[Inquiry] Re: Just In Time Logic

[Jon Awbrey]

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JITL.  Note 17

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| Chapter 11.  On Logical Breadth and Depth (cont.)
|
| By the "informed depth" of a term I mean all the real characters in
| contradistinction to mere synonimous names which can be predicated of
| it with logical truth in the supposed state of information no character
| being counted twice over knowingly.  The depth like the breadth will be
| certainly doubtful and there is a comprehensive distinctness corresponding
| to extensive distinctness.
|
| The informed breadth and depth suppose a state of information which lies
| somewhere between two imaginary extremes.  There are first the state of
| knowledge in which no fact should be known but only the meanings of terms
| and, second, the state of information in which every fact should be known.
| This suggests two other sorts of breadth and depth corresponding to the two
| essential states of information which I shall term accordingly the essential
| and the substantial breadth and depth.
|
| The essential depth of a term which is sometimes called
| its essence consists of the really conceivable qualities
| predicated of it in its definition.  This is one of the
| most important features of logic.
|
| Suppose the definition of the term T be this:  "In T is at once
| P_1, P_2, and P_3".  This sums up the whole meaning of T.  It may
| not be known that there is no such thing as P_1 and therefore the
| meaning of T does not imply its existence.  On the other hand we
| must know that P_1, P_2, and P_3 are neither of them coextensive
| with the whole conception of being for we know the qualities of
| things only by comparison with their opposites hence we must
| know that there is something which is not P_1 and that this
| is not T, that there is something which is not P_2 and that
| this is not T, and that there is something which is not P_3
| and that this is not T.
|
| Accordingly if we define the essential breadth of a term as "those real things
| of which according to its every meaning a term is predicable" then "not T" has
| an essential breadth that is to say its very meaning implies that there are
| things of which it is predicable.  Thus T is a term which has essential depth
| but no essential breadth -- "not T" is a term which has essential breadth
| but not essential depth and all terms may be divided into two classes,
| the "essential positive" and "essential negative", the former having
| essential depth but not essential breadth, the latter having essential
| breadth but not essential depth.  There are some terms which are
| affirmative in form but which according to this definition are
| essentially negative and vice versa.  As examples of this we
| may allude particularly to the terms "being" and "nothing"
| both of which are terms of second intention.
|
| As every term has breadth and the breadth of one term is greater
| than that of another we may conceive of a term the breadth of
| which includes that of every other other term so that it is
| predicable of anything whatever.  This is the definition
| of the term "being".  Its definition therefore gives it
| breadth but not depth and accordingly it is essentially
| negative.
|
| We may also conceive of a term whose depth includes the depth of all
| other terms so that anything whatever may be predicated of it without
| any falsity and this is the definition of the term "nothing".  For you
| may say what you please of nothing and if it is clearly understood that
| what you speak of has no existence there is no falsity in what you assert
| because you have not made any assertion whatever.  "Nothing" therefore is
| a term which has essential depth without any breadth and is according to
| our definition essentially affirmative.
|
| C.S. Peirce, 'Chronological Edition', CE 3, 100-101
|
| C.S. Peirce, "On Logical Breadth and Depth", MS 233, Spring 1873,
| Chapter 11 from ["Toward a Logic Book, 1872-1873"], pp. 14-108 in:
|'Writings of Charles S. Peirce:  A Chronological Edition, Vol. 3, 1872-1878',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.

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