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# Reasoning

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Reasoning Reasoning What is reasoning The world typically does not give us complete information Reasoning is the set of processes that enables us to go beyond the information given What types of reasoning are there Validity vs Truth Valid argument true premises guarantee a true conclusion It does not necessarily correspond to the truth in the world Deductive reasoning Allows us to draw conclusions that must hold given a set of facts premises Inductive reasoning Allows us to expand on conclusions Conclusions need not be true given premises Category based induction Analogical reasoning Mental models The logic of the situation You have tickets to the football game Go Mean Green You agree to meet Bill and Mary at the corner of Fry and Hickory or at the seats If you see Mary on the corner of Fry and Hickory you expect to see Bill as well If you do not see either of them at the corner you expect to see them at the seats when you get to the stadium The agreement has a logical form Bill AND Mary will be located at corner OR Bill AND Mary will be located at seats AND and OR are logical operators They have truth tables The logic of the situation Simple logical arguments If you see Mary Bill AND Mary You expect to see Bill Limits of logical reasoning We are good at this kind of reasoning We do it all the time We can do it in novel situations Are we good at all kinds of logical reasoning What are our limitations Conditional Reasoning Modus Ponens Modus Tollens Conditional Reasoning Each card has a letter on one side and a number on the other Which Cards must you turn over to test the rule If there is a vowel on one side of the card then there is an odd number on the other side Conditional Reasoning Who do you have to check If you have a beer then you must be 21 or older Conditional Reasoning These cases are logically the same Valid Arguments If premises are true conclusion must be true Affirming the Antecedent P Q P Q Modus Ponens Denying the Consequent P Q NOT Q NOT P Modus Tollens Conditional Reasoning Invalid Arguments Conclusion need not be true even if premises are true Affirming the Consequent P Q Q P Denying the Antecedent P Q NOT P NOT Q The ambiguity of if In everyday language sometimes implies a bidirectional relationship between P and Q i e if and only if Logical thinking Pure logic says that we should be able to reason about any content The Ps and Qs in the argument could be anything However we are more likely to accept an argument when the conclusion is true in the real world whether it is valid or not All professors are educators Some educators are smart Some professors are smart This conclusion may be true The argument is not valid It is possible that the smart educators are not professors Logical thinking We are good with simple logical operators AND OR NOT Earlier we saw content effects Wason selection task Social schemas are easy to reason about and may be context dependent rather that Cheng Holyoak Tooby Cosmides With neutral content it is more difficult With familiar content it is easier E g Permission Some precondition must be filled in order to carry out some action More complex argument forms can be difficult especially in unfamiliar contexts Why do we see these content effects Valid deductive arguments ensure that a conclusion is true if the premises are true Truth cannot be determined with certainty thus we must generally reason about content We will look at how people reason about content later Inductive Reasoning Luci s presentation Abductive Reasoning Say what Another form of reasoning is provided by the philosopher C S Peirce It essentially provides a means for coming up with rules based on new instances experiences One way you might think of it is coming up with hypotheses based on new findings whereas deduction would deal with outlining the consequences of a hypothesis and induction in testing the hypothesis Observation the grass is wet Explanation it rained The explanation is consistent with the domain of the problem Abuduction Deduction Necessary inferences if A leads to B and B leads to C then A leads to C All balls in this urn are red All balls in this particular random sample are taken from this urn Therefore All balls in this particular random sample are red Peirce regarded the major premise here as being the Rule the minor premise as being the particular Case and the conclusion as being the Result of the argument The argument is a piece of deduction necessary inference an argument from population to random sample Abuduction Induction Interchange the conclusion the Result with the major premise the Rule Argument becomes All balls in this particular random sample are red All balls in this particular random sample are taken from this urn Therefore All balls in this urn are red Here is an argument from sample to population and this is what Peirce understood to be the core meaning of induction argument from random sample to population Abuduction Abduction New argument Interchange the conclusion the Result with the minor premise the Case Argument becomes All balls in this urn are red All balls in this particular random sample are red Therefore All balls in this particular random sample are taken from this urn This is nothing at all like an argument from population to sample or an argument from sample to population it is a form of probable argument different from both deduction and induction Would later see these as three aspects of the scientific method Scientific reasoning Scientific reasoning Combination of reasoning abilities Hypothesis testing Generate an explanation for some phenomenon Develop an experiment to test the hypothesis Seek disconfirming evidence How good are people at this type of reasoning How good are scientists at living up to this ideal Hypothesis Testing Deductive side conditional reasoning If the null hypothesis is true this data would not occur The data has occurred The null hypothesis is false This is true by denying the consequent modus tollens Unfortunately this is not how hypothesis testing takes place If the null hypothesis is true this data would be unlikely The data has occurred The null hypothesis is false The problem is that we make the first statement probabilistic and that changes everything Hypothesis Testing If a person is an American If a person is an American then he is not a member of Congress FALSE This person is a member of Congress Therefore he is not an American then he is probably not a member of Congress TRUE

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