Peirce on Information:
“If a sign, B, only signifies characters that are elements (or the whole) of the meaning of another sign,
A, then B is said to be a predicate (or essential part) of A. If a sign, A, only denotes real objects that
are a part or the whole of the objects denoted by another sign, B, then A is said to be a subject (or
substantial part) of B. The totality of the predicates of a sign, and also the totality of the characters it
signifies, are indifferently each called its logical depth. This is the oldest and most convenient term.
[Synonyms are: comprehension, content (Inhalt), force, connotation.] The totality of the subjects, and
also, indifferently, the totality of the real objects of a sign, is called the logical breadth. [Synonyms are:
extension, sphere (Umfang), scope, denotation.] Besides the logical depth and breadth, I have proposed
(in 1867) the terms information and area to denote the total of fact (true or false) that in a given state of
knowledge a sign enbodies” (305, New Elements).
“Symbols which directly determine only their grounds or imputed qualities, and are thus but sums of
marks or terms” (8). “Symbols which also independently determine their objects by means of other
term or terms, and thus, expressing their own objective validity, become capable of truth or falsehood,
that is, are propositions” (ibid.). “Symbols which also independently determine their interpretants, and
thus the minds to which they appeal, by premising a proposition or propositions which such a mind is
to admit. These are arguments” (ibid.).
“In a proposition, the term which separately indicates the object of the symbol is termed the subject,
and that which indicates the ground is termed the predicate” (9).
“The other division of terms, propositions, and arguments arise from the distinction of extension and
comprehension. I propose to / treat this subject in a subsequent paper. But I will so far anticipate that,
as to say that there is, first, the direct reference of a symbol to its objects, or its denotation; second, the
reference of the symbol to its ground, through its object, that is, its reference to the common characters
of its objects, or its connotation; and third, its reference to its interpretants through its object, that is, its
reference to all the synthetical propositions in which its objects in common are subject or predicate, and
this I term the information it embodies. And as every addition to what it denotes [e.g. what else is a
dog], or to what it connotes [e.g. what other qualities dogs have], is effected by means of a distinct
proposition of this kind, it follows that the extension and comprehension of a term are in an inverse
relation, as long as the information remains the same, and that every increase in information is
accompanied by an increase of one or the other of these two quantities. It may be observed that
extension and comprehension are very often taken in other senses in which this last proposition is not
true” (11, On a List of New Categories).
(A synthetic proposition is a proposition that is capable of being true or untrue based on facts about
the world.)
The information in a term (to a speech community, or for a speaker):
What counts as a dog: new referents can be added to the extension (e.g. fluffy is a dog)
What properties dogs have: new qualities can be added to the intension (e.g. dogs are mammals)
The totality of extension and intension: new referents or new qualities can be added to information.
And so any utterance may precisely convey new extension or intension to a speaker and, over time, to a
community. Every quality can then be predicated of every referent. And information is precisely the
‘newness’ property of the conjunction. And for Peirce, it can be quantified. Indeed, he speaks of
equality and increase and decrease. And even of multiplication. (And these can be true of unique
referents (e.g. Peter, that lion) as much as classes (e.g. men, lions).
Information = Denotation x Connotation.
Interpretants: reference to all propostions in which term is subject or predicate.
The information in a proposition (to a speech community, or for a speaker)