presides over this product of Thought, as over the Judgment. No valid Concept can be formed, unless from Judgments which have either identical subjects or identical predicates. The Concept arises from the Synthesis of the different under the same; of different subjects having the same predicate, or of different predicates having the same subject. In other words, in the Basc is to be found the identifying principle governing in the Concept.

"It will have been observed, moreover, from the mode of its formation that a Concept is essentially a relative cognition. It is not only the result of a synthesis, not only the aggregate of a plurality of Judgments, and accordingly of relative cognitions, but the cognitions that are brought together in this synthesis sustain a determined and peculiar relation to one another. If the Concepts be formed from the subjects of the Judgments, those Judgments must have a common-the same predicate; if from the predicates, the Judgments must have the same subject. Concepts are thus from their very nature relative cognitions, and the principle of relation is in the sameness of the term of the Judgment which is not synthesized into the Concept-in its Base.

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Concepts, however, differ from Judgments, as relative cognitions, in this respect that in the Judgment the relation is explicit, while in the Concept it is only implied. Thus in the Judgment, Man is a rational animal, the relation is articulately declared; but in the Concept,

Man, the relation to the other term of the Judgment from which it is derived, although real, is not expressed, but only implied. The Base of the Concept, although real, is not expressed.

"Still further, a Concept is essentially a onesided cognition. It is formed from but one side of a Judgment, from the Subject or from the Predicate. It may be regarded, indeed, as an aggregate of Judgments, that is, a synthesized or composite Judgment, with the single termthe Base, and the Copula dropped.

"A Concept, however, always implies the Judgments from which it is derived; it implies the other term, which has been dropped, but which is the indispensable condition of its being formed, and is, therefore, appropriately denominated the Base of the Concept; and also implies that this Base has been identified with each of the terms which compose the Concept.

It will occur to the reflecting mind, on this exposition of the mode in which Concepts are formed, that they are mere products of Thought, aggregates of Subjects, or aggregates of Predicates, and do not imply necessarily any exactly corresponding aggregates in the reality of things. How many individual subjects of Judgments shall be combined, or how many predicates, are questions that will be determined by such considerations as those of extent of observation, practicability of aggregation, convenience of use, the needs of occasion, and the like. The extent of the aggregation, therefore, varies indefinitely with the occasions of Thought; and it is

not to be supposed that the constitution of things around us fluctuates precisely with the fluctuations of Thought. As the mathematical analyst, in the progress of his demonstration, finds it convenient to substitute single letters or symbols to denote a number of quantities in some respect of like character, so Thought, for its own manifold conveniences, often aggregates like elements and signalizes them by single words." (Day, Elements of Logic, ed. 1868, pp. 62-66.)

185.The Third gradation of Thought is the Reasoning. Like the Concept, it is derived from the Judgment. It differs from the Concept in its form, as, unlike that, it retains the full forms of the Judgment, and accordingly, also, to a certain extent, it differs from it in the mode of its derivation. It differs from the Judgment proper in this respect, that it is a derivation from a Judgment—a traced movement of Thought, supperadded to that which constitutes the Judgment. It is not the derived Judgment, not the mere terminus, the point at the end of the line over which the Thought has moved, but the line itself as traced in the movement of the Thought. When viewed as a resultant product of Thought, therefore, it must be regarded as the track of Thought left marked by the movement, not the mere attained object or goal of the movement, which is nothing more than a Judgment. We are carefully to distinguish, therefore, a Reasoning from the Conclusion-from the Judgment which is attained by the reasoning.

'A Reasoning, thus, is a derivation of a Judg

ment from another Judgment or Judgments. 'Reasoning is a modification from the French raisonner (and this is a derivation from the Latin ratio), and corresponds to ratiociatio, which has indeed been immediately transferred into our language under the form of ratiocination. Ratiocination denotes properly the process, but improperly, also, the product of reasoning; Ratiocinium marks exclusively the product. The original meaning of ratio was computation, and from the calculation of numbers it was transferred to the process of mediate comparison in general. Discourse (discursus, diavola) indicates the operation of comparison, the running backward and forward between the characters or notes of objects (discurrere inter notas, diavoεio@ai). The terms discourse and discursus, Savoia, are, however, often used for the reasoning process, strictly considered, and discursive is even applied to denote mediate, in opposition to intuitive, judgment, as is done by Milton. compound term, discourse of reason, unambiguously marks its employment in this sense. gumentation is derived from argumentari, which means argumentis uti; argument again, argumentum-what is assumed in order to argue something-is properly the middle notion in a reasoning-that through which the conclusion is established; and by the Latin Rhetoricians it was defined, probabile inventum ad faciendamfidem. It is often, however, applied as co-extensive with argumentation. Inference or Illation (from infero) indicates the carrying out into the

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last proposition what was virtually contained in the antecedent judgments. To conclude (concludere), again, signifies the act of connecting and shutting into the last proposition the two notions which stood apart in the two first. A conclusion (conclusio) is usually taken, in its strict or proper signification, to mean the last proposition of a reasoning; it is, sometimes, however, used to express the product of the whole process. To syllogize means to form syllogisms. Syllogism (σvλу16μos) seems originally, like ratio, to have denoted a computation-an adding up; and like the greater part of the technical terms of Logic in general, was brorrowed by Aristotle from the mathematicians. Zulloуioμos may, however, be considered as expressing only what the composition of the word denotes a collecting together; for ovλλογίζεσθαι comes from συλλέγειν,, which signifies to collect. Finally, in Latin, a syllogism is called collectio, and to reason, colligere. This refers to the act of collecting, in the conclusion, the two notions scattered in the premises.'

"A Reasoning is composed of two parts-the original Judgment or Judgments which are the original datum in the process, and the movement of the Thought in the process. As the datum is regarded as logically determining and preceding, it is called the Antecedent, and the other part, regarded as logically determined, or following, is called the Consequent. Its proper sign is therefore. These are the parts of a Reasoning regarded as an Integrate Whole.