This idea that there is generality in the specific is of far-reaching importance. - Douglas Hofstadter

Godel showed how a statement about any mathematical formal system (such as the assertion that Principia Mathematica is contradiction-free) can be translated into a mathematical statement inside number theory (the study of whole numbers). In other words, any metamathematical statement can be imported into mathematics, and in its new guise the statement simply asserts (as do all statements of number theory) that certain whole numbers have certain properties or relationships to each other. But on another level, it also has a vastly different meaning that, on its surface, seems as far removed from a statement of number theory as would be a sentence in a Dostoevsky novel.

We have a very hard time “seeing” our cognitive activity because it is the medium in which we swim. The attempt to put our finger on what counts in any given situation leads us at times to making connections between situations that are enormously different on their surface and at other times to distinguishing between situations that on first glance seem nearly identical. Our constant jockeying back and forth among our categories runs the gamut from the most routine behaviors to the most creative ones.

Categorization thus helps one to draw conclusions and to guess about how a situation is likely to evolve.