Characteristics OF Inductive Reasoning PDF

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Heuristics are simple and quick strategies (cognitive shortcuts), which aim to reduce the complexity of a task by assessing probabilities, and predicting values that simplify the operations needed to make judgments. Such simple and fast strategies are of a non-logical type ! this leads us to reason ...

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CHARACTERISTICS OF INDUCTIVE REASONING There is no unanimous criterion when determining what is meant when talking about inductive reasoning but, from a broad perspective, inductive processes are considered, all those processes of inference that expand knowledge with uncertainty (possible but not necessarily correct conclusions). From a more restricted perspective, Johnson - Laird through his taxonomy, defined induction as any thought process whose conclusion increases or increases, the semantic information contained in the initial premises. Inductive reasoning involves a process of generalization from concrete experiences from which possible, plausible or probable but not necessary conclusions are generated or derived from logic. An induction draws possible conclusions, although not necessarily valid, and in general, an inductive argument would be based on assumptions and an incomplete argument. Unlike a deductive argument, the argument may be stronger or weaker as new information confirming or not confirming the generalization performed is added. Although in the literature there is differentiation between induction and deduction, subjects in everyday life continuously generate inductive and deductive processes. In addition, we usually make decisions or reason or make a prediction under uncertain conditions; in such situations, there is a theorem that tries to investigate the performance of subjects when they are to make a prediction and have to generate a probable conclusion "the Bayes theorem": normative theory (regulatory method) that serves to be able to evaluate hypotheses ; consists of a mathematical formula that calculates the probability of a given event or hypothesis starting, from a series of parameters such as previous probability and conditioned probability. Subjects in everyday life, we do not use these kinds of formal criteria but, we use another type of more intuitive reasoning, cognitive shortcuts, simple, non-logical strategies that lead to sometimes making correct and sometimes not correct judgments ! Heuristic. Biases and heuristics in Inductive Inference. Heuristics are simple and quick strategies (cognitive shortcuts), which aim to reduce the complexity of a task by assessing probabilities, and predicting values that simplify the operations needed to make judgments. Such simple and fast strategies are of a non-logical type ! this leads us to reason properly on occasions and sometimes to make mistakes or biases. Thus, an error

or bias is a systematic error (not due to chance) in relation to a regulatory system such as standard logic. They originally arise in the field of Inductive Reasoning with authors such as Kahneman and Tversky (1972) who studied their use in areas such as problem solving, decision-making... being the reference point for other authors to address the studies of heuristics in the field of deductive reasoning: authors such as Pollard (1982) or Evans (1982, 1984) translate this into the field of Deductive Reasoning. Pollard focused on studying the Heuristicof Accessibility (assessing the frequency of a fact based on the ease with which we are able to evoke from memory examples related to that fact) in deductive reasoning tasks such as the task of the four Cards. Evans raises the Analytical Heuristics Theory: it says that accessibility is a necessary but not sufficient condition to reason. Part of the concept of Relevance (all the information that we can have, the subject filters it according to what is most relevant to him). This theory originates from another theory proposed by Wason and Evans (1975), which is the Dual Process Theory which says that there are two types of processes in reasoning. Kahneman and Tversky (1972) studied the strategies used by subjects when asked to estimate the probability of a particular event. For example./ when you ask what is the probability that a particular object A belongs to a class B, the authors observed the tendency of the subjects to launch the "Heuristics of Representativeness" ! to the extent that A, like B, will judge that the estimated probability that A belongs to B will be high and otherwise low. Which of the following events do you think is most likely? Let the smoking men have a heart attack. Let men over 55 have a heart attack. That men smoking over 55 years of age suffer a heart attack. Let men have a heart attack. If statement 3 is answered, a bias is made. One of the most commonly used problems that the Heuristic of Representativeness made clear was "Linda's Problem": it carries implicit principles of probability; in it, a story is presented with different alternatives; depending on the response given by the subject, it is studied whether or not it has adjusted to the normative theory of normality:

"Linda is 31 years old, single, she is an open and very cheerful girl. He graduated in Philosophy. As a student, she was very committed to non-discrimination and social justice, and also used to participate in anti-nuclear demonstrations." Sorts the following statements according to their degree of probability, using the 1 for the most likely and the 8 for the least likely: Linda is a basic teaching teacher. Linda works in a bookstore and attends yoga classes. Linda is associated with the feminist movement. Linda works in a health center as a psychiatrist. Linda is a member of the Feminist Party. Linda's a bank cashier. Linda's an insurance agent. Linda is a bank cashier and is associated with the feminist movement. One of the most frequent trends, is that the subjects selected the alternative "Linda is bank teller and is associated with the feminist movement", they judged it as more likely that the alternative "Linda is bank teller" ! committed the Falacia of the Conjunction that constitutes the violation of the Conjunction Rule which says that: the probability of two events occurring together is always going to be less than the probability that each of them will occur separately. The character of the fallacy implies that the subjects do not consider the task as a statistical calculation but that they evaluate the representativeness of the elements in the task with respect to a model, in this case, with respect to Linda's personality. Therefore, subjects solved the problem using the heuristic of representativeness; to verify that they were indeed judging based on this heuristic, what the authors did was present a new version of the problem: they were not given data on Linda's personality, only that she was cheerful, that she was single and that she was 31 years old: subjects selected with a higher percentage, who was a cashier and this, confirmed that in the first version, they actually used the Heuristics of Representativeness. This heuristic is said, sometimes it leads to committing biases and so, for example, one of them is "The Falacity of the Player" according to which, a sequence of losses must be followed by a sequence of victories to compensate; an example that illustrates this fact is the "problem of the bet": a coin is thrown into the air 10 times obtaining the sequence CXXXXXXXXX (the 1st is expensive and the other 9 are cross).

If you had to bet 60 euros, what option would you do it? (face will come out, cross will come out); subjects say face because they tend to expect that the sequence of facts that takes place from a process that is random, represents the characteristics that we all recognize in a random process: that it is not repeated many times in a row of the same event. Another example is the problem of tiles: on a floor that has 25 tiles, 5 balls have been thrown at random; the tiles on which a ball has fallen, have been pointed out by painting them, which of the two floors we present to you is most likely to appear? AB Soil A is more likely than B because It is judged more random a. The fact that the same event is not repeated many times in a row may be true if the sample size was very large, but it may not occur when we base our judgments on only a few cases. That is, in general, how much > is the sample size, the more the result tends to stabilize and this is known as The Law of the Great Numbers. In the light of this, one has to wonder, what is going on? and so, many of the works showed that subjects do not use statistical concepts but do what they do is develop inductive (heuristic) reasoning. A second heuristic of those studied by Kahneman and Tversky is the Heuristic of Availability or Accessibility: to assess the probability of a certain event based on the ease with which examples can be evoked from memory related to that event. In this heuristic, familiarity and salience are two variables that influence judgments around the frequency (with which it occurs) of an event. As a consequence of this heuristic skewed skewed skeletals such as the so-called Illusory Correlation devised by Chapman and Chapman (1969): it is to overestimate the frequency with which two events occur in reality (they occur at the same time in reality). A third heuristic is the Anchor and Adjustment Heuristic: tendency of subjects to make estimates from an initial value or anchor that adjusts to give rise to the final response. It is a particular effect of the accessibility of information that is irrelevant either that it is present in the task, or that is generated by the subject himself from an incomplete computation. To make this clear, a simple experiment was developed: two groups, group 1 was asked to estimate in 5 seconds the result of multiplying 1x2x3x4x5x6x7x8 and group 2, which in 5 seconds estimated the result of multiplying 8x7x6x5x4x3x2x1; the first group made an average estimate of 512 and the second group of 2250. As

subjects have a few seconds to do the mental calculation what they do is estimate the result by extrapolation or adjustment and so, those in group 1, give an approximate value lower than those in group 2 because the values are lower. Decision-making. The decision-making process involves some complexity because it depends both on a judgment of probability made by the subjects and on their personal desires. TD - Probability Judgments + Desires Not all decisions are of the same type; fundamentally there are two types and so some decisions involve risks and others involve uncertainties: Decisions that involve Risks ! decisions where the probability of a given outcome is known, although the actual (concrete) result cannot be predicted. E.g./ roll of a dice: I can know the probability but not the actual result. Decisions under Uncertainty ! you can't even know the probability of a result because I can't quantify it, as in the previous case. They're the ones in everyday life. There is a normative theory in the decision-making process which is savage's Expected Subjective Utility Theory (USE) (1954): it includes a set of ideas or axioms that provide subjects with a foundation (or basis) to try to maximize what is the subjective utility of a result for each of the possible alternatives in a decision to be made. Plant a series of rigid axioms that have not always been accepted: Transitive Axiom ! if a subject prefers an event A to event B, and event B is preferred to another C, this would indicate that A is preferred to C. Axiom related to subject preferences ! in a decision to be made, a subject's preferences are always fixed, stable and well-ordered. The Expected Subjective Utility Theory (USE) is a formal theory and has therefore received criticism: Actually, in everyday life, often the preferences of the subjects, will depend on the way in which the subjects are presented the alternatives (the different options) that may suggest arguments for or against them. Kahneman and Tversky proposed the following example to explain this: Two arguments, You plan to go to the theater, on the way to the theater, you've lost the ticket that cost you 5000 Ptas., would you buy a new one?

You feel like going to the theater, you still haven't bought tickets so you're on your way to the theater and along the way, you realize you lost 5000 Ptas,would you change your plan? In situation B I would buy the ticket and in situation A, no ! decisions are not fixed, it depends on how the situation arises. Mr. Crane and Mr. Tees' experiment: both subjects were planning to catch two different flights, at the same time. They took the same limousine to the airport, but got stuck in a traffic jam and arrived at the airport thirty minutes late over the scheduled departure time of their flights. Crane is told that his flight departed on time. Tees is told that his flight was delayed and that he departed only five minutes ago. Who's going to be more upset? Most subjects respond that Mr. Tees even though the situation is identical, they both miss the plane. With these examples, Kahneman and Tversky wanted to demonstrate the difficulty of explaining decision-making processes based on a normative theory such as the Expected Subjective Utility Theory (USE). From this idea were developed different theories that took into account the importance of psychological, emotional variables in the decision-making process: Theory of Perspective, Kahneman and Tvesky (1979) Theory of Repentance, Bell (1982, 1985) Summary and conclusions. The decision-making process that subjects carry out in everyday life, as well as reasoning processes, are far removed from the ideas that are proposed from normative theories and so, for example, when a subject makes a decision in everyday life , it does so in a situation of uncertainty and that is why, it does not make the decision using statistical criteria but mostly, using heuristics that often lead to committing biases. The most studied heuristics by Kahneman and Tversky are: Representative Heuristics ! it can lead to committing biases such as the Fallacy of the Conjunction, the Falacia of the Player or the difficulties in understanding the Law of the Great Numbers. Availability or Accessibility Heuristics ! judge the likelihood of an event based on how easily we can evoke from memory examples related to that event. Sometimes it leads to committing the Ilusory Correlation Bias.

Anchor ingetic and Adjustment. From a broad perspective, inductive processes are all those processes that expand knowledge with uncertainty (generalization conclusions). From a smaller perspective, Johnson-Laird defines it as a "thought process whose conclusion increases the semantic information included in the premises, so that it is a process of generalization from concrete experiences to conclusions possible or plausible, but not necessarily formally valid." Inductive reasoning has two fundamental characteristics; 1-. It's a reasoning that's based on assumptions 2-. These are incomplete reasoning; the more elements the subject finds to conclude, the more likely it is to come to the conclusion. There is a normative theory that allows to evaluate at a formal level the probability of a prediction being fulfilled: The Bayes Theorem. It consists of a mathematical formula that calculates the probability of a knowledge or hypothesis being given from a series of parameters known as pre-probability and conditional probability.

Previous probability; How likely am I to find a job at the end of my career? Statistics from the last 5 years say that a person's chance of finding a job at the end of the race is .35. The probability complementary to the previous probability (probability of not finding a job) would be .65. Conditional probability; is the degree of association between the hypothesis and a significant data observed, such as, for example, having a good record. Thus, the associated probability would be; P (E/H) . . . . . . . . . . . . . . . . . . . . . . . . . . His complementary probability (probability of not finding him having a good record) would be; P (E/H) . . . . . . . . . . . . . . . . . . . . . . . . . . The Bayes theorem is a normative theory, but we, in everyday life, use other nonlogical methods or cognitive shortcuts to estimate the likelihood of a certain event occurring, methods that will sometimes lead to correct reasoning and others to incorrect reasoning. Those non-logical methods or cognitive shortcuts would be heuristics. E.g. Which of the following events do you think is most likely? That a man over 55 has a heart attack. Let a man have a heart attack.

Let a smoking man have a heart attack. If we used Bayes's theorem to make a decision, possibly our answer would be two, since it is more likely that this event will take place than the other two. However, the subjects did not respond to this. Biases and Heuristics in Inductive Inferences Kahneman and Tversky studied how subjects reason when asked to estimate any probability, for example, to estimate the probability that a particular object A would belong to class B. they had to set in motion the "heuristic of representativeness", that is, to the extent that A resembled B the subjects judged that the probability that A belonged to B was high; and else it goes down. One of the most commonly used problems highlighted by the use of representative heuristics was Linda's problem. This problem was presented to the subjects and, depending on the response they gave, they were studied whether or not they had adjusted to the normative theory of probability. The problem is as follows; "Linda is a cashier, she's 31, she's single, she's an open girl and very cheerful. He graduated in Philosophy. As a student, she was very committed to nondiscrimination and social justice, and also used to participate in anti-nuclear demonstrations." The subject's task was to sort a series of statements according to their degree of probability, using the 1 for the most likely the 8 for the least likely. The series of statements were: -Linda is a basic teaching teacher -Linda works in a bookstore and attends yoga classes. -Linda is associated with the feminist movement. -Linda works in a health center as a psychiatrist. -Linda is a member of the Feminist Party. -Linda is a bank cashier -Linda is an insurance agent. -Linda is a bank cashier and is associated with the feminist movement. Subjects used to choose as most likely the alternative of "Linda is a bank cashier and is associated with the feminist movement" that the alternative "Linda is bank cashier". With this result, the subjects were making a mistake called "Conjunction's Fallacy", which is a violation of the conjunction rule. The conjunction rule says that the conjunction of two events could not be more likely than the fact that there is only one of them.

Thus, the subjects did not consider the task as a statistical calculation, but involved the representativeness of the elements of the task with respect to a model, in this case with respect to Linda's personality. The subjects were using the heuristic of representativeness. To verify that this was the case, that is, to check that the subjects were using the heuristic of representativeness, they were given the same problem without highlighting traits of Linda's personality. The subjects in this case judged that Linda was more likely to be only cashier and not cashier and feminist at the same time. This heuristic sometimes leads us to commit biases: Playerfallacy; According to this fallacy, a sequence of losses must be followed by a sequence of victories to compensate. For example, if you throw a coin into the air 10 times and, of those 10 times, nine comes out cross; if you had to bet 10000 Ptas. what it's going to do on the next spin, possibly most subjects would answer that it would come face, although the probability of it coming out face remains the same (0.5). Normally, subjects tend to expect that a sequence of events, produced from a random process, represent scant stakes in a random process: that the same event is not repeated many times in a row. This fact may be true if the sample size is very large; but it may not happen when we are basing our judgments on a few cases. For example, if I throw a coin into the air three times the face-face-face combination is likely to come out; but this is more likely that if I throw the coin into the air 100 times and, of those 100 times, three will come out face and 97 come out cross. Thus, the larger the sample size, the more the result tends to stabilize. This is what is known as the law of big numbers. Heuri...