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Passing on to the classification of the character of the intension of terms, we find:

Difference , a term denoting: "The mark or marks by which the species is distinguished from the rest of the genus; the specific characteristic." Thus the color of the skin is a difference between the Negro and the Caucasian; the number of feet the difference between the biped and the quadruped; the form and shape of leaves the difference between the oak and the elm trees, etc. Hyslop says: "Whatever distinguishes one object from another can be called the differentia . It is some characteristic in addition to the common qualities and determines the species or individual under the genus."

Property , a term denoting: "A peculiar quality of anything; that which is inherent in or naturally essential to anything." Thus a property is a distinguishing mark of a class. Thus black skin is a property of the Negro race; four feet a property of quadrupeds; a certain form of leaf a property of the oak tree. Thus a difference between two species may be a property of one of the species.

Accident , a term denoting: "Any quality or circumstance which may or may not belong to a class, accidentally as it were; or, whatever does not really constitute an essential part of an object, person or thing." As, for instance, the redness of a rose, for a rose might part with its redness and still be a rose—the color is the accident of the rose. Or, a brick may be white and still be a brick, although the majority of bricks are red—the redness or whiteness of the brick are its accidents and not its essential properties . Whately says: " Accidents in Logic are of two kinds—separable and inseparable. If walking be the accident of a particular man, it is a separable one, for he would not cease to be that man though he stood still; while, on the contrary, if Spaniard is the accident connected with him, it is an inseparable one, since he never can cease to be, ethnologically considered, what he was born."

Arising from the classification of the meaning or content of terms, we find the process termed "Definition."

Definition is a term denoting: "An explanation of a word or term." In Logic the term is used to denote the process of analysis in which the properties and differences of a term are clearly stated. There are of course several kinds of definitions. For instance, there is what is called a Real Definition , which Whately defines as: "A definition which explains the nature of the thing by a particular name." There is also what is called a Physical Definition , which is: "A definition made by enumerating such parts as are actually separable, such as the hull, masts, etc., of a ship." Also a Logical Definition , which is: "A definition consisting of the genus and the difference. Thus if a planet be defined as 'a wandering star,' star is the genus, and wandering points out the difference between a planet and an ordinary star." An Accidental Definition is: "A definition of the accidental qualities of a thing." An Essential Definition is: "a definition of the essential properties and differences of an object, person or thing."

Crabbe discriminates between a Definition and an Explanation, as follows: "A definition is correct or precise; an explanation is general or ample. The definition of a word defines or limits the extent of its signification; it is the rule for the scholar in the use of any word; the explanation of a word may include both definition and illustration; the former admits of no more words than will include the leading features in the meaning of any term; the latter admits of an unlimited scope for diffuseness on the part of the explainer."

Hyslop gives the following excellent explanation of the Logical Definition , which as he states is the proper meaning of the term in Logic. He states:

"The rules which regulate Logical Definition are as follows:

1. A definition should state the essential attributes of the species defined.

2. A definition must not contain the name of word defined. Otherwise the definition is called a circulus in definiendo .

3. The definition must be exactly equivalent to the species defined.

4. A definition should not be expressed in obscure, figurative, or ambiguous language.

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.

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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 .

In the above illustration of the comparison between the concepts horse and animal we find that the second concept animal is broader than the first, horse , so broad in fact that it includes the latter. The terms are not equal, for we cannot say, in truth, that "an animal is the horse." We may, however, include a part of the broader conception with the narrower and say: "some animals are horses." Sometimes both concepts are of equal rank, as when we state that: "Man is a rational animal."