PROPOSITION. This is the technical name for the final constituent or ultimate ele ment of whatever we call knowledge—what we can believe or disbelieve. " Fire melts wax ;" "the harvest is good:" "Rome stands on the Tiber;" " the moon is not inhabited" —are propositions. All information, whether historical, scientific, or practical, may be resolved at last into simple statements such as these; and all such statements are propo sitions. In every proposition there are two parts: something spoken about, called the subject; and something said, affirmed, or declared of what is spoken about, called the predicate. In the first examplegiven " fire " is the subject, "melts wax" is the predicate or affirming part, to which a verb is necessary. In the second example "harvest" is the subject, " is good " the predicate. But sometimes this last part is resolved further into predicate (good) and copula (is). The predicate then simply means the quality or fact affirmed, while the copula gives the affirmation. In the previous case the copula is con tained in the predicate (melts).
Propositions are affirmative or negative, according as we declare that a thing is, or that it is not; "the moon is (not) inhabited." As some propositions contain the form of a condition, and some the form of an 'alternative, these are called hypothetical, in oppo sition to which the rest are called categorical. If A is B, C is D, is the conditional form of the hypothetical class. Either A is B, or C is D, is called the disjunctive form.
Propositions are further divided, according to their. quantity, or according to the extent of the subject, into universal, particular, singular, and indefinite : " all the moving powers are originally derived from the sun" (universal); "some men are wise" (particu lar); "Socrates is wise" (singular). The "indefinite" means the uncertain or ambiguous in form, as "wine is good;" many of this form are known to be universal, as " man is mortal." In inquiring into the ultimate import or meaning-of propositions, Mr. John Stuart Mill came to the conclusion that they fall under five classes, distinguished according to the nature of the quality predicated. The five universal and comprehensive predicates
are—existence, co-existence (sometimes taking the form of order in place), succession (order in time), causation, resemblance. Every fact, or piece of information consists in the affirmation of some one of these five general attributes. Existence by itself expresses a very limited class, since we usually specify circumstances of time, place, etc., in the same assertion: " There is an ether for conveying light anct hunt," is a proposition of existence; but it would be more usually stated as having locality (order in place, or co-existence), "an ethereal medium is diffused over all space." Existence is the only one of the five attributes that can be affirmed of one thing; all the rest require at least two things. The attribute of co-existence appears in a very large number of propositions: all geographical statements and local descriptions; all the natural conjunctions of properties (the animal frame consists of digestive organs, a nervous system, etc.), affirm co-exist ence. The attribute of succession is seen in history, and in all the changing aspects of things. The attribute of causation is a special case of succession, so important as to be raised to the rank of a first-class predicate. The facts of physical and mental science involve not merely succession, but cause and effect: " Heat expands bodies;" "practice improves the human faculties." The concluding attribute—resemblance—is of very wide occurrence. The propositions of numerical or mathematical scieneo all involve some assertion of equality or inequality, proportion or disproportion: " Twice three is. (equal to) six ;" "triangles in the same base and between the same parallels are equal." Throughout all our knowledge, the'affirmation of likeness, or of unlikeness, is a funda mental fact; but in mathematics it constitutes the characteristic predicate, or the sole. affirmation.