In the previous chapter we saw the mechanisms that we use in decision making, something very linked to how we pose a problem. In cognitive psychology a problem is a situation in which there is no immediate and standardized way to reach a goal, a fact that is further complicated by the anxiety it triggers and emotional aspects of our unconscious.
Structure of a problem
Faced with a problem, our mind initiates a process of identification, represents it, often with an image and then looks for a line of action that makes its resolution possible (I visualize the problem and see how to solve it).
This way of acting rationally and for all makes logical sense, we will see how it is not always the human being, sometimes looking for "shortcuts", heuristics, less reliable but with less expenditure of energy and resources.
A problem can be structured in three parts:
- Target state or goal.
- Initial or starting state.
- Operations that can be applied for its resolution.
An example of a problem that follows this classical structure is in the Tower of Hanoi, where there is an objective state of resolution of the problem, a starting situation and a series of operations to move from the initial state to the final state.
Types of problems
To the problems in which the initial state and the final objectives are clear, they are called "well-defined problems", The Tower of Hanoi or chess are examples of this type. When this does not happen, they are called "ill-defined problems"And in these cases it is important to find the limitations, the restrictions of the solution or the means at our disposal.
Some ill-defined problems are characterized by a spontaneous resolution, we find the solution as a "light that makes them manifest", we see it clearly. This phenomenon is known as "insight", something that also relates to the visual system. We can only visually imagine that which makes sense, that it is possible, mental representations related to the information that we keep in the long-term memory.
Strategies to solve problems
Although there are differences in the strategies used to solve problems, there are a series of steps that are common to all of them. The basic steps are shown in the following flow chart.
First we must form a representation of the problem and then plan a solution and verify it. If the proposed solution fails, we must represent the problem again from another perspective and look for a solution that solves it. If the solution is successful, it is executed and the problem is concluded.
In case of not finding the solution, the question arises how many times we must rethink the problem, look for new representations and new solutions. There is no clear answer but, in what most researchers agree, it is to change the resolution strategy, using some of the paths that we expose next.
The problem space
Currently, the "problem space theory" is used as the most valued strategy for problem solving (Newell and Simon, 1972). It is about looking at each step of the problem structure what we call the "problem space", which it is the set of states or possible alternatives faced by the person who has to solve the problem. In scientific research, where the problems are generally complex, we work in several spaces simultaneously, the space of the hypotheses, to formulate theories, an experimental space and a data space to interpret the results.
Algorithms
In most cases, before a certain type of problems, a safe way to solve them is looked for, we try to follow a series of standardized steps, a formula, what we know as an algorithm, which always, sooner or later, will give rise to the correct answer. The rules for solving a square root is an example of an algorithm.
Algorithms are very effective but require a lot of time and resources, both operational memory and long term, so it has been seen that most people do not use algorithms but prefer faster but less secure approaches, are the heuristics, which could be considered as "shortcuts" to solve problems, so heuristics tend to focus on the resolution of the problem "moving" towards the objective or, through a random search type trial-error.
Heruistics
Within the strategies based on heuristics, what we call "means-end analysis" is usually used, in which the problem is divided into parts and attempts are made to resolve each of the parts separately, understanding that the partial resolution is more feasible than the attempt to solve the problem as a whole.
In the resolution of problems, the working memory, fact confirmed by the activation of dorsolateral prefrontal areas as well as clinical experiences with patients with lesions in this region, unable to resolve situations such as the Tower of Hanoi.
One fact that interested the researchers is whether there were differences in the structuring and resolution of problems comparing expert subjects and beginning subjects. The main difference was the ordering of knowledge, more superficial in the beginners and deeper and with more abstract structures in the experts (Chi, 1981). Another interesting difference was the direction followed in the search for the problem space. Experts tend to look forward, from the initial state to the objective state of resolution, for example, an expert doctor goes from symptoms to diagnosis, while beginners do a backward search, first diagnosis and then move forward towards the symptoms that confirm it.
Analogical reasoning
It is one of the most used strategies to solve problems. We do not start from scratch as in the previous case, it is about thinking about a problem with similar characteristics that has been solved previously and the solution is used or adapted to the current problem. A classic example of analogical reasoning is the one used by the solar system to explain the structure of the atom or the case of the design of the antivirus that we use in computers, where experiences with antiviral vaccines are used in animals and humans.
The analogical reasoning allows identifying and transferring structural information of a known system, biological viruses, stored in long-term memory, to a new system, computer viruses, housed in the working memory, where information is processed, elaborated hypothesis and it is evaluated if the analogy is useful to solve the problem. Visual mental representations are again used in this type of reasoning, which is important when working with these models in learning tasks, both for children and adults, for example to overcome a phobia or in athletes who must correct certain errors in the movements.
Theories of analogical reasoning
To explain the analogical reasoning two theories have been proposed:
- Theory of the cartography of the structure, TCE, (Falkenhainer 1989).
- Theory of learning and deduction with schemes and analogies, ADEA, (Hummel 1997).
Theory of structure cartography
The TCE model consists of two stages, in the first one looking in the long term memory possible sources that have the superficial characteristics that appear in the objective and in the second stage, there is the evaluation of how good is the matching between what He has recovered in the first stage and the goal.
Theory of learning and deduction with schemes and analogies
The ADEA model uses a different computing mechanism that resembles neural networks. The objective is represented in terms of the activations of the characteristics of the source: the computer virus will activate, for example, the characteristics of malfunction, be harmful and be replicating. This simultaneous activation of a series of similar characteristics in long-term memory is what leads to the recovery of an analogous source, such as the influenza virus.
Limits of analogical reasoning
One of the questions that remained to be determined was the question of whether analogical reasoning could be merely a product of attention and operational memory or it would be something else.
By means of neuroimaging it was demonstrated that in tasks where the load of the operative memory was increased, the parietal cortex and the dorsolateral prefrontal cortex were activated, as expected, but the situation changed when the structural complexity was increased while the load was kept constant of the operative memory, in this case the left anterior prefrontal cortex was activated exclusively.
With these data it is deduced that the analogical reasoning represents a cognitive capacity that recruits the activity of neural tissue in greater degree than the attention and the operative memory so, in fact, it is something more.
Inductive reasoning
We can define it as a thought process that uses our knowledge of specific, known circumstances to make a deduction about unknown circumstances.
The main peculiarity of this type of reasoning is that you can not know all the cases that exist as well, we are adding new knowledge, which although possible, may be incorrect. Inductive reasoning can be general or specific.
General or general inductive reasoning
The global or general induction it tries to generalize from known circumstances to all possible circumstances. Burner in 1956, was one of the most studied general induction, worrying greatly about the way we introduce the hypothesis in the problem. A hypothesis is an idea or proposition that we can evaluate or verify by gathering evidence that supports or refutes it. This seems simple and obvious, it is not always like that.
Questions of the type can be asked, how can a subject that has deduced a rule through general induction, find out if that rule is incorrect?
A classic example is the one proposed by Peter Watson: before the triad of numbers: 2, 4, 6, most respondents point out as a rule that relates to the three numbers, that of being even numbers with increments of two units and, when they are told that it is not correct, they go to look for new rules like, any number with increment of two units and they give as examples, 1-3-5 and, before the new refusal of success, they will reach rules with less and less sense, they move away more and more from the correct answer, the simplest and the most logical, in this case, "numbers of increasing magnitude".
In this example of the general induction, of the triad, we see that a general induction must be made from a set of particular cases, but the subjects usually fall into what we call, "error of confirmation bias", Which gives weight to the previous information that we have, to pre-existing beliefs. A solution is found, apparently valid, and it is not confirmed if there are other better solutions and when they are told that it is not correct, it becomes much more difficult to find the error in the rule, to discover that the rule they have proposed was incorrect.
Specific inductive reasoning
The specific induction we can represent it with the fact that, assuming that a member of a category has a particular characteristic, any other member of that category must have it as well. This has a trampa obvious, the characteristic involved may not be common for all members of the category. Although this is true, the specific induction allows us to make useful deductions about a new or unknown member of that category.
Inductive reasoning allows us to update our knowledge, it is not necessary to have to search case by case if that particular characteristic is true for all members of the category. To the extent that we categorize an object in a certain category, we assign the characteristics of that category.
Neurophysiological bases of inductive reasoning
Looking for the neural network that could explain the inductive reasoning, it was observed that the frontal lobes played a fundamental role. When there was a lesion in the left dorsolateral prefrontal cortex, patients were unable to order letters or other objects, although the rule to follow was very simple, as in the Wisconsin test (Monchi, 2001).
With neuroimaging studies it was observed that along with the activation of the frontal areas, there was also activation of the left hemisphere, specifically medial and parahippocampal temporal regions, which indicates that in this type of reasoning long-term memory intervenes. Induction requires that information pertinent to long-term memory be actively recovered and that information be kept in working memory. These processes demand resources mediated by the frontal and temporal lobes.
Induction and learning
An important issue was that of experience, the fact that the underlying cognitive process can change with experience. Neuroimaging studies show that when a subject is asked to perform an object classification task, the frontal and parietal regions of the right hemisphere are stimulated, but as the learning process progressed, activity in the right hemisphere began to register. the regions of the left hemisphere, specifically in the left parietal lobe and the left dorsolateral prefrontal cortex. This suggests that in the first phase of the classification task, these are basically done by processing the visual models of the stimulus, while when learning progresses, an abstract rule that improves the classification process begins to accelerate learning.
Fungelsang and Dunbar (2005) examined with functional magnetic resonance the mechanisms by which we integrate the data when we are testing specific hypotheses. They found that when the subjects were examining the data of interest for a plausible hypothesis, preferentially activated regions of the caudate nucleus and the para-hippocampal circumambulation were activated. Conversely, when subjects examined data related to an implausible hypothesis, regions of the anterior cingulate cortex, the precunus, and the left prefrontal cortex were selectively activated.
In the case of plausible hypotheses, activated neural regions are those that intervene in learning, long term memory and the process of integrating information. With these data we can infer that the learning process, of integrating new information, improves if it is consistent with a credible hypothesis. In the same way, the anterior cingulate cortex, activated in cases of implausible hypotheses, has been involved to a large extent in the detection of errors and conflict situations.
These authors suggest that during inductive reasoning, the human brain recruits regions related to learning, when it evaluates data that are coherent with preexisting hypotheses, while it recruits other regions when it comes to error detection, when evaluating data that are not coherent. with the hypotheses. This distinction is important when considering, for example, curricula in childhood.
Deductive reasoning
In this type of reasoning we go from top to bottom, we start from premises that we consider true and therefore, the conclusion can not be false (unlike in the inductive reasoning). This type of reasoning is the one that most faithfully represents rational thought. The mental process is closely related to syllogisms, an argument consisting of two statements and a conclusion. The conclusion can be both true and false but, if it follows the laws of deductive logic, it will always be a valid conclusion.
The syllogisms
The syllogisms can be categorical or conditional.
The categorical have the form:
- Premise 1: All A's are B
- Premise 2: C is an A
- Conclusion: C is B
The relationship between the terms of a categorical syllogism can be described by four types of statements:
- Universal Affirmation: All A's are B
- Universal Denial: No A is B
- Particular Affirmation: Some A is B
- Particular Denial: Some A is not B
In the example of buying a car we could write the syllogism like this:
- Premise 1: All Porches are reliable
- Premise 2: The Boxster is a Porch
- Conclision: The Boxster is reliable
Conditional syllogisms
In the case of conditional syllogisms, they echo the situation: the fact that an event occurs can be conditioned by the occurrence of another. As in the categorical ones, the conditional syllogisms consist of two premises and the conclusion.
The first premise is always of the type, "if P then Q", where P is an antecedent condition and Q a consequent condition.
The second premise can have one of the following four forms: Affirmation of the antecedent: P is true, Negation of the antecedent: P is not true, Affirmation of the consequent: Q is true, and Negation of the consequent: Q is not true.
In this case, the example of buying the car would be:
- Premise 1: If the car is a Porch, then it is reliable
- Premise 2: The Boxster is a Porch
- Conclusion: The Boxster is reliable
In the P1, "Porche" is the antecedent and "is reliable" the consequent. In the P2, in the example, the antecedent affirms, therefore, the conclusion "is reliable", follows logically.
Errors in deductive reasoning
Although deductive reasoning is very reliable, we can make mistakes, generally because we raise it badly, but it is difficult to see why we think that it is the most truthful type of reasoning. Basically there are two types of errors: errors of form (errors of the structural form or format of the relation between the premise and the conclusion) and errors of content (when the content of the syllogism is too influential).
Form errors
In the errors of form, a type of error very frequent is the one that we denominate "effect of the environment", In which a conclusion is accepted as valid if it contains the same quantifier (some, all or not), that appears in the premises. This situation leads to a general mood or "environment", hence its name, which leads us to accept a conclusion in a wrong way.
Upon the conclusion "all A are C", the following premises are necessarily followed, "all A are B" and "all B are C". If we change the quantifier "all" to "none" we have: "no A is B", no B is C and the conclusion: no A is C. This other form seems equally valid, like the first, but we will see that it is.
If we take real examples, the syllogism with "none" would be:
- Premise 1: No human is a car
- Premise 2: No car is a doctor
- Conclusion: No human is a doctor
It is obvious that the conclusion is valid but it is incorrect in the real world.
Matching bias
Within the errors of form, we also have what is known as "match bias", Very frequent in the conditional reasoning and in which a conclusion is accepted as valid, if it contains the syntactic structure of the premises or some of the terms of these.
Both the effect of environment and the pairing bias point to the strong impact of the syntactic structure. In both cases we are very influenced by the quantifiers that are used in the premises. It seems that this is because certain objects in categorical and conditional statements, such as formal quantifiers, would strongly capture our attention. We always expect that the information we receive is adequate and therefore, we expect the quantifier to be critical, therefore, in view of the preference to attend to the words of the quantifier in the premises, and to give these as valid, when the same quantifier appears in the conclusions, they are also accepted as valid.
Content errors
Along with the errors of form are the errors of content that we often make when we focus on the certainty or falsity of the individual statements of the syllogism, ignoring the logical connection between the affirmations. We see it in studies that present false syllogisms whose conclusions contained, at times, certain statements. (Markovits 1989). We are prone to accept as valid, logically, a conclusion if the premises and the conclusion are true statements.
Along with these errors we also find those that are committed when we give credit to our beliefs. The tendency to be more inclined to accept a "credible" conclusion than that which is "incredible" is a very frequent fact in everyday life and is strongly rooted in our cultural beliefs.
Finally, it seems increasingly accepted that many of the errors that are made in deductive reasoning are due to limitations in working memory.
Studies on theories of deductive reasoning, lead to admit that there is a natural process of mental analysis that assesses the validity of the premises and conclusions, which are born with this substrate, with this skill however, the limitation that marks the capacity of the operative memory, does not always use the rules of logic and we go to the heuristics, shortcuts that save energy and resources but that easily make us fall into errors, such as those we have seen when describing environmental errors , that of pairing bias and those based on beliefs. We end up choosing what seems more credible to us.
Neurophysiological aspects of deductive reasoning
Studies with neuroimaging during the deductive reasoning process showed initially contradictory results. It was thought that areas related to a linguistic base would be activated but it was observed that areas related to spatial models were also activated. The conclusion reached is that when deductive reasoning occurs with material that is familiar, neural resources of the left hemisphere are used, related to linguistic models, while if the material is more complex, visuospatial construction models are required. and the right hemisphere regions are activated.
The implication of linguistic bases in deductive reasoning, in the generation of errors, is something well known and highlighted by various authors, especially Chomsky in his transformational grammar, when he deals with ambiguous phrases and their capacity to generate errors of interpretation. I believe that the subject is so important as to make a monographic article. I hope to fulfill this promise later.
Decision making and the visual system
We have already seen how vision models that go from top to bottom, like those proposed by the Gestalt researchers, would have a certain similarity with the deductive models.
The information that we store in the long-term memory, the construct that is generated by experience, the mental representation of the objects that we keep, exercises the function of "guide" on the new information that is entering at every moment.
The internal representational model helps identify the objects that appear in front of us. The filtering of data, edges, colors and forms, supposes a great information that must be integrated to identify the objects and in that process of constitution, of categorization, the internal representations mark the grouping rules to "deduce" from which objects it is.
This mechanism of top-down vision is fundamental because it requires much less energy and allows an identification of objects much faster, almost automatically. We see the importance in examples of daily life as is the case of proposing an overtaking car, we identify the vehicles that circulate in both directions, we calculate the trajectories, the distances and the time that we need to advance, almost immediately, what it means to gain in efficiency and security.
Once we have seen the mental mechanisms that we use in decision making and problem solving, we are already in a position to address the mental processes that lead to action, especially with the help of the visual system, something that we will develop in the next chapter.
