ReasoningSlide 2What types of reasoning are there?The logic of the situationSlide 5Limits of logical reasoningConditional ReasoningSlide 8Slide 9Slide 10Slide 11Logical thinkingSlide 13Inductive ReasoningAbductive ReasoningAbuductionSlide 17Slide 18Scientific reasoningHypothesis TestingSlide 21Hypothesis testingSlide 23Slide 24Slide 25MC’s experience at Research and Statistical SupportMC’s Suggestions for Having Fun with ScienceImportance of ContentSlide 29Contrast modelAnalogyStructure mappingAnalogical InferenceSlide 34Slide 35Similarity and cognitionReasoning and Mental ModelsMental Models and Intuitive TheoriesLogical and Analogical ModelsCausal ModelsIntuitive TheoriesSlide 42How deep are our models?SummaryReasoningReasoningWhat is reasoning?The world typically does not give us complete informationReasoning is the set of processes that enables us to go beyond the information givenWhat types of reasoning are there?Validity vs. TruthValid argument: true premises guarantee a true conclusionIt does not necessarily correspond to the truth in the worldDeductive reasoningAllows us to draw conclusions that must hold given a set of facts (premises)Inductive reasoningAllows us to expand on conclusionsConclusions need not be true given premisesCategory-based inductionAnalogical reasoningMental modelsThe logic of the situationYou 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 seatsIf 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 seatsAND and OR are logical operatorsThey have truth tablesThe logic of the situationSimple logical argumentsIf you see MaryBill AND MaryYou expect to see BillLimits of logical reasoningWe are good at this kind of reasoningWe do it all the timeWe can do it in novel situationsAre we good at all kinds of logical reasoning?What are our limitations?Conditional ReasoningModus PonensModus TollensConditional ReasoningEach card has a letter on one side, and a number on the otherWhich 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 sideConditional ReasoningWho do you have to check?If you have a beer, then you must be 21 or older?Conditional ReasoningThese cases are logically the sameValid Arguments: If premises are true, conclusion must be trueAffirming the AntecedentP QPQ (Modus Ponens)Denying the ConsequentP QNOT QNOT P (Modus Tollens)Conditional ReasoningInvalid Arguments: Conclusion need not be true, even if premises are true.Affirming the ConsequentP QQPDenying the AntecedentP QNOT PNOT QThe ambiguity of if. In everyday language, sometimes implies a bidirectional relationship between P and Q (i.e. if and only if)Logical thinkingPure logic says that we should be able to reason about any contentThe Ps and Qs in the argument could be anythingHowever, we are more likely to accept an argument when the conclusion is true (in the real world) whether it is valid or notAll professors are educatorsSome educators are smartSome professors are smartThis conclusion may be trueThe argument is not validIt is possible that the smart educators are not professorsLogical thinkingWe are good with simple logical operatorsAND, OR, NOTEarlier we saw content effectsWason selection taskWith neutral content it is more difficultWith familiar content it is easierSocial schemas are easy to reason about and may be context dependent rather thatCheng & Holyoak; Tooby & CosmidesE.g. Permission: Some precondition must be filled in order to carry out some actionMore complex argument forms can be difficult, especially in unfamiliar contextsWhy do we see these content effects?Valid deductive arguments ensure that a conclusion is true if the premises are trueTruth cannot be determined with certainty, thus we must generally reason about content We will look at how people reason about content laterInductive ReasoningLuci’s presentation!Abductive ReasoningSay what?Another form of reasoning is provided by the philosopher C.S. PeirceIt essentially provides a means for coming up with rules based on new instances experiencesOne 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 wetExplanation: it rainedThe explanation is consistent with the domain of the problemAbuductionDeductionNecessary inferences (if A leads to B and B leads to C, then A leads to C)All balls in this urn are redAll balls in this particular random sample are taken from this urn Therefore All balls in this particular random sample are redPeirce 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.AbuductionInductionInterchange the conclusion (the Result) with the major premise (the Rule). Argument becomes: All balls in this particular random sample are redAll balls in this particular random sample are taken from this urnTherefore, All balls in this urn are redHere 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 populationAbuductionAbductionNew 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 redTherefore, 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
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