What in logic is called a "proposition" is the expression in words of a logical judgment. Hyslop defined the term "proposition" as follows: "Any affirmation or denial of an agreement between two conceptions." For instance, we compare the concepts "sparrow" and "bird" and find that there is an agreement, and that the former belongs to the latter; this mental process is a _judgment_. We then announce the judgment in the _proposition_: "The sparrow is a bird." In the same way we compare the concepts "bat" and "bird," find that there is a disagreement, and form the judgment that neither belongs to the other, which we express in the proposition: "The bat is not a bird." Or we may form the judgment that "sweetness" is a quality of "sugar," which we express in the proposition: "Sugar is sweet." Likewise, we may form the judgment which results in the proposition: "Vinegar is not sweet." While the process of judgment is generally considered as constituting the second great step of thinking, coming after the formation of the concept, and consisting of the comparing of concepts, it must be remembered that the act of judging is far more elementary than this, for it is found still farther back in the history of thought processes. By that peculiar law of paradox which we find everywhere operative in mind processes, the same process of forming judgments which is used in comparing concepts also has been used in forming the same concepts in the stage of comparison. In fact, the result of all comparison, high or low, must be _a judgment_. Halleck says: "Judgment is necessary in forming concepts. When we decide that a quality is or is not common to a class, we are really judging. This is another evidence of the complexity and unified action of the mind." Brooks says: "The power of judgment is of great value in its products. It is involved in or accompanies every act of the intellect, and thus lies at the foundation of all intellectual activity. It operates directly in every act of the understanding, and even aids the other faculties of the mind in completing their activities and products. * * * Strictly speaking, every intelligent act of the mind is accompanied with a judgment. To know is to discriminate and, therefore, to judge. Every sensation or cognition involves a knowledge and so a judgment that it exists. The mind cannot think at all without judging; to think is to judge. Even in forming the notions which judgment compares, the mind judges. Every notion or concept implies a previous act of judgment to form it; in forming a concept we compare the common attributes before we unite them, and comparison is judgment. It is thus true that 'Every concept is a contracted judgment; every judgment an expanded concept.'"