[Inquiry] Re: Logic Of The Sciences

[Jon Awbrey]

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LOTS.  Note 9

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Here is a passage that I initially skipped over, as it presents us
with an exercise in broken field reading that I judged too extreme
for a first pass.  On further consideration, however, it does give
us a clear case of interaction between extensional and intensional
reasoning, a feature that will, in the fullness of time, come to
distinguish Peirce's "Logic of Relatives" from the syllogistic
horde of past and present barbarisms.

| It would be impossible to analyze representation into its inward constituent
| characters since any elements into which it might seem to be separated would
| be, themselves, representations.  Representation implies contrast;  hence it
| has an inward character only so far as that can be contrasted with something.
| Now, as all things are representations alike, they can only be contrasted in
| their relations.  Hence, the only inward character of representation is the
| relation of anything to itself, -- 'identity'.  But the different essential
| external relations of representation can be distinguished very well, because
| all things do not stand in essential relation to any one representation.
| It is true, that these relations are themselves representations and so
| involve each other.  But though they cannot be separated in the
| nature of things, they can in representation.
|
| To understand representation as a mark, we must consider the different orders
| of marks.  By a mark of the 1st, 2nd, 3rd order is meant one which indicates
| a state of things which essentially supposes one thing, two things, or three
| things.  A mark of the second order determines the subject in two ways, viz.:
| 1st to relate to a certain object and 2nd to relate to it in a certain respect.
| Hence it consists of two marks of the first order which are essential to each
| other;  viz.:  1st a mark which the subject has in common with the correlate
| and 2nd the distinction which the subject has from the correlate.  For example;
| "on my right hand" consists 1st of being relatively to 'me' and 2nd of being at
| the right hand.
|
| A mark of the third order, implies two things beside the subject;
| it therefore 1st determines the subject to stand in a certain relation
| to the first thing, 2nd to stand in a certain relation to the second thing,
| 3rd to stand in such relations to the two that these relations shall involve
| each other, for otherwise we should have merely two marks of the second order
| and not any of a different order.  Hence, a mark of the third order consists
| of three mutually involved marks of the 2nd order.  Each of these marks of
| the second order must consist of two marks of the 1st order.  Accordingly
| the mark of the third order consists of
|
|    1 Being relatively to 'A'
|    2 Being of a kind 'a'
|    3 Being relatively to 'B'
|    4 Being of a kind 'b'.
|
| C.S. Peirce, 'Chronological Edition', CE 1, 324-325
|
| C.S. Peirce, "Logic of the Sciences", MS 113 (1865), pp. 322-336 in:
|'Writings of Charles S. Peirce:  A Chronological Edition, Vol. 1, 1857-1866',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.

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