[Arisbe] Re: Inquiry Into Information

[Jon Awbrey]

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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 that "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, "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.

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