ONT Re: Inquiry Into Information -- Cats Not Blue
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
I am going to run through the series of concrete illustrations
that Peirce lays out to explain his take on the conceptions of
extension, intension, and information. It is a mite long, but
helps better than anything else I know to bring what Peirce is
talking about down to earth. For ease of comprehension I will
divide this extended paragraph into more moderate-sized chunks.
| For example, take 'cat'; now increase the extension of that greatly --
| 'cat' or 'rabbit' or 'dog'; now apply to this extended class the
| additional intension 'feline'; -- 'feline cat' or 'feline rabbit'
| or 'feline dog' is equal to 'cat' again. This law holds good as
| long as the information remains constant, but when this is changed
| the relation is changed. Thus 'cats' are before we know about them
| separable into 'blue cats" and 'cats not blue' of which classes 'cats'
| is the most extensive and least intensive. But afterwards we find out
| that one of those classes cannot exist; so that 'cats' increases its
| intension to equal 'cats not blue' while 'cats not blue' increases its
| extension to equal 'cats'.
|
| Again, to give a better case, 'rational animal' is divisible into 'mortal rational animal'
| and 'immortal rational animal'; but upon information we find that no 'rational animal'
| is 'immortal' and this fact is symbolized in the word 'man'. 'Man', therefore, has at
| once the extension of 'rational animal' with the intension of 'mortal rational animal',
| and far more beside, because it involves more 'information' than either of the previous
| symbols. 'Man' is more 'distinct' than 'rational animal', and more 'formal' than
| 'mortal rational animal'.
|
| Now of two statements both of which are true, it is obvious that
| that contains the most truth which contains the most information.
| If two predicates of the same intension, therefore, are true of
| the same subject, the most formal one contains the most truth.
|
| Thus, it is better to say Socrates is a man, than to say Socrates
| is an animal who is rational mortal risible biped &c. because
| the former contains all the last and in addition it forms
| the synthesis of the whole under a definite 'form'.
|
| On the other hand if the same predicate is applicable
| to two equivalent subjects, that one is to be preferred
| which is the most 'distinct'; thus it conveys more truth
| to say All men are born of women, than All rational animals
| are born of women, because the former has at once as much
| extension as the latter, and a much closer reference to
| the things spoken of.
|
| CSP, CE 1, pages 187-188.
|
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤