Psychology of Logic and Cognition Research Paper

1. Reasoning

The pervasiveness of reasoning has captured the interests of cognitive psychologists who seek to understand universal principles of human cognition. Early in the twentieth century, psychologists were surprised at how poor people are in solving academic logic problems, yet how perfectly adequate the same people are in their reasoning with everyday materials—and without special training (Wilkins 1928). People tend to feel alienated from the prescriptive logic of the classroom, as well they might since from its very beginnings it had little to do with the rationality of the human mind and very much to do with creating a didactic device for educating students. Aristotle, in an effort to express to his students how to think clearly and how to draw conclusions from data, created a set of idealized conditions (called Figures) from which certain conclusions could be unequivocally drawn; and he contrasted these with conditions from which a conclusion could only be equivocally drawn. From these simple didactic beginnings, the field of philosophy of logic was born. Over the centuries, innovations in understanding human logical or rational abilities have continued to come from efforts at teaching: Euler, who invented the circles to represent sets, did so within the context of tutoring in logic (Euler 1775). Venn (1880), who expanded on the circle representation, introduced the notion of a universe of discourse and analyzed the overlapping of multiple sets circles and did so within the context of trying to teach logic to his students at Cambridge University. Some of these didactic techniques have inspired modern cognitive psychologists to theorize about natural human inference. Erickson (1978) and Guyote and Sternberg (1981) borrowed Venn diagrams as an approximation to how students may interpret and mentally represent quantified sentences in their combinatorial theories of reasoning. One of the major cognitive accounts of the processes of human reasoning is called ‘Mental Models’; it was developed by Johnson-Laird (1983) and had its origins in the efforts at the beginning of the twentieth century by Storring (1908) to teach his students how to reason by drawing pictures. Throughout the centuries, the impoverishment of didactic logic has been so daunting to students that they have argued they should not have to study it. After all, they say that ‘we should only study things that are relevant to human life; syllogistic reasoning is not relevant, so we shouldn’t be studying syllogisms.’ This itself is a type of logical argument that could be rewritten in syllogistic form (the standard form for logic):

We should only study things that are relevant.

Syllogistic reasoning is not relevant.

Therefore: we should not study syllogistic reasoning.

Clearly this argument is self-refuting, but illustrates that even though we may wish to avoid the intricacies of prescriptive logic, some aspects may be descriptive of an underlying system of natural inference processing that becomes manifest even by people untutored in the philosophical tradition. Take a four-year-old, for example. We know that if you tell the child (in the form of a syllogism):

If you brush your teeth, I’ll read you a story before bed and

The child brushes her teeth

You can be sure that the child will expect a story.

The structure of this argument is formally described as If P, then Q; P therefore Q and is termed modus ponens (positive mode) and is an argument that is accurately understood by children and adults, without any special instructions (e.g., Taplin et al. 1974). Just as Moliere’s Bourgeois Gentilhomme was surprised that he spoke prose all of his life, so too are the students of the psychology of logic surprised to find that people seem to be inherently rational (at least under specifiable circumstances) and follow a kind of psycho-logic which is illustrated below with three different forms of inference: linear, categorical, and conditional reasoning.

1.1 Linear Reasoning

One of the simplest forms of inference compares the extent of things and draws a conclusion about the item that has the most or least of the extent. For example:

Scott is taller than Paul.

Paul is taller than Nancy.

Who’s tallest shortest?

These kinds of syllogisms found their way on to the early measures of intelligence (e.g., Burt 1919) because reasoning skill with these problems seemed to increase with chronological age during adolescence (e.g., Hunter 1957). Interestingly, the pattern of difficulty shown on series problems by children is similar to that shown by adults (Huttenlocher 1968, Clark 1969) which suggests that linguistic processes (and the complexity of the terms: older–younger, taller–shorter, etc.) rather than inference per se contributes to the development of reasoning skill with age (JohnsonLaird and Steedman 1978).

These problems are called ‘linear syllogisms’ because one way to draw inferences from them is to imagine that the information is placed on a line or on an analogue scale (a continuously varying scale). When such a scale is used, it is possible for the reasoner simply to ‘read-off’ the mental image to find the answer. Consistent with this idea is students’ expectation that the information will be presented in a linear form (left-to-right or right-to-left order), called the canonical form. When the information flow fits the canonical form, reasoning is fast and accurate and when it does not fit it, reasoning is labored and error prone (Hunter 1957). A similar effect has been observed for problems with more than just three terms in it. For example, Potts (1974) had students reason with relations among five items embedded in a passage (e.g., A is greater than B, which is greater than C, which is greater than D, which is greater than E) and discovered that terms that are further apart on the linear scale are easier for students to evaluate (e.g., Is A greater than E? was faster and more accurately judged than Is A greater than B?, even though the latter was actually presented in the narrative and the former inference was not). This effect of the way you mentally represent information has been termed the semantic distance effect (Holyoak and Mah 1981) and requires primarily that the information be coded on a uniform scale (such as size, intelligence, etc.).

1.2 Categorical Reasoning

Perhaps the simplest form of reasoning with categories is the categorical syllogism:

All men are mortal.

Socrates is a man.

Therefore: Socrates is mortal.

The ability to draw the appropriate inference is nearly universal, does not require knowledge of logical forms, or even to know the meaning of the term ‘men’ and ‘mortal.’ It requires only a basic willingness to cooperate to do the task. For example, Cole and Scribner (1974) showed that unschooled adults in Liberia will occasionally decline to draw an inference, but their explanation reveals basic inferential skills:

All men in Kpelle town are farmers.

Joe is a man in Kpelle town.

Therefore: Joe is a farmer.

‘I cannot answer the question, because I only speak about people I know and I don’t know this Joe.’ In the canonical form, the man’s explanation looks as follows:

I only speak of people I know.

I don’t know Joe.

Therefore: I cannot speak of Joe.

So the justification for failing to do syllogistic reasoning takes the form of a perfectly phrased logical argument and is an example of the universality of this form of reasoning.

The critical factor in the willingness to solve syllogisms seems to be whether a person has had more than 2 years of basic schooling. When asked to solve categorical syllogisms, such educated people, while not necessarily tutored in logic, show the following profile. When they reason about everyday sorts of things, they are more accurate than when they reason about symbolic or abstract relations (Wilkins 1928). Reasoning on symbolic material can be enhanced by having a mental image of how many elements are contained in the sets—the sizes of the sets allows people to represent the relations more like concrete than like abstract materials (Revlin and Leirer 1978). When their beliefs about the world are consistent with the syllogism’s conclusion, they are more accurate than when logic and belief are in conflict. When there is a definite unambiguous conclusion to be drawn, people are confident in the conclusion, but when no such conclusion is to be drawn, people are tentative and somewhat capricious in their answers. When reasoners are asked to draw inferences from a multitude of category relations as in the following narrative, they show a kind of semantic distance:

All members of the Fundala Party are members of the Outcast Coalition. All members of the Outcast Coalition are members of the Hill People Union … members of the Peace Front.

The more distant the relation, the more accurate the judgment—just as with linear relations. A completely different pattern is seen when the categories do not readily fit in a common scale, as in the following (from Griggs 1978):

All Fundala are Outcasts. All Outcasts are hill people. All hill people are farmers. All farmers are peace loving.

Reasoners view these relations as di ergent, dealing in succession with a social group, geographic entities, occupational categories, and a political orientation. The very same people who performed optimally with the first passage are at near chance levels when asked to reason about this second narrative (Nguyen and Revlin 1993).

Reasoning with categories shows a developmental sequence somewhat akin to that shown for linear relations. The critical factor seems to be in the interpretation of the terms rather than possession of inferential processes. For example, when seven-yearolds are told that all of the squares in a display are yellow, they anticipate that the display will only contain yellow squares and no other kind of object. This is called an ‘order-neutral interpretation.’ Slightly older children interpret the quantified sentence as implying that all squares are yellow and that all of the yellow things will be squares. However, they are not surprised that there are nonsquares and these will have colors other than yellow. This is called a ‘converted interpretation.’ Finally, most adults (but not all of them) interpret such quantified sentences as true setinclusion, that all squares are yellow, but some yellow things may not be squares (Bucci 1978). This ontogeny in the interpretation of quantifiers corresponds to the development of logical competence with categorical relations and suggests that the interpretative processing and not inferential ones may be what is developing.

1.3 Conditional Reasoning

Conditional syllogisms have as their central statement, a conditional expression of the form If P is true, then Q is true. Although conditional syllogisms are logically equivalent to categorical syllogisms, they have a communicative property that makes them especially interesting to psychologists in studying how people reason with them. The external marker If allows for an incredible range for conjecture: the reasoner can interpret it to mean let’s suppose that … , or someone belie es that … (e.g., Paul belie es that if P, then Q, even though he may be wrong), or to perform some action, there is a set of conditions that must be followed (e.g., If you’re drinking alcohol, you must be the right age), and so forth. That is, conditional syllogisms reveal the very property that makes human inference so dynamic: an ability to consider truth at many levels. When adults are presented with conditional syllogisms that have an unambiguous conclusion to be drawn, they are rapid and accurate:

If P then Q If P then Q.

P is true not Q is true.

Therefore: Q Therefore not P.

These problems are called modus ponens and modus tolens, respectively. The former tends to be more accurately solved than the latter, but people demonstrate real skill in solving these problems without any special training. In cases where the conclusion is ambiguous, students take longer to reach a decision and tend to equivocate and generally draw an incorrect conclusion:

If P then Q If P then Q.

Not P Q.

Therefore: ? Therefore: ?

Just as with other forms of inference, interpretation of the relational terms is critical to accurate judgment.

A common error among adults is to assume that a kind of unique causal structure holds when they hear If P then Q. That P somehow causes Q and that it uniquely does this. This typically goes by the name biconditional interpretation: If P is true then Q is true and if Q is true, so must P (Taplin 1971). You will notice that this is similar to the ‘converted interpretation’ on categorical syllogisms. It has been argued that there is a developmental sequence in the ability to solve conditional syllogisms which is linked to the child’s interpretation of the conditionals. Very young children treat conditionals as conjunctions, slightly older children treat them as biconditionals, and adolescents and adults are able to treat them as oneway conditionals. Just as with categorical reasoning, conditional inference is sensitive to the content of the material reasoned about. This is particularly striking when people have to test conditional rules (Cox and Griggs 1983). When the rules and situations match a type or schema (e.g., a permission rule: If you meet the requirements, you can perform an action), reasoning can be sharply more accurate than if the conditional rule is arbitrary (Cheng and Holyoak 1989, Cosmides and Tooby 1997). The ease and ubiquity of this kind of reasoning suggests it may actually be a part of the human cognitive apparatus, part of our biological heritage that permits us to engage in effective social interactions.

2. Where are the Rules?

These findings from cognitive research in three areas of logical reasoning show that people are far more rational than is often assumed. Our inability to solve some impoverished symbolic problems does not mean that we are not rational. It does mean that if there is a logic within us—and we must be following some set of rules or procedures to allow us to be rational under normal circumstances—it is probably not the standard logic we are taught in schools. The logic of the head need not be the same as the philosopher’s logic because human inference occurs in rich and varied contexts, with cognitive and social constraints operating all around us and directing our attention to critical assertions and providing us with just the right inference procedures to evaluate them. These pragmatic influences may at first sight seem impurities in the crystal clarity of inference, but we must be mindful that even logic rules can propagate errors. Rationality and the possession of general reasoning rules do not assure us that the premises are not false, or that situations are not misinterpreted, or that cognitive load will not contribute to erroneous processing. While natural logic may be the basis for rational judgments (Rips 1994, Braine and O’Brien 1998), this does not mean we cannot make errors and do irrational things. An error in the input can be propagated promiscuously throughout our knowledge. Without some pragmatic knowledge to direct our processing or the identification of degrees of truthfulness of propositions, our knowledge base would be completely suspect. To provide a kind of cognitive firewall (Cosmides and Tooby 2000), our inference system relies on the myriad of special representations of information that codes those things that are conjectures, possible truths, fantasies, and what other minds might know and how they may seek to influence us. These not only comprise the fabric of human inference, they are also domains of investigation of modern cognitive psychology. To understand human logical thought, we must also understand our system of knowledge and how it is able to represent the world as it is and as we imagine it to be.

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