[Inquiry] Re: Extension x Comprehension = Information

[Jon Awbrey]

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ECI.  Note 24

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Nota Bene.  In the Table below the form "XY" indicates a premiss of
a classical syllogism where X is the subject and Y is the predicate.
Also, I suspect that the Third Figure syllogism ought to be XY & XZ.

| What we have to distinguish, therefore, is not so much the
| quantity of extension from the quantity of intension as it
| is the object of connotation from the object of denotation.
| In analytical judgments there is no denotation at all.  In
| a synthetical judgment the subject is an object of denotation.
|
| o----------------------o-------------------------o-------------------o
| |                      |                         |                   |
| |                      |  (    Subject:  O of C  |            (  XY  |
| | Analytic             |  <                      |  2nd Fig.  <      |
| |                      |  (  Predicate:  O of C  |            (  ZY  |
| |                      |                         |                   |
| o----------------------o-------------------------o-------------------o
| |                      |                         |                   |
| |                      |  (    Subject:  O of D  |            (  YX  |
| | Synthetic Intensive  |  <                      |  1st Fig.  <      |
| |                      |  (  Predicate:  O of C  |            (  ZY  |
| |                      |                         |                   |
| o----------------------o-------------------------o-------------------o
| |                      |                         |                   |
| |                      |  (    Subject:  O of D  |            (  YX  |
| | Extensive            |  <                      |  3rd Fig.  <      |
| |                      |  (  Predicate:  O of D  |            (  ZX  |
| |                      |                         |                   |
| o----------------------o-------------------------o-------------------o
|
| There cannot be a judgment whose subject is an object of connotation and
| whose predicate is an object of denotation.  For a symbol 'denotes' by virtue
| of 'connoting' and not 'vice versa', hence the object of connotation determines
| the object of denotation and not 'vice versa', in the sense in which the subject
| of a proposition is the term determined and the predicate is the determining term.
| Whence if one of the terms is an object of connotation and the other is an object
| of denotation, the latter is the subject and not the former.
|
| In the other two cases, there is no difference between subject and predicate;
| except that one may be regarded as taken first.
|
| Thus these cases in which both terms are of the same kind are two kinds of
| twists of the first kind, just as the 2nd and 3rd Figures of Syllogism are
| right-handed and left-handed twists of the 1st.  This is expressed in the
| above Table.
|
| A proposition would usually be called intensive if its
| predicate were an object of connotation;  hence we have
| three kinds of propositions given by these two;  namely,
|
|    Analytic.
|
|    Synthetic Intensive.
|
|    Extensive.
|
| There is no such thing as an analytic extensive proposition.
| For an analytic proposition containing no object of denotation
| is merely the expression of a relation of comprehension.  Of course
| from an analytic proposition a synthetic one may be immediately inferred.
| From
|
|    Man is mortal
|
| we may infer
|
|    All men are mortals
|
| but the predicate 'mortals' is not a mere result of the analysis of 'men'.
| I have here slightly narrowed Kant's definition of the analytic judgment so
| as to make it not merely needless but impossible to test one by experience.
|
| CSP, CE 1, pages 272-274.
|
| Charles Sanders Peirce, "On the Logic of Science",
| Harvard University Lectures of 1865, pages 161-302 in:
|
|'Writings of Charles S. Peirce:  A Chronological Edition',
|'Volume 1, 1857-1866', Peirce Edition Project,
| Indiana University Press, Bloomington, IN, 1982.

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