Bibliography

Chap. XI. On Logical 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.

The first intention is the mental act by which an object is conceived.

By the ‘informed breadth’ of a term I shall mean all the real objects of which it is predicable with logical truth in the supposed state of information as our knowledge is never absolute but consists only of probabilities that all the information at hand must be taken into account and those things of which there is not on the whole reason to believe that the term is truly predicable are not to be reckoned as part of its breadth.

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…

…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…

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 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.

Two of the most important characters of general terms are their logical breadth and depth. [—] The depth of a term is that which can be predicated of it. [—] 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.

…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.

Substantial depth is the real character as it exists in the object, which belongs to every thing of which a term is predicable with absolute truth.