PART III. OF REASONING. THE third operation of the mind employed in argumentation is Reasoning, which is that process by which we infer or deduce a conclusion from given premises. It often happens that we cannot at once perceive the relation which subsists between our ideas; we, therefore, compare them with some common medium, and, from their agreement or disagreement with this medium, decide whether or not they agree with each other. In this way we draw inferences; and when the process is regularly carried on, it is called Discourse or Reasoning. It is to be particularly kept in mind, that in every instance in which we reason, whether it be to refute an adversary, or to convey instruction, or to satisfy our own minds on any particular subject, a certain process takes place in the mind, which is, when correctly carried on, in all cases, and on all subjects, one and the same. Every one may not be aware of this process, nor be able to explain the principles on which it proceeds; but this is not to be wondered at. It is the case with all our mental operations, and with every process that has been reduced to regular system. The practice must have preceded the theory-just as men must have been able to speak grammatically before Language was reduced to a system of Grammar. It is indeed customary to speak of mathematical reasoning, and metaphysical reasoning, and political reasoning, and theological reasoning, as if they were essentially different. But these are not different kinds of reasoning, founded on different principles. The process is the same in all these instances; and it is no more affected by the nature of the subject to which it is applied, than is an arithmetical process affected by the nature of the objects that are the subject of calculation. If, then, the process of reasoning is in all cases the same, it must be an interesting employment to analyse this operation, and become acquainted with the principle on which it rests, and the laws by which it is regulated; and since an unsound and inconclusive mode of reasoning is often employed, it must be of great service to be acquainted with some general rules, applicable to all cases, which may be employed either to convince, or to confute; and by which we may judge of the validity of any reasoning process. This is what Logic furnishes. Its principal object is to guard us against inconclusive reasoning. The third part of Logic, therefore, treats of Argumentation, which is Reasoning expressed in words. When an argument is stated at full length, and in its regular form, it is called a syllogism; the nature and properties of the Syllogism must, therefore, now be considered. CHAPTER I. OF THE SYLLOGISM. EVERY Argument consists of two parts; that which is proved, and that by means of which the proof is given. The former, before it is proved, is called the question; but after it is proved, it is called the conclusion. The means of proof, if stated last, is called the reason; but if stated first, it is called the premises. Every conclusion is deduced from two premises, either expressed or understood, which are granted to be true, and from which the conclusion necessarily results or follows. A syllogism has therefore been defined, an argument so expressed, that the conclusiveness of it is manifest, from the mere form of the expression, without considering the meaning of the terms in which it is expressed." Thus, in the syllogism, "A is B: C is A; therefore, C is B;" the 66 conclusion is inevitable, whatever the terms A, B, C, may be considered respectively to indicate. The order generally observed in stating a syllogism, is first to lay down the premises, and then to draw the conclusion; thus, All A is B: All C is A; therefore, All C is B. or, All tyrants deserve death: Every syllogism has only three terms,-denoted above by the symbols A, B, C,-viz., the middle term, and the two terms found in the conclusion; for though each syllogism has three propositions, and each proposition has three terms, yet, it will be seen, by examining the above syllogism, that each term occurs twice in every syllogism. The middle term, A, is the medium of comparison with which each of the terms is separately compared, in order to ascertain their agreement or disagreement with each other. The other two terms, B and C, are called the extremes, and are always found in the conclusion, in the following order : 1. The subject of the conclusion, C, is called the minor term; and, 2. The predicate of the conclusion, B, is called the major term, because it has the greater extension. Every syllogism has only three propositions : 1. The proposition in which the major term is compared with the middle term, is called the Major premise. 2. The proposition in which the minor term is compared with the middle term, is called the Minor premise. 3. The proposition in which the minor term is compared with the major term, is called the Conclusion, because concluded from the other two propositions, which are called the Premises. These several parts of a syllogism will be best illustrated by an example; take therefore the following: Every reasonable being is accountable : Man is accountable. This syllogism consists of three propositions; the first and the second are the premises; the third is the conclusion. "Man" is the subject of the conclusion, and is therefore the minor term; "accountable" is the predicate of the conclusion, and is therefore the major term; and "reasonable being" is the middle term, because it is with this that the other two terms are compared. In the first proposition the major term is compared with the middle term; it is therefore the major premise. In the second proposition the minor term is compared with the middle term; it is therefore the minor premise. The validity of such a syllogism may be made evident to the eye by means of a diagram. Thus : Every X is B: Every A is X; therefore, Enclose the A's (the minor term) in right margin; and the triangle in the circle, as on the left, it follows that the triangle must be contained within the square, thus: The conclusion of the foregoing syllogism is a universal affirmative; that is to say, the class of things denoted by the predicate is asserted to contain the whole of the things denoted by the subject. The following has a universal negative as its conclusion. Thus : No X is B: Every A is X; therefore, This may be represented by a diagram, thus: where all the X's in the circle are outside of the square containing the B's; whilst all the A's in the triangle are included within the circle of X's hence the square and the triangle have no portion in common. The conclusion in the next example is a particular affirmative. Thus : : Every X is B: Some A's are X; therefore, This may be seen in the diagram on the right margin, or on the left. The whole semicircle of X's is contained in the square of B's; therefore so the square. The conclusion in the next example is a particular negative. Thus : No X is B: Some A's are X; therefore, Some A's are not B. Here the whole circle of X's is excluded from the square of B's; hence whatever portion of the triangle of A's falls within the circle, must be outside of the square. The propositions of the syllogism do not inform us whether or not the triangle and the square coincide in any other portion of their extent. The argument may be represented C thus, as on the right margin; or thus, as on the left. Or thus, as on the right margin; or thus, as on the left. |