[Inquiry] Re: Peirce's Logic Of Information

[Jon Awbrey]

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

PLOI.  Note 4

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Let's jump in and see if we can tackle a couple of the more concrete examples
that Peirce gives us of processes that change an agent's state of information,
in the present application exemplifying the properties of inductive reasoning.

The run up to the first example begins as follows:

| We come next to consider inductions.  In inferences of this kind
| we proceed as if upon the principle that as is a sample of a class
| so is the whole class.  The word 'class' in this connection means
| nothing more than what is denoted by one term, -- or in other words
| the sphere of a term.  Whatever characters belong to the whole sphere
| of a term constitute the content of that term.  Hence the principle of
| induction is that whatever can be predicated of a specimen of the sphere
| of a term is part of the content of that term.  And what is a specimen?
| It is something taken from a class or the sphere of a term, at random --
| that is, not upon any further principle, not selected from a part of
| that sphere;  in other words it is something taken from the sphere
| of a term and not taken as belonging to a narrower sphere.  Hence
| the principle of induction is that whatever can be predicated of
| something taken as belonging to the sphere of a term is part of
| the content of that term.  But this principle is not axiomatic
| by any means.  Why then do we adopt it?
|
| To explain this, we must remember that the process of induction is a
| process of adding to our knowledge;  it differs therein from deduction --
| which merely explicates what we know -- and is on this very account called
| scientific inference.  Now deduction rests as we have seen upon the inverse
| proportionality of the extension and comprehension of every term;  and this
| principle makes it impossible apparently to proceed in the direction of
| ascent to universals.  But a little reflection will show that when our
| knowledge receives an addition this principle does not hold.
|
| Thus suppose a blind man to be told that no red things are
| blue.  He has previously known only that red is a color;
| and that certain things 'A', 'B', and 'C' are red.
|
|    The comprehension of red then has been for him   'color'.
|    Its extension has been                           'A', 'B', 'C'.
|
| But when he learns that no red thing is blue, 'non-blue'
| is added to the comprehension of red, without the least
| diminution of its extension.
|
|    Its comprehension becomes   'non-blue color'.
|    Its extension remains       'A', 'B', 'C'.
|
| Suppose afterwards he learns that a fourth thing 'D' is red.
| Then, the comprehension of 'red' remains unchanged, 'non-blue color';
| while its extension becomes 'A', 'B', 'C', and 'D'.  Thus, the rule
| that the greater the extension of a term the less its comprehension
| and 'vice versa', holds good only so long as our knowledge is not
| added to;  but as soon as our knowledge is increased, either the
| comprehension or extension of that term which the new information
| concerns is increased without a corresponding decrease of the other
| quantity.
|
| The reason why this takes place is worthy of notice.  Every addition to
| the information which is incased in a term, results in making some term
| equivalent to that term.  Thus when the blind man learns that 'red' is
| not-blue, 'red not-blue' becomes for him equivalent to 'red'.  Before
| that, he might have thought that 'red not-blue' was a little more
| restricted term than 'red', and therefore it was so to him, but
| the new information makes it the exact equivalent of red.
| In the same way, when he learns that 'D' is red, the
| term 'D-like red' becomes equivalent to 'red'.
|
| Thus, every addition to our information about a term is an addition
| to the number of equivalents which that term has.  Now, in whatever
| way a term gets to have a new equivalent, whether by an increase in
| our knowledge, or by a change in the things it denotes, this always
| results in an increase either of extension or comprehension without
| a corresponding decrease in the other quantity.
|
| C.S. Peirce, 'Chronological Edition', CE 1, 462-464.
|
|"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 (eds.),
| Indiana University Press, Bloomington, IN, 1982.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
inquiry e-lab: http://stderr.org/pipermail/inquiry/
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o