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?SummaryReasoningReasoning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 givenWhat 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 modelsThe 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 tablesThe logic of the situationSimple logical argumentsIf you see MaryBill AND MaryYou expect to see BillLimits 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 TollensConditional 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 sideConditional 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 professorsLogical thinkingWe are good with simple logical operatorsAND, OR, NOTEarlier we saw content effectsWason selection taskWith neutral content it is more difficultWith familiar content it is easierSocial schemas are easy to reason about and may be context dependent rather thatCheng & Holyoak; Tooby & Cosmides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 laterInductive 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 problemAbuduction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 populationAbuduction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