ONT Re: Information = Comprehension x Extension -- Discussion
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ICE. Discussion Note 34
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One of the distinctive characteristics of Peirce's treatment of
information is the way that he makes comprehension and extension
relative to the state of information or the state of knowledge of
the interpreter. For example, consider the following statements:
ICE 12. http://suo.ieee.org/ontology/msg03770.html
| It is important to distinguish between the two functions of a word:
| first to denote something -- to stand for something -- and second to
| mean something -- or as Mr. Mill phrases it -- to connote something.
|
| What it denotes is called its Sphere.
| What it connotes is called its Content.
|
| Thus the sphere of the word "man" is for me every man I know;
| and for each of you it is every man you know.
|
| The content of "man" is all that we know of all men, as being two-legged,
| having souls, having language, etc., etc. It is plain that both the
| sphere and the content admit of more and less. ...
|
| Now the sphere considered as a quantity is called the Extension;
| and the content considered as quantity is called the Comprehension.
|
| Extension and Comprehension are also termed Breadth and Depth.
|
| C.S. Peirce, Lowell Lecture 7, CE 1, 459.
ICE 16. http://suo.ieee.org/ontology/msg03775.html
| 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.
|
| C.S. Peirce, Lowell Lecture 7, CE 1, 462.
|
| Charles Sanders Peirce,
|"The Logic of Science, or, Induction and Hypothesis",
| Lowell Institute Lectures (1866), 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.
How can we give this principle of relativity to a state of information
its due representation in our interpretive modeling of Peirce's theory?
Jon Awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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