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

seems to have maintained it from what he says in many parts of his 'Elements1, nevertheless what he really meant is, that Logic does not treat of reasoning apart from, but only as expressed in, language. "If any process of reasoning," says he, "can take place in the mind without any employment of language, orally or mentally, such a process does not come within the province of the science here treated of 2." Whately really adopted the subject-matter of the first view, and only the phraseology of the third. This is also evident from his definition of Logic 'as the science and also as the art of reasoning.'

§ 5. Hamilton adopts the first view, and defines Logic as "the science of the laws of thought as thought, or the science of the formal laws of thought, or the science of the laws of the form of thought," that is, as the science of those universal laws or principles to which thought must conform in order that its products, viz., concepts, judgments, and reasonings, may be valid. Hamilton uses the word valid to mean free from inconsistency or self-contradiction, and by laws of thought he means only the fundamental principles of consistency, that is (1) the Principle of Identity, (2) the Principle of Contradiction, and (3) the Principle of Excluded Middle. The first means that A is A, that a thing is what it is, that while 'A' is 'A,' it cannot be anything else. The second means that A cannot be both B and not-B, at the same time, in the same place, and in the same respect. If the proposition ‘A' is ‘B' be true, then the proposition “A is

1 Whately writes, for example:-"Logic is entirely conversant about language." Again, "It (Logic) is, therefore (when regarded as an art), the art of employing language properly for the purpose of reasoning and of distinguishing what is properly and truly an argument from spurious imitations of it.”—Elements, 9th Edition, p. 37. 2 Whately's Elements, 9th Edition, p. 37. 3 Lectures, Vol. г. pp. 25, 26. See also pp. 4, 17, 24. On p. 24 Hamilton defines Logic as 'the science of the necessary forms of thought,' and afterwards developes this definition into the expression given in the text. By 'thought as thought' Hamilton means 'the form of thought to the exclusion of the matter' (p. 15).

not-B" cannot be true. If a thing be red, it cannot at the same time be not-red. It may lose redness afterwards, or, it may not be red in all its parts; but if any part of it be red, that same part cannot be not-red at the same time, The third means that one or other of two contradictory terms must be true of one and the same thing, the middle or the mean between them being excluded. 'A is either B or not-B'. Here 'B' and 'not-B' are two contradictory terms, and A must be one or other of the two. It cannot be neither. "This thing is either red or not-red'; this proposition means that the thing must be one or the other, 'red' or ‘not-red’—¿. e. if not 'not-red' then 'red'; and if not 'red,' then 'not-red.' It cannot be anything else than either 'red' or 'not-red.' The two concepts, 'red' and 'not-red' cover the whole sphere of thought and existence; and every possible as well as real object must be one or the other. It is evident that the concept not-red' is so indefinite, that it, in fact, includes every thing real or imaginary except 'red'.

According to Hamilton, if a thought does not violate any of the above three laws of thought, then it is valid; and the science of Logic is entirely conversant about the forms or the uniform and constant modes of thinking in conformity to those laws, to the entire exclusion of the matter of thought. He does not require that the products of thought must agree with actual realities; the only condition which they must fulfil, according to him, is that they must be free from self-contradiction or inconsistency.

§ 6. In his Examination of Hamilton's Philosophy, Mill adopts the first view with the qualification that the products of thought must not only be formally valid, but true or objectively real. He defines Logic as "the art of thinking, which means of correct thinking, and the science of the conditions of correct thinking," that is, "the science of the conditions on which right concepts, judgments, and reasonings depend."

The products of thought, according to Mill, should be not only free from inconsistency or self-contradiction, i. e., valid in Hamilton's sense, but must also be true, i. e., 'agree with the