Page:An Investigation of the Laws of Thought (1854, Boole, investigationofl00boolrich).djvu/68

52 CHAPTER IV. OF THE DIVISION OF PROPOSITIONS INTO THE TWO CLASSES OF "PRIMARY" AND "SECONDARY;" OF THE CHARACTERISTIC PROPERTIES OF THOSE CLASSES, AND OF THE LAWS OF THE EXPRESSION OF PRIMARY PROPOSITIONS. HE laws of those mental operations which are concerned in the processes of Conception or Imagination having been investigated, and the corresponding laws of the symbols by which they are represented explained, we are led to consider the practical application of the results obtained: first, in the expression of the complex terms of propositions; secondly, in the expression of propositions; and lastly, in the construction of a general method of deductive analysis. In the present chapter we shall be chiefly concerned with the first of these objects, as an introduction to which it is necessary to establish the following Proposition: All logical propositions may be considered as belonging to one or the other of two great classes, to which the respective names of "Primary" or "Concrete Propositions" and "Secondary" or "Abstract Propositions" may be given. Every assertion that we make may be referred to one or the other of the two following kinds. Either it expresses a relation among things, or it expresses, or is equivalent to the expression of, a relation among propositions. An assertion respecting the properties of things, or the phænomena which they manifest, or the circumstances in which they are placed, is, properly speaking, the assertion of a relation among things. To say that "snow is white," is for the ends of logic equivalent to saying, that "snow is a white thing." An assertion respecting facts or events, their mutual connexion and dependence, is, for the same ends, generally equivalent to the assertion, that such and such propositions