[Inquiry] Re: Extension x Comprehension = Information

[Jon Awbrey]

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Note 4

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| 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.
|
| CSP, CE 1, pages 468-469.
|
| Charles Sanders Peirce,
|"The Logic of Science, or, Induction and Hypothesis",
| Lowell Institute Lectures of 1866, pages 357-504 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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