[Inquiry] Re: Logic 101

[Jon Awbrey]

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LOG.  Note 6

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| Logic Chapter 1 (cont.)
|
| Relations on account of their double reference, will
| be separable again into two kinds;  and representations
| on account of their triple reference, will be separable
| into three kinds.
|
| To begin with relation.
|
| Every relate has both a reference to a correlate and also necessarily
| connected with that a reference to a ground.  If no reference to an
| interpretant is involved, the reference to a ground may be prescindible
| from reference to the correlate, that is, it may be in itself a simple
| quality, or it may require the introduction of reference to a correlate
| in order to be represented and then it may be termed a relative quality.
|
| Let it be remembered that we speak here only of real relations, that is to
| such as can be prescinded by position from all reference to a comparer or
| 'correspondent'.  We have already seen that the correlate to which a simple
| quality refers, is such a one as makes a generalization possible;  that is to
| say it is a correlate of 'agreement'.  A reference to a ground which implies
| a reference to a correlate is such as killing, approaching, etc.  It is, thus,
| a ground of difference 'in actu'.  Difference in predicates merely, as 'larger',
| etc., can only be considered as an ideal relation, because the two terms cannot
| be represented as having any connection thereby except to a 'correspondent'.
| It thus stands on a different footing from agreement, which can be prescinded
| by position from all such reference, and still be a relation.  Agreement, then,
| and difference 'in actu' are the two kinds of real relations.
|
| We may here note a few of their peculiarities.  If 'A' agrees with 'B',
| 'B' also agrees with 'A' upon the same ground;  but if 'A' differs from 'B',
| 'B' differs from 'A' upon the contrary ground.  This is true of all relations,
| real or ideal.*  Agreement involves a setting over against, which is possible
| when there is a difference, real or ideal, between the agreeing terms.  At the
| same time, if no real diversity between the two terms is supposed, agreement may
| be prescinded by position from difference.  But the converse proposition does not
| hold.  For, in the first place, total exclusion in comprehension, that is absolute
| unlikeness is an absurdity, since things so unrelated could not be brought under
| one conception, whereas it is the only possible justification of a hypothesis
| that it makes the manifold comprehensible.  Now we may take for granted, for
| argument's sake, what only 'may' be justified;  but we cannot suppose that
| our own supposition is unjustifiable, and still continue to make the
| supposition.  In order, therefore, to suppose or conceive an exclusion
| in comprehension, we must neglect what nevertheless is contained in the
| conception, namely that it is unjustifiable;  that is to say we can only
| conceive of real difference without agreement by confusion but not by
| position.  Since then real difference involves agreement, but not
| conversely, we must understand agreement, first, in order to
| understand real difference.
|
|* Contrariety has proved difficult to define.  The essence of it
|  seems to be the relation  between a pair of relative qualities
|  which are the grounds of the two reciprocal differences of two
|  differing things.  Thus if 'A' is light relatively to 'B',
|  'B' is heavy in comparison with 'A';  and hence 'heavy'
|  and 'light' are termed contraries.
|
| C.S. Peirce, 'Chronological Edition', CE 1, 354-355
|
| C.S. Peirce, "Logic Chapter 1", MS 115 (1866), pp. 351-356 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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