CONCEPT PARAMETERS

by F. Richard Singer III Edition date: 7/2010

Website conceptualstudy.org Email: mailto:richardsinger3@sbcglobal.net

Note: Papers referenced only by title can be found on the above website.

Abstract: This is a conceptual paper written from the perspective of Descriptive Psychology, altho without presupposing its concepts. The focus is on the role that a concept may have in a person’s world, with special emphasis on ways to think about a person’s mastery of a concept. The role a concept has in a person’s world is conceptualized as complex personal state of affairs, using five parameters for thinking about its various features. Moreover these parameters are used to indicate ways in which a person’s concept may be a variant of a public concept, i.e. a concept as used in some community. The paper begins with some conceptual remarks. Having a concept is conceptualized as form of behavioral competence that involves at least a minimal ability to act on some distinction that the concept entails. This is the related to having the concept of a concept. It then introduces the parameters, followed by comments illustrating each of them. These parameters are used to consider a person’s mastery of a concept and a person’s understanding of a concept, where understanding a concept is conceptualized as an aspect of concept mastery. Rather than thinking of the mastery of a concept as a matter of degree, parameters give a diverse qualitative perspective. A distinction is drawn between what are called type concepts and specific concepts, and some relationships between them are considered. Finally most of these parameters are illustrated and discussed in detail. The parameters selected here merely provide one of many ways that could be used to describe the mastery and understanding of a concept by some person and the role they play in that person’s world.

Conceptual Nets: Concepts are acquired by using them, and it is important to stress that this involves using them in the context of a network that includes various conceptual distinctions and relationships. The term ‘net’ denotes such a conceptual network. A net can be used to think and communicate about various matters in some realm of interest. This includes organizing or obtaining information, proposing conjectures, suggesting questions, etc. Such use will be called paraceptual. Thus, saying Ann is Meg’s younger sister is an ordinary paraceptual use of the sister concept. Conceptual use is independent of any state of affairs in a realm of application. For instance, saying that full biological sisters have the same parents is a conceptual remark about the relationship between concepts used in our public net for family relationships. A net will be regarded as a kind of complex concept. For instance, chess can be regarded as a complex concept that includes a network of concepts relating to the game of chess. It is this concept that we are referring to when we say that a person understands chess.

Conceptual Papers: We can acquire concepts and knowledge of their relationships even if our sole use of them is paraceptual. This often involves interacting with others who are competent in using them. In fact, this the way most children acquire their concept of a sister and often of the conceptual relationship between being sisters and having the same parents. On the other hand, the concept of a first cousin twice removed is less likely to be acquired solely by paraceptual use. A direct focus on a concept, even if not necessary, is more efficient and is more likely to bring it into sharper focus. This is the purpose of a conceptual paper. The remark below is a modification of one given by Tony Putman in his preface to Place (Ossorio 1998). It indicates a major reason that a conceptual paper or other form of purely conceptual use of a concept makes a difference. Some specific difference this present conceptual paper could make will be indicated later.

Formulating concepts in a net encapsulates our understanding of how we use its concepts, which we already understand but might not know we understand - and “knowing that we understand” makes a significant difference, both in understanding the net and in using it.

Terminology: For the most part, concepts do not exist independently, but rather support each other within some net. Altho we could think of concepts individual building blocks, they are more like nodes for interwoven relational strands that are not supported by some base. This is why the word net was chosen instead of a word like system or structure. It is suggestive of the flexible nature of conceptual relationships. However the visual connotations of ‘net’ should not be taken too literally. In particular a conceptual net is multi-dimensional, and it nodes may be fairly complex dynamic nets or structures in their own right. The connotation as used in ‘Internet’ is more appropriate than that of a physical net.

Concept Potential: Many concepts are flexible in the sense that they indicate similar but different distinctions in different contexts. Consider the concept indicated by ‘somewhat less than’. I might say that the distance from my house to the library is somewhat less than two miles. I might also say that the distance between the earth and the moon is somewhat less than a quarter of a million miles. In the first case ‘somewhat less’ than refers to some unspecified distance that is a small compared to a mile. This is clearly not intended in the second case. We could regard the locution ‘somewhat less than’ as indicating different concepts in different contexts. However the essential core is the same in these two case and the distances involved are of minor significance in comparison to this core. Thus I chose to regard the ‘somewhat less than’ concept as a single flexible concept potential. The specific concepts that this potential yields are also less precise than a ‘less than but within a range of 10%’ concept. However they need not be as precise to serve many ordinary purposes. In fact, the lack of precision is what makes them more useful for many such purposes, as it can take more effort to check a precise claim than a more open-ended one.

Having a Concept: Altho concepts may seem to be dependent on language, perhaps this is largely due to the way we discuss-analyze-formulate them. This is not how a human usually acquires concepts. They are mainly acquired thru use rather than discussion and analysis, and we recognize that a person has a concept when that person can act on a distinction that the concept entails in at least one of the ways in which it makes sense to act. For instance, at age 1½ Ellie picked up a book, took it to Angela, crawled up on her lap, and looked expectantly. This was followed by her attentive expression as Angela began reading to her. Saying that Ellie had some concept of a book not only seems reasonable, no other account of her actions would seem even somewhat plausible to most of us. She could even have had the concept of a book without knowing what it is called. On the other hand, had she called it a book, but showed no inclination to treat it as one, we would have been justified in doubting that she had this concept. A short time later, she repeated this pattern of behavior with another book, indicating that her concept of a book is a type concept rather than being limited to a single item. Moreover it was more a functional concept than a physical one. She recognized books by physical appearance, but her book concept involved how it functions to enhance her world.

The Concept of a Concept: Having the concept of a concept is also something we recognize from behavior, namely when a person can act in one of the ways in which it makes sense to act on the concept of a concept. The act of reading a conceptual paper is one such way. At a more basic level, the main way it makes sense to act on the concept of a concept is to think about making or being able to make distinctions. These are often linguistic ways of acting. In fact, Ossorio (2006b, p124) indicates that he thinks that the ability to verbalize that one is making a distinction is tantamount to having the concept of a concept.

Without language, I can distinguish the red triangle from the blue square, but I can’t know that is what I am doing. I can’t know that what I am distinguishing is the red triangle from the blue square, and I also can’t know that what I’m doing is distinguishing something from something.

Altho there are other perspectives, I conceptualize a concept is as a type of tool, namely as a cognitive tool that a person can use for in relation to some realm of interest. I will suppose readers have some concept of a concept that is compatible with this, altho this is something they may seldom consider.

Note: For more about this concept of a concept, see the appendix.

Variants of a Concept: Altho it is often reasonable to talk as if a person either has or does not have a concept this is an oversimplification. Different people will often have different variants of a concept, but these may be similar enough to think of them as variants of a public concept as used in some community. In this paper, the terms ‘our culture’ and ‘our concepts’ will refer to American culture and concepts as used by the general public in this culture, altho examples of concepts from any other communities could have been used an at times will be mentioned. More about what is meant by a public concept is discussed in the appendix. For a given person, we can consider to what extent the concept a person is using is a variant of some public concept. In the books that Ellie brought to Angela, pictures predominated. There were some words, but Ellie only pointed to pictures when she said a word. Since she had no concept of written language, her variant of the book concept was only a limited variant of our concept of a book. Still it included enough of that concept that we would generally say that she had a variant of our book concept rather than that she used a different book concept. Moreover we expected that her variant would expand to our public one.

Example 0a: There are variants of a concept that are more sophisticated than some public variant. Galileo’s concept of acceleration was more sophisticated than the public concept of acceleration of his time. His concept was a mathematical one that became the one used in physics. Even now, it seems clear that our concept of acceleration is only a limited variant of this mathematical concept, altho a large number of people may have this more precise concept. Consider an automobile enthusiast who can tell you the time it takes for his car to go from zero to sixty mph.

Example 0b: In a movie a woman is driving her car and the man beside her is an alien from another planet. He has never before seen an automobile or a traffic light. Conditions arise that make it difficult for her to continue driving. He assures her that he has observed her and can take over. On coming to a red light he stops. Saying that he has some concept of a traffic light and some concept of a brake seems reasonable, altho he does not know what either is called. He proceeds as expected, stopping on red continuing on green. She supposes he has her variant of the traffic light concept. Of course there may be other explanations for his actions. In fact as he approaches the next light, he speeds up rapidly and then stops suddenly. When quizzed he explains that yellow means speed up, but then it turned red. His variant is not exactly the public concept, altho it is reasonable variant obtained by observing her behavior. Moreover, altho she had been speeding up when a light turned yellow, we would not conclude that her concept of a traffic light was not the public one. As most of us know, speeding up on yellow makes sense for another reason, altho making sense does not mean that it is prudent. In general, having a concept only means being able to act on it in at least one of the ways in which it makes sense to act. It does not mean there is only one way that makes sense to act. Nor does it mean that having a concept entails always acting on it in one of those ways. Moreover just responding to various signals in a way that makes sense does not guarantee that a person has the concept of a traffic light. Our public concept includes not only what the signal tells us to do but that the purpose of this is to regulate traffic. Perhaps he has gleaned this. To find the claim that he is acting on our concept plausible, we may need to determine more information about his behavior. In general, observing a person’s behavior gives us reasons to consider what concepts a person has, but our judgements are fallible. A woman who stops on green and looks both ways might seem not to have the public variant of a traffic light, but there are other possible explanations of her behavior. For instance suppose we know that she was recently hit by a truck that ran a red light, or suppose we know that that light is not working correctly.

Example 0c: When Ann was four she knew that her father stopped when the light was red but not when it was green. Altho she could not act on the concept as her father did, she acted on it vicariously. Seeing a light turn green, she expected her father to go. Once when he was on his cell phone, she even reminded him that the light was green. However, Ann had no idea that the purpose of the traffic light was to regulate the flow of traffic. Altho we can say that she had a concept of a traffic light, we would
also say that she her variant of this concept was only a limited case of the public concept. Still, her mastery of this concept was adequate for the role it was playing in her world. Her sister Meg understood the relationship between traffic lights and regulating the flow of traffic. She even asked her father why he needed to stop on red when he could see that there were no cars on the other street. This enabled her to relate the concept of a traffic light to some ordinary legal concepts. Unlike Ann’s world, Meg’s world demanded not only the public traffic light concept but also a network of related concepts, altho she was also too young to drive.

Specific Concepts and Type Concepts: A specific concept is the concept of a specific object or specific event or specific process or some other kind of specific state of affairs. For instance, Meg has the concept of her bed. On the other hand, she has the type concept of a bed. It includes her bed as an instance, but it has a multitude of instances beyond any bed she is likely to encounter. In general, a type concept is an abstraction that can be used for classifying something (object, event, process, state of affairs, etc.) according to attributes or the place it can have in some realm. Type concepts are flexible in the sense that they have the potential to be used to formulate other concepts as needed. She has a process type concept of making a bed, which she uses to form the specific process concept of making her bed this morning. She has a specific state of affairs concept of her bed being neatly made this morning. This is only a sample of a multitude of type concepts and related specific concepts that Meg can easily relate to her ordinary experience. Moreover for most such concepts, she know the realms to which they can be applied, has them at least adequately connected to other concepts, find them useful in relevant settings, can explain them in an appropriate manner, and has them in fairly clear focus. Similar remarks could be made about most persons. The concept parameters to be introduced shortly provide a way to systematize such remarks. First, I make a few more remarks about specific and type concepts.

A concept C is manifest to a person P to the extent that aspects of it relate closely to P’s easily accessible or easily imagined experiences. Altho we do not remember many of our experiences, they sometimes give rise to specific concepts that are highly manifest and stable and easy to describe. This is especially the case when the specific concept involved is of lasting significance. For instance most residents of St. Louis have a Gateway Arch concept that has been abstracted from a number of similar experiences, and it will be highly manifest. We often have proper names for specific concepts of major significance to some community. However other specific concepts of major significance are referred to by phases, such as ‘the stock market crash of 1939’. Specific concepts of lasting significance for only one person are also often designated by that person using some phrase.

Altho a type concept may be acquired without direct experience of any instance that type, it is likely to remain somewhat remote until some direct experience with instances of that type occurs. We may then obtain a highly manifest concept of some instances of that type and also develop a manifest type concept linked to these, but not necessarily limited to these. Specific instances of a type may remain manifest even if no longer experienced, but they may become less manifest. If other instances of that type are still frequently thought about then our type concept is likely to become even more manifest than our concepts of the instances that we no longer encounter. For instance my concept of a horse is highly manifest, altho at this point no specific instance of a horse seems very manifest. On the other hand, altho the concept of an ax seems highly manifest, it is not quite as manifest as my concept of the ax I used yesterday. Other persons will use these type concepts much as we do, whether or not they have thought about the same instances. All of this makes type concepts for specific instances that we frequently encounter among our most manifest concepts. Some of our specific instance concepts may remain even more manifest, especially if our experience of them is frequent or highly significant. For instance, altho occurring only once, the concept of a wife’s funeral is likely to be more manifest to a man than his concept of a funeral.

Many type concepts can be referred to by a single word or a fairly simple term, and this may make them seem highly manifest. This can be misleading. For instance, I doubt that the object type concept quark is manifest to most people. The same can be said of the state of affairs type concept of global harmony. However many of our highly manifest concepts are of types that are abstractions from what we think of as significant features specific manifest concepts. A child’s bed concept begins as a specific concept referring to a specific bed. It soon evolves in to a type concept that includes at least her parents bed and which can be used to talk about beds.

Acknowledgement: The parameters that follow apply only to concepts. However some of them were partially suggested by {Knowledge, Comprehension, Application, Analysis, Synthesis, Evaluation} from Bloom’s Taxonomy of Educational Objectives for the Cognitive Domain. See (http://faculty.washington.edu/krumme/guides/bloom.html).

Parameters: Altho the idea of parameters did not originate in Descriptive Psychology, seeing how parameters have been used there suggest a wider usage than most people have imagined. The parameters below are used to indicate a relationship between a person P and a concept C, and specifically the ways in which to consider P’s mastery of C.

¨ proximity: indicates the extent that C is close to or remote from P’s ordinary experience

¨ integration: indicates how C is connected to other concepts within the nets used by P

¨ explanation: refers to way P could or would be able to explain C

¨ focus: refers to the ways P understands various conceptual features of C

¨ utility: indicates any noteworthy uses or types of uses that P has for C

Parameters as Attributes: These parameters can also be used as if they were attributes of a public concept as used in some community. A concept is remote to the extent that aspects of it do not relate closely to easily accessible or easily imagined experiences for persons in that community. A concept is highly connected to the extent that most people in the community connect it to a wide variety of other concepts. A concept is analytic to the extent that most people in the community would explain it in terms of more basic concepts. A concept is in focus to the extent that most people in the community can use it in the same manner and can recognize the extent that the concept is precise, flexible, etc. A concept has use for a realm if most people in the community could apply it to that realm. A concept is easily expendable for a community to the extent that little or nothing in their lives would be different if nobody used the concept.

For the community of mathematicians, the octillion concept is only somewhat remote, is easily expendable, is analytic, is adequately integrated, is precise, applies to the realm of natural numbers. For the general public, this concept would seem to be remote, at most barely explainable, at most loosely connected, at least somewhat imprecise, numerically applicable but easily expendable.

Altho the vast majority of people might not find the of atomic fusion concept essential, it has too much impact on our lives to be classified as easily expendable. We can probably also classify our concept of atomic fusion as remote, primarily analytic, weakly connected, highly imprecise, applicable to physics and the military. On the other hand, the community of physicists would find their concept of atomic fusion (more likely to be referred to as nuclear fusion) somewhat manifest, essential, precise. It would also apply to more realms, such as the realm of stellar evolution. It would have many more connections than our concept of atomic fusion.

The Proximity Parameter: This parameter indicates how close various features a concept are to a person’s ordinary experience or to specific features of experience that a person finds easy to identify. Proximity can vary from highly manifest to extremely remote, altho this is not intended to be subject to numerical analysis. A concept C is manifest to a person P to the extent that features of it relate closely to P’s easily accessible or easily imagined experiences. C is remote for P to the extent that P finds its features removed from such experiences. For P to have a concept, some feature of it must seem at least somewhat manifest to P.

The world for a person is conceptualized as all of the objects, processes, events, states of affairs, and relationships that person is likely to take account of when doing something. A person’s world includes a number of specific worlds, i.e. various realms of interest; such as ordinarily referred to by phrases like ‘the sports world’ or ‘the business world’. Since imagining is a form of doing, a person’s world includes anything a person tends to imagine, and so some of a person’s world may be classified as fictitious. For instance, the Easter Bunny may be part of the world of both a parent and a child, altho it differs in status in their worlds. What constitutes ordinary experience for a person depends on a person’s world. What is ordinary experience for one may not be ordinary experience for another. For instance a child in the city may have never observed a brown egg while a farm child may have seen many such eggs. Some people have seen an ostrich egg. Others have not even heard of them. Effects that this could have on a person’s egg concepts are illustrated in detail in Various Egg Concepts. If a person’s world includes a realm that seems extremely remote to most people in our culture, what that person takes as ordinary experience may not even seem imaginable to most of us. For instance, a physicist may find the realm of subatomic particles included in her ordinary experience and thus her concept of them may be fairly manifest.

Altho a type concept tends to be less manifest than many specific concepts that are instances of that type, we often use type concepts to refer to such instances. The concept of a computer can be referred to by a single word, yet it is somewhat less manifest than the concept of the particular computer that a person is using to write a term paper. In order to refer to one of these specific objects we use a phrase describing it in terms of slightly less manifest concepts such as word processing or my office, but we do not understand this concept by analysis of these less manifest concepts. They are merely pointers.

Example 1a: When Meg was about two, her concept of my baby sister Ann was highly manifest. Altho she called Ann ‘my baby sister’ it seems reasonable to say that she did not even have a variant of our sister concept, altho she did have some highly manifest variant of our baby concept. Meg soon learned that she is Ann’s sister. As Meg gained further experience, aspects of our sister concept became manifest to her, mostly as she used other manifest concepts involving particular sisters. The bed Meg used was the highly manifest concept of ‘my bed’ for Meg. The concept of a bed was almost as manifest to her, since the function of a bed was easy to understand in terms of ordinary experience, and since other examples of bed were easy to observe. Likewise Meg soon found (and continues to find) a multitude of direct abstractions highly manifest. These included not only object type concepts such as bicycles and rocking chairs, but also other type concepts such as fear, holidays, hunger, etc. She also obtained fairly manifest concepts not as directly related to ordinary experience but that she easily imagined in terms of ordinary experience, such as a great white shark or a saber-tooth tiger. At a slightly higher remoteness level, but still manifest, was her concept of a unicorn. On the other hand, even when she took a course in general science, the concept of an ion was one that she found extremely remote. Science was not one of her interests, and it is doubtful that she ever acquired this concept. This does not mean that all complex concepts were remote for her. Altho many people find the concept of dialectical materialism remote, this concept seemed manifest to Meg. Due to many discussions with her father, she found a multitude of social and political concepts manifest.

Example 1b: Jed can give the definition of a proton that he memorized in his science class. This alone does not mean that he has our public proton concept. However since he relates the concept of a proton to a very small billiard ball, at least one aspect of his proton is manifest to him, and so he has some variant of this concept. Altho he can tell you that protons repel each other because they are positively charged, he cannot relate this to anything he experiences about billiard balls. To make this aspect more manifest he relates it to being repelled by spiders, altho this does not make the idea of being repelled by like attributes seem manifest. His classmate Jo, who later became a mathematician with little interest in physical science, had a more manifest concept of a proton. Having a good grasp of large numbers she found ways to at least relate the make the size of a proton to her ordinary experience.

Example 1c: Altho, different people may have somewhat different concepts of a democracy, there maybe enough in common to consider a public concept of democracy. By voting on their first grade class project and by electing a class president at least one aspect of this concept was manifest to Ann. Of course, at that time, her concept of democracy was a limited variant of our public concept. She had heard that our government was a democracy, but had only a vague idea of what this meant. On the other hand, altho Meg was only in the third grade at that time, she had already acquired a concept of democracy that was an adequate variant of the concept used in the community of politically active adults. She followed both national and local elections, knew who held various offices, could discuss the articles of the constitution, etc. All of this made the concept of democracy seem very close to her ordinary experience. Note that communicating about something or merely thinking about something can be part of our ordinary experience. This can make a concept seem manifest, even if a person never uses it for any other form of activity.

The Integration Parameter: This parameter indicates the place a concept has within a person’s nets, and especially how the concept is connected to other concepts within these nets. Most of a person’s concepts will be variants of a public concept. Such a concept C is appropriately connected for a person P to the extent the connections used by P are coherent and correspond to those used in public nets. C is integrated to the extent that C is appropriately connected and these connections include those needed for using C in order to understand and communicate with others in the communities to which P belongs and cares about. C is adequately integrated if these connections include most of those that P would commonly need for such purposes. An adequately integrated concept for P may also have connections other than these if P is aware of how P’s variant differs from C. Moreover a person may have a concept that is not a variant of some public concept. For such a concept C to be adequately integrated its connections to other concepts must be coherent and these connections must serve the purpose for which P uses C.

Example 2a: For Ann in grade 1, democracy was connected primarily to the concept of voting. Altho her concept was appropriately connected, many other connections will need to be made before it will be adequately integrated for use in our culture. For instance, she did not have the concept of a legislature, nor could she have been expected to have such a concept at that time. On the other hand, her older sister Meg had a much stronger interest in the adult world. Even two years earlier, when she had been in first grade, her concept of democracy was appropriately connected and exhausted the way it was integrated for most adults in our culture.

Example 2b: Meg’s my sister concept began as connected only to her concept of Ann. Thus it was appropriately connected but only minimally connected. It became slightly more connected when she thought of herself as Ann’s sister. Only when she understood the relationship between concepts in {sister, brother, male, female, same parents} did it become adequately integrated for most purposes. As she matured, it became adequately integrated, as this concept was related to a vast number of concepts in a net for family relationships, such as aunt, half sister, stepsister, cousin, etc.

Example 2c: Jed’s concept of a proton was appropriately connected to his concept of an electron. It was far from adequately integrated if he were to be even a novice in a scientific community. He could not even connect it to the concept of valence, nor could he connect it to the concept of atomic weight. However since the concept of a proton has few connections in our public net, his concept of a proton was adequately integrated in relation to our general public concept.

Example 2d: Galileo’s concept of acceleration of acceleration differed so much from the more primitive public concept of acceleration that we could classify it as a new concept rather than a variant of that public concept. His concept was more precise and connected to mathematical concepts in ways not previously imagined.

The Explanation Parameter: This parameter refers to the way a person could or would be able to explain a concept. This includes explanations that involve other parameters. For instance a person P may indicate the realms in which a concept C can be used and it utility in these realms. P may be able to explain how C is connected to other concepts. P can explain C analytically to the extent that P understands how to reduce C to concepts that are more basic. P can explain C synthetically to the extent that P understands how C can be explained in some other way, perhaps by giving a multitude of examples or relating C to a number of ways that it is used. A person may be able to explain a concept both analytically and synthetically. In fact, altho some concepts may not lend themselves to an analytic explanation, any analytic can be augmented by various synthetic ones. Moreover, the ability to give both a clear analytic explanation and various synthetic explanations of a concept indicates a high level of mastery for the concept.

Example 3a: Kate teaches third grade. She can explain the concept of a million analytically as 10⁶. With her class she normally uses the alternative analytic explanation of a thousand a thousands, sometimes writing this as the more tedious expression 1000´1000. She also places this within the context of our base ten numeration system, indicating that 1000 = 10´100 and 100 = 10´10. She has previous preceded her analytic explanations 1000 with a synthetic one using base ten blocks. It is visually apparent that this block is a 10by10by10 cube of smaller centimeter cubes. This had provided a manifest explanation of a thousand. For another manifest explanation she had used two reams of paper. Her brief synthetic explanation is the number of small cubes that can fit on the card table in the corner of her classroom. To make this manifest, she has her students explain how to fit a thousand base ten blocks on this table. It is only then that she focuses on an analytic definition of a million. One of her students volunteers another explanation of a million, as the number of pages in the books that would fill a bookshelf reaching from the school to his house. He adds that it would take a stack of about 40 billion such pages to reach the moon.

Example 3b: Recall that Jed can give the definition of a proton that he memorized in his science class. Thus in spite of having a weak understanding of this concept, he explains it analytically. He can do little beyond this, altho in saying that it is likes a very small billiard ball, his concept is somewhat synthetic. He added that by very small he meant less than an angstrom. However, this was only a pseudo-explanation since he had no idea that ten billion angstroms was a meter.

Example 3c: Meg’s early sister concept was almost totally synthetic and she would have explained it almost exclusively by giving examples. Her sister concept became analytic for her when knew how to reduce it explicitly to the concepts of female and same parent. Moreover, it became primarily analytic for her when this became the way she would usually explain it. However it was also remained somewhat synthetic for her, since she explained it to Ann by giving familiar examples. Meg’s bed concept became analytic when she learned to explain it as an item of furniture used for sleeping. Challenged about why the couch was not a bed, she added that it was not just that a bed is used for sleeping, but that this is its primary use. She also added that beds only belonged in the bedroom.

The Focus Parameter: The role main role of the focus parameter is to indicate the extent to which a person P has a concept in focus. A concept C is implicitly in focus for P to the extent that P knows exactly when and how to use C and also understands various limitations in using it. C is precise for P to the extent that P applies it consistently and coherently without having to allow for indeterminate cases. C is fuzzy to the extent there are indeterminate or borderline cases for C. A person’s fuzzy concepts serve important purposes, especially when they are in focus and used with caution. If C is too fuzzy or too imprecise to be used consistently and coherently by P then C is said to be vague. C is flexible for P to the extent that C can be used to make different distinctions in different contexts. For instance the ordinary concept of small is flexible in a way that allows a small point guard to differ in size from a small center. Flexible concepts allow a conceptual net to easily incorporate new concepts. For instance, without the concept of small many more specific concepts would be tedious to formulate. C is explicitly in focus if P has the ability to tell to what extent C is precise, fuzzy, flexible, etc. This can also be indicated as part of the explanation parameter. To say that a concept is in focus for P is a competence claim that means that P can use the concept coherently and effectively for certain purposes in a multitude of situations.

Example 4a: Altho it might seem that Jed had a precise concept of a proton, back when he had its definition memorized, he did not know what was meant by all of the concept used in that definition. Thus while this concept may have been precise for his teacher, it was still fuzzy for Jed. Moreover, the proton concept was explicitly in focus for his teacher, but it was not even implicitly in focus for him.

Example 4b: As with most extremely manifest concepts, Meg’s early my sister concept was precise. This concept was only implicitly in focus. Her later concept of my sister was explicitly in focus. Meg’s current concept of a heavy rock is somewhat imprecise, but it is implicitly in focus. Moreover, with little effort she can bring it explicitly into focus.

Example 4c: Ann’s first grade concept of democracy only meant voting on what to do and who was to fill class roles. Altho this concept was fairly precise and implicitly in fairly good focus for her, it was not explicitly in focus. Much later, as she acquired our related public concept, her democracy concept was somewhat vague. Since she did not realize this, her concept was not even implicitly in clear focus. On the other hand, Meg’s concept of democracy was somewhat fuzzy, but also in focus. Meg would say that being a democracy was a matter of degree and that there was no exact demarcation between being or not being a democracy. She could also indicate that the concept of a democracy was not restricted to a form of government, altho its range of application might be somewhat fuzzy.

The Utility Parameter: This parameter indicates the realms and type of realms that P can relate to C. Suppose P has a ‘larger than’ concept. This concept is likely to be included in the net P routinely uses for a variety of ordinary matters. P may be able to use it in the realm of linear measurement, population comparisons, playing card ranks, etc. This parameter goes beyond merely knowing realms of application by indicating anything that might provide a perspective on how a person might be able to use a concept. This includes the kinds of uses a person has for a concept. One noteworthy way of using a concept is in communicating with others. This can vary in it range from being used to communicate widely to being only used to communicate in some small community. For instance Meg uses the concept of a hiding place with many of her friends, but she uses the concept of their special hiding place only to communicate with her sister Ann. P can also use C merely to think about something. For instance Meg can use chess concepts to think her next move without communicating this to anyone. This parameter also includes the extent of the utility of C for P. At one extreme, C may be crucial for P, i.e. P could not effectively imagine doing without it. A concept that P needs for one of P’s important worlds or realms of interest will be called an essential concept for P. Since what is important to a person can change, which concepts are essential can also change. Clearly crucial concepts are and remain essential, but other routinely used concepts are also essential to various persons. At another
extreme P may use C so seldom that C may be easily expendable. In between, there are concepts that have varying degrees of utility. Of course a concept that is easily expendable for one person could be essential for another or have only some limited utility.

Example 5a: Meg has our standard ace of diamonds concept and knows that this concept applies only in the realm of playing cards. The integration parameter for her would also include the connection of this card to the concepts of rank and suit. Currently she uses it both in playing poker and blackjack. The way in which she uses this concept these two games is different.

Example 5b: Try to imagine living the without the ability to act on some distinction that the concept of food entails. I suspect this concept is one that most humans would find crucial, both for communicating and for planning what to do.

Example 5c: Meg’s concept a sister is essential for her, as are many other concepts from the realm of family relationships. She can use the concept of a first cousin once removed, but it is far from essential to her. However she hears others use it enough that it is not easily expendable. An extension her sister concept applies to personal relationships that are thought of as family-like but not as family. Altho Ann was Meg’ only biological sister, when she joined a sorority she called them her sorority sisters. Some hermits might find all of these concepts easily expendable.

Example 5d: Jill uses her ax and a sledgehammer to split wood. These concepts are essential, but since her world would still make sense without them, they are not crucial. She also uses the concept of a maul, but until recently this concept was expendable. She acquired it as an amateur who normally split just enough wood for her wood burning stove, and her other tools are sufficient for this purpose. Such information could be included as parts of the utility parameter for her ax and maul concepts. Currently her concept of a maul, altho still not essential, is useful enough not to be easily expendable. She occasionally talks with Zak about splitting wood and he uses a maul, but talking with him about splitting wood in not important to her.

Example 5e: Tim is an average person with our usual concept of a bed. His bed applies to the realm of furniture. It also applies to the realm of personal use and maintenance his wellbeing. Both of these are personal realms. When his concept of a bed relates to its physical features rather than on its use, it relates to impersonal realms. Beth works in furniture store. Her concept of bed also applies to the realm of pricing and selling furniture.

Example 5f: The forward pass concept is essential for a football player. It has limited utility for someone who is not a football fan but whose son is. It is expendable for someone who totally ignores the realm of football, assuming that person even has this concept.

Personal and Impersonal Realms: Two types of realms that are broad and especially noteworthy are the personal and impersonal. A realm is personal to the extent that it is used to think about persons and their actions. For instance, our usual concept of frugality makes sense only in personal realms. An impersonal realm is one in which the actions of persons do not seem central. Our concept of volcanic action is impersonal, altho there have been cultures in which this was not the case. Personal concepts are not restricted to humans. For instance, the usual concept of Satan relates both to a personal realm and to a supernatural realm. However some people may have an impersonal concept of an evil force pervading the world, which they call Satan. Having a concept does not involve an existential commitment. Those who find the existence of Satan highly implausible can use it either to communicate with some other people or to read certain materials. Altho all concepts are acquired thru personal experience, some have little else to do with persons. This is especially the case with many concepts that are primarily perceptual, such as red or wet.

Interrelationships: As remarked earlier, altho these parameters are conceptually independent, they are often interrelated. For instance, concepts that are in focus tend to have greater utility than those that are not. Moreover their realms of application may be better understood. Likewise highly manifest concepts tend to be in focus. There are exceptions. Some manifest concepts may merely seem clear because the user feels they are so familiar, but familiarity can result in careless usage. While many persons find remote concepts fuzzy or even vague, remote mathematical concepts are analytically mastered and precise for mathematicians. Some mathematicians have acted as if all useful remote concepts must be highly analytic. The alternative seemed to be remote concepts that were extremely fuzzy. However the conceptual clarification techniques, such as those used in Descriptive Psychology, allow us to formulate remote concepts that are not analytic and are precise enough for many purposes. Altho analytic concepts have considerable utility, many of the main concepts we need cannot be analytic. There is a price to pay for the use of analytic concepts. They usually must deal with highly idealized states of affairs. They often achieve precision by making artificial simplifications.

The Utility of Fuzzy Concepts: Concepts are expressed by words or phrases, but what concept is being expressed may vary depending on context. This is a feature of many ordinary concepts that makes them easy to use without inventing a large number of tedious locutions. Altho we may often recognize that the concept expressed by certain locutions may be fuzzy, they may well serve of our purposes. Recall the ‘somewhat less than’ concept. It is intentionally fuzzy and in many contexts more useful than a more precise distance concept. It is also less likely to convey incorrect information due to faulty measurements. As with many ordinary somewhat fuzzy concepts, it is normally used to convey information that is clear enough for the purposes at hand. So it is more useful to use fuzzy concepts judiciously, rather than discard them. One such purpose is to try to understand language that we are likely to encounter even if we avoid initiating it. Another reason for using fuzzy concepts is that this can be a prelude to using more precise ones. Consider the somewhat different concepts that might be indicated by the term ‘the truth’ in some of the statements below.

(1) Which of you is telling me the truth?

(2) Always tell the truth, even though this may sometimes be painful.

(3) Tell the truth, the whole truth and nothing but the truth.

(4) You shall know the truth and the truth shall set you free.

(5) The truth is eternal an immutable.

Using (1) in some situation where two people make ordinary incompatible claims seems to involve a concept that is precise enough for the purposes at hand. We might then focus on the claims and examine them in more detail. Etc. An ordinary concept ‘the truth’ in (2) is more remote and somewhat fuzzy. Does telling the truth involve telling someone that you think he is boring? Does it involve telling a secret you promised not to reveal? We do not need a precise concept to make effective use of this advice, as it is often clear enough for the purposes at hand. Similar remarks apply to (3), as long as we realize that the language in this command is conventional and not to be taken in a literal sense. Altho the concept of the truth in (4) may be fairly fuzzy, the sentiment involved come thru well enough to give some utility to the statement. I personally find the concepts involved in (5) vague, and when others make statements like this, I seem to be incapable of understanding what they mean. However even if I must rely on vague concepts in this situation, this is better than not trying to conceptualize it. The majority of my concepts are less clear than my concept of a finite cyclic ring and less fuzzy than my concept of the truth. For instance, my concept of conceptual clarity is somewhat fuzzy, but it is often clear enough for my purposes in many situations. Conceptual clarity is a matter of degree, and this is context dependent in various ways.

Mastery of a Concept: Mastery by a person P of any concept C is a mater of extent, and the concept parameters can be used to indicate the extent to which P has mastered C. Having C was conceptualized as form of behavioral competence. This involves at least a minimal ability to act on some distinction that C entails. We may judge this by merely looking at the utility parameter. Having C is at least a low level of mastery. To the extent that the mastery of a public concept C is at a high level for P, all of the parameters are likely to be describable as indicated below.

¨ C seems highly manifest to P, even if many others find the concept remote.

¨ C appropriately integrated for P, and perhaps more highly connected than average.

¨ P can give an explanation of C to the extent that this is called for on various types of occasions.

¨ C is explicitly in focus for P

¨ P can explicitly indicate the realms in which C can be applied by various communities, and perhaps imagine realms others have not consider.

¨ P can explicitly indicate the ways in which C has utility, and can also implement such applications in a various ways in situations where the use of C is appropriate.

It should be noted that the extent to which a concept is mastered is often opened ended, i.e. given any level of mastery, some higher level might be obtained. For instance, however many appropriate connections P might understand for C, some new connection might be imagined.

The mastery considerations above need to be modified somewhat in order to think about the mastery of a variant of a public concept. For instance, a variant of a concept can be mastered at a high level even if it is a limited variant of a broader public concept. For instance as young child Ann had a high level of mastery of her variant of the concept of a story, altho it was limited to the stories that were in the books that were read to her. The fact that she easily expanded this to stories that were told to her and to stories on TV is one indication of this. These parameters can also be used to consider concepts that are not even variants of public concepts.

My main reason for formulating concept parameters is because altho concepts permeate almost everything we do, we usually acquire concepts with little thought about the role they play or the extent to which we have mastered them. I first formulated them in my book entitled A Personal Approach to Conceptual Philosophy, where I use them to think about the most fundamental conceptual nets that persons use. See Singer (2007). I also used these parameters to reflect on some ideas that teachers and parents might use to help students master concepts. Singer (2008) focuses on making one the main processes used in solving algebraic equation seem more manifest. Singer and Pais (2005) discuss how these parameters relate to constructivist learning.

Understanding Concepts: The phrase ‘P understands a concept C’ will be used mainly to indicate the conceptual aspect of mastery, which usually involves focusing on the first four parameters. To say that P understands means that at a minimum C is integrated for P and that P is able to recognize at least one explanation that someone might give for C. The understanding aspect of mastery is also a matter of extent. To have C adequately integrated indicates a greater understanding than having C be minimally integrated. The ability to give various explanations of C indicates a greater understanding that merely being able to recognize them when given by others. The focus parameters can also be used to indicate important aspects of understanding, since being in focus indicates understanding. Altho not as directly an aspect of understanding, finding C manifest can be indicative of a greater understanding than finding C remote. This is especially the case for a concept that P finds manifest but that the general public finds more remote, as in Galileo’s time with the concept of acceleration.

Altho understanding concepts was conceptualized with no attention to the utility, it would be strange to say that P understands C but cannot use it in any manner. Clearly conceptual competence is seldom divorced from paraceptual competence in using C. However P can understand a concept and find it expendable. Being a mathematician Jo had a high level of mastery of the concept of an octillion, which she almost never uses. However in a situation where it would be useful she would be able to apply it, altho her understanding of the concept was acquired without applying it.

Concepts and a Person’s World: A person P’s world consists of everything P is willing to treat as real in the sense of taking account of it in relations to P’s actions. What P can take account of depends on the concepts that P has and the extent to which P has a mastery of these concepts. Altho all the concept parameters would normally be used to indicate the role that a concept C may have in a person P’s world, there would normally be much more elaborate attention of the utility parameter (and perhaps the integration parameter). The utility parameter would tend to be more fully developed than it would have been when merely indicating P’s mastery of C. In order to indicate the role of a concept that was essential to a person’s important world, a fairly extensive development of this parameter could be given. Consider what in might be like to give an account of the role of the concept forward pass in the world of a quarterback.

A concept can be may play significant role in a persons’ world primarily on the basis of conceptual utility. When Jo was in grade 3 she was fascinated with naming what she thought of as large numbers. At that time concepts such as septillion and an octillion played a larger role in her world than they did when she was older. The role was primarily conceptual, as there was nothing outside of her imagination that called for such numbers.

Note: The rest of this paper is a detailed presentation of considerations that helped shape the concept parameters. Most of these are introduced by examples that are simplified fictional personal observations or experiences. The purpose is to illustrate the use of the parameters. To better illustrate them make up examples that relates to something from your own experiences and observations.

Example 6a: Early in 1988 Mat took a blood test that gave rise to a lasting concept. Altho this event remains of major significance to Mat, he does not have a brief term for his concept of this experience. Mat refers to it with a partial description, as the blood test that changed his attitude toward blood tests. This concept includes his apprehension, his impressions of the room, his anticipation of the needle pricking his skin, etc. Any description misses the essence of his concept of this experience. It has a holistic quality that Mat can recall but cannot describe. While this experience has become more remote, his concept of it is still highly manifest. The utility of this concept is narrow but significant. It enhanced Mat’ behavior potential. Mat still uses it to cope with any medical procedure he encounters. He also occasionally uses it to think about doing other things that he finds difficult. This indicates the main things we might say about the utility and integration parameters. Mat’s explanation of the concept would be an account of his personal experience, perhaps with an attempt to relate it to some experience of his listener. His concept is precise and in focus.

Example 6b: Tim regularly sits in the same chair for dinner, and refers to it as ‘my dinner chair’. When sitting there, his concept of that specific chair is highly manifest, altho often only implicitly. When he latter talks about his chair, his concept of it is slightly more manifest to him than his concept of a chair, altho he uses the concept of a chair along with several other highly manifest type concepts in order to refer to his dinner chair. The slightly more general concepts of dinner and of a chair are manifest enough to Tim that they seem as close to his ordinary experience as does his experience of this particular chair. Several years after this chair was replaced, his concept of it became somewhat less manifest. However other examples of chairs were easy to observe, and the concept of a chair remained highly manifest, as it would for almost anyone in our culture. His chair type concept is connected to his

furniture type concept. The concept of furniture, altho initially not as manifest as the concept of a chair, also seems highly manifest to him. Since Tim can relate furniture to a variety of kinds of furniture, his furniture concept is appropriately connected. His next door neighbor Beth works in a store selling furniture. The concept of furniture has greater utility for Beth and applies to the realm of selling furniture. Her furniture concept is vastly more connected that his. If this was not so, then her concept of furniture would not appropriately her connected for her, since being a member of the community of furniture salespersons is something she cares about.

Concepts in Ordinary Nets: Different people are likely to have some different ordinary nets. For instance, a net for selling furniture is an ordinary net for Beth but not for Tim. In general, all concepts in a person’s ordinary nets will seem manifest for reasons like those given in Example 6b, regardless of their level of abstraction. They are also likely to be adequately integrated and at least implicitly in focus. Similar remarks could be made about how the other parameters apply to such concepts, i.e. altho there are exceptions, the level of mastery for concepts in a person’s ordinary nets is likely to be high enough for using them effectively. It is the abstract concepts that a person has heard about but does not use that will seem remote and not mastered well enough to be very useful. For instance, the concept of a galaxy is likely to be at least somewhat remote to most people, altho some people will find it more remote than others. This concept will be part of an ordinary net for an astronomer, who will find it manifest, highly integrated, etc.

Distinctive Concepts: A distinctive event concept is a specific concept of a distinct event, usually formed as it happens. A concept of a specific state of affairs can also be distinctive. Tim has a distinctive concept of his dinner chair having a broken leg. Distinctive concepts are among our most manifest concepts, at least as long as they last. Most distinctive concepts are mastered easily but not retained. They may have considerable utility in the moment but they apply primarily to the limited realm of current activity. They quickly become easily expendable and are seldom explained to anyone. They quickly fade from focus. When useful they are likely to be adequately integrated. In fact, to be useful they usually need to be at least appropriately connected to a number of type concepts. They also reinforce the type concept to which they are connected. For instance, Tim’s concept of his dinner chair having a broken leg is connected to the concept of chair and a broken chair leg. Moreover after experiencing this state of affairs the concept of a broken chair leg will be in sharper focus and more manifest to Tim.

Some distinctive concepts so significant we retain them. The essence of what was said about Mat’s distinctive blood test concept applies to most of our noteworthy distinctive concepts. To appreciate the manifest quality and other features of a distinctive concept, focus on some experience you vividly recall. This will provide a much better example than any that someone else can describe.

It is not easy to effectively communicate about a distinctive concept, perhaps because the general human need to do so was not great enough to influence the evolution of natural language. It often takes a complex descriptive phrase to refer to it, while other manifest concepts can be referred to by a single word or simple phrase. We may use language to point to our distinctive concepts, but language only gives a shadow of them. They are too rich to be captured by linguistic abstractions, and we understand them primarily by recalling the experiences. We may neglect this, since they usually seem clear enough for our purposes and since they seldom seem relevant to anyone else. Altho ignoring our most distinctive concepts usually seems harmless, bringing them into focus is one way to help deepen our understanding of less distinctive concepts. To do this effectively we must concentrate on using these concepts rather than their shadows. This means selecting a number of relevant distinctive concepts that relate to our other concepts and try to develop an understanding of how they are related.

Unlike specific objects which we may frequently encounter, specific events occur only once. A few may make such an impression that our concepts of them will remain highly manifest for a long period of time. Most will become less manifest and even remote. The related event types may remain highly manifest. My specific event concept ‘looking at the snow just before I first drafted this paragraph’ was manifest, but this concept is now remote because that particular event has faded from memory. On the other hand, my event type concept ‘looking at the snow’ is likely to remain manifest for a long time. It is linked to experiences that have occurred a number of times.

Example 6c: Mat has a blood test concept that is only mildly less manifest than his concept of those he remembers having taken, yet whose level of proximity is close enough that it would be classified as highly manifest. This concept can be described as a process that involves using a hypodermic needle to draw blood and then having someone with the appropriate expertise examine this blood. If he had more biological knowledge he might have a more elaborate and widely connected concept of a blood test, but it would probably still be fairly manifest. His concept of a blood test is somewhat abstract because it ignores features specific to any particular experience. It ignores personal feelings, who is taking or giving the test, how sharp the needle is, etc. However being abstract does not necessarily make a concept remote. This blood test concept is not remote because it is easy to link it to a very specific type of situation, and it is really his imagining of this type of situation, rather than his verbal description, which makes this concept manifest.

Example 6d: Pat acquired a pony concept before he ever encountered a pony or even saw a picture of one. He had seen a horse and had a manifest horse type concept, altho he no longer had any memory of the first horse he had encountered. Being told that a pony was like a small horse, Pat felt like he understood what was meant by a pony. Since he thought a colt was a pony, it was not appropriately connected, altho this was not a problem because this concept was easily expendable for him. This pony concept remained somewhat remote and easily expendable until age seven when he had a friend who owned two ponies and took him on some pony rides. In addition his previous realm of application, he added the additional realm of recreation, also making the pony concept more useful. Occasional encounters with ponies and thoughts about them have kept the pony type concept manifest, while the once highly manifest concept of the pony he first rode became less manifest. The related object type zebra concept is about manifest as his pony type concept, but he does not have a manifest concept of any particular zebra, altho it is linked somewhat to zebras he has seen in pictures and those he has seen at a zoo. Integrating these type concepts yields a somewhat less manifest type concept of equine animals, altho he just called them horse-like animals. In fact, all of these type concepts and concepts of specific instances are linked to experiences that he find easy to identify and understand. Thus we could classify them all as manifest to Pat.

Comment: The next example focuses on the utility parameter. One use of this parameter is to indicate the magnitude of the utility. In how many realms is C used and how important are these realms to P? There are several types of utility that can be indicated by this parameter. Of special importance is the behavioral utility of C in relation to some realm of interest R. Indicating behavioral utility involves describing what behavior options C allows P in relation to R. To have behavioral utility C must have at least some paraceptual utility in relation to R, i.e. it must help P comprehend some aspects encountered in R. An essential thing this parameter can indicate is the purely conceptual utility of C in a net that P uses in relation R, i.e. it can indicate the role C plays for P within that net. Without some conceptual utility, it is hard to imagine any other utility, but conceptual utility does not guarantee paraceptual or behavioral utility. It might seem that, the more elaborate are the values that can be assigned to the utility parameter the greater is the mastery of the concept. This is true of concepts with great potential utility. However there are concepts of small utility that can be highly mastered, Consider the concept of a rotten egg. What matters for mastery is the extent C can be used when applicable.

Example 6e: Bo is an ordinary bridge player. Sue only occasionally observes bridge games. Each will have a net for bridge. In both nets the concept T of a trick is connected to the concepts of bidding, opening lead, trumping, going set, etc. In fact T is essential to understanding these other concepts, altho a person can have some mastery of T without understanding all of these other concepts. A mastery of T is also essential to knowing what is actually going on in any particular game of bridge. For Bo, the realm of application for T includes both playing and observing bridge. Sue’s realm of application for T is more limited. Bo can also give a more detailed explanation of T than can Sue, mostly because T is in better focus for him. T may have no behavioral utility for Sue, altho it would if she wants to discuss the game being played. The concept F of a finesse has conceptually utility in relation to playing strategies, but its broader conceptual role is minor. So F is at least somewhat expendable. A person can understand many concepts of bridge playing without F. However without F some of what happened in many bridge games would not be understood. Having F clearly gives a playing advantage over players who do not have F. In fact the behavior utility is such that Bo needs F in order to make many of the bids that should be made. Similar remarks apply to the concept of saving entries. Altho Sue finds this concept easily expendable, it has considerable behavior utility for Bo. The magnitude of F for Sue is minor. Its magnitude for Bo depends on how important playing bridge and winning is to Bo.

Comment: It should be noted that being adequately integrated depends on the realms in which a person participates. A person for whom the realm of bridge is irrelevant can have an adequately integrated ‘finesse’ concept without knowing how this concept relates to playing bridge. This would be an inadequately connected concept for a person talking to a bridge player. Since one way that concepts can be connected is thru support, the integration parameter may also indicate how a concept supports other concepts in a person’s conceptual net for a realm of interest.

Example 6f: In our ordinary net F for family relations the concept of aunt and uncle are supported by the brother and sister concepts, and these are supported by parent and gender concepts. The concept of a sibling is connected primarily to brother and sister concepts. It could be used as support for these concepts, but it is normally learned later and most of us more often think of being a brother or a sister rather than as having the same parents. The concept of parent is essential in F, and it provides some support for any other concept in F. The brother-in-law concept is supported in addition by the concept of marriage. Jan’s tells of a time when someone told her father Jack he had just seen his brother-in-law. Jack was puzzled, saying he did not have any sisters. He was somewhat chagrined when reminded that his wife had several brothers. Clearly his brother-in-law concept was connected, but not connected as adequately as it might have been. Marriage is a basic concept in F, but altho it supports many other concepts it is not absolutely essential because a major part of F would remain without it. As a child, Jack had a well-connected cousins concept that was not appropriately connected in relation to the official cousins concepts (altho it was appropriately connected to concepts as used by a number of people). He had been told that his second cousin Karen was his third cousin, because her mother and his mother were first cousins. Lacking the concept of a first cousin once removed, he was told that Karen was his mother’s second cousin.

Example 6g: Jo is a competent mathematician. Her successor concept for a natural number is essential and adequately integrated. On the other hand, her concept of a googolplex is minimally connected and easily expendable. Her concept of a googolplex does not support any other concepts and is directly connected to very few other concepts. Still it is adequately integrated by being explicitly linked to the concept of powers of ten. Similar comments apply to almost any other contemporary mathematicians.

Example 6h: Zoe understands the concept of oxidation in relation to a number of realms. The primary realm for her understanding is chemistry. She also knows that oxidation involves the transfer of energy and so part of her mastery of this concept relates to the realm of energy physics. She can relate this concept to realm of food energy for animals. In addition there are realms involving fire in which she can use this concept, for altho in building a campfire she would not normally talk about oxidation, she could if it seemed relevant. Likewise in the realm of caring for metal tools, she might talk about preventing rust, and she knows how to describe this in terms of oxidation. Her concept of oxidation is supported both by a number of ordinary concepts and by some scientific ones. Recalling the integration parameter, Zoe has an oxidation concept that is highly connected and adequately integrated.

Comment: Part of what is involved in mastering a concept is to understand how it relates to one or more realms or types of realms. As indicated earlier, two especially significant realm types are the personal and the impersonal. Concepts are used by persons, and thus belong to their nets, but this is not what is meant by the phrase ‘a personal concept’. By a highly personal concept, I mean one whose use has been influenced primarily by experience of persons. In particular, they are those on which we focus when thinking about the actions of persons or situations in which persons play a central role. A highly impersonal concept is one whose use has been influenced primarily by experience in which the actions of persons does not seem central. These are concepts we focus on when thinking impersonally. They include natural types, such as the physical and biological. The concepts of mathematics are also impersonal. So are the concepts of chess, for altho the pieces in chess are named as if they were persons, they are not conceived that way.

Example 6i: Bob knows that a lever can be used as tool. Saying this indicates a value of the utility parameter in his mastery of his lever concept. Being regarded as a tool makes his lever concept somewhat personal, because he often thinks about a person using a lever this way. He also thinks of a lever as conceptualized in physics, this being another realm of application for his lever concept. As such it is impersonal because he classifies something as a lever basically because of its potential to produce an effect on a state of affairs that is largely impersonal. Furthermore he can recognize something as acting as a lever even when no person is involved. Thus his lever concept is intermediate between being personal and impersonal. This is typical of many concepts that are primarily functional.

Example 6j: When Jay explained the concept of a meter to his class he illustrated it by showing them a meter stick and having them measure the length and width of their classroom. He also explained the concept analytically as 40 inches. This suggests that his net for linear measure was not appropriately connected. He gave also gave them a synthetic explanation of a centimeter by pointing to marks on the meter stick and having them makes some measurements using centimeters. He supplemented this by indicating that it took 100 centimeters to make a meter. Altho he could explain a centimeter analytically as one hundredth of a meter, he did not think this would be useful.

Example 6k: The concept of a chair is partially analytic for Tim because he would explain it as furniture used for sitting. However this does not totally explain the concept because it does not eliminate other types of furniture used for sitting. With effort, Tim might totally reduce his chair concept to more basic concepts, but he would be more likely to give a partial analysis with some counterexamples.

Comment: Since many concept can be explained both analytically and synthetically , some concepts can be regarded as being composed of analytic and synthetic components or even as composed of a cluster of concepts that are referred to using the same term. For instance, a person may have a sister concept that allows both for a full sister and a half sister, and even for a spiritual sister. Altho the terms ‘analytic’ and ‘synthetic’ was suggested by Kant, it is a different distinction. Other terminology might be more appropriate. Analytic explanations could be called static or extensional. Synthetic one could be called dynamic or intentional.

Concepts that are most likely to remain true to the complexity of experience would either be primarily synthetic or at least have major synthetic components. Unlike analytic components, which tend to be static, synthetic components are more dynamic and tend to evolve with experience. Even when abstracted from ordinary experience they may be somewhat remote because they are broad and difficult to isolate or restrict. Examples include such ordinary concepts as reality, love, justice, change, beauty, happiness, etc. These concepts are highly experiential, but they are not easy to identify with narrow features of experience, nor can they be adequately analyzed into concepts that are more basic and that can be simply described. This does not mean they must be vague or mysterious. What is needed to bring these concepts into sharper focus is a variety of examples or paradigm cases, carefully organized. To understand concepts that are primarily synthetic, carefully examine how they are used. Unlike analytic concepts, do not expect that such an examination will result in their reduction to concepts that are more basic.

Example 6l: A narrow analytic concept of an aunt can be given as a sister of either one of a person’s parents. However there is a much broader aunt concept consisting of a cluster that would be tedious to articulate analytically. Acquisition of this concept is often synthesized from using this concept a multitude of times to indicate this relationship. This usually involves sorting out the use of the word aunt from this narrow concept and from its other uses for what more precisely would be called an aunt-in-law or a grandaunt or a great grandaunt or an honorary aunt. In fact it is this broader concept that many children first acquire, and they usually acquire it prior to having the more remote analytic concept in sharp focus.

Example 6m: The concept of the chair on which Tim is currently sitting is precise for Tim and easy for him to bring into focus. Because of borderline case possibilities, his concept of a chair is less precise, but still precise enough for most purposes. This is because there are some situations in which his concept of a chair seems applicable. There are also times when he vacillates on how to apply it. When he sits on a log, he may or may not think of it as a chair. Still his concept of a chair is precise enough that he uses it coherently and effectively for all practical purposes, and in indeterminate cases, he could clarify it further if this was important enough for some reason. Similar remarks could be made for most adults in our culture.

Example 6n: Jo’s concept of the class of all sets is vague, but it is more precise her concept of fairness. In fact, her general concept of fairness is precise only in very ordinary situations. She can use it coherently in relation to playing a game with clear rules. She also knows what she means when she says that when a referee unintentionally makes the wrong call he is not being unfair, even if the result is unfair. In situations where what to do is not specified by exact rules, Jo thinks that the concept of being fair can still be used precisely enough for some purposes, but not for others. If a teacher and a student disagree about whether a grade was fair, they may be using the same concept but disagreeing about a matter of fact. On the other hand, they may agree on the facts but be using different concepts of fairness. Jo is not even sure that she uses the concept of fairness in similar ways in different situations. Moreover when other people talk of life as not being fair, she is often unsure to what extent the concept they are using relates to what she might be thinking. In general, extremely vague concepts are those that a person uses in ways that lack coherence within or between situations.

Example 6o: Jan’s concept of a modern art is extremely vague. She would only know that something was modern art if she was told so by a reliable critic. She also has only a vague concept of a reliable critic. Altho vague, these concepts are in focus. She understands that she would only know that something was modern art if told so by a reliable critic, and she knows that she only has a vague concept of a reliable critic. Her concept of modern art still has some utility. It at least allows her to listen to certain discussions.

Example 6p: Recall from Example 0b that Meg understood the relationship between traffic lights and regulating the flow of traffic. Thus even at a young age her concept of a traffic light was connected to some ordinary legal concepts. In fact, the role that her traffic light concept had in her world was fairly broad. She also understood the concept of a light being triggered by traffic on a side street and of a sequence of light being synchronized for a constant speed.

APPENDIX: THE CONCEPT OF A CONCEPT

Private and Public Concepts: In using concept parameters, the focus has been on the role concepts, play for persons. This should not suggest that a person’s concepts bear no relation to the concepts of others. In illustrating the use of the integration parameter, we considered ways in which a person’s concept may be a variant of a concept as used in some community. In fact, our private concepts are usually acquired thru the social practices that involve public concepts as used in some community. Without having public concepts, we should not expect our attempts to communicate to be successful. Moreover knowing that people can communicate is part of our basic reliable knowledge. I also noted that concepts are like interwoven strands that support each other within some net. Taken together, this indicates my perspective on the status of concepts. Concepts have their place as tools in some public or private net. Before further considering the concept of a concept, consider an example of public and private nets given below.

Example: Ron is a football fan. Peg is not. They clearly have different variants of a football net. Their nets are private in the sense that she alone has direct access to her net and he alone has direct access to his. Of course being private in this sense does not mean they have no information about each other’s football nets. If they were not similar in many ways, we would not use the term football for them. In general, we all think of our private football nets as variants of some public football net. That Ron’s football net is a rather faithful copy of that public net is apparent by observing his use of football concepts. That Peg’s is a copy of a small part of that net, but one sufficient for her purposes, is also apparent from her use of these concepts. For instance, altho Ron told Peg what is meant by a safety blitz in a way that any football fan would understand, she did not integrate this concept into her net. However Peg knows that not only is her football net different from Ron’s, but that his net is much more like the public one that is hers. That the community of football fans has a public football net can be conceptualized as a state of affairs for that community. In this sense, this public net is an unproblematic object of thought for both of them, and there are reasonable ways to gain and confirm information about it. Either of them may make incorrect conceptual claims about this net, but there are ways to find out that these claims are incorrect.

Private and Public Nets: Having a private net is a state of affairs that is power for some person P. It involves a type of understanding that is integrated with P’s competence. Other people can recognize that a person not only has concepts but also has a net for these concepts by seeing how the person uses these concepts in the context of that net. A public net T for some realm is a net for some group of people, who often form one or more communities. T includes the conceptual distinctions that are similar to those used in most of the private nets that members have for this realm. Most members’ private net for R will normally be a bona fide partial copy of T. A mature public net T for a community is one in which the main shared components are similar for most members. Moreover each of the individual partial copies will contain all the essential concepts of T, and as individuals expand their partial private copies of T they will tend to remain bona fide partial copies of T.

Having the Concept of a Concept: Earlier I said that having the concept of a concept is also something that we recognize from a person’s behavior, namely when the person can act in one of the ways in which it makes sense to act on the concept of a concept. Moreover the main way that it makes sense to act on the concept of a concept is to think about making (or being able to make) distinctions. This is compatible with the condensed staement below of some comments by Ossorio (2005, p27).

A concept is not to be reified as a kind of something. A concept is not an object, process, or etc. Rather “concept” is a logical derivative from the more complex “P act on concept X”. Concepts have a place in behavior because the concept ‘concept’ has a place in the concept ‘behavior’.

Concepts as Objects: This focus on recognizing when a person has the concept of a concept does not explicitly consider what a concept is. I informally addressed this by indicating that I conceptualize a private concept as a type of tool, namely as a cognitive tool that a person can use in relation to some realm. From this perspective, a private concept is an object of thought whose place is within some net of some person. Unlike persons, communities do not think, at least not in the sense that persons think. What kind of object (if any) then is a public concept? Since concepts are normally understood in relation to other concepts in some net, a short answer to this is that a public concept also has its place as an object in a net. This takes a somewhat different perspective form the above comment by Ossorio, since in calling a concept a tool, I am thinking of a concept as a kind of thing or object, altho with no intention to reify concepts. Being a tool merely seems to capture the essence of the way an individual uses a concept. It also meshes easily with the notion of public concepts, since conceptual distinctions are community tools that have been shaped and acquired thru social practices.

I am somewhat puzzled by Ossorio’s reluctance in to regard concepts as objects and his references to the trouble with concepts, since in various places he has referred to types of objects such as mental objects, mathematical objects, physical objects etc. In particular, see Ossorio (2005, p16). If we adopt a broad concept of an object, it seems reasonable to think of a person’s concept as objects of thought. This allows concepts to be covered by the basic reality concepts of Descriptive Psychology, i.e. {objects, events, processes, states of affairs}. This would seem to be desirable, as much of our thinking about concepts involves these reality categories. Saying that Ann has a concept of a democracy is clearly a state of affairs. Saying that Meg just expanded her traffic light concept is an event. Using arithmetic concepts to calculate 34·27 is a process. Etc.

In using the term ‘object of thought’, I am making only ordinary ontological commitments to our reliable knowledge that people engage in the activity of thinking. To say that the score of a last night’s game is an object of my thought only entails it being something that I can think about in relation to that game. It does not mean that this score has some kind of transcendent existence in some platonistic realm of ideas. I assume Ossorio’s use of ‘mental object’ is like my use of ‘object of thought’.

A Broad Object Concept: One dictionary entry defines an object as a material thing that can be seen or touched. This narrow concept of an object cannot be what Ossorio has in mind, since he includes mathematical object and mental objects. Another entry says that an object is a focus of somebody’s attention. A third says anything that can be known or perceived by the mind. This last entry suggests the kind of broad object concept I am using when I refer to a concept as an object of thought.

Using a broad concept, almost anything can be conceptualized as an object in what Julian Jaynes call our mind space. We say that the demonstration was massive, metaphorically ascribing a kind of attribute to it that we ascribe to a physical object. We use the metaphor of seeing, in saying that I see what you mean, as if your meaning was an object to be seen. We talk about the impact of his culture on his actions, again thinking of his actions and his culture as things that we can individualize in our thinking about certain matters. In fact, most of a person’s world makes sense only in terms objects that are conceived in terms of the roles they play. Even an object like a basketball, which we normally identify by its physical attribute, is a basketball only by having a role in the realm of sports. In the physical realm, it is a spherical object of a certain size and composition. That the player made a 3 point shot is likely to seem more significant than that a spherical object passed thru a circular rim while coming from etc. In general, to be an object (using a broad concept) is to have a place in some realm of interest, and realms may vary considerably in the extent to which physical aspects are significant.

Perhaps one reservation about calling a concept or a net an object is that a concept cannot be directly transferred from one person to another as can objects that have more physical attributes such as a coin or a basketball. Concepts must be acquired by the person or community who needs them. However this

is the case with many objects that we do not ordinarily think of as physical, such as beliefs, attitudes, traits, ideals, laws, principles, rules, institutions, etc. Whatever reluctance there may be in the Descriptive Psychology community, I will adopt an object concept that allows anything to be conceptualized as an object, at least for some purposes. This will include those just mentioned. In fact, these objects are much more significant in our important worlds than are the objects that we identify as primarily physical.

The reality concepts of Descriptive Psychology are crucial for thinking about what actually happens, i.e. without these or similar concepts we could not think about our world is any systematic manner. Thus they cannot be reduced analytically to more basic concepts. They can be partially explained by conceptual specifications. Below is one that I use to think about our broad object concept.

Anything that we can individualize as having a place in some realm of interest and which can be thought of as maintaining its individuality for our purposes in thinking about matters can be conceptualized as an object within that realm.

There are various reasons that this should not be regarded as an analytic definition. In particular, it involves the concept of individuality, which could be regarded as intertwined with (rather than more basic than) the concept of an object. A similar remark could be made about the concepts of anything, a realm, etc. For instance, we individualize something by the role it plays in our thinking. So the individuality aspect is not intended to mean that something is unchanging in terms of its physical composition. This is not how zero can be individualized in the realm of natural numbers. Nor is this the way we individualize the United States Constitution. This is not even the way we normally think about objects whose composition we regard as physical. For instance, I think of certain large rocks in Barbin Branch (a creek branch running thru my land) as maintaining their individuality, altho I know they are probably being physically changed by the water. I maintain the individuality of Barbin Branch, not thinking of it as the water, in spite of the Greek philosopher who said that you couldn’t step in the same river twice.

Things: I have probably already belabored my reaction to Ossorio saying that a concept is not an object. However I will also respond to his Ossorio (2006a, p29) remark that there is no such thing as a concept, followed by a quote from well-known architect, “If a concept were something then it would have to be a very peculiar something.” Ossorio then adds a concept is not a something and it is not something peculiar. Perhaps this is because the word ‘thing’ has a narrower connotation for him that than it does has for me. As Paul Zeiger once said to me, being a mathematician, you can thingify anything. This is not surprising, since mathematicians conceptualize the empty set as something (some thing) rather than nothing (no thing). After all, it is an element of the set whose only element is the empty set. As regard to a broad thing concept (which relates to conceptualizing a concept as an object), consider some things indicated by Lewis Carroll (from Through the Looking-Glass and What Alice Found There, 1872). Note that the last two things are states of affairs.

"The time has come," the Walrus said,
"To talk of many things:
Of shoes--and ships--and sealing-wax--
Of cabbages--and kings--
And why the sea is boiling hot--
And whether pigs have wings."

Using the term ‘thing’ for a broad concept is compatible with its incorporation into words like ‘anything’, ‘something’ etc. In a narrow sense, the word ‘thing’ has a narrow physical connotation. In that sense a shoe is a thing, but in spite of what the walrus said, a king is not a thing. Likewise I learned that a noun names a person, place or thing. Perhaps the word ‘or’ is not being used in an

exclusive sense. In other contexts the word ‘thing’ does not have these physical connotations. Consider ‘things are not what they seem’, ‘there are more things in the world than’, ‘a strange thing happened’ etc. As occurring in the root of other words ‘thing’ can mean almost anything. When my great grandson Caleb was about 3 years old, he asked Charmayne what granddaddy was doing at the cabin. She said that she did not know. He remarked that granddaddy was at the cabin doing something. Clearly his concept of something allowed for almost anything.

Side Remarks of a Mathematician: As Paul indicated, my predilection for a broad concept of an object may relate to the fact that I am a mathematician. Not having a platonistic realm in which to place the empty set, I want to regard it as a concept. Even if I imagined it and other mathematical objects as have a place in some platonistic realm, what I know best are mathematical concepts. Moreover since the empty set is a member of every ordinal and since the ordinals form the backbone of the universe of sets I want to regard it as an object. Our mathematical talk sounds like we are talking about objects and none of it refers to objects that are in any way physical.

Since mathematical discourse does not indicate whose mathematics is being considered, it seems to suggest those mathematical objects are independent of individual persons, and perhaps even of all persons. Perhaps such language could be reduced to language about private mathematical objects, but mathematicians have no inclination to make such a reduction. This impersonal mode of speech is convenient. It helps point towards the conceptual strands used for thinking about common element in our mathematical experience. For this purpose we need the primary concept of a mathematical object to be an object either in our public math net or in some platonistic realm. As a mathematician who is agnostic with respect to a platonistic ontology, I prefer the former perspective.

References: Formulations of many of the concepts from Descriptive Psychology can be found in the file entitled Concept Encyclopedia on the Descriptive Psychology section of conceptualstudy.org. For a comprehensive introduction to these concepts, see Persons, Behavior, and the World, by Mary Shideler. For a deeper perspective, see various books from the collected works of Peter Ossorio. Also see the Society for Descriptive Psychology website sdp.org.

Bloom’s Taxonomy of Educational Objectives for the Cognitive Domain. (http://faculty.washington.edu/krumme/guides/bloom.html).

Pais, John and Singer, F. Richard III (2005), Constructivist Learning Resources, conceptualstudy.org in the Constructivist Learning Section.

Ossorio Peter (1998) Place. Ann Arbor MI: Descriptive Psychology Press.

Ossorio Peter (2005) What Actually Happens. Ann Arbor MI: Descriptive Psychology Press.

Ossorio Peter (2006a) In A World Of Persons And Their Ways. In K. Davis & R. Bergner (Eds), Advances in Descriptive Psychology (Vol 8, pp 7-32). Ann Arbor MI: Descriptive Psychology Press.

Ossorio Peter (2006b) Out of Nowhere. In K. Davis & R. Bergner (Eds), Advances in Descriptive Psychology (Vol 8, p124). Ann Arbor MI: Descriptive Psychology Press.

Shideler, Mary (1988) Persons, behavior, and the world. New York: University Press of America

Singer, F. Richard III (2008) A Constructivist Bridging Example. conceptualstudy.org in the Constructivist Learning Section.

Singer, F. Richard III (2007) A Personal Approach to Conceptual Philosophy. conceptualstudy.org in the Philosophy Section.