5. A definition must not be negative when it can be affirmative."
A correct definition necessarily requires the manifestation of the two respective processes of Analysis and Synthesis.
Analysis is a term denoting: "The separation of anything into its constituent elements, qualities, properties and attributes." It is seen at once that in order to correctly define an object, person or thing, it is first necessary to analyze the latter in order to perceive its essential and accidental properties or differences. Unless the qualities, properties and attributes are clearly and fully perceived, we cannot properly define the object itself.
Synthesis is a term denoting: "The act of joining or putting two or more things together; in Logic: the method by composition, in opposition to the method of resolution or analysis." In stating a definition we must necessarily join together the various essential qualities, properties and attributes, which we have discovered by the process of analysis; and the synthesized combination, considered as a whole, is the definition of the object expressed by the term.
CHAPTER VIII.
JUDGMENTS
The first step in the process of reasoning is that of Conception or the forming of Concepts. The second step is that of Judgment, or the process of perceiving the agreement or disagreement of two conceptions.
Judgment in Logic is defined as: "The comparing together in the mind of two notions, concepts or ideas, which are the objects of apprehension, whether complex or incomplex, and pronouncing that they agree or disagree with each other, or that one of them belongs or does not belong to the other. Judgment is therefore affirmative or negative."
When we have in our mind two concepts, we are likely to compare them one with the other, and to thus arrive at a conclusion regarding their agreement or disagreement. This process of comparison and decision is what, in Logic, is called Judgment.
In every act of Judgment there must be at least two concepts to be examined and compared. This comparison must lead to a Judgment regarding their agreement or disagreement. For instance, we have the two concepts, horse and animal. We examine and compare the two concepts, and find that there is an agreement between them. We find that the concept horse is included in the higher concept of animal and therefore, we assert that: "The horse is an animal." This is a statement of agreement and is, therefore, a Positive Judgment. We then compare the concepts horse and cow and find a disagreement between them, which we express in the statement of the Judgment that: "The horse is not a cow." This Judgment, stating a disagreement is what is called a Negative Judgment.