ONT Re: Just In Time Logic
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JITL. Note 15
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| Chapter 11. On Logical Breadth and Depth
|
| As Logic is the study of the laws of signs so far as these denote things --
| those laws of signs which determine what things they denote and what
| they do not -- it is necessary in Logic to pay especial attention to
| those terms which denote signs. Such terms are genus species &c.
| No thing is a genus but as there are terms such as man and tree
| which denote some one thing leaving it more or less indeterminate
| what one so we may speak of whatever may be denoted by such a general
| term as a genus or class. Such terms are called 'terms of second intention'.
| The first intention is the mental act by which an object is conceived. The
| second intention is the mental act by which the first conception is made an
| object of conception in reference to its relation to its object. A term of
| second intention does not so much signify the sign itself as it signifies
| whatever is denoted by a sign of a certain description. As signs differ
| in their logical characters we may define an object by means of the
| logical characters of the sign which denotes it and in that case
| it is pointed out with a peculiar kind of generality which
| requires special attention. Two of the most important
| characters of general terms are their logical breadth
| and depth. The breadth of a term in general is that of
| which the term can be predicated. The depth of a term is
| that which can be predicated of it. The breadth therefore
| may be considered as a collection of objects -- real things --
| though it can also be considered as consisting of the terms
| which may be made subject of a true proposition of which
| the given term is the predicate. The depth of a term
| cannot be considered as a collection of things but
| can only be considered as a complex of terms or of
| attributes. The term attribute, character, mark, or
| quality is a term of second intention. Two things are
| alike in a certain respect that is to say the same predicate
| can be applied to either of them. Then the capacity of having that
| predicate applied to it with truth is called an attribute that is a thing
| to which it can be applied. The attribute is therefore an abstract term.
| Terms are divisible into concrete and abstract. The concrete are such
| as white virtuous &c. the abstract such as whiteness virtue, etc.
| Abstract terms do not denote any real thing but they denote
| fictitious things. An object's being white is conceived
| as being due to its being in some relation with a certain
| fictitious thing whiteness. In point of fact that the object
| is white may in a certain sense be said to be due to its connection
| with the sign or predicate white that is to say it must be in such a
| relation to the name white that this name may be applied to it with
| truth or else it cannot be white. There is no falsity in this
| statement although it is more natural to state the matter
| in the inverse way and to say that its having that
| connection with that name is due to the fact
| that it is white. One statement is as true
| as the other. In the latter more natural mode
| of statement the existence of the thing is looked
| upon as the ultimate fact but we have seen in the chapter
| upon reality that the final information is the ultimate fact,
| that final information consisting in applying a certain sign
| to certain objects in the predication and therefore it is
| perfectly correct to say that the thing's being white
| is due to and consists of the applicability of
| a certain predicate to a certain thing.
| A attribute or quality is not precisely
| the same as a predicate inasmuch as when we
| use the word predicate we have in mind the fact
| that the predicate is something extraneous to the thing
| which does not belong to it as it exists but belongs to it as it is
| thought whereas an attribute is considered as belonging to a thing whatever
| is thought. But upon our view of the nature of reality this is a distinction
| of very slight moment because existence is thus not independent of all thought
| and what is affirmed in the final judgment is the same as what really exists.
|
| C.S. Peirce, CE 3, pp. 98-99.
|
| C.S. Peirce, "On Logical Breadth and Depth", MS 233, Spring 1873, pp. 98-102 in:
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 3, 1872-1878',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
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