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may be remarked, that they are necessarily all of them imperfect. It is not within the capability of the wit and power of man to frame a perfect circle, or a perfect triangle, or any other figure which is perfect. We might argue this from our general knowledge of the imperfection of the senses; and we may almost regard it as a matter determined by experiments of the senses themselves, aided by optical instruments. "There never was," says Cudworth, "a straight line, triangle, or circle, that we saw in all our lives, that was mathematically exact; but even sense itself, at least by the help of microscopes, might plainly discover much unevenness, ruggedness, flexuosity, angulosity, irregularity, and deformity in them."*

Our reasonings, therefore, and our conclusions, will not apply to the figures before us, but merely to an imagined perfect figure. The mind can not only originate a figure internally and subjectively, but can ascribe to it the attribute of perfection. And a verbal statement of the properties of this imagined perfect figure is what we understand by a DEFINITION, the use of which, in this kind of reasoning in particular, has already been mentioned.

CHAPTER XI.

MORAL REASONING.

190. Of the subjects and importance of moral reasoning. MORAL REASONING, which is the second great division or kind of reasoning, concerns opinions, actions, and events; embracing, in general, those subjects which do not come within the province of demonstrative reasoning. The subjects to which it relates are often briefly expressed, by saying that they are matters of fact; nor would this definition, concise as it is, be likely to give an erroneous idea of them.

Skill in this kind of reasoning is of great use in the formation of opinions concerning the duties and the gen* Treatise concerning Immutable Morality, bk. iv., ch. iii.

eral conduct of life. Some may be apt to think, that those who have been most practised in demonstrative reasoning can find no difficulty in adapting their intellectual habits to matters of mere probability. This opinion is not altogether well founded. Although that species of reasoning has a favourable result in giving persons a command over the attention, and in some other respects, whenever exclusively employed it has the effect, in some degree, to disqualify them for a correct judgment on those various subjects which properly belong to moral reasoning. The last, therefore, which has its distinctive name from the primary signification of the Latin MORESs, viz., manners, customs, &c., requires a separate consideration.

191. Of the nature of moral certainty.

Moral reasoning causes in us different degrees of assent, and in this respect differs from demonstrative. In demonstration there is not only an immediate perception of the relation of the propositions compared together; but, in consequence of their abstract and determinate nature, there is also a knowledge or absolute certainty of their agreement or disagreement. In moral reasoning the case is somewhat different.—In both kinds we begin with certain propositions, which are either known or regarded as such. In both there is a series of propositions successively compared. But in moral reasoning, in consequence of the propositions not being abstract and fixed, and, therefore, often uncertain, the agreement or disagreement among them is, in general, not said to be known, but presumed; and this presumption may be more or less, admitting a great variety of degrees. While, therefore, one mode of reasoning is attended with knowledge, the other can properly be said to produce, in most cases, only judgment or opinion.-But the probability of such judgment or opinion may sometimes arise so high as to exclude all reasonable doubt. And hence we then speak as if we possessed certainty in respect to subjects which admit merely of the application of moral reasoning. Al though it is possible that there may be some difference between the belief attendant on demonstration and that produced by the highest probability, the effect on our

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feelings is, at any rate, essentially the same. who should doubt the existence of the cities of London and Pekin, although he has no other evidence of it than that of testimony, would be considered hardly less singular and unreasonable than one who might take it into his head to doubt of the propositions of Euclid.-It is this very high degree of probability which we term moral certainty.

192. Of reasoning from analogy.

MORAL REASONING admits of some subordinate divisions; and of these, the first to be mentioned is reasoning from analogy.-The word analogy is used with some vagueness, but, in general, denotes a resemblance, either greater or less. Having observed a consistency and uniformity in the operations of the physical world, we are naturally led to presume that things of the same nature will be affected in the same way, and will produce the same effects; and also that the same or similar effects are to be attributed to like causes. ANALOGICAL REASONING, therefore, is that mental process by which unknown truths or conclusions are inferred from the resemblance of things.

The argument by which Sir Isaac Newton establishes the truth of universal gravitation is of this sort. He proves that the planets, in their revolutions, are deflected towards the sun in a manner precisely similar to the deflection of the earth towards the same luminary; and also that there is a similar deflection of the moon towards the earth, and of a body projected obliquely at the earth's surface towards the earth's centre. Hence he infers by analogy, that all these deflections originate from the same cause, or are governed by one and the same law, viz., the power of gravitation. There are a variety of subjects, both speculative and practical, in respect to which we may reason in this way, and sometimes with considerable satisfaction. It is nevertheless true, that much care is necessary in arguments drawn from this source, especially in scientific investigations. The proper use of analogical reasoning in scientific inquiries seems to be, merely to illustrate and confirm truths which are susceptible of proof from other sources of evidence, either by casting a direct additional light or by answering objections.

§ 193. Of reasoning by induction.

We now come to another method of moral reasoning, viz., by induction. Inductive reasoning is the inferring of general truths from particular facts that have fallen under our observation. Our experience teaches us that nature is governed by uniform laws; and we have a firm expectation, (whether it be an original principle of our constitution, or whatever may be the origin of it,) that events will happen in future, as we have seen them happen in times past. With this state of mind we are prepared to deduce inferences by induction.

When a property has been found in a number of subjects of the same kind, and nothing of a contradictory nature appears, we have the strongest expectation of finding the same property in all the individuals of the same class; in other words, we come to the conclusion that the property is a general one. Accordingly, we apply a magnet to several pieces of iron; we find, in every instance, a strong attraction taking place; and we conclude, although we have made the experiment with only a small number of the masses of iron actually in existence, that it is a property of iron to be thus affected by that substance, or that all iron is susceptible of magnetical attraction. This is a conclusion drawn by induction.

The belief which attends a well-conducted process of inductive reasoning bears a decided character; it is moral probability of the highest kind, or what is sometimes termed moral certainty; and is at least found to be sufficient for all practical purposes. We obtain all the general truths relating to the properties and laws of material objects in this way.

And we thus not only acquire a knowledge of material objects, but apply the same inductive process also in the investigation of laws which govern the operations of the mind. It is by experience, or observing what takes place in a number of individuals, that we are able to infer the general law of association, viz., when two or more ideas have existed in the mind in immediate succession, they are afterward found to be mutually suggested by each other. It is the same in ascertaining other general laws

of the mind.

§ 194. Of combined or accumulated arguments. When a proposition in geometry is given to be demonstrated, it sometimes happens that two or more solutions may be offered leading to the same end. The theorem or the problem is one and the same, as also the conclusion; but there may be more than one train of reasoning, more than one series of intermediate steps connecting the proposition which is to be investigated with the result. But as the conclusion in each of these different cases is certain, it does not strengthen it, although it may gratify curiosity to resort to a different and additional process.

It is not thus in moral reasoning. The great difference between the two kinds of reasoning, as before observed, is not so much in the mental process as in the subjects about which they are employed. Now, as the subjects in moral reasoning are not of a purely abstract nature, and are, therefore, often attended with uncertainty, our belief, when we arrive at the conclusion, is not always of the highest kind. More frequently it is some inferior degree of probability. Hence, in any moral inquiry, the more numerous the series of arguments which terminates in a particular conclusion, the stronger will be our belief in the truth of that conclusion.

Thus we may suppose a question to arise, Whether the Romans occupied the island of Great Britain at some period previous to the Saxon conquest? In reference to this inquiry a number of independent arguments may be brought forward. (1.) The testimony of the Roman historians. (2.) The remains of buildings, roads, and encampments, which indicate a Roman origin. (3.) The coins, urns, &c., which have been discovered. Although these arguments are independent of each other, they all bear upon the same conclusion; and, being combined together, they very essentially increase the strength of our belief.

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