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Inductive Arguments, Sept 28th.docx

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Brian Lightbody

th PHIL 1F91 September 28 , 2012 Lecture Four: Inductive Arguments - We now know that in order for a deductive argument to be valid, it must conform to a valid logical form - We also examined a number of fallacious forms of reasoning. Such inference patterns are fallacious because they are invalid - We will now examine how to assess inductive arguments Inductive Arguments: Probability - Inductive arguments are arguments that are not necessarily or absolutely true. They only have a high degree of probability 1. Every swan that I have seen has been white Therefore: all swans are white - Even if we accept premise one to be true, the conclusion may still be false Three Types of Inductive Arguments TYPE ONE: Enumerative - As the name implies, enumerative inductive arguments make a universal claim about something (like a swan) based on an observation of that thing What makes for a good enumerative inductive argument?  Three components: 1) A large sample size 2) An unbiased sample 3) A causal connection  Take the following (outdated) example: The next Prime Minister of Canada will be Michael Ignatief. Our justification? The majority of people we polled the day before election day said they would vote Liberal Enumerative inductive arguments  Large sample size: Out of a poll of 3,000,000 people 75% claimed they would vote Liberal  Unbiased sample: These 3,000,000 people were selected at random  Causal connection: We only took into account those factors that had a direct causal relation to our prediction Fallacies and enumerative inductive arguments  1) Fallacy of the small sample size: predicting Ignatief will become the next Prime Minister based on a poll of 20 people  2) Biased sample: polling only Liberal delegates 1 th PHIL 1F91 September 28 , 2012  3) Questionable cause: Claiming there is a causal connection between a person‟s favorite color and the party the person will vote for TYPE TWO: Analogical Inductive Arguments - Analogical arguments compare something that is very well known to something that is less known to draw a conclusion: 1) The human heart is like a motor pump 2) Every motor pump can be repaired when it fails Therefore: the human heart can be repaired when it fails Analogical Arguments continued  An analogical argument is considered strong when there are a number of similarities between the two things being compared  What do you think? Is this analogy particularly strong?  We answer the question by examining the similarities and dissimilarities between the two things being compared Fallacy: Questionable Analogy  We criticize an analogical argument if we can show that there are more dissimilarities between the two things being compared than similarities 1) A human being is like a dog 2) Every dog can be trained to be obedient Therefore: a human being can be trained to be obedient TYPE THREE: Inference to the best explanation or Abductive Arguments - Inference to the best explanation usually combines two of the following rules: 1) Principle #1: Ockham‟s razor or the K.I.S.S : an explanation A is better than explanation B if (all other things being equal) explanation A is simpler than explanation B Ockham’s razor  Think about the Simpson‟s episode “Grandpa‟s Love Tonic”  The adults of Springfield have been mysteriously disappearing at dinner time for the past week. Unknown to the children of Springfield, they have been “going to bed” early thanks to Grandpa‟s Love Tonic  The more components you add on to an explanation, the more improbable the explanation becomes. It is unlikely that the saucer people exist and unlikely that reverse vampires exist. Let us give each of these possibilities 1/1000 probability. However, when we claim that both of these things exist and are „working together‟ the probability jumps to 1/1000 x 1/1000 = 1/1,000,000 (Bayes‟ Restricted Conjunction Rule) 2 th PHIL 1F91 September 28 , 2012 2) Principle #2: The principle of Conservatism  Definition: “An explanation A is better than explanation B if (all other things being equal) explanation A fits together better with the rest of my other beliefs about the world”  Example: From this distance it appears as though there is a giant dog on my neighbor‟s lawn. Am I correct to assume that there is a real, giant dog on my neighbor‟s lawn based on my distant observation? The Principle of Conservatis
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