Monday, April 15, 2013

What is a "concept"?

(Translated from: Qu'est-ce qu'un concept ?)

"What is a concept? " asked once a friend of mine. I had used this word while we were talking about economy.

 This friend has suffered like me philosophy in the last year in high school. She may not have been paying attention, it may be that his teacher was a mediocre philosopher or poor teacher. To understand the philosophy, told me a philosopher who thought of his own experience, one must have reached at least the age of thirty years, have formed a family, have children and practice a profession ... What can we understand at the age of eighteen?

 I admire the choice and depth of the readings of this friend, if not their extent, but this fine and intelligent person kept so unpleasant memories of the course of philosophy that she close her ears when she hears one of the terms of the technical vocabulary, in particular "concept".

It is therefore normal that she does not know what it means. I begun to understand it when, working at INSEE, I questioned the relevance of the classification of activities and the relationship between statistics and economic theory.
*     *
"A concept, I said, that's an idea associated with a definition." As it meant nothing to her, I had to develop.
"Everyone, I said, has an idea of what a circle is: it is a regular round whose nature provides examples. The outline of the full moon, the section of a branch of a tree are circles. This idea, which is associated with an image, helps to recognize a circle when we see it but not reason about the circle in order to explore its mathematical properties.

 "For this, it must be defined. Several definitions are possible: the circle is the set of points in the plane equidistant from a given point, or the set of points in the plane from where we see a segment at a right angle, or the closed line with a given length which encloses the largest planar surface, etc. These definitions are equivalent because we can pass from one to the other by a demonstration.

"To possess the concept of a circle, one has to know one of these definitions. It may be that one of these definitions provides a more convenient starting point for the demonstrations: it is this one that will retain a mathematician concerned with elegance, that is to say efficiency.

"It is the same for the triangle: we easily recognize one of them when we see it, but it must be defined if we want to show that the sum of the angles is 180 °, determine the formula for the surface, say whether two triangles are equal or similar, and so on.

 "Ideas do not lend themselves to any conceptualization: Aristotle himself said that we should not try to define everything. Of all the faces we recognize that of the beloclassification of activitiesved person, but it would be impossible to condense it into a definition."

*     *
Having said that concepts are, I thought I should go further to show what they do.

"The concepts, have I said, are a fundamental element of any theory. In economic theory, for example, the basic concepts are the consumer, the company and the product, and they still cover other concepts. "Product" for instance develops in final product, intermediate product, capital good, which develop themselves in a nomenclature that could go to infinity if we did not have to abstract the detail in order to reason. The grain of the nomenclature depends on what you should do: when the hiker of the city sees only "trees," a forester sees "birch, beech, oak, pine etc." among which he still distinguishes subcategories.

"To the nomenclature of concepts theory adds causality: in economics, the value of consumption is thus a function of household income and savings behavior, the production cost will depend on factor prices and quantity produced, the investment will depend on the cost function, anticipated demand and interest rates, etc.

"Concepts and theories are not reserved to the intellectual life: they are present in everyday life and practice. When we learned to drive a car it took us assimilate concepts and causalities to use gearbox, brake, accelerator, and to know how to select in the image that appears on our retina the signals necessary for driving.

 "It is therefore wrong to believe that concepts are a matter of pure philosophy and that the theory can be used only by theoreticians. Our daily work is based on the concepts and patterns of causality that education and experience have formed. The intellect relies however, to illuminate a special area on few concepts that bind long chains of reasoning while everyday life, which confronts us with the diversity of nature, involves many concepts on which reasoning process with quick little steps or even short-circuit.

"Concept" and "theory" are instruments of our daily lives. Isn't it true, moreover, for the intellectual activity itself? When we claim that there is a bulkhead between theory and practice, aren't we the victims or accomplices of the interested pedantry of academic corporations? "

*     *
My friend said she understood what I was saying but it would take her time to "realize" it, to "understand that it is real." I conceive that she needs to think at leisure: didn't it took me a few decades to clarify what is a concept, what is a theory, and what they serve?

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