WHAT IS A THING?

street and to talk with people, With a cobbler. for instance,
over what a shoe is. Socrates had no other topic than what
the things are. "Are you still standing there," condescendingly
asked the much traveled Sophist of Socrates, "and
still saying the same thing about the same thing?" "Yes,"
answered Socrates, "that I am. But you who are so extremely
smart, you *never* say the same thing about the
same thing!"

The μαθήματα, the mathematical, is that "about" things which we really already know. Therefore we do not first get it out of things, but, in a certain way, we bring it already with us. From this we can now understand why, for instance, number is something mathematical. We see three chairs and say that there are three. What "three" is the three chairs do not tell us, nor three apples, three cats nor any other three things. Moreover, we can count three things only if we already know "three" In thus grasping the number three as such, we only expressly recognize something which, in some way, we already have. This recognition is genuine learning. The number is something in the proper sense learnable, a μάθημα, i.e., something mathematical. Things do not help us to grasp "three" as such, i.e., threeness. "Three"—what exactly is it? It is the number in the natural series of numbers that stands in third place. In "third"? It is only the third number because it is the three. And .. place"—where do places come from? "Three" is not the third number, but the first number. "One" isn't really the first number. For instance, we have before us one loaf of bread and one knife, this one and, in addition. another one. When we take both together we say, "both of these," the one and the other, but we do not say, "these two," or 1 + 1. Only when we add a cup to the bread and the knife do we say "all." Now we take them as a sum, i.e., as a whole and so and so many. Only when we perceive it from the third is the former one the first. the former other the second. so that one and two arise, and "and" becomes "plus," and there arises the possibility of places and