the fallacy is really involved. An example illustrative of this subject is familiar to those who are acquainted with the controversy respecting our idea of cause and effect. Mr. Hume stated in a clear manner the doctrine that this idea is derived entirely from our experience of a uniform sequence of two events; and founded upon this an argument against our belief in a great First Cause. This led to a controversy respecting the original doctrine itself; and it is not many years since it was contended by respectable individuals that it is nothing less than the essence of atheism to maintain that our notion of cause and effect originates in the observation of a uniform sequence. It is now, perhaps, universally admitted that this doctrine is correct, and that the sophism of Mr. Hume consisted in deducing from it conclusions which it in no degree warranted. This important distinction we formerly alluded to; namely, that our idea of cause and effect in regard to any two individual events is totally distinct from our intuitive impression of causation, or our absolute conviction that every event must have an adequate cause.

XI. A sophism somewhat connected with the former consists in disproving a doctrine, and on that account assuming the opposite doctrine to be true. It may be true, but its truth does not depend upon the falsehood of that which is opposed to it; yet this will be found a principle of not unfrequent occurrence in unsound reasonings.

XII. Fallacies are often introduced in what may be termed an oblique manner; or, as if upon a generally admitted authority. The effect of this is to take off the appearance of the statement being made directly by the author, and resting upon his own authority, by which we might be led to examine its truth. For this purpose it is put, perhaps, in the form of a question; or is introduced by such expressions as the following:-"it is a remarkable fact," "it is somewhat singular,"—" it has

Example. Mr. Hume's doctrine, and his inference from it? Former opinion of his doctrine? Present opinion of the doctrine and the inference? Disproving a doctrine and inferring the opposite to be true? Fallacies introduced in an oblique manner? Examples.

been argued with much justice," "it will be generally admitted," &c.

XIII. Fallacy may arise from leaving the main subject of discussion, and arguing upon points which have but a secondary relation to it. This is one of the resources of the casuist when he finds himself in the worst of the argument. Nearly allied to this is the art of skilfully dropping part of a statement, when the reasoner finds he cannot support it, and going on boldly with the remainder as if he still maintained the whole.

XIV. Much of the fallacy and ambiguity of processes of reasoning depends entirely, as formerly stated, on the use of terms. This may consist in two contending parties using the same word in different meanings without defining what their meanings are; in one or both using terms in a sense different from their commonly recognised acceptation, or in using them in one sense in one part of the argument, and in another in a different part of it. Such disputes, accordingly, are often interminable; and this mode of disputation is one of the great resources of the casuist, or of him who argues for victory, not for truth. The remedy is, that every reasoner shall be required clearly to define the terms which he employs; and that in every controversy certain premises or preliminaries shall be fixed in which the parties are agreed. The ambiguity of terms is in fact so extensive a source of fallacy, that scarcely any sophistical argument will be found free from it; as in almost every language the same term is used with great diversity of meanings. Let us take, for example, the term faith. It means a mere system of opinions, confidence in testimony, reliance on the integrity, fidelity, and stability of character of other beings, an act of the understanding in regard to abstract truth presented to it, and a mental condition by which truths of another description exert a uniform influence over the moral feelings, the will, and the whole character. In the controversies which have arisen out of this word, it will probably be found that these various meanings have not been suffi

Wandering from the question? Wrong use of terms? Consequences of it? Reme. dy? Example; term faith?

ciently distinguished from each other. A celebrated passage in the "Spirit of Laws" has been justly referred to as a remarkable example of the same kind of sophism. "The Deity," says Montesquieu, "has his laws; the material world, its laws; intelligences superior to man, their laws; the brutes, their laws; man, his laws." In this short passage the term laws is employed, probably, in four senses, remarkably different.

XV. There are various other sources of fallacy, consisting chiefly in the use of arguments which cannot be admitted as relevant in regard to the process of reasoning, though they may carry a certain weight in reference to the individuals concerned. Among these may be reckoned appeals to high authorities, to popular prejudices, or to the passions of the multitude; and what is called the argumentum ad hominem. If a person, for example, be arguing in support of a particular rule of conduct, we may retort upon him that his own conduct in certain instances was in direct opposition to it. This may be very true in regard to the individual, but can have no influence in the discussion of the question.

XVI. One of the most common sources of fallacy consists of distorted views and partial statements;-such as facts disguised, modified, or collected on one side of a question; or arguments and authorities adduced in support of particular opinions, leaving out of view those which tend to different conclusions. Misstatement, in one form or another, may indeed be considered as a most fruitful source of controversy; and, amid the contests of rival disputants, the chief difficulty which meets the candid inquirer after truth, is to have the subject presented to his mind without distortion. Hence the importance, in every inquiry, of suspending our judgment, and of patiently devoting ourselves to clear the subject from all imperfect views and partial statements. Without the most anxious attention to this rule, a statement may appear satisfactory, and a de

Example from the "Spirit of Laws." The argumentum ad hominem. Example of this? Incorrect views and statements? Frequency of it?

duction legitimate, which are in fact leading us widely astray from the truth.

After every possible care in any process of reasoning, we may still find, in many cases, a degree of doubt, and even certain varieties of opinion in regard to the import and bearing of the argument. This arises partly from actual differences in the power of judging, or what we call, in common language, vigor of mind; and partly from differences in attention, or in the habit of applying the judgment closely to the elements of an inquiry. Hence the varieties of opinion that may be held by different individuals on the same subject, and with the same facts before them; and the degree of uncertainty which attends various processes of reasoning. There is one species of reasoning which is free from all this kind of uncertainty, namely, the mathematical; and the superiority of it depends upon the following circumstances:

1. Nothing is taken for granted, or depends upon mere authority; and, consequently, there is no room for fallacy or doubt in regard to the premises on which the reasoning is founded. No examination of facts is required in any degree analogous to that which is necessary in physical science. The mathematician, indeed, proceeds upon assumptions of such a kind that it is in his own power to clear them from all ambiguity, and from every thing not connected with the subject.

2. In the farther progress of a mathematical argument, if we have any doubt of a proposition which is assumed as the result of a former process, we have only to turn to the demonstration of it, and be immediately satisfied. Thus, if any step of a process be founded upon the principle that all the angles of a triangle are equal to two right-angles, or that the square of the hypotenuse is equal to the sum of the squares of the two sides, should we have any doubt of the truth of these conclusions, the demonstration of them is before us. But if an argument be founded on the principle that the heavenly bodies attract one another with a force which is directly as their quantity of matter, and inversely

Some uncertainty unavoidable. Reason for it? Exception. Grounds of the superiority of mathematical science? Nature of the premises? Evidence easily accessible? Illus trations of this?

as the square of their distance; this great principle must be received on the authority of the eminent men by whom it was ascertained, the mass of mankind having neither the power nor the means of verifying it.

3. All the terms are fully and distinctly defined, and there is no room for obscurity or ambiguity in regard to them.

4. The various steps in a process of mathematical reasoning follow each other so closely and consecutively, as to carry a constant conviction of absolute certainty; and, provided we are in possession of the necessary premises, each single step is short, and the result obvious.

5. The proper objects of mathematical reasoning are quantity and its relations; and these are capable of being defined and measured with a precision of which the objects of other kinds of reasoning are entirely unsusceptible. It is, indeed, always to be kept in mind, that mathematical reasoning is only applicable to subjects which can be defined and measured in this manner, and that all attempts to extend it to subjects of other kinds have led to the greatest absurdities.

Notwithstanding the high degree of precision which thus distinguishes mathematical reasoning, the study of mathe matics does not, as is commonly supposed, necessarily lead to precision in other species of reasoning, and still less to correct investigation in physical science. The explanation that is given of the fact seems to be satisfactory. The mathematician argues certain conclusions from certain assumptions, rather than from actual ascertained facts; and the facts to which he may have occasion to refer are so simple, and so free from all extraneous matter, that their truth is obvious, or is ascertained without difficulty. By being conversant with truths of this nature, he does not learn that kind of caution and severe examination which is required in physical science, for enabling us to judge whether the statements on which we proceed are true, and whether they include the whole truth which ought to enter into the investigation. He thus acquires a habit of too great facility in the admission of data or premises, which is

Use of terms. Regular succession of steps. Objects of mathematical reasoning? Effects of mathematical studies on the mind ? "Common error? Explanation of the facts?