Divine Illumination and Revelation 

Section One




Part One

Chapter One 

Chapter Two

Chapter Three

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Knowledge is a product of the processes of thought, but there has been little understanding of the way in which the subjective mind achieves knowledge. The Western philosophical tradition has seen the processes of the mind to be logical, but this approach has always been fraught with problems and the Postmodernists have, on good grounds, denied its validity. Karl Popper has suggested that knowledge is produced by certain psychological processes. The understanding of these processes of the mind is fundamental to any theory of knowledge.

The nature of the human mind has been the subject of long-running philosophical disputes. Materialists see the mind as a state of matter. For them the "brain" and the "mind" are different ways of looking at the same entity. Rene Descartes is credited with the first statement, within the Western tradition, of the separate natures of mind and matter, and Karl Popper has more recently restated the theory.

In this epistemological project the investigation of the human mind is pursued independently of the brain. Compatibility with Cognitive Psychology is maintained by an approach based on the study of observable behaviour. This is supplemented by the study of experience. Experience gives the problems and behaviour represents the response. The mental actions that relate the problems and the behavioural solutions may be inferred, where inference is a problem solving activity. Speech is an observable behaviour and the individual's explanation of his understanding of particular experience and his reasons for selecting particular behaviours in response to the experience are valid and valuable evidences to support the inferences.

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Hume's Empirical Approach

Psychology and subjective epistemology have a common interest in the functioning of the human psyche. The interest of subjective epistemology is limited to the question of how knowledge is achieved. David Hume (1711-1776) proposed to investigate the nature of mental processes to discover how the intellect reached knowledge. This was to be carried out using the experimental method employed so successfully in physics by Isaac Newton. The study would result in a "science of man" which would be the only solid foundation for all other sciences. Hume's own investigation of mental entities and processes has been heavily criticised and is now discredited. Hume's programme is taken up, with the substitution of scientific methodology for Hume's method of reasoning. Hume's epistemological project, as amended, is a scientific investigation of how experience is processed within the human intellect to produce knowledge. The investigation of the human mind is broken down into more basic studies concerned with how the problems of experience are reduced to knowledge, how this knowledge is retained, more or less permanently, by the individual, and how retained knowledge is deployed to deal with the reality of experience. These questions are discussed in the three parts of this section. The results of the studies provide the foundation for a scientific theory of epistemology.

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Thinking is Problem Solving Behaviour

Mental behaviour is usually called thinking. Thinking is often associated by psychologists with problem solving. In successful thinking the individual moves from the awareness of a problem to the achievement of the solution. Problems occur in the experience of the individual. The form for problem solving is given by:- 


The solution determines the mental and physical behaviours of the individual with regard to the problem. Mental and physical behaviours are parts of the same behavioural program. 

The form is:- 


Further experience tells the individual if those behaviours were successful and therefore appropriate. Inappropriate and unsuccessful behaviours bring the validity of the thinking process into question.

To successfully manipulate reality to achieve specific ends the behaviours must be correct. To achieve correct behaviours the individual must understand reality through the careful observation and analysis of experience. The thinking process that leads to the solution must be based on a valid problem solving method that takes all relevant experience into consideration. The correct solution to the problem of experience is called knowledge. 

The form is then:- 


Knowledge is therefore the consequence of the correct execution of the problem solving method applied to the problems of experience.


Experience and Knowledge of Reality 

Part One


The study of subjective knowledge is concerned with how individuals gain knowledge. Human beings come into the world understanding almost nothing and yet within a short period of time every child has acquired some understanding of its environment and by the end of its life may be very knowledgeable indeed. The process by which the intellect develops is based on experience. The world of experience exhibits order and this order may be learned through observation. Everyday living and experiencing in the world leads to understanding.

The worlds of the Inuit, the Somali herdsman, the Polynesian fisherman, and the New Yorker, all seem so radically different that their experiences may appear to have little in common. However, the basic experiences of human beings do not differ. All human beings learn the rudiments of space and time, they learn how to analyse their environments, and to use a general purpose language to communicate information about their world. They learn to recognise people, human relationships and the conventions of social behaviour. They learn the explanations given by their cultures for the existence of people in the world, and the history of their own group which gives them their identity. The technology of the modern world is a superstructure built upon this basic set of experiences.

The unit of experience is the problem. New experience is not understood simply by observation but occupies that intermediate area between the known and the unknown. It is recognised intellectually as new experience but has not been assimilated into the class of experiences which are understood. It therefore constitutes a problem to the individual intellect. The problems of experience beset human beings throughout their lives. The living of each day brings its quota of new problems. The solving of problems has the benefit that the individual gains solutions in the form of understandings. Knowledge is the true understanding of the problem of experience, and the behaviour, both mental and physical, that follows from knowledge is that most likely to achieve the objectives of the individual.


Experience and Knowledge of Reality 

The Problems of Experience

Chapter One


The point of departure is Aquinas's argument that knowledge starts with experience. St.Thomas took the senses and sense impressions to be the starting point for knowledge. From the point of view of the conscious intellect there is no awareness of sensory data or of any category of events of experience such that those data or events can be distinguished from understanding. St.Thomas recognised that raw sense data was not the stuff of thought and proposed a psychological process whereby sense data became understandable in itself and then intelligible to the intellect as a part of the understanding of reality.

The conscious intellect can deal only with understandings and experience of reality always takes the form of understanding within the intellect. Individuals either understand the events of experience or they understand that they have a problem of understanding an experience in a way that would allow them respond with correct behaviours, both mental and physical. The set of understandings may therefore be divided into two subsets which are:- 

1. understandings of the existence of problems of experience, and 

2. understandings of solutions to problems of experience.

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The Classes of Experience

Human experience covers all sensory, aesthetic, feeling, emotional, intellectual, moral and spiritual events which appear to intellects. Perceptions of the physical world appear to the intellect as understandings related to its model of physical reality. Physical feelings represent emotional reactions to perceived physical events and are intellectual rather than physical in origin. Emotions such as love, happiness, fear, and depression may be triggered by external events but their expression lies in the spiritual nucleus of the human entity. All these forms of experience appear as intellectual experience. Individuals understand that they are experiencing physical, emotional, and spiritual events but their real experience is one of understanding. Pain, as an experience, is non-existent to the unconscious intellect since it is not understood. It is meaningful only to the conscious understanding.

Analysis of experience in the intellect reveals differences which allow classification. Experience may be arranged into five classes:- 

1. Physical experience is the earliest and commonest form met with by the human intellect. 

2. Cultural experience in the forms of social training and education are part of a child's upbringing and the culture forms the medium for human interaction. 

3. Moral experience, in the forms of behavioural training and the learning of respect for others, is also an early factor in intellectual development. Morality is a first consideration in dealings with other people. 

4. Religious or spiritual experience is met with in childhood but its depth and quality are the result of study in later years. 

5. Intellectual or ideal experience is superficial in most intellects, and is mainly the province of philosophers, psychologists, and theologians. The world of ideas may be seen as one of the components of the understanding of human nature.

Events of experience may have multiple subunderstandings within the intellect. The visual experience of a victim of murder may give rise to a simple biological understanding that a life process has ceased due to a certain cause. Seen against a normative model of individual human life it may be understood as a premature and unnecessary termination of a valuable life process. Viewed from a model of social order it may be understood as a contravention of law. Looked at as a reconstruction of the events of the termination of the life it may give rise to emotional reactions of horror, outrage, and anger. Seen as an event affecting family and friends it may be understood as a permanent loss and a matter for grief and sorrow. Upon moral reflection it may be seen as an evil. All experiences are not understood in the same ways by all individuals.

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Reality as the Source of Experience

The human individual has only a set of experiences to work with. Treating these experiences as problems he arrives at the solutions to those problems which are understandings of the experiences. Reality is the explanation for the origin of experience. Since he has experiences of physical, intellectual, spiritual, moral, and social events, he may come, through the problem solving method, into understandings of the realities which gave rise to those experiences. Reality is therefore more than the physical environment.

The cultural subreality is explained as the set of objective knowledge, both formal and informal, and theoretical and applied, resulting from the solutions of problems common to all members of a group. Ideal reality is the reality of the rationalist tradition, as described by Rene Descartes. There are few responsible individuals who would deny the fact of morality. Moral experience is a consequence of living a life and moral considerations are primary in all behavioural decision making. The moral universe has been recognised from antiquity and Confucius defined his understanding of it several hundred years before the beginning of the Christian era. Moral experience translates to moral knowledge when processed by normal problem solving methods. Religion recognises and explains the supernatural reality and the relationship of humanity to this reality.

Scientific epistemological theory sees five subdivisions of reality, adding to the physical subreality, the universe of intellects and thought, the human created reality which is the culture, the moral universe, and religious reality. Each of these subrealities, or natural environments, is valid in that true knowledge of them can be obtained by the correct application of the methods of knowledge.

These five subrealities account for the totality of human experience. They form parts of a more fundamental reality which links the universe of experience with the ultimate or supernatural. Knowledge is the correct understanding of any part of the five subdivisions of reality, and of the total or fundamental reality.

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Experience and Knowledge of Reality

The Problems of Experience

Chapter Two


Cultures as Sets of Problem Solutions

The relationship between experience, problems, the culture and the set of intellects is given by the thesis is that experience gives rise to problems, and the set of solutions to the problems of experience is what is called the culture. The label of culture may be applied both to the problem solutions of the group and to those of individuals. Here the word "intellect" is used to refer to the set of individual solutions, reserving the word "culture" to its group meaning.

Problems have their origin in the human situation of living as a group on a small planet in a three-dimensional universe. Some problems are common to mankind; others to groups in particular geographical regions. The problems that are common to the group give rise to common purposes and objectives, and from there to common solutions. These solutions constitute group understandings and the set of common solutions forms the culture.

The culture, in the form of particular solutions to particular problems, is taught to the young as the subject matter of education. The cultural solutions to problems, in the forms of objective knowledge and paradigms of behaviour, give the student intellect greater understanding of reality and enhanced power to achieve purposes.

Not all group problems have ready-made solutions. Those cultural problems which have not been solved as yet, or not solved satisfactorily, must be solved at the level of the individual intellect. These problems are reduced to understanding by the use of a valid problem solving procedure and may later be incorporated into the set of objective knowledge.

For any intellect experience may be direct or interpreted through cultural conventions. Conventionally interpreted experience is filtered by education within a culture and is subject to conventional problem understandings and solutions. While the individual is free to reject cultural interpretations of experience and cultural solutions to the problems of experience there must be some significant motivation to do so. Commonly such interpretations are rejected on the grounds of alleged immorality.

There is a class of problems which are peculiar to people as individuals. They have no group equivalent and therefore no culturally normal solution. These subjective problems are also solved using a valid problem solving method, and the solutions are annexed to the intellect as subjective knowledge.

Personal experience is of two sorts. The first sort includes all those events of experience which the individual has met before, and which therefore he understands and can respond to with appropriate mental and physical behavioural sequences. The second includes all those events of experience which are new to the individual and therefore constitute problems. These problems are to be solved and thereby understood, and then to be responded to behaviourally in an appropriate way. The intellect in dealing with problems of experience achieves new and enhanced understandings.

People approach experience purposefully, seeing the events of experience as relevant or irrelevant to their objectives. The behaviours that are expressed in response to purpose-relevant experience have the aim of furthering those objectives. The variety of human purposes falls under one of two headings which are survival and self-fulfilment. The problems selected by the individual for solution are real problems. Real problems are those which bar the progress of the individual intellect towards the achievement of its purposes, and which the solution, as intellectual and physical behaviour, will overcome. While experience follows the observation of reality, problems of experience are a feature of cultures, both of the individual and the group, and not of reality itself. A problem arises only when the correct understanding and behaviours for dealing with reality are unknown.

Problems of experience fall into the categories given by the natural environments. A group culture or individual intellect, which has no purposes that fall within a given environment, cannot have a real problem within that segment of reality. A primitive culture has problems of survival and its primary environment is the physical. Its interest in other divisions of reality is minimal. A rational culture has problems of truth and morality and must extend its interest into the ideal and moral environments.

At the subjective level the individual may or may not have understandings within every category of reality. Where there is understanding within a category there will also be a philosophy. The philosophy may see something of interest and significance within the category and the intellect may evolve a purpose, for example, to find out more. Conversely, the category may be viewed by the philosophy as non-significant and the individual may seek to promote this view as a purpose. For example, morality or religion may be little understood by an individual who may have no interest in those categories. He may reject any claims with regard to them and this behaviour is consistent with his experience and understanding, although it will be contradicted by those with knowledge in these categories.

Although problems may be commonly regarded as undesirable, intellectual problems are, by and large, beneficial. Problems are the means of intellectual development. The intellect reacts to the problems posed by experience which are the indicators of inadequacy of understanding. Understanding develops by the solution of problems which cease to exist when the intellect extends itself to include their solutions. The growth of individual intellects therefore proceeds from problems and the successful projects to solve them.

An obvious value of problems lies in cases of error of understanding. It is the sign of errors of understanding that anomalies will arise in consequence of attempts to act according to those understandings. Anomalies fall outside normal understanding and constitute problems. They are therefore the safeguard against the persistence of human error. The presence of problems of ignorance and error motivate changes in the understanding through creative problem-solving. As the understanding changes, so the appearance of reality and the quality of experience change.

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Problems are Violations of Models of Reality

The individual analyses his experience and makes distinctions. These are related logically into a model of the segment of reality that he is observing. Where David Hume saw only "bundles of impressions" there are in fact logically structured models of reality. The individual may describe aspects of reality when not actually observing them by referring to his internal models.

The model of reality describes a natural subset of the field of experience in such a way that rules may be derived. These rules are predictive, and the ability to predict, to some extent, the processes of reality constitutes, in part, the individual's understanding of it. The operation of the individual intellect in any segment of the field of experience is based on what his model tells him, and the rules that govern its operation. Models enable the individual to interface with his environment in a way that permits him to influence that environment in the direction of his objectives. The extension of this is that the individual bases all behaviour on what his model of reality tells him is the case. It follows that if the model of reality is inadequate or wrong the consequences of behaviours based upon it are unlikely to be successful. The successful achievement of human objectives requires the detailed and accurate modelling of the set of environments.

All trained people have mental models and behavioural procedures which support their work, and they view their problems in the light of the understandings given by these models. For example, a physician in making a diagnosis, will call to mind mental models of the human body, and of its parts and systems, and models of the malfunctions to which the body is liable. The problem is first defined by the symptoms described by the patient. The doctor endeavours to match the symptoms with the known symptoms of the various ailments, as given by the models. Where possible matches are found behavioural routines are operated to test for other confirmatory symptoms. The use of stethoscopes is a behaviour long associated with doctors. This is the problem investigation stage, which may proceed through a set of tests to eliminate all but the real cause. The model of the real problem, as learned in medical training, specifies those behaviours available to the physician to assist in the cure of his patient.

Problems are recognised as such because they violate the expectations of the intellect. The understanding either allows an event of experience as a normal type requiring a selection from a predetermined range of behaviours, both mental and physical, or it disallows the event as non-processable intellectually. The inbuilt model of reality is then incapable of predicting the origins and consequences of the event of experience. The nature of the problem is determined by the individual's subjective philosophical understanding, and constitutes a puzzle or counter-instance to the model of reality on which that philosophical understanding is based. The recognition of problems is related to the degree of sophistication of the model of reality. The more advanced intellect sees a greater variety of problems of greater complexity.

When models of reality fail there is a need for judgment regarding the nature of the cause. The model is in some way inadequate to its purpose. The problem may be minor and may be overcome by a modification of the model. On the other hand, a major change may have occurred in the environment making the model of reality and the understanding that explains it, obsolete. If problems must be solved, the individual's understanding of what constitutes a problem solving process must be invoked and applied.

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The Understanding is formed by Problem solving

All knowledge disciplines are dependent for new knowledge on advances in subjective knowledge. All theorists and research workers are faced with problems in their work, and they must solve these problems correctly. This is true whether the knowledge worker is a philosopher, theologian, or scientist. The problems are recognised as such in light of the models of the field of knowledge. A worker with no models of the field of study is not qualified to engage in knowledge development. For example, a linguist working on the problems of language, will have, as a minimum, models of the structures and application rules for one or more general purpose languages. In addition, he will have models of the various problems under investigation. Typically, if the problem is how languages are learned, the investigator will have a number of case studies, each modelling a particular state of affairs in the field of language-learning. The task is then to reduce the study models to one general model which explains the problem. This is achieved through the application of a problem solving method.

Problems are solved every day by everybody. Most problem solving is intuitive and informal but this does not prevent successful solutions. In important and complex matters the individual will attempt to structure the problem as best he can, as a basis for rational working. Problem investigation and analysis involves behaviour aimed at the better understanding of the problem as the precursor to problem solution and the determination of the best course of action. Better understanding follows from a more detailed model of the problem.

The areas where the problem of formal problem solving can be studied are science and technology, education and business. A survey of these areas will show that failures to reach correct solutions may be ascribed to errors like not understanding the reality in which the problem reveals itself, trying to solve the wrong problem, trying to solve a problem that was not properly understood, making assumptions which are not valid, and failing to test intermediate conclusions as well as end solutions. For example, a failure to understand the realities of the stock market may be the cause of financial losses which are seen as a problem. Ignorance of true reality implies that problem solving is carried out in a universe of illusions and the resulting "solutions" will have unpredictable consequences in the real world. A valid problem solving method will require procedures that will effectively prevent these errors. A valid problem solving method gives true solutions to real problems.

There is a problem solving method which, if carefully applied, will always give true solutions to the problems of the intellect. This method is based on the investigation of the problem, the achievement of problem understanding, and the requisitioning of the solution. The process of development of understanding commences with the real problems of the field of study and ends with the production of the solution in the form of an understanding, the formula being:- 


A complete and correct understanding of the problem is necessary to correct problem solving. This is achieved by careful execution of the problem solving method. The solution of problems involves a learning process in which the investigator's understanding of the problem is continually widened and deepened. New ideas emerge in the individual intellect as a result of the probing of the problem, and the consideration of the experiences that follow. Problem-Solution theory shows how a problem is structured and carried to a solution, which is new understanding. The omission of any stage of the problem investigation reduces the problem solver's ability to understand the problem. If all the stages are omitted the problem-solver can only resort to that pseudo problem-solving process usually associated with armchair philosophy, opinion and other forms of non-factual speculation.

The result of the problem solving process is both an understanding of the problem solution and a new or modified model of reality. Better understandings are achieved through better models and the continual need to improve understanding results in increasing depth of environmental modelling. Models are subject to continual improvement in interaction with the flow of experience. Problems lie outside the horizon of understanding given by the existing set of models of reality and the aim of the intellect is to solve them and to assimilate their solutions into an existing more general model, or failing that, to include the new problem solution as an addition to the set or library of particular understandings. The set of understandings available to the intellect develops in range and power with each correct solution to problems of experience.

The problem solving method is also the self-programming method and produces those procedures which are executed as intellectual and physical behaviour. These procedures form behavioural programs which are based on models of reality. The solution to a real problem, based on a model of reality and amounting to an executable procedure or program, is called an understanding. As an understanding it is annexed to the database of understandings which is the intellect.

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Experience and Knowledge of Reality

The Problems of Experience

Chapter Three


The intellect solves problems and, in thereby gaining knowledge, extends its power to deal with experience. There is a valid method for the solving of problems, which, if it is applied rigorously, will result in the development of knowledge. The problems of objective knowledge are solved at the subjective level and the problem solving method discussed here is applicable to both subjective and objective problem solving.

Problems should be distinguished from puzzles, as defined by Thomas Kuhn. The general solution model for a puzzle is already known. For example, the multiplication of 9975 x 93 is a puzzle for most individuals since they already know how to solve it. However, the multiplication would constitute a problem for an individual who has not learned a multiplication method. Education allows the individual to move directly from the understanding of the problem to the understanding of the solution, but the problem must always be understood first. All knowledge is produced, in the first instance, by the problem solving method.

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The Solving of Problems

The method for solving problems consists of a number of stages which are:- 


* Problem Determination: 

      Problem detection 

      Problem identification 


* Problem Understanding: 

      Problem investigation 

      Problem analysis 

      Problem definition 


* Solution Formation: 

      Solution specification 

      Solution creation 

      Solution recognition

In the real world the individual is rarely conscious of passing through specific stages of problem solving. However, no rational individual would consider himself as being in a position to attempt a solution without first being assured that his understanding of the problem was correct and complete. Each stage of the problem solving method is necessary to the full understanding of the problem.

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The Stages of the Problem-solving Method

Problem detection

At some point an individual becomes aware of the possible existence of a problem. Generally some understanding is being violated. The awareness that a problem may exist may start simply as a feeling that something is wrong. Scanning of the events of experience may detect signals indicating problems. For example a bank employee may notice unusual customer credit card account activity. This may be perfectly legitimate but enquiries would need to be made to ensure that the credit card was not being misused. The outcome of the problem detection stage is confirmation that a problem exists.

Problem Identification

The awareness of the existence of a possible problem or problems does not necessarily include the ability to isolate the correct problem. The right problem needs to be identified. A prerequisite for identifying problems is a model or understanding of the overall situation in which the problem can reveal itself. A problem is only a problem when it runs counter to our expectations as given in our model of reality. Without such a model it is impossible to recognise the occurrence or nature of a problem. At the subjective level the model is supplied by the intellect. The intellect either understands the event of experience or it does not. Where failure to understand occurs a problem exists.

For example, the awareness that a patient has a high temperature does not identify the problem, but is only a symptom or signal of the problem. Two understandings are necessary here; the first to recognise the symptom as indicating a possible problem, and the second to tie the symptom to its cause. The first understanding is a common one; the second may require medical training. Medical knowledge supplies models of reality from which a diagnosis may be possible. Even for trained people identifying the real problem may require an investigation. The first attempts to identify the problem may all be wrong. Even the final identification of the problem may be incorrect. People are often aware of problems without being able to say exactly what the problem is, and a problem may stand unidentified indefinitely.

It is a form of error to treat a symptom of a problem as the real problem. In a business situation treating falling sales volumes, or rising production costs as problems may fail to get to an effective solution if the real problem is obsolescent products or out-of-date production facilities. Problem situations may be over-determined; this is to say, there is more than one factor or problem causing the problem situation. Solving only one of a set of contributory problems, if that is possible, rarely produces a valid or satisfactory solution.

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The Process of Understanding the Problem

Once the problem has been correctly identified the next stage is to understand it. This involves the stages of investigation, analysis, and definition.

Problem Investigation

The task of understanding the problem involves finding out everything about the problem that is relevant to its appearance in experience. The investigation of problems involves a learning process in which the investigator's understanding of the problem is continually expanded and deepened.

The nature of the problem determines the investigation methods. In general, the scientific approach which involves breaking the problem down into manageable units is usually fruitful, providing the problem can later be reconstituted through a method of integration. For example, an investigation of an ailing commercial undertaking may be broken down into investigations of the various departments of the company, all of which may show symptoms of problems. An attempt to solve the many departmental problems would be the wrong approach if the true problem is the bad management of the enterprise as a whole.

Problem Analysis

The factors that have a bearing on the problem must be understood in a way relevant to the purpose and objectives being pursued so that a valid structured problem definition may be formed in the understanding. The problem analysis results from insights formed during the investigation, although not necessarily prompted by any particular part of the investigation. It is aided by previous experience in dealing with similar problems. The problem structure may be logical, mathematical, or both. This model explains the occurrence of the problem in experience. For example, a mechanical problem may be traced to metal fatigue. The problem analysis shows how this fatigue occurs after a period of use.

Problem Definition

In the problem definition the problem solver sets out his understanding of the problem based on his problem model, and supported by the evidences obtained in the problem investigation. If this definition is correct the problem is now completely understood. The writing of the problem definition has the twin advantages of improving the precision of the problem solver's understanding, and improving the accuracy of the problem definition through the opportunity it gives for criticism.

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The Solution Stage

In the solution stage the problem understanding is replaced by the solution understanding. The descriptions of the entities and processes involved in the problem situation have been produced by the problem investigation and definition phase. The problem is understood in terms of the old understanding of reality, but cannot be assimilated into that model. This follows from the definition of a problem. The requirement now is to understand them in a way that overcomes the problem. A new model of reality is therefore required to explain both the old understanding and the problem. This understanding is supplied by the solution.

Solution Specification

From the problem definition the problem-solver moves to a position of forming an understanding of what would count as a solution to the problem. The problem definition is a statement of fact and the solution specification is a question based on that statement. The solution specification sets out that which one wants to know, and is the bridge between the understanding of the problem and the solution. It establishes the criteria by which the solution is evaluated. Without the solution specification it is impossible to say if the solution answers the problem.

The meanings of the problem definition and the solution specification, as stages in the solution of a problem, are determined solely by the problem-solver's intellect. The solution specification is formed by the individual in furthering his purposes and constitutes a definition of an objective which is the achievement of the solution. The solution specification therefore imports the philosophy of the individual into the problem solving process. Different philosophies, based on opinions and ideologies, will interpret the same problem definition in different ways and will ask different questions. The problem of social poverty can be well-defined by researchers and generally agreed, but the solution specification and solution may be very different for different individuals.

As the intellect is commonly inadequate, and to some degree confused and erroneous, the interpretation of the specification may be less than perfect. For example, all solution specifications in which the nature of Time is of the essence are not likely to be absolutely correct. The nature of Time is one of the least understood areas of physics. Solution specifications which employ the term "God", where that term has a substantial meaning within the intellect, are likely to result in an answer, all other things being equal. Where no meaning of any worth can be attached to the term within the intellect, the solution, if there is one, is likely to be confusing and even erroneous. The individual has to know what he is talking about. Given that the solution specification is valid a solution will be returned.

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The Relationship of Solution Specification to Solution

A specification is not a definition. The solution specification describes the conditions that the new understanding must satisfy. It may be compared to a specification of a new house which is no more that a page of requirements, where the definition is the set of plans produced by an architect. The relationship between the meaning of the specification and the meaning of the solution is exact in the same way that an arithmetic equation is exact. The solution is precisely limited by the specification. On the other hand, a carefully considered solution specification may be almost open-ended in its knowledge requirements and may produce a solution which exceeds the boundaries of the problem. A solution specification which grossly exceeds the problem definition may produce a solution which cannot be tied back to the reality of known problems of experience, and being untestable against a known problem, may have an unknown truth status.

If the solution specification is badly drawn up so that it cannot be reduced to a valid meaning or understanding, no solution will follow. This is often the explanation for prolonged struggles to solve particular problems. As an example, the solution specification might require a solution to a problem of subnuclear physics, in terms of Newtonian mechanical concepts. The requirement could not be met and the result is that the transformation of the solution specification to a solution is aborted without a result. Generally failures to reach solutions are either the consequence of inadequate understandings of elements of the problem, or the insistence of the researcher that the solution must conform to some existing theory or ideological understanding when that is impossible.

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The Emergence of the Solution

The solutions to problems are found within the intellect at some time subsequent to the process of problem solving. The appearance of a solution is an event of experience and is followed by the understanding of that solution. The act of understanding the solution happens when an individual says, "now I understand". The "I" grasps and assents to the new understanding. The understanding is annexed as an improvement to, or extension of, the intellect.

Problems may be particular or general, and solutions are likewise specific or generic. General solutions may be in the form of prototypes. An arithmetic problem requires a specific solution. The law governing the behaviour of bodies subjected to gravitational force is a prototypical solution in which certain variables are unknown. For the solution to be useful it must be related to a specific problem of a real body existing in physical reality by a set of informational data.

All class constructions are prototypical and are made specific by information. The term "body" may be applied to wide variety of objects. Prototypes may be related to virtual realities. A reality in which there are no impressing forces is virtual, and represents a rational construction for a purpose. An unspecified body free of impressed forces is a prototype existing in a virtual reality.

A representative problem taken together with a protypical solution is a model solution and amounts to a paradigm in Kuhnian terminology. Paradigms are not separated from real world states of affairs. As described by Kuhn, scientists articulate paradigms into other problem areas by abstracting the paradigm's prototypical model and reapplying it to the new problem.

Prototypical solutions give the intellect the power to solve a range of problems. The problem solving method defined above is, itself, a prototypical solution.

The new solution or understanding, being new, is different from any understanding already incorporated into the problem understanding or solution specification. The new solution imports a new model of reality into the intellect. Where the new model replaces an older one the difference may be described in Kuhnian terms as a transformation of reality, where such transformations may be minor as well as major. The model of reality which was the basis of the problem understanding has changed in a manner that the problem no longer exists in its original form. The intellect which has annexed the new understanding may think of the problem area in an altogether different way.

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The Expert Understanding

Once the problem solution method has been operated the problem-solver may then understand the general problem area or field of study. He may then ask supplementary questions, based on his understanding of the field. There may be no need to research the problem field over again even when new problems arise.

The formula then becomes 


where each new solution broadens and deepens the understanding of the expert in that field. For example, a problem in the field of Economics may be new but its origins and probable consequences may be determined from an existing understanding of the field. The expert may correctly describe it and prescribe relevant and probably effective behaviours to deal with it without further empirical study. The problem in this case is, in Kuhnian terms, a puzzle, for which a prototypical solution or paradigm already exists in the intellect of the problem solver.

Specialists in any field who find they can arrive at solutions to problems without the necessity of applying any formal problem solving method may tend to think that they do not use a method, and that, therefore, methods are unnecessary. An attempt to solve a problem in an unfamiliar field would quickly prove the necessity of method.

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Intuitive Problem solving

The stages of problem solving do not require consciously formal execution. Problems may be solved at the intuitive level by passing through the same stages as above. These stages may be seen as puzzlement, problem recognition, growth of problem understanding, questioning, and then solution. Intuitive problem solving is a common human activity applied to the myriad of problems that human beings overcome in the course of their lives. It is the method of problem solving used by infants in the first stages of building their intellects and it is simple and easy to apply. But problems which are correctly solved are always solved by the methodology defined above, whether formal or intuitive.

Complex problems may be solved either intuitively or formally, but generally the more complex the problem the more the formal method is likely to be successful compared with the intuitive. The solutions to the problems of objective knowledge have to face criticism and a record of the progression from problem identification through to solution is valuable evidence of truth. Problems in the field of knowledge should always be solved formally.

The problem solving method given above is the only road to new knowledge. This has always been the case for human knowledge and yet there is ample evidence of error and confusion in intellects and in the culture. The explanation is that the method has either been ignored or carelessly or cynically applied. The result is the generation of opinions and ideologies which masquerade as knowledge.

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The Problem Solving Method and the Scientific Method

Objective knowledge is a development of subjective knowledge. In a situation where there are competing candidates for the status of objective knowledge some procedure must exist to determine the best theory. This procedure is science. Science lays down conditions that must be satisfied by all acceptable candidates for objective knowledge status. There is a relationship between the general problem solving method and the scientific method such that the latter is a more rigorously enforced case of the general method. Science is, therefore, the objective equivalent of the subjective way of reaching knowledge.

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The Source of Problem Solutions

The problem definition and solution specification are transformed by the problem solving method into the new understanding or solution. The new solution is found in the intellect at some time subsequent to the attempt to solve the problem. The description of the psychological process in which the new understanding is created, in response to its requisition in the form of the solution specification, is given in the next section.