evident or too well known to require statement, is shown by the word therefore, which marks the conclusive nature of the inference drawn. The suppressed premiss would, in fact, be the answer, should the use of that word be questioned, i.e. :

"A is a good mother, therefore she will watch over her children's education." "Why do you say she will therefore watch over her children's education ?" Ans." Because all good mothers watch, &c."

The general fact, or axiom, or principle expressed in the major premiss of the syllogism, and implied, though not always stated in the common form of argument, is then the basis, the assumed, or proved, or self-evident, truth from which we proceed to further conclusions. It may require itself to be proved, as in the instance above given, or it may contain a self-evident maxim, as in the following :—

Things that are equal to the same are equal to one another. A and B are each equal to C;

Therefore, A is equal to C.

But in either case the process of reasoning is the same.

The syllogism, then, is not a form for scholastic disputation, or a peculiar mode of reasoning adapted to particular subjects; but the detailed form of every process of reasoning, of that operation which the mind performs every time it draws an inference or a conclusion on any subject whatever. When we speak, therefore, of logical, or mathematical, or moral reasoning, we mean no more (as far as the expression is correctly used) than to distinguish between different classes of subjects, with reference to the different kinds of proof they are susceptible of; that is, to the nature of the premises we reason from, while the mode of reasoning remains the same in all. The identity of logical principles with geometrical axioms is a further proof of this fact. When the logician says: "If two terms agree with one and the same third, they agree with each other," it is evidently only another mode of expressing the axiom in geometry, referred to above, "Things which are equal to the same, are equal to each other." These are not peculiar principles of particular sciences, but formulæ of the essential laws of thought itself.*

To determine then the character of the reasoning, we must look to that of the premises. If either of these be assumed, the conclusion will be a simple assumption. If they be proved, the conclusion will carry all the force of that proof. If they be selfevident, the conclusion is a demonstrated truth. In the former cases the reasoning is termed moral or contingent; in the latter it

*Whateley's Logic, Introduction and Book I., Sec. 1, 2, 3, 4.

INDUCTIVE REASONING.

247

is termed demonstrative. By demonstrative reasoning alone do we obtain absolute certainty. The conclusion is necessary, that is, a contrary conclusion would involve a contradiction or an absurdity. We will take the instance given by Mr. Bailey.* "This man was in Edinburgh at the time he was accused of committing a crime in London, therefore he is not guilty. The ground of the conclusion here is the self-evident fact that no man can be in two places at once, and the conclusion is demonstrative, that is, a contrary conclusion involves an absurdity.

When we reason, not from self-evident axioms, but from facts known to us by our own experience or the testimony of others, the process of reasoning is precisely the same, but the conclusion is no longer necessary, that is, the contrary does not involve an absurdity; it has therefore been called contingent. For instance, the sun rises every morning, therefore it will rise to-morrow; here we reason from an intuitive belief in the human mind that what has been will continue to be, but there is no absurdity in the contrary supposition that the sun may not rise to-morrow. In all cases of contingent reasoning (and they make up nine-tenths of all our reasoning) the validity of the conclusion depends on the previously established validity of the premises. The latter are, as we have said, facts derived from our own observation, or from the testimony of others, or from both combined. From the observation and comparison of a large number of facts, we arrive at a collective fact, or as it is more commonly termed, a general law, such, for instance, as that all men are mortal; then, from the collective fact or general law thus obtained, we infer a particular fact, i.e., all men are mortal, therefore we, being men, are also mortal. The first part of this process, i.e., the inferring a general law from the observation and comparison of particulars is termed inductive reasoning, and to it we owe most of the great conquests of modern science, over physical nature. But the whole process is liable to errors which cannot affect demonstrative reasoning, resting, as the latter does, on self-evident premises, or necessary conclusions from self-evident premises. Hence the superior certainty of mathematical over moral or contingent reasoning. In the latter the major premiss, which is the collective fact obtained by observation and generalization, may be false or uncertain; or the minor premiss, or particular fact inferred from the general law, may be improperly classed under it, e.g.:-Such and such medicines relieve fever; this man has fever, therefore they will relieve him. The syllogism is perfect, but the conclusion may nevertheless be erroneous. We may have inaccurately observed the symptoms of the man's disease, and thereby made

*Theory of Reasoning.

†See Bailey,-Theory of Reasoning, ch. 9.

a false application of the general law; or the latter may itself be false. If after observing the efficacy of the medicine in two or three cases, we at once draw the conclusion that it will be efficacious in all, our generalization will be too hasty to be depended upon. Of all errors in reasoning, hasty generalization is the most common; and we should guard against it with the more care that it not only vitiates the judgment, but has in it an element of dishonesty. When from a few instances only we assume a general principle, we indulge our indolence or our impatience, and we are apt to reason from this assumed principle, and act upon our conclusions as dogmatically as if they were the result of the most careful induction. If a man should say, "I have been cheated several times by my servants;-all servants are rogues, and unworthy of trust," and act upon this as a true general principle, he will be sure to commit injustice, and his own mind will be poisoned by universal suspicion; the only conclusion warranted by the premises being, "Some servants are rogues, therefore I must be cautious." A large number of the assertions put forward in conversation or in books as undoubted truths, from which farther conclusions may safely be drawn, are hasty generalizations of this kind. In testing, therefore, the validity of any train of reasoning, whether our own or another's, our first care must be to analyse the assertions it contains, and ascertain on what grounds they rest. Very few, if any, general propositions can rest on our own experience only, because the experience of an individual is seldom wide enough to justify an assertion broader than this: In some cases, in many cases, or in all cases that have come under my knowledge, it is so and so, which still falls far short of a general principle. The conclusions deduced from premises of this nature are only probable; for instance: "In every imprudent marriage I have known the result has been unfortunate; therefore it is highly probable it will be so in this;" or, "I have generally found servants trustworthy; therefore it is probable this one will prove so;" or, where experience is narrower still, "I have known one or two cases of people surviving this operation; therefore it is possible such an one may survive." Here bare possibility is admitted below the lowest degree of probability. The accurate estimate of probabilities is that which in daily life is called good judgment, and which constitutes the main element of success in a world where, as Bishop Butler truly observes, probability is the rule of life. Almost all the decisions we have to make in daily life, not involving moral principle,-are judgments on probabilities; and how much of our happiness depends on those judgments being correct, and our expectations squared to the reasonable probabilities of events.

In the vast majority of cases, where our own experience is too

EVIDENCE AND AUTHORITY.

249

narrow to form the basis of a general principle or proposition, we must rely upon evidence; and here we are called upon for a double exertion of care and accuracy, for we have to test the evidence we reason from, as well as to guard against errors in our own reasoning from it.* When we receive facts or general principles solely on evidence, the latter is called authority. Both in theory and action, it is of the first importance that we should clearly know on what authority we reason or act, and what is the value of that authority; since its validity is the exact measure of the validity of the conclusions we build upon it. We have alluded to this already, and shall have occasion to do so again; but the point we wish to insist upon here is the importance of clearly knowing on what basis we found our reasonings, that we may be also clearly aware of the character of the conclusions we arrive at. If we accept the conclusions of others, as we must continually do, we must be careful to ask ourselves the question, How did they arrive at these conclusions? and strive to trace back the process to its original principle. If we cannot do this we are thrown back on authority alone, and it is then doubly necessary to ascertain the character of our authority, as the only test of the truth or falsehood of the facts and principles we receive from it.

The best mode of training the reasoning faculty is by analysing the conclusions we find in our own minds or in books, till we arrive at the original facts or principles on which they rest, or the authority whence we received them. We should state the conclusion we wish to verify, as a proposition to be affirmed or denied,† and then trace back each step by which it was arrived at. Suppose, for instance, the proposition to be, A is B. The first question is-Why does my author or why do I say, A is B? the answer will lead to another question till we reach the ultimate fact or principle which was the basis of the whole process. Here we have again to ascertain the character of this fact or principle, whether self-evident, or collected from observation; in the latter case, whether correctly observed, by whom, on what evidence admitted. This process

of proof must necessarily expose the loose, vague notions and beliefs which are too commonly dignified with the name of opinions and principles; and when we have learnt to distinguish what we know from what we only believe, and what we believe from what we merely conjecture; to ascertain

See Appendix, B.

See in Bailey's Theory of Reasoning, Appendix, sec. 2, the analysis of a passage from Burke's Letter on the French Revolution.

why we know, or believe, or conjecture,-we shall be comparatively safe from the manifold errors which spring from confusion and sophistry, and our conduct will gain in steadiness as much as our judgment in accuracy, because the grounds of both will be clear and firmly established. In many cases we shall, indeed, be obliged to stop far short of proof, but it is of no small importance that we should know the limits and degrees of our certainty. We may add, in the words of Burke :- "If any inquiry thus carefully conducted should fail at last in discovering the truth, it may answer an end, perhaps, as useful, in discovering to us the weakness of our own understandings. If it does not make us knowing, it may make us modest. If it does not preserve us from error, it may from the spirit of error; and may make us cautious of pronouncing with positiveness or with haste, when so much labour may end in so much uncertainty."

In attempting by the method we have indicated to prove the conclusions we have formed for ourselves or admitted from others, the detailed logical form will assist us by ensuring that the process of reasoning itself shall be fairly conducted; that from the data given, such as they are,-the relation of ideas shall be clearly traced, and the conclusion fairly drawn. It strips a proposition of the disguise, which either rhetoric or clumsy statement may have thrown over it, by showing in what part of the argument confusion or ambiguity may have crept in; it leads to the detection of their source, and thus exposes the fallacy or sophistry that may lurk under apparently coherent and undeniable propositions. It is for its use in this respect that some acquaintance with the principles of logic is so essential to all who would train themselves to reason closely and correctly, and to guard against being misled by the inconclusive or sophistical reasonings of others. Error, in reasoning as in action, seldom stands alone; every false argument that we accept is too likely to become the ground of further conclusions, which in their turn must be equally false; it is a vicious link in the chain which connects all our knowledge on one subject, and vitiates, therefore, in a greater or less degree, the value of the whole.

The perfect accuracy of mathematical terms, each being strictly defined, the indisputable grounds of the reasoning employed, the clearness and certainty of the results obtained, make the study of mathematics the best school for strengthening the reason and giving precision and certainty to its operations. Even if other studies may be allowed to be of equal advantage in training the mind to acuteness, to searching investigation and power of ab

Essay on the Introduction to the Sublime and Beautiful.