[Inquiry] Re: Extension x Comprehension = Information

[Jon Awbrey]

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ECI.  Note 23

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If you dreamed that this inquiry had come full circle then I inform
you of what you already know, that there are always broader circles.
I revert to Peirce's Harvard University Lectures of the year before,
to pick up additional background material and a bit more motivation.

| We are already familiar with the distinction between the extension and
| comprehension of terms.  A term has comprehension in virtue of having
| a meaning and has extension in virtue of being applicable to objects.
| The meaning of a term is called its 'connotation';  its applicability
| to things its 'denotation'.  Every symbol 'denotes' by 'connoting'.
| A representation which 'denotes' without connoting is a mere 'sign'.
| If it 'connotes' without thereby 'denoting', it is a mere copy.
|
| It is universally held that extension and comprehension
| are in reciprocal relation;  thus if 'horse' be divided
| into 'black horse' and 'non-black horse', 'black horse'
| has more intension and therefore less extension than
| 'horse'.
|
| It behooves me to say what the distinction between extension and
| comprehension is upon my view of logic.  Before doing so, however,
| I must remark that the distinction extends to propositions;  there
| are extensive and intensive propositions.
|
| An extensive proposition is defined to be one which
| states the relation between the extension of two terms.
|
| An intensive proposition is one which states the relation
| between the intension or comprehension of two terms.
|
| Subordination in extension is expressed by the term 'contained under'.
|
| Subordination in intension is expressed by the term 'contained in'.
|
| Hence in the case of affirmatives;
| an extensive judgment is expressed
| by the formula
|
|    'A' is contained under 'B'
|
| an equivalent intensive proposition
| by the formula
|
|    'B' is contained in 'A'.
|
| Thus 'black horse' is contained under 'horse',
| and 'horse' [is contained in 'black horse'].
|
| CSP, CE 1, page 272.
|
| 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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