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Language, Cognition and Cognitive Mastery. Logic and Reasoning. Logic is the science of thinking – although 2 people may think of the same thing but their conclusions may differ, one being logical and the other illogical.
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Logic and Reasoning • Logic is the science of thinking – although 2 people may think of the same thing but their conclusions may differ, one being logical and the other illogical. • Syllogism (Syllogistic reasoning) – a logical problem in which the goal is to determine the validity of a conclusion given 2/more premises (true conclusion); consists of 3 major steps (a major premises, a minor premises, a conclusion)
Logic and Reasoning Predicate (P) • Major premises All men are mortal. • Minor premises Socrates is a man. • Conclusion Therefore Socrates is mortal. • A conclusion reached by means of syllogistic reasoning is considered valid (true) if the premises are accurate and the form is correct. • The major premises links the predicate of the conclusion, P (mortal) with the middle term, M (man) • The minor premises links the subject of the conclusion, S (Socrates) with the middle term, M (man) • The conclusion links the subjects, S (Socrates) with the predicate of the conclusion, P (mortal) Middle Term (M) Subject (S)
Logic and Reasoning • Syllogism is a type of reasoning (logical technique) based on deductive reasoning. • Logic is a formal system (set of rules) deriving valid conclusions about events or things. • All Proton are Malaysian cars; All Malaysian cars are cheap; A Proton is cheap. • People are rational to the extent that they are capable of going beyond what is given in their direct sensory experience and memory. • Reasoning research focuses on how a person reaches and evaluates the validity of a conclusion from either explicit or implicit premises. The difference between the validity of a conclusion and its empirical truth is crucial as it has implications for the question of rationality.
Logic and Reasoning • Validity – whether a conclusion can be logically deduced from the premises and is independent of whether that conclusion is true of the real world, eg valid but not true deductive argument. • if the earth is flat, you eventually would sail off the end; The earth is flat; therefore, you would sail off the end if you traveled too far. • Correctly judging the validity of logical arguments requires that the form of the argument be separated from the content (the abstract process of reasoning should be independent of the particular prior experiences that you have had with the content of the problem)
Logic and Reasoning • Deductive reasoning – the rule system of formal logic, in which particular/ specific conclusion is drawn from a set of more general principles/ premises assumed to be true (drawing a logical. Specific conclusion from a set of general premises) • Besides syllogistic reasoning, conditional reasoning is also a deductive reasoning, conditional reasoning takes the form of “if-then” propositions. Eg • If I buy Emirates air ticket, then I will receive a free accommodation and Holland-Argentina football match ticket. In fact, “I buy the Emirates air ticket” by the rules of logic we can conclude that “therefore I will receive a free accommodation and Holland-Argentina football match ticket”.
Logic and Reasoning • Mary Henle – people do not always base their judgments on their attitude but, in fact, actually perform according to the rules of logic on some occasions. Attitudes, beliefs, and prior experiences sometimes assume priority over logic and affect our decision. • Inductive reasoning results in conclusions often expressed in probability statements (decisions are based on past experiences, and conclusions are based on what is perceived as the best choice of a number of possible alternatives). • Inductive reasoning corresponds more to everyday decision-making than does syllogistic or deductive reasoning (drawing probabilistic conclusion from a set of specific premises – lead to a decision about how to respond). Eg • I may noticed that it is a cloudy day and try to decide whether to take an umbrella when I leave. • Specific premise – “it is cloudy day” – leads to “some cloudy days in the past it has rained.” • Conclusion – “it may rain today” and decide to take umbrella.
Logic and Reasoning • The rules of logic doesn’t apply (cloudy day – will rain) – it is based on probability (on any given cloudy days, some probably that it will rain but on most occasion, no rain occurs) • Inductive reasoning is something that is likely to be true on the basis of past experience but not absolute.
Creativity • Creativity is cognitive activity resulting in a new/ novel perspective or way of viewing a problem/ situation and is not restricted to pragmatic outcomes. • In the absent of a dominant/ unified theory on the studies of creativity, one conceptual framework by Wallas – proposes 4 sequential stages/ phrases: • 1. preparation – formulating the problem and making initial attempts to solve it, eg based on biographs of famous people, even since early childhood, ideas were being developed, knowledge was being acquired and tentative thoughts in a specified direction were being tried out. These early ideas frequently shape the ultimate destiny of the creative people.
Creativity • 2. incubation – the period when no direct attempts to solve the problem are made and attention is diverted elsewhere (leaving the problem while considering other things). This period of interruption of the problem unconsciously as well as forgetting inappropriate/ old unsuccessful approaches to a problem. • 3. illumination – occurs when understanding is achieved (insight to the problem) • 4. verification – testing of the insight/ carrying out the solution.
Creativity • Sternberg and Lubart have developed a theory of creativity based on a multivariate approach which is built around 6 attributes: • Processes of intelligence; intellectual style; knowledge; personality; motivation; environmental context. • Assessing human creativity is not a simple matter of identifying the amount of each attribute but rather it is a matter of identifying and assessing the strengths of the interactions among attributes.
Creativity • J. P Guilford has distinguished 2 tyoes of thinking: • 1. convergent thinking: straightforward manner to a particular conclusion. Eg, what is the capital of Bulgaia? • 2. divergent thinking ability to generate many different answers to a question, the “correctness” of the answers being somewhat subjective. Eg, how many different things can you use a brick? • Hayes has suggested that creativity can be enhanced by: • 1. developing a knowledge base • 2. Creating the right atmosphere for creativity. Eg, brainstorming • 3. searching for analogies. Eg, considering similar problems you may have encountered.
Decision making • Amos Tversky suggests that in making decisions we select alternatives by gradually eliminating less attractive choices based on a sequential evaluation of the attributes/ aspect of the alternatives – this notion is known as elimination by aspects • Some of the failures in logical analysis when considering a decision: • A) the fallacy of reification – to reify an idea is to assume that it is real when, in fact, it may be hypothetical/ metaphoric. Eg, a student who was having difficulty completing a degree may assumed that the university acted as an individual would act.
Decision making • B) Ad hominem and personal argument – those that attack a person’s character rather than the substance of an argument. Eg, a candidate with well-reasoned ideas may be rebutted on the basis of his/her moral character or based on individual’s experience/ knowledge. • C) arguments that appeal to force and power – eg, the US was justified to attack Iraq because of its involvement with Al-Qaeda. • D) appeal to authority/ fame – eg, the use of movie starts to endorse products about which they have no special knowledge • E) the majority-must-be-right argument.
Decision making • Studies of decision making by Amos Tversky and Daniel Kahneman show that problematic solutions are influenced by: • Memory factors (the availability hypothesis) – sometimes the consideration of options are influenced by publicity/ option exposure. • Point of reference/decision frames (conception of the acts, outcomes and contingencies associated with a particular choice) that affect problem formulation Problem: an outbreak is expected to kill 600 people, 2 alternatives were proposed. 1 . If program A is adopted, 200 people will be saved (majority choice 72%) 2. If program B is adopted, there is a 1/3 probability that 600 will be saved and a 2/3 probability that no people will be saved (minority choice – 28%)
Decision making • Given the choice, the majority will select program A as the prospect of saving 200 lives is more attractive than the more risky alternative, although both save same number of lives (assuming more will be saved in program A) • If program C is adopted, there is a 1/3 probability that nobody will die and a 2/3 probability that 600 will die (majority choice – 78%) • Given the choice, majority will select program C as the certain death of 400 people is less acceptable than the 2-in-3 chance that 600 will die (assuming less will died in program C) • Choices involving gains are frequently seen as risk aversive whereas choices involving losses are perceived as risk taking.
Decision making • C) representativeness – failure to consider how similar an event is to its population, eg, is selecting 600 boys in a sample of 1000 children = selecting 60 boys in a sample of 100 children? Majority would report that both samples were equal, but in reality the 1st statistics is far less than the 2nd one. • D) underestimating the mathematical is significance of a possible event.
Problem-Solving • Problem solving is thought that is directed toward the solving of a specific problem that involves both the formation or responses and the selection among possible responses. • Gestalt Psychologists – perceptual events are not perceived as a series of individual elements but as a whole configuration made up of these events (organizational factors); thinking about a problem, or by examining it from different angles (how problems were viewed), the “correct” view can emerge in an moment of insight (new perception of the relations among the elements of a problem)
Problem-Solving • A fundamental aspect of the Gestalt approach was a distinction between productive thinking and reproductive thinking. • Productive thinking (structural understanding) – use of abstract thought processes in problem solving; relations between components of the problem that led to insights into the problem solution); yields general principles that would then transfer to future problems. • Reproductive thinking (rote memory – set of particular rules) – the use of particular prior experience in solving problem; not relevant to the Gestalt theories
Problem-Solving • Insight – the result of productive thinking that successfully arranged the parts of the problem in a new way and representing the solution to the problem; it is the key step in thinking that produces solutions to problem =illumination (understanding) • The concept of functional fixedness by Karl Duncker, held that there is a tendency to perceive things in terms of their familiar uses (function) and that tendency often makes it difficult to use them in an unfamiliar way (interference to problem-solving due to prior experience and habitual aspects). Eg, using a brick as a measuring device; thus, the objects/ideas become set in their functions; to use them as part of a problem-solving task, the subject must overcome that “set-effect” (persistence of an old way/ strategy, even in new situation)
Problem-Solving • In contrast, the information-processing approach – focused on the reproductive thinking (based on the tool of computer simulation in solving problem); efficient problem solving is a product of prior experience; led to Artificial Intelligence discipline. • Information-processing perspective – 3 characteristics of problem solving • Aspects of the task environment – the description of the problem as presented to subject and includes the information, assumptions and constraints given, as well as the context in which the problem is set.
Problem-Solving • Information-processing perspective – 3 characteristics of problem solving • Aspects of the task environment – the description of the problem as presented to the subject and includes the information, assumptions and constraints given, as well as the context in which the problem is set. • Mental representation of the problem as a problem space – various ideas/ hypotheses/ solutions that may be attempted to solve the problem; mental representation is a central feature of effective problem solving.
Problem-Solving • Information-processing perspective – 3 characteristics of problem solving • Aspects of the task environment – the description of the problem as presented to the subject and includes the information, assumptions and constraints given, as well as the context in which the problem is set. • Mental representation of the problem as a problem space – various ideas/ hypotheses/ solutions that may be attempted to solve the problem; mental representation is a central feature of effective problem solving. • Selection of an appropriate operator – sequence of operations that takes the problem solver from the initial state to the goal state.
Problem-Solving • One of the models of problem solving – production systems (a condition-action pair in the form of an IF_THEN_statement) • The conditions following IF specify some situations • The action following THEN describe something to do. • A collection of productions, all related to a class of problems (each production is an operator, as it moves toward the goal, conditions change, different productions come into play) • Theory applying production systems – ACT (Adaptive Control of Thought – John Anderson); efficient problem solving results from learning a cognitive skill (a matter of converting declarative knowledge into procedural knowledge) • The role of prior experience in problem solving – expert performance (excel n their own domain)
Problem-Solving • Mayer (1992) – 4 aspects of problem solving that distinguish the expert from the novice • Expert stores factual knowledge relevant to the problem in larger units (pattern of many pieces as one meaningful unit) and can access those units more quickly. • Expert is capable of relating a particular problem to general underlying concepts (semantic knowledge) • Expert performance is guided by superior schematic knowledge (ability to discriminate types of problems) • Expert develops a global strategy for solving the problem (strategic knowledge) but works forward by considering alternatives to the global strategy as progress is made toward the solution.
Problem-Solving • The way information is represented in solving problem seems to follow a well-ordered pattern and almost always unconscious. • Hayes suggested that the stereotypical sequence of problem solving are: • Identifying the problem • Representation of the problem • Planning the solution • Executing thee plan • Evaluating the plan • Evaluating the solution
