A.—The Canons or Axioms of the Syllogism according to § 1. Lambert's Canons for the so-called Imperfect Fi- is an Objective Science, while the Theory of Rea- NOTE. Mr Carveth Read's View, Dr Venn's 4. Lewes's View:-His distinction of the different INTRODUCTION. CHAPTER I. THE DEFINITION, PROVINCE, AND PARTS OF LOGIC. § 1. LOGIC may be defined as the science of the regulative principles of thought, that is, the science of the axioms and laws to which thought must conform in order that it may be valid. The word science means coherent or systematized knowledge as distinguished from unconnected or detached knowledge. Thus Algebra is a science, or a consistent body of knowledge of number, that is, of numbers and their relations; Geometry is a science, or a system of knowledge of space, that is, of the modes of space and their properties; Physics is a science of the general properties of matter; while a register of births and deaths, or of the observations of atmospheric temperature and pressure, is not a science, but a mere collection of unconnected knowledge of individual subjects and particular facts. The word principle means a general truth as distinguished from a particular one; the former holds good universally in all cases, while the latter is true in a single case, or in a few cases only. A principle may be self-evident like the axioms of Geometry, or proved by observation and generalization like the law of gravitation. The word regulative means that the principles constitute, determine or underlie all thought, that is, no thought can, properly speaking, be called thought unless it conforms to them; or, in other words, 1 R In no thought is valid unless it is conducted in accordance with them. The word thought is used in, at least, three senses. the widest sense it means any mental state or phenomenon, whether of knowing, feeling, or willing. In a narrower sense it means an act or product of knowledge, whether of perception, memory, inference, imagination, &c. As used in logic, thought means sometimes the process, and sometimes the product of comparison in the former sense it stands for conception, or judgment, or reasoning; and in the latter sense, it is a concept, or a judgment, or a reasoning. Logic treats of these processes and products, and lays down the laws and rules to which they must conform in order that they may be valid. A concept is the product of comparing two or more individual things with a view to find out the attribute or the attributes in which they all agree. Regarded subjectively, that is, as a thought, it is an idea or notion corresponding to an attribute or collection of attributes possessed in common by a number of individual things. For example, the concept 'man' is an idea corresponding to those attributes in which all individual men agree. Suppose that those attributes are 'animality' and 'rationality,' then the concept 'man' is the idea or notion corresponding to these two attributes. Similarly, the concept 'triangle' is the idea or notion corresponding to the attribute of 'being bounded by three lines,' possessed in common by all triangles; the concept 'horse' is the idea or notion corresponding to the collection of attributes in which all horses agree; the concept 'animal' is the idea or notion corresponding to the attribute or attributes possessed in common by all animals; the concept 'metal' is the notion corresponding to the collection of attributes which is found in all metals. A judgment is the product of comparing two concepts with a view to affirm or deny one of them of the other. Regarded subjectively, that is, as a thought, it is a mental recognition of a certain relation (agreement or disagreement, according to some logicians) between two notions or concepts. In the judgment 'man is mortal,' for example, there are two concepts, 'man' and 'mortal,' and there is a recognition of a certain relation (agree 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." |