{ Information = Comprehension × Extension } Revisited • Selection 3

Selection 3 opens with Peirce remarking a critical property of genuine symbols — the class of symbols is not closed under combinations.  In particular, there are logical conjunctions of symbols and logical disjunctions of symbols which are not themselves genuine symbols.

Applying this paradigm to terms, Peirce introduces two sets of examples under the headings of conjunctive terms and disjunctive terms designed to illustrate the correspondence between manners of representation and modes of inference.

Yet there are combinations of words and combinations of conceptions which are not strictly speaking symbols.  These are of two kinds of which I will give you instances.  We have first cases like:

man and horse and kangaroo and whale,

and secondly, cases like:

spherical bright fragrant juicy tropical fruit.

The first of these terms has no comprehension which is adequate to the limitation of the extension.  In fact, men, horses, kangaroos, and whales have no attributes in common which are not possessed by the entire class of mammals.  For this reason, this disjunctive term, man and horse and kangaroo and whale, is of no use whatever.  For suppose it is the subject of a sentence;  suppose we know that men and horses and kangaroos and whales have some common character.  Since they have no common character which does not belong to the whole class of mammals, it is plain that mammals may be substituted for this term.  Suppose it is the predicate of a sentence, and that we know that something is either a man or a horse or a kangaroo or a whale;  then, the person who has found out this, knows more about this thing than that it is a mammal;  he therefore knows which of these four it is for these four have nothing in common except what belongs to all other mammals.  Hence in this case the particular one may be substituted for the disjunctive term.  A disjunctive term, then, — one which aggregates the extension of several symbols, — may always be replaced by a simple term.

Hence if we find out that neat are herbivorous, swine are herbivorous, sheep are herbivorous, and deer are herbivorous;  we may be sure that there is some class of animals which covers all these, all the members of which are herbivorous.  Now a disjunctive term — such as neat swine sheep and deer, or man, horse, kangaroo, and whale — is not a true symbol.  It does not denote what it does in consequence of its connotation, as a symbol does;  on the contrary, no part of its connotation goes at all to determine what it denotes — it is in that respect a mere accident if it denote anything.  Its sphere is determined by the concurrence of the four members, man, horse, kangaroo, and whale, or neat swine sheep and deer as the case may be.

Now those who are not accustomed to the homologies of the conceptions of men and words, will think it very fanciful if I say that this concurrence of four terms to determine the sphere of a disjunctive term resembles the arbitrary convention by which men agree that a certain sign shall stand for a certain thing.  And yet how is such a convention made?  The men all look upon or think of the thing and each gets a certain conception and then they agree that whatever calls up or becomes an object of that conception in either of them shall be denoted by the sign.  In the one case, then, we have several different words and the disjunctive term denotes whatever is the object of either of them.  In the other case, we have several different conceptions — the conceptions of different men — and the conventional sign stands for whatever is an object of either of them.  It is plain the two cases are essentially the same, and that a disjunctive term is to be regarded as a conventional sign or index.  And we find both agree in having a determinate extension but an inadequate comprehension.

(Peirce 1866, pp. 468–469)


  • Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.


cc: CyberneticsOntolog ForumStructural ModelingSystems Science

This entry was posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Information Theory, Inquiry, Intension, Logic, Logic of Science, Peirce, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations and tagged , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

8 Responses to { Information = Comprehension × Extension } Revisited • Selection 3

  1. Pingback: Survey of Pragmatic Semiotic Information • 4 | Inquiry Into Inquiry

  2. Pingback: { Information = Comprehension × Extension } Revisited • Selection 4 | Inquiry Into Inquiry

  3. Pingback: { Information = Comprehension × Extension } Revisited • Comment 1 | Inquiry Into Inquiry

  4. Pingback: { Information = Comprehension × Extension } Revisited • Comment 2 | Inquiry Into Inquiry

  5. Pingback: Survey of Pragmatic Semiotic Information • 4 | Inquiry Into Inquiry

  6. Pingback: Survey of Pragmatic Semiotic Information • 5 | Inquiry Into Inquiry

  7. Pingback: C.S. Peirce and Category Theory • 4 | Inquiry Into Inquiry

  8. Pingback: Survey of Pragmatic Semiotic Information • 6 | Inquiry Into Inquiry

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.