…second intentions are the objects of the understanding considered as representations, and the first intentions to which they apply are the objects of those representations.
…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.
The scholastic doctors used to talk of first intentions and second intentions. First intentions were conceptions obtained by generalizing ordinary experiences. Second intentions were conception[s] obtained by generalizing conceptions themselves considered as objects of logical comparison. Now an abstract notion, that is, the name of a quality, is the first fruit of second-intentional thought.
The sort of idea which an icon embodies, if it be such that it can convey any positive information, being applicable to some things but not to others, is called a first intention. The idea embodied by an icon which cannot of itself convey any information, being applicable to everything or to nothing, but which may, nevertheless, be useful in modifying other icons, is called a second intention.
Characters of second intention are characters which are brought to our knowledge, not by observation of their subjects, but by observation of logical forms. Relatives of second intention are of high importance in logic, as might be anticipated. Especially so are those which express the numbers of collections. All such arithmetical relatives are expressible in terms of three fundamental arithmetical relatives, a monad, a dyad, and a triad.
Without these the most elementary requisites of logic cannot be fulfilled.
By logical reflexion, I mean the observation of thoughts in their expressions. Aquinas remarked that this sort of reflexion is requisite to furnish us with those ideas which, from lack of contrast, ordinary external experience fails to bring into prominence. He called such ideas second intentions. It is by means of relatives of second intention that the general method of logical representation is to find completion.
Second intentions are those which are formed by observing and comparing first intentions. Thus the concept “class” is formed by observing and comparing class-concepts and other objects. The special class-concept, ens, or what is, in the sense of including figments as well as realities, can only have originated in that way. Of relative second intentions, four are prominent–identity, otherness, co-existence, and incompossibility.
Every rhema whose blanks may be filled by signs of ordinary individuals, but which signifies only what is true of symbols of those individuals, without any reference to qualities of sense, is termed a rhema of second intention. For second intention is thought about thought as symbol. Second intentions and certain entia rationis demand the special attention of the logician.