ment) between them. In the judgment 'no man is perfect,' there are two concepts, 'man' and 'perfect,' and a recognition of a certain relation (disagreement) between them. Similarly, in the judgments 'all metals are elements,' 'all sensations are feelings,' 'all material bodies are extended,' 'matter gravitates,' there are two concepts, and a recognition of a certain relation between them.

It is evident that our definition of concept or of judgment does not include any concepts or judgments that are intuitive, or as they are called à priori, that is, not the result of experience, but due to the very nature, constitution, or original forms of the mind. Logic, as defined above, does not inquire into the truth or falsity of these à priori concepts and judgments, the existence of which is affirmed by some and denied by others. It does not lay down the conditions to which these must conform in order that they may be true. It treats of the principles and conditions to which those concepts and judgments which are products of comparison must conform in order that they may be free from error and self-contradiction.

A reasoning is the product of comparing two or more judgments, with a view to arrive at another which is contained in or warranted by them. It is the recognition of a relation between two or more judgments, or the establishment of a relation between two concepts, by means of a third. In the reasoning "All men are fallible, philosophers are men; therefore philosophers are fallible," there are the three concepts, 'philosophers,' 'man,' and 'fallible,' and a relation between the first and the last is established by means of the second. In the first judgment, there is the recognition of a relation between the two concepts 'man' and 'fallible.' In the second, between 'philosophers' and 'man.' In the third, between 'philosophers' and 'fallible,' as the result of a comparison between the first two judgments. In the simplest form of reasoning, that is, in immediate inference, a judgment is inferred from another judgment, while in the most complex form, in induction, for instance, a judgment is the result of the comparison of a number of judgments. In the inference

“All men are mortal, therefore no man is immortal,” we have an example of the former. In the inference "John is dead, James is dead, all men of past ages have died; therefore, all men now living will die, or all men are mortal," we have an example of the latter.

§ 2. Regarded objectively, that is, as something existing in things or objects, a concept is an attribute or a collection of attributes in which a number of individual things or objects agree1, For example, the concept 'man' viewed objectively, that is, as something existing in men, is the aggregate of attributes in which all individual men agree. Similarly, the concept 'triangle' is objectively the attribute of 'being bounded by

1 With reference to this passage, Mr Keynes, reviewing this work in Mind for October, 1884, has remarked that it "involves a confusion of phraseology if nothing more," and that "it is calculated to suggest to the student a metaphysical doctrine which it is hardly probable that the author himself holds." There is, I maintain, no confusion of phraseology; but there is a change in the meaning of the word concept necessitated by a change in the meaning of the term Logic. If Logic is an objective science "formulating the most general laws of correlation among existences considered as objective," and if the term concept is to be retained in that science, a concept must be something existing in things or objects. The concept, like the science itself, must be objective; and what is an objective concept? I hold that it must be an attribute or collection of attributes in which a number of individual things agree. Nor is the change in the meaning of the word concept so great as I have admitted. Munsel, for instance, defines a concept "as a collection of attributes united by a sign, and representing a possible object of intuition." The second charge brought against the passage is that "it is calculated to suggest to the student a metaphysical doctrine which it is hardly probable that the writer himself holds." I suppose that the metaphysical doctrine here alluded to is the Hegelian doctrine of the Identity of Thought and Being or of Logic and Metaphysics. If this doctrine is suggested by that passage, this is not due to any accident but to great correspondence or resemblance between the Logic of Hegel and the Objective Logic of English Logicians. See Appendix E, "The Nature and Province of Objective Logie."

three lines'; the concept 'flower' the attribute or collection of attributes in which all individual flowers agree. Thus every concept is objectively an attribute or a collection of attributes, and subjectively an idea or notion corresponding to that attribute or collection of attributes.

A judgment, regarded objectively, is, according to some writers, a relation between two attributes; according to others, a relation between two things; and according to others again, a relation between a thing and an attribute. For example, the judgment ‘all men are mortal,' objectively regarded, has been variously considered as a relation between the attribute ‘mortality' and the collection of attributes 'humanity,' between the two groups of things 'all men' and 'mortal,' and between the group of things 'all men' and the attribute 'mortality'; that is, in that judgment the attribute 'mortality' is affirmed of the attribute ‘humanity,' or, the group of things called 'mortal' is affirmed of the group of things called 'man,' or, the attribute 'mortality' is affirmed of the groups of things called 'man.' In the judgment 'all metals are elements,' a relation is expressed between the two collections of attributes, namely, those of 'metal,' and of 'element'; or between two groups of things, namely, 'metals,' and 'elements,' &c. Similarly, every judgment, objectively regarded, is an affirmation or denial of a certain relation between things and attributes.

A reasoning, objectively regarded, is the establishment of a relation between two things or attributes by means of a third, or, the inference of a relation between two things or attributes from one or more given relations of things and attributes. For example, in the reasoning "All men are mortal, kings are men; therefore, kings are mortal," a relation between 'kings' and 'mortal' is inferred from two given relations between things, namely, (1) a relation between 'men' and 'mortal' expressed in the first judgment, and (2) a relation between 'kings' and 'men' expressed in the second judgment. Similarly, in all reasonings, objectively regarded, a relation universal or particular between two things or attributes or between a thing and an

attribute is inferred from one or more given relations of things and attributes.

From this direct and close connexion between thought, and things and attributes, or, between concepts, judgments, reasonings, on the one hand, and attributes, relations of attributes and things, and inferences, on the other, Logic may be regarded (from the objective point of view) as the science of the most universal relations and correlations of things and attributes, that is, the science of the principles and laws to which we must conform in order that a relation established by comparison of things and attributes, or inferred from one or more given relations between them, may be true.

§ 3. A concept is expressed in language by a single word, or a combination of words, called a term or name. For example, the concept 'man,' or, the aggregate of attributes in which all men agree as well as the idea or notion corresponding to it, is signified or expressed by the word man. The concepts 'metal,' 'flower,' 'animal,' 'horse,' that is, both the aggregates of attributes, and the ideas corresponding to them, are expressed by those words, respectively. Similarly, the combinations of words 'good man,' 'elementary substance,' 'red flower,' 'round table,' are names or symbols for certain concepts.

A judgment is expressed in language in the form of a sentence, called a proposition. For example, the judgment explained above as expressing a relation between the two concepts 'man' and 'mortal' is expressed in the sentence 'man is mortal.' A reasoning is expressed in language in a series of connected sentences called, an argument. The reasoning explained above as establishing a relation between the two concepts 'philosopher' and 'fallible' by means of a third concept 'man' is expressed in the argument "All men are fallible, philosophers are men; therefore, philosophers are fallible."

From the direct and close connexion between thought and language, between concepts, judgments and reasonings on the one hand, and words and sentences, or names, propositions and arguments on the other, Logic has been regarded as conversant

about language, as the science of the use of names, propositions, and arguments, that is, the science of the principles and rules to which we must conform in order that we may be right and free from fallacy and self-contradiction in the use of names, propositions, and arguments.

Logic has been thus defined from three distinct points of view. The first definition we have given above is from the psychological or subjective point of view, the second from the objective point of view, and the third or last from the linguistic point of view. These definitions reveal also the relations of Logic to the other sciences according as it is regarded from one or other of these three stand-points. The first places it among the mental sciences, and makes it dependent upon the psychology of cognition. The second places it among the objective sciences, and makes it the most general of all sciences, treating of those principles and laws which are equally true of all phenomena and things, both mental and material. The third places it among the linguistic or philological sciences, and makes it dependent upon grammar and language generally. On the first view, Logic treats of the processes and products of conception, judgment, and reasoning. On the second, it treats of the most universal relations and correlations of things, that is, of the most general aspects of things, of their fundamental relations, and of relations between relations; on the third, it treats of language, that is, of the use of names, propositions and arguments, or rather of words and sentences.

§ 4. Most logicians have adopted one or other of these views to the exclusion of the other two. A philosopher of mind will naturally adopt the first view and its appropriate phraseology. A scientific man will adopt the second and its appropriate phraseology; while a practical man, with a knowledge of mental philosophy as well as of physical science, will try to combine the first or the third with the second. He will adopt the phraseology of either of the former, but constantly refer to the second for its real meaning, signification, or import. The third view cannot really be held by itself, and though Whately