5. Inductive Reasoning copy.docx

CRITICAL READING: CORNELL NOTES Inductive Reasoning Name: Date: 29 August 2023 Section: Lecture 5 Period: Questions/Main Ideas/Vocabulary Notes/Answers/Definitions/Examples/Sentences Induction One of the important uses of conceptual representations is to make generalisations and infe...

CRITICAL READING: CORNELL NOTES Inductive Reasoning Name: Date: 29 August 2023 Section: Lecture 5 Period: Questions/Main Ideas/Vocabulary Notes/Answers/Definitions/Examples/Sentences Induction One of the important uses of conceptual representations is to make generalisations and inferences about novel stimuli. I can reason that my neighbour’s new dog will behave in a manner that is similar to other dogs. If I encounter a dog-like animals such as a wolf, I can reason that this will also behave in a dog-like manner. Deductive Reasoning Involves using given true premises to reach a conclusion that is also true. All men are mortal. Socrates is a man. Therefore, Socrates is mortal. Inductive Reasoning Is probabilistic. It only states that given the premises, the conclusion is probable. 7 – 10% of males are red-green colour blind. Joe is a male. Therefore, the probability that Joe is red-green colour blind is 7 – 10%. Category-Based Induction Rips (1975) category-based induction experiment: Employed blank predicates – these are predicates that individuals would be unlikely to have strong beliefs about ‘robins have sesamoid bones’ and ‘birds have sesamoid bones’. Using blank predicates in this way enables Rips to understand the processes underlying category-based induction in general, without having to rely on any prior knowledge regarding the predicate. Participants are presented with a premise and a conclusion. Premise: Ducks are susceptible to Reinholf disease. Conclusion: Geese are susceptible to Reinholf disease or robins are susceptible to Reinhold disease. The participants rate the degree to which they agree with the conclusion (0% - 100%). Rips found that the likelihood of extending a predicate from a premise to a conclusion varied within a category. Once again, this suggest that category representations have graded structure. Members of a category aren’t all equally representative of that category. Multi-Dimensional Space Rips modelled the participants’ responses using distances in a multi-dimensional space: Typicality was the distance from category prototype. Similarity was the inverse of distance in the space. This data was used to compare a set of different regression models. On the basis of these analyses Rips concluded that the participants’ willingness to extend the blank predicate to the conclusion category varied as a function of: The similarity between the premise and conclusion category. The typicality of the premise category. The Similarity Between the Premise & Conclusion Category Participants would be more likely to accept that geese could get Reinholf disease than robins because ducks are more similar to geese than to robins. The Typicality of the Premise Category Ducks aren’t highly typical birds, so the premise wouldn’t tend to have a high level of extension. If the premise was “robins are susceptible to Reinholf disease”, then the degree of extension would be a lot higher (robins are more typical). It is important to note that the typicality of the conclusion category appeared to play a little part in the likelihood of extension. In other words, just because robins are typical, doesn’t mean that we are more likely to extend from the premise to the conclusion. Replication of Rips’s Findings Rips’s findings have subsequently been replicated in numerous studies, with a wide range of target participants including different cultural groups and children as young as 4, and with a wide range of different stimulus categories. In other words, the finding that induction likelihood is based upon the typicality and similarity relations between premise and conclusion categories appears highly robust. The Rips study employed a single premise category, but subsequent studies sometimes used more than premise category. Premise Monotonicity When more categories are added to the premise, the argument is stronger. Foxes, pigs and wolves have sesamoid bones. Gorillas have sesamoid bones. Will be stronger than: Foxes and pigs have sesamoid bones. Gorillas have sesamoid bones. Adding more categories should only ever increase the similarity between the premises and the conclusion, and can only ever increase the coverage of the category. When more positive evidence is added, the likelihood of accepting the conclusion should increase. Premise Diversity The more diverse the premise categories are, the stronger the argument. The smallest category that can encompass all of these items is mammal. The first argument has a greater coverage of the category mammal than the second argument. When the premises are distributed across the category (have greater coverage or diversity), we can be more confident that the property is true of the entire category. Dolphins, cows and rabbits all use Dihedron. Therefore, all mammals use Dihedron. Is stronger than: Dolphins, seals and whales all use Dihedron. Therefore, all mammals use Dihedron. Because the second argument only covers aquatic mammals, whereas the first covers both aquatic and terrestrial animals. The Inclusion Fallacy Osherson et. al demonstrated a reasoning error similar to Tversky and Kahneman’s (1982) conjunction fallacy. Robins have an ulnar artery. Therefore, birds have an ulnar artery. Will be rated as stronger than: Robins have an ulnar artery. Therefore, penguins have an ulnar artery. This is an error of reasoning because if something is true for all birds, then it must also be true for penguins. What About Negative Evidence? So far all of the experiments have used premises based upon positive evidence. Sharks have vertebrae. Stingrays have vertebrae. But we also learn about the world via negative evidence. Squid don’t have vertebrae. Stingrays have vertebrae. Surprisingly, very few studies looked at the role of negative evidence in inductive reasoning. Heussen et. al (2011) Demonstrated that sometimes negative evidence can actually increase argument strength. This is a violation of the assumption of premise monotonicity. None of the models of inductive reasoning above can account for this effect (but they can, in some cases, be modified to account for this). Why? Brahms, Shostakovich, Bach and AC/DC are all members of the superordinate category Music. However, this category can be further divided, in this case, into Classical Music and Rock Music. Because Brahms is classical music and yet, it doesn’t induce alpha waves, it decreases the likelihood of extending the premise to Bach. Because AC/DC isn’t classical music, it suggests that alpha waves have something special to do with classical music, therefore, adding negative evidence actually strengths the likelihood of extension.