1. Τὰ φυσικά: The things insofar as they originate and come forth from themselves.

2. Τὰ ποιούμενα: The things insofar as they are produced by the human hand and stand as such.

3. Τὰ χρήματα: The things insofar as they are in use and therefore stand at our constant disposal-they may be either φυσικά, rocks and so on, or ποιούμενα, something specially made.

4. Τὰ πράγματα: The things insofar as we have to do with them at all, whether we work on them, use them, transform them, or we only look at and examine them--πράγματα, with regard to πρᾶξις: here πρᾶξις is taken in a truly wide sense, neither in the narrow meaning of practical use (χρῆσθαι), nor in the sense of πρᾶξις as moral action: πρᾶξις is all doing, pursuing, and enduring, which also includes ποίησις; finally:

5. Τὰ μαθήματα: According to the characterization running through these four, we must also say here of μαθήματα: The things. insofar as they ... but the question is: In what respect?

In every case we realize that the mathematical concerns things, and in a definite respect. With the question concerning the mathematical we move within our original question "What is a thing?" In what respect are things taken when they are viewed and spoken of mathematically?

We are long used to thinking of numbers when we think of the mathematical. The mathematical and numbers are obviously connected. Only the question remains: Is this connection because the mathematical is numerical in character, or, on the contrary. is the numerical something mathematical? The second is the case. But insofar as numbers are in a way connected with the mathematical there still remains the question: Why precisely are the numbers something mathematical? What is the mathematical itself that something like numbers must be conceived as something mathematical and are primarily brought forward as