I don't know where else to put this question but I'm hopeful some of the smart people here can help.
My question concerns language or the relation between language and concepts or ideas. I've been reading and rereading Skemp's "The Psychology of Learning Mathematics" and after referring to some other books on cognition, realize that in sixty years I never realized that a "concept" is an _abstraction_. Benjafield's book "Cognition" says on p 63 that abstraction is "the process of including recurring attributes and excluding nonrecurring attributes. A particular thing or object is a "positive instance" of a concept if it has all the "criterial attributes" of the concept.
This is all fine and good. What I don't understand is this:
Is my idea of the sun a concept? I don't mean my idea of the sun as "positive instance" of the (abstract) concept "star." Primitive people didn't know the sun was a star, anyway. I speak of the sun as a unique thing which I have an idea or memory of in my mind once I've perceived it. So, if a concept is an abstraction, then my idea of the sun as a unique thing must not be a concept. I must say it is simply an "idea." (?) Is it a contradiction in terms to speak of a "concrete concept"?
I'll give another perhaps better example. I'm a translator, and I'm interested in the way concrete concepts underlying some words (which symbolize the concepts) such as "stomach," "the sun" and the like can be "translated" merely by looking it up in a dictionary. Other more abstract concepts can not be understood in this way but instead can only be understood by genuine abstraction from a number of instances, namely sentences in which the word is used. One of Skemp's points is that math teachers should stop using definitions and teach students concepts by helping the students "abstract" the concept themselves from a number of examples. In fact in my experience I'd say this is true in the case of most words. For example, you could have a glossary of anatomical terms in English and Japanese and you would't need any explanation at all since the concepts or rather the objects represented by the words are precisely the same in both cultures (leaving aside physical differences arising from race). But the English word "rice" and the Japanese word "kokoro" (heart-mind) could only be understood through the abstraction approach since they concepts don't correspond exactly.
In short, the ideas in our minds which represent the image of some particular external object are not abstracted from numerous instances but from a _single_ perception of one unique thing, which we give a name. Of course, we could classify that thing in other ways, but the abstract concept would be the name of the class (star, organ, structure, etc.) and not the unique thing.
So if these unique things are not concepts, which are by definition abstractions, what are they? Ideas?
A side thought: Skemp says that "understanding" something means fitting it into one's mental schema, which I suppose means being able to classify it in a number of ways. Thus had primitive people been able to classify the sun as a star, and as a star with a solar system and the like, they would perhaps not have worshipped as a god.
My question concerns language or the relation between language and concepts or ideas. I've been reading and rereading Skemp's "The Psychology of Learning Mathematics" and after referring to some other books on cognition, realize that in sixty years I never realized that a "concept" is an _abstraction_. Benjafield's book "Cognition" says on p 63 that abstraction is "the process of including recurring attributes and excluding nonrecurring attributes. A particular thing or object is a "positive instance" of a concept if it has all the "criterial attributes" of the concept.
This is all fine and good. What I don't understand is this:
Is my idea of the sun a concept? I don't mean my idea of the sun as "positive instance" of the (abstract) concept "star." Primitive people didn't know the sun was a star, anyway. I speak of the sun as a unique thing which I have an idea or memory of in my mind once I've perceived it. So, if a concept is an abstraction, then my idea of the sun as a unique thing must not be a concept. I must say it is simply an "idea." (?) Is it a contradiction in terms to speak of a "concrete concept"?
I'll give another perhaps better example. I'm a translator, and I'm interested in the way concrete concepts underlying some words (which symbolize the concepts) such as "stomach," "the sun" and the like can be "translated" merely by looking it up in a dictionary. Other more abstract concepts can not be understood in this way but instead can only be understood by genuine abstraction from a number of instances, namely sentences in which the word is used. One of Skemp's points is that math teachers should stop using definitions and teach students concepts by helping the students "abstract" the concept themselves from a number of examples. In fact in my experience I'd say this is true in the case of most words. For example, you could have a glossary of anatomical terms in English and Japanese and you would't need any explanation at all since the concepts or rather the objects represented by the words are precisely the same in both cultures (leaving aside physical differences arising from race). But the English word "rice" and the Japanese word "kokoro" (heart-mind) could only be understood through the abstraction approach since they concepts don't correspond exactly.
In short, the ideas in our minds which represent the image of some particular external object are not abstracted from numerous instances but from a _single_ perception of one unique thing, which we give a name. Of course, we could classify that thing in other ways, but the abstract concept would be the name of the class (star, organ, structure, etc.) and not the unique thing.
So if these unique things are not concepts, which are by definition abstractions, what are they? Ideas?
A side thought: Skemp says that "understanding" something means fitting it into one's mental schema, which I suppose means being able to classify it in a number of ways. Thus had primitive people been able to classify the sun as a star, and as a star with a solar system and the like, they would perhaps not have worshipped as a god.
