[Inquiry] Re: Extension x Comprehension = Information

[Jon Awbrey]

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ECI.  Note 31

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| The difference between connotation, denotation, and information
| supplies the basis for another division of terms and propositions;
| a division which is related to the one we have just considered in
| precisely the same way as the division of syllogism into 3 figures
| is related to the division into Deduction, Induction, and Hypothesis.
| Every symbol which has connotation and denotation has also information.
| For by the denotative character of a symbol, I understand application
| to objects implied in the symbol itself.  The existence therefore of
| objects of a certain kind is implied in every connotative denotative
| symbol;  and this is information.
|
| Now there are certain imperfect or false symbols produced
| by the combination of true symbols which have lost either
| their denotation or their connotation.
|
| When symbols are combined together in extension,
| as for example in the compound term "cats and dogs",
| their sum possesses denotation but no connotation
| or at least no connotation which determines their
| denotation.  Hence, such terms, which I prefer to
| call 'enumerative' terms, have no information, and
| it remains unknown whether there be any real kind
| corresponding to cats and dogs taken together.
|
| On the other hand, when symbols are combined together in
| comprehension, as for example in the compound "tailed men",
| the product possesses connotation but no denotation, it not
| being therein implied that there may be any 'tailed men'.
| Such conjunctive terms have therefore no information.
|
| Thirdly, there are names purporting to be of real kinds,
| as 'men';  and these are perfect symbols.
|
| Enumerative terms are not truly symbols but only signs;
| and Conjunctive terms are copies;  but these copies and
| signs must be considered in symbolistic because they are
| composed of symbols.
|
| When an enumerative term forms the subject of a grammatical proposition,
| as when we say "cats and dogs have tails", there is no logical unity in the
| proposition at all.  Logically, therefore, it is two propositions and not one.
| The same is the case when a conjunctive proposition forms the predicate of a
| sentence;  for to say "hens are feathered bipeds" is simply to predicate two
| unconnected marks of them.
|
| When an enumerative term as such is the predicate of a proposition, that
| proposition cannot be a denotative one, for a denotative proposition is one
| which merely analyzes the denotation of its predicate, but the denotation of
| an enumerative term is analyzed in the term itself;  hence if an enumerative
| term as such were the predicate of a proposition, that proposition would be
| equivalent in meaning to its own predicate.
|
| On the other hand, if a conjunctive term as such is the subject of a proposition,
| that proposition cannot be connotative, for the connotation of a conjunctive term
| is already analyzed in the term itself, and a connotative proposition does no more
| than analyze the connotation of its subject.
|
| Thus, we have
|
|    Conjunctive, Simple, Enumerative
|
| propositions so related to
|
|    Denotative, Informative, Connotative
|
| propositions that what is on the left hand of
| one line cannot be on the right hand of the other.
|
| CSP, CE 1, pages 278-279.
|
| 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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