The concepts of definition and determination converge in their concern for setting bounds to the point where they coincide at a certain level of abstraction. One avenue of approach to determination may then begin from a consideration of definition.
The moment, then, that we pass from nothing and the vacuity of being to any content or sphere, we come at once to a composite content and sphere. In fact, extension and comprehension — like space and time — are quantities which are not composed of ultimate elements; but every part however small is divisible.
The consequence of this fact is that when we wish to enumerate the sphere of a term — a process termed division — or when we wish to run over the content of a term — a process called definition — since we cannot take the elements of our enumeration singly but must take them in groups, there is danger that we shall take some element twice over, or that we shall omit some. Hence the extension and comprehension which we know will be somewhat indeterminate. But we must distinguish two kinds of these quantities. If we were to subtilize we might make other distinctions but I shall be content with two. They are the extension and comprehension relatively to our actual knowledge, and what these would be were our knowledge perfect. (Peirce, CE 1, 462)
- Peirce, C.S. (1866), “The Logic of Science; or, Induction and Hypothesis”, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.