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 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 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 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, then he is not a member of Congress FALSE This person is a member of Congress Therefore, he is not an American This is a valid argument but untrue as the first premise is false If a person is an American, then he is probably not a member of Congress TRUE This person is a member of Congress Therefore, he is not an American This is the form of hypothesis testing we undertake, and is logically incorrect

Hypothesis testing Induction Take a sample, calculate a statistic Generalize to the population Problem: often no real reason to believe the population statistic is a constant Example: though the transformed score is of course a mean of 100 IQ, IQ raw scores have been improving over the past couple decades Begs the question, to what are we generalizing? Just this population at this time?

Hypothesis testing People tend to have a confirmation bias We seek confirming evidence Scientists also show a confirmation bias They tend to be more critical of evidence that is inconsistent with their beliefs. This always may not be a bad thing (Koehler) Wason 246 task You are told to find a rule that generates “correct” three number sequences. You are told that is a “correct” sequence You search for the rule by testing as many sequences as you want until you are confident you know the rule

Hypothesis testing Confirmation bias Many people initially assume the rule is “Sequences increasing by 2” They try sequences like “4-6-8” and “ ” These are sequences that would confirm their hypothesis Few people try sequences that would disconfirm their hypothesis (e.g., “1-2-3” or “3- 2-1”) The actual rule is “Any increasing sequence” Few people find the correct rule

Hypothesis testing Scientists ignore base rates (prior research) Bayes theorem allows for incorporating prior probabilities to give a (posterior) probability about a hypothesis Yet most of social science does not use Bayesian methods Some do not realize that the end of their scientific efforts is a probability about data, not a hypothesis Not p(H|D) But p(D|H)

MC’s experience at Research and Statistical Support People (students and faculty) come in with: No clear hypothesis to test Lack of knowledge regarding the methods that would allow a hypothesis to be tested Heavy reliance on prescribed ‘rules’ which do little to aid their reasoning about the problem Vague notion as to which population they are generalizing to And a host of other issues…

MC’s Suggestions for Having Fun with Science Have clear ideas Regarding concepts (operational definitions), their implications, and the coherency of hypotheses regarding them Sounds easy but is probably the hardest part and the source of most problems Do not ignore prior efforts Sorry to break it to you, but much has been done in your area of research Don’t be afraid to explore Engage your natural curiosity (try new methods and really investigate your data) Think causally Every method is an investigation of a causal model, what’s yours? Remember the big picture Your research should speak well beyond its specific results (esoterism ≠ progress)

Importance of Content Analogy and Similarity How do we use past experience? What are analogies? Structural alignment Similarity

What to do... How do you decide what to buy? Use your past experience How do you figure out which experience is relevant? Using prior knowledge Use of prior knowledge is guided by similarity How can we study this process? Studying pairs of items Study perceptions of similarity when all information is available

Contrast model Tversky (1977) Had people list features of concepts Had other people rate the similarity of concepts Compared the feature lists Similarity increases with common features, similarity decreases with distinctive features Similarity ratings were positively related to the number of common features Similarity ratings were negatively related to the number of distinctive features

Analogy Often, things being compared are not very similar. Atom vs. Solar system Analogies preserve relations The Atom and the Solar System have similar relations among their parts. The Atom cause( greater(charge(nucleus) charge(electron)), revolve(electron,nucleus)) The Solar System cause( greater(mass(Sun) mass(planet)), revolve(planet,Sun)) The attributes of the objects are not similar. The nucleus is not hot, the planets are not small etc.

Structure mapping Structured representations Relations connect the objects Items are placed in correspondence when they play the same role in a matching relational system

Analogical Inference Can make inferences about target domain Inferences based on correspondences between the base and target Allows us to learn from experience

Types of similarity

Focus on alignable differences Gentner & Markman (1994) Ss given 40 word pairs 20 highly similar, 20 highly dissimilar Hotel-Motel Magazine-Kitten List one difference for as many pairs as possible in 5 minutes More differences listed for similar pairs than dissimilar pairs Reflects that alignable differences are easier to find for similar pairs than for dissimilar pairs

Similarity and cognition Similarity enables us to use background knowledge Recognize how a new case is like an old one Structure mapping/structural alignment Relations are important in similarity comparisons Commonalities and Alignable differences are key Nonalignable differences are less important Differences are easy to find for similar things Structural alignment affects cognitive processing

Reasoning and Mental Models Mental models Intuitive Theories and Naïve physics

Mental Models and Intuitive Theories Mental models allow us to reason about devices Kind of like scripts and schemas discussed earlier People often have causal information about the way things work Used to allow us to get through the world Information may be flawed Three types of mental models Logical mental models Analogical mental models Causal models

Logical and Analogical Models Logical mental models Used to solve logic problems Johnson-Laird Contain “empty” symbols that are manipulated All Archers are Bankers No Bankers are Chemists ? Useful primarily for logic puzzles Analogical mental models Sometimes we understand one device by analogy to another Electricity and water flow Voltage Water pressure Current Flow rate Resistance Width of pipe

Causal Models Causal models allow us to explain and understand the world around us Note that it is not exactly clear what may be determined what a cause is, and that is a separate question from how we come to a determination of a causal relationship White 1990, Ideas about Causation in Philosophy and Psychology Nevertheless our (often flawed) notions of causal relationships can have profound effects on our ability to reason and understand

Intuitive Theories Naïve physics What would happen to a ball shot through this pipe? People often respond by assuming curvilinear momentum McCloskey and Proffitt Even happens if they carry out an action

Intuitive Theories Why do we err? Our naïve physics matches our observations The world has friction, and so there are unseen forces that act in opposition to seen forces Our naïve physics is often accurate for things we can do with our bodies Only when we create larger machines do the differences become important Should not be a surprise Newtonian physics is only a few hundred years old Aristotelian mechanics is closer to our daily experience

How deep are our models? Shallowness of explanation Keil People believe they understand more than they do Asked college students about devices Toilet, Car ignition, Bicycle derailleur Said they understood devices, but could not actually explain them Why does this happen? When we know how to use an object and it is familiar, we believe we know how it works

Summary Mental models Logical mental models Analogical mental models Causal mental models Naïve physics Physical beliefs sometimes diverge from truth Sufficient to get us around the world Scientific reasoning People generate pretty good tests Often show a confirmation bias