.
    17. 17. Opinion Polls A recent Gallop Poll reported that 74% of the American Public believes abortion should be legal. A poll is a form of empirical generalization, a general statement about an entire group made on the basis of observing some members of the group.
    18. 18. Questions to Ask About Polls  Is the sample known?  Is the sample sufficient?  Is the sample representative?  Do the conclusion seem reliable?  Why or why not?
    19. 19. Inductive arguments can include: • Part-to-whole: where the whole is assumed to be like individual parts (only bigger). • Extrapolations: where areas beyond the area of study are assumed to be like the studied area. • Predictions: where the future is assumed to be like the past.
    20. 20. Deductive Reasoning
    21. 21.  Deductive reasoning starts with a general case in order to draw conclusions about specific instances. Deductive reasoning starts with an assumed hypothesis, theory or truth. This assumption may be well-accepted or rather shaky—but if it’s true, the conclusion can not be questioned. Deductive reasoning is used by scientists to take a general scientific law and apply it to a certain case when they assume that the law is true.
    22. 22. All planets revolve around stars. The earth is a planet.Therefore the earth revolves around a star. The earth revolves around the sun. Therefore the sun is a star.
    23. 23.  Deductive reasoning assumes that the basic law from which you argue is applicable in all cases. Scientists will prove a general law for a particular case and then do many deductive experiments to demonstrate that the law holds true in many different circumstances. Using deductive reasoning usually is a credible and safe form of reasoning, but it is based on the assumed truth of the rule or law on which it is founded.
    24. 24. Deductive arguments aregenerally based on thefollowing:  laws  rules  widely accepted principles  theories  hypotheses
    25. 25. Deductive Reasoning Premise Premise Conclusion
    26. 26. Deduction begins with the general and ends with the specific. All men are mortal Socrates is a man Therefore Socrates is mortal. syllogism
    27. 27. A syllogism The syllogism isat the core of traditional deductive reasoning. cartoon
    28. 28. Valid Argument: An argument inwhich the reasons support theconclusions so that the conclusionfollows the reasons offered.Invalid Argument: An argument inwhich the reasons do not support theconclusion so that the conclusion doesnot follow from the reasons offered.
    29. 29. What’s Wrong with this? Penguins are black and white. Some old TV shows are black and white. Therefore some penguins are old TV shows.
    30. 30. All men are mortal.Socrates is mortal.Therefore Socrates is man. not a valid argument, why?
    31. 31. THE general Rule:
    32. 32. Syllogism: THE general Rule
    33. 33. Premise: Birds fly
    34. 34. Deductive Reasoning If the premises are true, the conclusion is also true.
    35. 35. A DEDUCTIVE ARGUMENT  Premise 1: Birds fly.  Premise 2: An owl is a bird.  Conclusion: Owls fly. owl flying
    36. 36. But Is the premise correct? Do birds fly?
    37. 37. Test Your PremiseRemember: The general rule tells usthat the basic law from which youare arguing must be applicable in allcases.
    39. 39. AN UNSOUND ARGUMENT: Valid structure, but invalid premise(s).
    40. 40. Checking our premises: Is a penguin is a bird? BBC: Do Penguins Fly? From the BBC BBC Explanation v=lzhDsojoqk8&feature=watch_response
    41. 41. Premises Birds. Class *Aves. Birds are feathered, winged, bipedal, warm-blooded, egg-laying vertebrates. Aves is Latin for birds and is universally used as the scientific term for the class of organisms to which birds belong.Either our premise that all birds fly is wrong, or our premisethat penguins are birds is wrong.
    42. 42. If, by definition penguins are feathered, winged, bipedal,warm-blooded, egg-laying vertebrates, then they arebirds. The next question has to be, do all birds fly orjust some?If the answer is “some,” then your premise, “birds fly”is wrong, and therefore your conclusion is wrong.From Wikipedia:“All living species of birds have wings—the now extinct flightlessmoa of New Zealand were the only exception. Wings are evolvedforelimbs, and most bird species can fly. Flightless birds includeratites, penguins, and a number of diverse endemic island species.”
    43. 43. In deductive reasoning you must expain and defend the premisesThere is no way to admit the truth of a premise and deny the truth of the conclusion. premise: birds fly premise: a penguin is a bird conclusion: penguins fly
    44. 44. Penguins (orderSphenisciformes,family Spheniscidae)are a group ofaquatic, flightlessbirds living almostexclusively in thesouthern hemisphere,especially inAntarctica.
    45. 45. True reasons, valid structure = Sound Argument False reasons, valid structure = Unsound ArgumentTrue reasons, invalid structure = Unsound ArgumentFalse reasons, invalid structure = Unsound Argument
    46. 46. modus tollens denying the consequence• If Michael is a good friend, he will loan me his car for the weekend.• Michael won’t loan me his car.• Therefore Michael is not a good friend.
    47. 47. Silver Blaze
    48. 48. modus tollens denying the consequence From Sherlock Holmes, Silver Blaze Dogs bark at strangers. The dog didn’t bark when the horse disappeared. Therefore whoever took the horse away was not a stranger.