III. In deducing from a large collection of facts a general fact or general principle; when this induction is made from a full examination of all the individual cases to which the general fact is meant to apply, and actually does apply to them all,-this is truth. When it is deduced from a small number of observations, and extended to others to which it does not apply,-this is falsehood. As in the former case, however, a general principle may be produced hypothetically or by conjecture; that is, it may be assumed as general so far as we at present know. This process is often legitimate and useful as a guide in further inquiry, if it be employed for this purpose only, and the result be not received as truth until it be established by sufficient observation. A great and not unfrequent error is, that when such hypothetical principles are proposed in a confident manner, they are very often received as true; and the consequence is, that a degree of observation is required for exposing their fallacy, perhaps as extensive as, if properly employed, might have been sufficient to discover the truth. Those who are acquainted with the history of medical doctrines will be best able to judge of the accuracy of this observation, and to estimate the extensive influence which this error has had in retarding the progress of medical science. The proper rules to be observed, in deducing a general principle, are therefore opposed, in the first place to the error of hasty generalizing, or deducing such a principle from a limited number of facts. They are further opposed to another error, prevalent in the hypothetical systems of the old philosophy, by which phenomena were referred to principles altogether fictitious and imaginary, or, in other words, which could not be shown to be facts. In opposi tion to both these errors the great rule of induction in modern science is, that the principle which is as sumed as general shall be itself a fact, and that the fact shall be universal. Thus, what we call the law of gravitation is primarily nothing more than the fact that bodies fall to the earth; and that this is true of all bodies, without a single exception. Of the cause of this fact, or the hidden principle on which it depends, we know nothing; and all the investigations of Newton were carried on independently even of the attempt to discover it. "When Newton," says Mr. Stewart, "showed that the same law of gravity extends to the celestial spaces, and that the power by which the moon and planets are retained in their orbits is precisely similar in its effects to that which is manifested in the fall of a stone; he left the efficient cause of gravity as much in the dark as ever, and only generalized still further the conclusions of his predecessors." False investigation may be briefly referred to three heads, fallacies in facts,-false inductions,—and false reasoning. I. FALLACIES IN FACTS. A statement of facts is fallacious when any of the alleged facts are not true, -when it includes facts not relating to the subject, -and when important facts are omitted. This last error is most frequently exemplified in those cases in which facts are collected on one side of a question, or in support of a particular doctrine. To the same class we may likewise add those instances in which statements are received as facts, which are not facts but opinions. II. FALSE INDUCTION includes false causation and false generalization. False causation is, when two events are considered as cause and effect without sufficient reason, and which are, in fact, only incidentally combined :—when events are considered as cause and effect which are only joint effects of a common cause; and when, of two events really con rrected as cause and effect, we mistake the order of the sequence, considering that as the cause which is really the effect, and that as the effect which is really the cause. The error of false causation is most apt to occur in those sciences in which there is peculiar difficulty in tracing effects to their true causes, and causes to their true effects. These, as formerly mentioned, are exemplified by medicine and political economy. A physician, for example, ascribes the cure of a patient to a remedy which he has taken, though it perhaps had no influence on his recovery; and a political declaimer refers some circumstance of national distress or commercial embarrassment to certain public measures which happened to correspond in time, but were in fact entirely unconnected. False generalization, again, as was lately stated, includes general principles which are deduced from a limited number of facts; and hypotheses which cannot be shown to be facts, but are entirely fictitious and imaginary., III. FALSE REASONING. This consists either,—in applying to the explanation of facts, principles which are unsound,-in applying sound principles to facts which have no relation to them, or in deducing conclusions which do not follow from these facts and principles. REASONING is usually divided into two parts which have been called the intuitive and the discursive. Intuitive reasoning, or intuitive judgment, is when the truth of a proposition is perceived whenever it is announced. This applies to axioms or self-evident truths, and to first truths or fundamental articles of belief, formerly referred to, which rest upon the absolute conviction of the whole mass of mankind. In discursive reasoning, again, some of these axioms or first truths are applied to particular facts, so as to deduce from the connexion new conclu sions. Thus, when we say that "every event must have an adequate cause," we state a principle of intuitive judgment. When we then collect from the phenomena of nature various examples of adaptation and design, and, applying that intuitive principle to these facts, arrive at the conclusion that the universe is the work of an intelligent and designing First Cause, this is discursive reasoning. The new principle or conclusion thus deduced may be applied in a similar manner to the deduction of farther conclusions, and so on through what we call a chain of reasoning. Any particular piece of reasoning, then, may generally be resolved into the following elements : 1. Certain principles or propositions which are stated either as axioms, as first truths, or as deduc tions from some former process of reasoning. 2. Certain facts or relations of facts, derived either from observation or testimony, which are stated as true, and to which the principles are to be in some manner applied. 3. Certain new conclusions deduced from the ap plication of the principles to the facts. In examining the validity of such a process, we have not only to attend to the correctness of the principles and the authenticity of the alleged facts, but likewise to inquire whether the facts are of that class to which the principles are legitimately applicable; for the principles may be true, and the facts authentic, and yet the reasoning may be unsound, from the principles being applied to the facts to which they have no relation, This method of examining, separately, the elements of an argument, appears to correspond with the ancient syllogism; and this, accordingly, when divested of its systematic shape, is the mental process which we perform, whenever we either state, or examine any piece of reasoning. If I say, for example, "the greatest kings are mortal, for they are but men;" I appear to state a very simple proposition; but it is in fact a process of reasoning which involves all the elements of the syllogism; namely, 1. The general fact or proposition, that all men are mortal. 2. The fact referable to the class of facts which are included under this proposition,-that kings are men. ! 3. The deduction from this connexion, that kings are mortal. For the validity and efficacy of such a process, two things are necessary, namely, 1. That the general proposition which forms the first part of the statement, or, in logical language, the major proposition, be absolutely and universally true, or true without exception in regard to facts of a certain class, and be admitted as such by those to whom the reasoning is addressed. 2. That the fact referred to it, or the minor proposition, be admitted or proved to be one of that class of facts which are included under the general proposition. The conclusion then follows by a very simple process. If either of the two former propositions be deficient or untrue, the argument is false. Thus, if I had varied the statement as follows,-" Angels, like other human beings, are mortal;"-there is a fallacy which, when put into the syllogistic form, is immediately apparent; thus, All human beings are mortal, The general or major proposition here is true; but the minor is not one of the class of facts which are included under it; therefore the conclusion is false. If I had said again, “Angels, like other created beings, are mortal;" the fallacy is equally apparent, though from a different source; thus, |