[Inquiry] Re: Extension x Comprehension = Information

[Jon Awbrey]

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

ECI.  Note 16

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

| 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.
|
| Logicians have hitherto left the doctrine of extension
| and comprehension in a very imperfect state owing to the
| blinding influence of a psychological treatment of the
| matter.  They have, therefore, not made this distinction
| and have reduced the comprehension of a term to what it
| would be if we had no knowledge of fact at all.  I mention
| this because if you should come across the matter I am now
| discussing in any book, you would find the matter left in
| quite a different state.
|
| CSP, CE 1, page 462.
|
| Charles Sanders Peirce,
|"The Logic of Science, or, Induction and Hypothesis",
| Lowell Institute Lectures of 1866, pages 357-504 in:
|
|'Writings of Charles S. Peirce:  A Chronological Edition',
|'Volume 1, 1857-1866', Peirce Edition Project,
| Indiana University Press, Bloomington, IN, 1982.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o