Concepts.

In our short reading this week, we discussed the principles of open concepts and closed concepts. Open concepts are those which have no limit to the amount of defining conditions for the object at hand, closed concepts are those which have a set, clear limit to the amount of necessary defining conditions. One thing I've noticed is the specific objects tend to have closed concepts whereas the broader objects tend to have open concepts. This is expected, of course, since specific objects, such as an apple, require less "umbrella" features than broader concepts, such as food. When giving the necessary conditions for an apple, you give it's specific defining features. However, when giving the definition for food, each condition must satisfy every object that could be considered food, but at the same time no object that isn't food can contain all of the defining principles. For instance, if you were to define a healthy, growing empire apple, you may list its defining conditions as red and tart. However, under food, these conditions can't appear, since spaghetti is yellow and not tart at all, but is still considered food. Satisfying these conditions is difficult, but rewarding when the definition can finally become closed.

A second point that I've noticed about concepts is that those objects with mathematical basis tend to be closed concepts. This is because mathematical proof is indubitably fortifying evidence, provided the analysis is correct. For instance, in class Johnson used the triangle as an example, since triangles have specific parameters under which they can be called triangles (interior angles add up to 180 degrees, 3 sides, all connect at vertices.)

My question is this: Would you argue that broader concept have less conditions or more conditions than specific concepts?