[Inquiry] Re: Pure Symbols -- Discussion

Tue Mar 29 14:00:14 CST 2005

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PS.  Discussion Note 16

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I did not think that the mere idea that some symbols
are compound, complex, or complicated -- in some sense
of those words that may remain to be explicated, if ever
the exact sense looks like it's going to become critical,
which it may never be -- since the familiar homilies that
sentences, books, and people are symbols seems to go about
as far as we need in the direction of complexity for symbols.
And of course it seems 'prima facie' obvious that any symbol
as complicated as a sentence, a book, or a person could have
all sorts of other varieties of signs woven into its texture.

In this connection, if not directly, it may serve to remember
that complications of symbols not themselves symbols were one
of the prototypical ways that the early Peirce was led to his
studies of icons and indices in connection with the varieties
of approximate or synthetic inference.  For example, consider
the excerpts from the Lowell Institute Lectures of 1866 that
I copy below.

Jon Awbrey

ICE 3.  http://stderr.org/pipermail/inquiry/2004-January/001033.html
ICE 4.  http://stderr.org/pipermail/inquiry/2004-January/001034.html
ICE 5.  http://stderr.org/pipermail/inquiry/2004-January/001035.html
ICE 6.  http://stderr.org/pipermail/inquiry/2004-January/001036.html
ICE.    http://stderr.org/pipermail/inquiry/2004-January/thread.html#1031
ICE.    http://stderr.org/pipermail/inquiry/2004-February/thread.html#1122

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ICE.  Note 3

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| For this purpose, I must call your attention to
| the differences there are in the manner in which
| different representations stand for their objects.
|
| In the first place there are likenesses or copies -- such as
| 'statues', 'pictures', 'emblems', 'hieroglyphics', and the like.
| Such representations stand for their objects only so far as they
| have an actual resemblance to them -- that is agree with them in
| some characters.  The peculiarity of such representations is that
| they do not determine their objects -- they stand for anything
| more or less;  for they stand for whatever they resemble and
| they resemble everything more or less.
|
| The second kind of representations are such as are set up
| by a convention of men or a decree of God.  Such are 'tallies',
| 'proper names', &c.  The peculiarity of these 'conventional signs'
| is that they represent no character of their objects.  Likenesses
| denote nothing in particular;  'conventional signs' connote nothing
| in particular.
|
| The third and last kind of representations are 'symbols' or general
| representations.  They connote attributes and so connote them as to
| determine what they denote.  To this class belong all 'words' and
| all 'conceptions'.  Most combinations of words are also symbols.
| A proposition, an argument, even a whole book may be, and
| should be, a single symbol.
|
| C.S. Peirce, 'Chronological Edition', CE 1, 467-468.
|
| 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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ICE.  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.
|
| C.S. Peirce, 'Chronological Edition', CE 1, 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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ICE.  Note 5

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| Accordingly, if we are engaged in symbolizing and we come to such
| a proposition as "Neat, swine, sheep, and deer are herbivorous",
| we know firstly that the disjunctive term may be replaced by a
| true symbol.  But suppose we know of no symbol for neat, swine,
| sheep, and deer except cloven-hoofed animals.  There is but one
| objection to substituting this for the disjunctive term;  it is
| that we should, then, say more than we have observed.  In short,
| it has a superfluous information.  But we have already seen that
| this is an objection which must always stand in the way of taking
| symbols.  If therefore we are to use symbols at all we must use
| them notwithstanding that.  Now all thinking is a process of
| symbolization, for the conceptions of the understanding are
| symbols in the strict sense.  Unless, therefore, we are to
| give up thinking altogeher we must admit the validity of
| induction.  But even to doubt is to think.  So we cannot
| give up thinking and the validity of induction must be
| admitted.
| 
| C.S. Peirce, 'Chronological Edition', CE 1, 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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ICE.  Note 6

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| A similar line of thought may be gone through
| in reference to hypothesis.  In this case we
| must start with the consideration of the term:
|
| 'spherical, bright, fragrant, juicy, tropical fruit'.
|
| Such a term, formed by the sum of the comprehensions of several terms,
| is called a conjunctive term.  A conjunctive term has no extension
| adequate to its comprehension.  Thus the only spherical bright
| fragrant juicy tropical fruit we know is the orange and that
| has many other characters besides these.  Hence, such a term
| is of no use whatever.  If it occurs in the predicate and
| something is said to be a spherical bright fragrant juicy
| tropical fruit, since there is nothing which is all this
| which is not an orange, we may say that this is an orange
| at once.  On the other hand, if the conjunctive term is
| subject and we know that every spherical bright fragrant
| juicy tropical fruit necessarily has certain properties,
| it must be that we know more than that and can simplify the
| subject.  Thus a conjunctive term may always be replaced by
| a simple one.  So if we find that light is capable of producing
| certain phenomena which could only be enumerated by a long conjunction
| of terms, we may be sure that this compound predicate may be replaced
| by a simple one.  And if only one simple one is known in which the
| conjunctive term is contained, this must be provisionally adopted.
|
| C.S. Peirce, 'Chronological Edition', CE 1, 470.
|
| 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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