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Inductive Reasoning

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Inductive Reasoning

Hello and welcome, Now I will talk in this week and in the next2 lectures, 3 lectures about 2 very important cognitive functions that basically form asignificant portion of why and this course is referred to as higher cognitive processes.ah I am going to talk about reasoning and I am going to talk about decision making acrossthe next 2 or 3 lectures. Now, life if you see it is really full ofmaking decisions. Now I am not really going to talk about ah perception, attention andmemory now, those are basic cognitive processes those are things that you need to deal withthe world let us move a little bit towards the realm of thought and realm of thinkingand deciding stuff. So, this whole ah point of life being full of decisions you have ahsometimes simple decisions to make like you know which flavor of the ice cream you wantah for your dinner or harder decisions to make that you know, which person to marryor what kind of job to get in and those kind of things.Now, in addition to ah. So, this is basically a very important aspect of life you know,making decisions is something very important that we tend to do. How do we come up withthese decisions? You know a lot of times our decisions are preceded by some sort of thinkingsome sort of reasoning, we will talk about reasoning also in this course, but what isreasoning? Reasoning is basically the process of drawing conclusions you know. So, you drawconclusions from sometimes from whatever is there in front of you whatever evidence isthere in front of you, whatever your past knowledge is, whatever the current scenariois telling you and you kind of process those kind of those things and you come up you doah you know a churning if you do a reasoning. And on the basis of that reasoning you kindof you know can make decisions. So, in this week basically or in the next 2 or 3 lecturesbasically we will talk about aspects of decision making and we will talk about aspects of reasoning.And we will try and see that how are these processes accomplished by ah you know us thecognate by which people start with a particular kind of information and they come to a certainkind of conclusions is referred to as reason. So, if I were to define reasoning is basicallywhen you take up some given information and you arrive at a particular conclusion. Whateveryou know technique or whatever strategy you use at arriving that conclusion is basicallywhat reasoning is about. So, we will talk about reasoning today a littlebit. Now reasoning is; obviously, it is involved in so, many arenas of life ah and also sometimesthat even when you do not really have to make a decision you know even when you do not haveto ah come up with a particular choice, you are still performing some kind of reasoningon or the other you know reasoning is a very important aspect of your thought processes.So, there are 2 kinds of reasoning that you might be engaged in at different points intime the first one is referred to as deductive reasoning. What happens in deductive reasoningis, that it involves a sequence of statements let us say let us called syllogism ah forjargon sake yes ah you have certain kinds of statements, and basically you compare thosestatements and then you come to a third part which is a conclusion.So, the 2 statements could be suppose for example, I tell you that you know a c is needed,a c is absolutely necessary to get a course x ok and then you come across a person thatyou know Rakesh has got the course x. So, it definitely you know it is automaticallyyou will conclude that Rakesh must have got either a c or some above grade that is whyhe is got the course x. So, you know automatically almost involuntary you will come up with thiskind of reasoning. This is what definite and deductive reasoning is about and the conclusionsyou come up generally are definitive conclusions. On the other hand sometimes you could basicallybe ah pitched with scenarios where you do not really have a definitive conclusion tomake. Sometimes you could arrive and you try to arrive at conclusions based on probablytrue evidence you know something you heard something you not 100 percent sure, but onthe basis of whatever you know you start making a a conclusion and again because the natureof evidence is not definite the nature of the conclusion is also probable. So, thiskind of reasoning is referred to as inductive reasoning and it is it is a bit more freeit is a bit more flexible and ah obviously, but it is its not definite.So, we will talk about how these 2 reasonings work. Let us talk a little bit about deductivereasoning first. Aristotle introduced the basic forms of an introductory reasoning calledsyllogisms. Syllogisms are statements, syllogism basically includes at least 2 statements whichI refer to as premises and followed by a third setting which is called a conclusion. So,there are 2 premises and there is one conclusion. So, let us consider a categorical syllogism.A categorical syllogism is basically in which the premises and conclusions describe therelationship between 2 kinds of categories and these categorical syllogisms basicallyinclude words like all none or same something idea.So, the first syllogism is again borrowing from Goldstein's book, ah the premises allbirds are animals all animals eat food is the second premise. So, on the basis of these2 premises you come up with a conclusion that therefore, all words eat food this is a categoricalsyllogism. Now, categorical syllogisms might or mightnot always be correct. In in the sense if you have to evaluate how good or bad a syllogismis you might want to look at its validity what is validity? A syllogism is valid whereits conclusion is following logically from the 2 premises ok.So, when it is fitting the logical operation, I will give you an example the example isall birds are animals ok all animals have four legs is the second one, and then theconclusion is all birds have four legs. Now if you look at this syllogism here the thirdstatement the conclusion follows logically from the first 2. So, the conclusion is followinglogically from the 2 premises; however, just will read it once again all birds are animalsor animals have four legs all birds have four legs. Now you know for a fact that all birdsdo not have four legs. So, now how is this possible? It is possiblebecause the idea is that even though the form of the 2 premises is correct and basicallyif you see the ah conclusion follows the 2 premi the form of the 2 premises almost ahcompletely. The whole point is that even though the conclusionis valid and is logically following from the premises, truth is a different thing truthis not only whether the syllogism is valid or not. When validity in that sense dependsupon the form of the syllogism and which determines whether the conclusion follows logically fromthe 2 premises; however, truth on the other hand refers to the content of this ah premises.So, it will also take into account what is the content actually saying, which have tobe also evaluated to determine whether they are consistent with facts.So, logically there are third sitting follows from the 2 you C all A are B all B are youknow by law of association all are C this is all very good, but if you look at the contentyou would know that; obviously, all are C is not correct in this case. So, you haveto evaluate the content of the syllogism at hand.So, one of the things we know now that there is a difference between validity and differentand truth. So, the difference between validity and truth sometimes; however, can make itdifficult to judge whether the reasoning that somebody is applied is logical or not. Notonly can valid syllogisms leads to false conclusions, but also syllogisms can be invalid thougheach of the premises and the conclusion still seem reasonable.For example all students are tired some tired people are irritable, some of the studentsare irritable now you do not really I mean logically it it is ok I mean you can actuallybecause it is not an all or none kind of statement, you can probably ah correctly derive someof the students are irritable from the above 2 premises.But again it is it is not really it is its not really correct in in some sense. Becauseeven though the premises and the conclusions are true still the conclusion is not reallylogically following from the 2 premises. So, there has to be some procedure for determiningthe validity or lack of validity and this procedure is slightly more difficult, I probablynot really get into it because this is better handled by a philosophic ah class and in acourse on logic. But I will just give you the main message in the main message is that,good reasoning and truth are not really the same thing. You know sometimes with good reasoningvery rationally you can come up with ah you know something, but it that thing might notbe that conclusion might not be the true conclusion. So, these 2 things a lot of times I I thinkpeople can you know confuse good reasoning with truth, but truth in good reasoning areslightly different things. Let us let us show this from this example.Now I am just putting a real world example here again borrowed from goldsteins book ahlisten to me ah I know for a fact that all members of the congress from new york areagainst the new tax law, I also know for a fact that some members of the congress whoare against the tax new tax law are taking money from special interest groups.So, what this means as far as I can tell is that, some of the members of the congressfrom New York are taking money from special interest groups. Now just examine this a littlebit more closely this earlier argument that I was just giving is very similar to thisthird syllogism that we were talking about. And as with the third syllogism it does notreally logically follow that because all members from New York are against the new tax lawand some members of the congress are taking money from that are against the new tax ortaking money from special interest groups. You cannot still conclude that some membersof the congress of New York are taking money from the special interest groups. It justdoes not really follow because those some in the second and third statements might notreally you know overlap with each other. So, even though the syllogisms may sometimesseem academic and people often you will find people often using syllogisms to prove theirpoint, they sometimes do not realize and you know people do not realize that this reasoningmight be invalid ok. ah You can actually see it a lot in the way newspapers operate a lotof you know media operates and a lot of people around us operate and again this should basicallyhelp you solve some of those things. Let us move to a different kind of syllogismssyllogisms for a while. So, there are conditional syllogisms conditionals syllogisms have 2premises and they have a conclusion like the ones we have been discussing, but here thefirst premise basically begins with the form if ok and this kind of deductive reasoningis very very common in our everyday life. Suppose for example, your friend comes toyou Steve comes to you and asks for 20 dollars again I am using an American example here,suppose you have a friend called Steve and it comes to you asking for 20 dollars ah,but you have known Steve for some time now and you know that even if you are if I givehim 20 dollars then he is not going to give me back.So, if I try and put this in a form of a syllogism, I can say if I lent it in a dollar twenty2 to Steve that I would not get it back I lend Steve dollar 20, I am not getting backmy and dollar 20. So, this is the conditional syllogism a conditionalsyllogisms are of four types and I am just talking about them right now. So, affirmingthe aunts antecedent, suppose I studied therefore, I get a good grade. So, my getting a goodgrade affirms the fact that I studied then there is denying the consequent, I did notget a good grade therefore, I did not study. So, basically the idea is that I did not geta good grade it is kind of denying the fact that I did not study. Then there is ah affirmingthe consequent I got a good grade therefore, I must have studied this is again something.Then there is denying the antecedent I did not study therefore, I did not get a goodgrade. So, it is kind of basically denying the first part. Now you can see here thatthere is this validity judgments here and only the top 2 were judged as valid the bottom2 words are judged invalid and 97 percent of people could the first syllogism, 60 percentpeople could judge the second solution, but a lot of people if only 40 percent of peopleah could judge the third and the four syllogisms correctly.Now, what is happening here syllogism one is called affirming the antecedent becauseantecedent p if I study is affirmed in the second premise that I studied. That I geta good grade the conclusion is therefore, valid syllogism 2 is called denying the consequentbecause consequent q, I will get a good grade is negated in the second device I did notget a good grade. The conclusion of this syllogism is again valid because I did not study becauseI did not get a good I must not have studied. Syllogism 3 is called affirming the consequent.So, what is happening here is because q that is the consequent? So, the form is if p thenq the consequent q is affirmed in the second premise. So, I got a good grade.Now, the conclusion of the syllogism, I studied is invalid because even if you did not studyit is still possible that you might have got a good grade. So, again this is this one istherefore, not valid now perhaps the exam was easier maybe you know the material becauseyou are familiar with it you had practiced something, you might not have studied it stillgot a good thing you know it is its like for example, if it is a robin, then it is a birdit is a bird therefore, it is a robin is not correct. Because if it is a bird it couldbe some other bird as well, but if it is a robin certainly it must be a bird you knowthis is the kind of comparison you got to make.Talking about syllogism four; syllogism four is called denying the antecedent. So, it hasto negate p ok because n p has to be negated in the second premise. So, the conclusionof the syllogism I did not get a good grade is also not valid because as in syllogism3 the last one; one can probably think of a situation that would contradict the conclusionyou know you study very hard, but you still did not get a good grade ok or a good gradewas got even by a person who did not really study so much.So, again I give you a simpler example, if it is a robin then it is a bird it is nota robin therefore, it is not a bird you know, it could be some other bird and not a robin.So, it is there because it is not a robin therefore, it is not a bird does not reallyfollow. So, this is this is again how the conditional syllogisms works.So, because we were talking about conditional syllogisms ah it only fits that we start talkinga little bit about conditional reasoning ok what is conditional reasoning? Now if reasoningfrom conditional syllogisms dependent only upon applying the rules of formal logic theones which we were talking about, does the conclusion follow from the premise that kindof thing. Then it would not really matter whether the syllogism was stated in termsof abstract symbols such as p and q or in terms of real examples.So, I could always say if p then q and if q would not be is something like that ah itdid not matter that I am talking about if it is a robin, then it is a bird or if itis not a bird and it is not robin those kind of things, ah it does not it would not reallymatter if it were just following logical notations. So, research shows that people are often betterat judging the validity of syllogisms, when real-world examples are used as opposed towhen p and q and these kind of if p then q kind of statements are used.Let us take an example. So, there is this very famous Wasons card sorting task. So,what happened was each card has a letter on one side and a number on the other, and thetask is to indicate which cards you would need to turn over to test the following rule.And the rule is if there is a vowel on one side then there is an even number on the otherside. Now the idea is you have to really check that if there is a you have to really checkwhich is the card that you will turn over to check this rule consistently.So, there these things are E K 4 and 7 what do you really need to check ok. So, I thinkhere there are at least 2 things that you can check you can either check E because itis a vowel, if there is no even number on the other side ah there will be a problemor you could just check for that because if it is four here and there should be an evennumber less. Let us let us check what happens. When Wason1966 ah posed this task to ah people 53 percent of his participants indicated that he mustbe turned over this is correct because turning e over we directly test the rule.So, if there is not an even over the other side the rule is you know falsified and therule is broken. So, if there is an e then there must be an even number. So, there isan odd number if there is an odd number on the other side kind of does not know; however,another card also needs to be turned over to fully test the rule.Which one 4 46 percent of the participants ah suggested that four would also need tobe turn over. Now the problem here is that if a vowel is on the other side of the cardthis is consistent with the rule, but if ah a constant is on the other side, turning fourwill not be able to tell us anything. So, it is kind of trying to lead you astrayhere. If you turn four and if there is a constant on the other side the rule does not reallytell you whether that there is no consonant on the even number. It just tells you if thereis a e if there is an vowel, then the other side should be even numbered. So, as shownin the figure only 4 percent of Wasons participants came up with the correct answer, that thissecond card that needs to be turned over is s7. Turning over 7 is important because revealinga vowel would disconfirm the rule when to turn 7, if you see a vowel there then therule is broken and the rule is test. So, what we are actually looking for hereis the falsification principle what we are trying to do is we have to find one instanceat least that falsifies the rule. So, if you want to test a particular rule, it is necessaryto look for situations that would falsify the rule rather than confirm the rule or tellus nothing about the rule. Here is ah the different kind of scenariosthat are there, again borrowed from goldsteins book and they say there are only 2 conditionsthat will test whether the rule is getting falsified. If you turn over E and find oddor if you turn 7 and find a vowel. So, this is one of the ways how conditionally reasoningwould work. Moving on you saw that people are in somesense following these rule kind of things. So, if you talk about regulations. So, theWason task basically had generated a great deal of research and you know ah one reasonfor the degree of interest is that, it is a conditional reasoning task and people whoare interested in knowing about different aspects of conditional reasoning.So, researchers basically they wanted to determine, if there are general mechanisms that are responsiblefor improved performance in real world terms. If conditional reasoning works better withreal examples one such versions of the Wasons card problem is the beer drinking age version.So, I will show you ah the problem now. So, the idea is the rule is if drinking beer youmust be over 19 years old now there are 2 age cards and 2 drinkers. So, there is a beercard, as a soda card, there is a 16 year old card and a 24 year old card. Now you haveto check which is the easier thing. You will see that people a lot of people easily detectedthat beer card must be turned over or the 16 card probably must be turned over.Let us see the beer drinking age version of the problem is basically identical to theproblem that you know except that concrete everyday terms are substituted for the lettersand numbers. You know the task we were talking ek 47 we have actual things here. Now Griggsand cox use the version of the stars and found a 73 percent of the ah participants providedthe correct response. It is necessary to turn the beer card andthe 16 year cards, both of which check for the falsification of the rule in contrastnone of the persons answered the abstract problem correctly you know the same ek 47problem was given to these people, none of them could actually answer that correctlyapparently relating the beer or drinking age problem to actual regulations help peoplebecause there is an actual regulation we know which restricts alcohol drinking in theseparticular countries. So, probably what they were doing is theywere relating this actual regulation with the conditional rule here, and that is whythey were able to solve this problem better using the real world example even though theycould not solve the abstract example. So, here is the finding. So, you see noneof the people could actually solve the problem with the abstract rules, but a good 73 percentof the people could solve the beer age drinking problem.Now, taking this task slightly further Cheng and Holyoak they took the Wason task a littlebit further and they basically proposed the concept of pragmatic reasoning. So, the ideais that the way of thinking about cause and effect in the world is learned as a part ofexperiencing everyday life. So, you know how you go about your life in the world, how youobserve events are around you, how you see that things are happening in the world aroundyou, that is basically going to you know give you an aspect of what is called pragmaticreasoning; what really happens in the world ok. So, your reasoning is not really basedon you know hard logic if x then y, it is basically based upon knowledge of whetherreally y happens if x is then you know. Things about suppose for example, you knowthere will be a fine if you are not wearing a helmet. Now somebody would know that youknow it is also sometimes there that even if you are not wearing an helmet you mightget away without giving a fine. So, this is basically ah the kind of adapted this Wasonscard for a sorting problem to a different thing, and they came up with what is calleda permission schema. What is the permissions capable camera is a rule that says that, ifa person satisfy his condition A then he or she gets to carry out the condition B ok.If aged this much then drinking is allowed something like that. The permission schemathat if you were 19, then you get to drink beer was learned by everybody through experience.So, they were able to apply that to the card task and that is that is how here the linkis being made. Apparently activating the permission schemahelps people focus attention on the card that would test the schema. So, they will automaticallygo to a scenarios that would basically test and falsify this, because you know this isa real world problem. Participants attention is automatically attracted to the 16 yearsold card, because they know that beer on the other side would be violating the rule. Totest this idea ah that permission schema may be involved in reasoning about the carters,Cheng and Holyoak again ran an experiment with 2 groups of participants. You see whatkind of cards they were presented with one of the groups read the following instructions.So, the cards are entering transient cholera typhoid hepatitis typhoid and hepatitis. So,3 diseases 2 diseases in entering or transient, and the rule is if entering then cholera islisted. So, basically and the instruction is thisis the scenario, the instruction is you are an immigration officer at the InternationalAirport in Manila that is the capital of Philippines among the documents you to check is a formcalled H, ah one side of this form indicates whether the passenger is entered in the countryor is in transit. And the other form lists the names of tropical diseases, you have tomake sure that if the form says entering on one side.The other side includes cholera among the list of diseases, which of the following ahforms would you have to turn over to check. Now again these are card these are cards orforms and you would turn over to check whether somebody is entering or is in transit. ahIt is very easy here because this is a pragmatic task to this check, either the entering cardor the cholera typhoid hyper hepatitis card. 62 percent of these participants in this groupchose the correct cards. Entering and typhoid hepatitis entering other side cholera musthave been listed typhoid hepatitis then entering should not be there.Participants in the other group saw the same cards there is another group and heard thesame instructions as the first group, but with the following changes. So, there wassome more instructions putting. Instead of saying that the form listed tropical diseasesthe instructions said the form listed inoculation that the travel had received in the past 6months. So, some kind of vaccinations ah must have been received in addition the followingsentence were added, this is to ensure that entering passengers are protected againstthe disease. So, this is again some more information is added.The changes in these instructions were calculated to achieve a very important effect what wasthat? Instead of checking just to see whether the correct diseases are listed on the form,the immigration officer is now checking to see whether the pyre pyre whether the travelershave the inoculations necessary to give him permission to enter the country. These instructionswere intended to activate the participants permission schema and to apparently and youknow apparently, it was found that this works because 91 percent of the participants asopposed to 62 percent earlier, participated in this condition and they picked up the rightcards. So, you see how invoking the real world example,how invoking the pragmatic reasoning or the permission schema a concept is helping peopleto do reasoning much more easily as compared to the abstract reasoning things.So, this is the results of the Cheng and Holyoaks in 1995 experiment.Now, people have also thought about an evolutionary approach towards solving this four card problem.The alternative to the earlier a possibility that, we are talking about is the fact thatperformance on the Wason card sorting problem is governed by what is called a built in cognitiveprogram that kind of detects cheating. You know that kind of detects every time you aregoing to violate a particular rule. So, Cosmides and Tooly ah there are 2 one of the 2 evolutionarypsychologists who have an evolutionary perspective on cognition, they basically argue that wecan trace many of the properties of our minds back to the evolutionary principles of naturalselection you know, only those things would have survived only those things would havestayed on with us across centuries that would have helped us to survive and propagate andcome to the next generation. So, according to natural selection adaptivecharacteristics like will overtime you know adaptive characteristics will, over time becomebasic characteristics of humans. Because these things have survived generations and generations,these things will become almost embedded in our psyches.So, they have tried to apply this idea. So, if you apply this idea to cognition it followsthat a highly adaptive feature of the mind would through an evolutionary process, becomea very basic characteristic of the mind. So, anything that we have now should have beenuseful for us to survive through the ages. Let us take an example; an example is thesocial exchange theory. Now the social exchange theory says that an important aspect of humanyou know behavior is the ability for 2 people to cooperate with each other, in such a waythat is beneficial to both of the people. If only one of them is getting benefited thenit is not evolutionally very useful you know one of them will die out and the other wayand as soon as they realize that you know I am losing in this bargain, they will stopcooperating. So, what cooperation do exist they should be benefit to both parties. So,evolutionary approach proposes the Wason card sorting problem can be understood in termsof cheating thus people do well in the cholera task, because they can detect someone whotreats the country by entering without a cholera shorts that is probably that what is helpingand not the permission schema. So, let us see they test they wanted to testthis idea. So, Cosmides and Tooly what they did was the device number of four card scenarios,involving unfamiliar situations. Now no real world problems, but unfamiliar situationsnot the abstract ones ah unfamiliar situations which they would not know of, but seeminglike real world problems. So, what they did was they basically came up with a hypotheticalculture called Kulwane and they said participants in these experiments you know were told toread a story ah about that culture, which led to the statement that if a man eats acassava root and he must have a tattoo in his face this is the rule. Participants wasseeing four cards Eats Cassava Roots, eat Molo Nuts has a Tattoo does not have a Tattoo.Now, they were asked to test this. And the task was to determine whether the conditionalstatement was being a adhere to whether it was being followed or not. Now this is a situationwhi