Mental Philosophy: Including the Intellect, Sensibilities, and Will

by Joseph Haven

CHAPTER II.

THE ANALYTIC PROCESS—REASONING.

Relation to the Synthetic Process.—We have thus far considered that form or process of the reflective faculty, by which we combine the elements of individual complex conceptions, to form general conceptions and classes, on the basis of perceived agreements and differences. This we have termed the synthetic process. The divisive or analytic process remains to be considered. This, as the name denotes, is, so far as regards the method of procedure, the opposite of the former. We no longer put together, but take apart, no longer combine the many to form one, but from the general complex whole, as already formed and announced, we evolve the particular which lies included in it. This process comprehends what is generally called analysis, and also reasoning.

In discussing this most important mental process, we shall have occasion to treat more particularly of its nature, its forms, and its modes.

§ I.—The Nature of the Process.

Conceptions often Complex.—It was remarked, in speaking of our conceptions, that many of them are complex. My notion of a table, for example, is that of an object possessing certain qualities, as form, size, weight, color, hardness, each of which qualities is known to me by a distinct act of perception, if not by a distinct sense, and each of which is capable, accordingly, of being distinctly, and by itself, an object of thought or conception. The understanding combines these several conceptions, and thus forms the complex notion of a table. The notion thus formed, is neither more nor less than the aggregate, or combination of the several elementary conceptions already indicated. When I am called on to define my complex conception, I can only specify these several elementary notions which go to make up my idea of the table. I can say it is an object round, or square, of such or such magnitude, that it is of such or such material, of this or that color, and designed for such and such uses.

Virtual Analysis of complex Conceptions.—Now when I affirm that the table is round, I state one of the several qualities of the object so called, one of the several parts of the complex notion. It is a partial analysis of that complex conception. I separate from the whole, one of its component parts, and then affirm that it sustains the relation of a part to the comprehensive whole. The separation is a virtual analysis. The affirmation is an act of judgment expressed in the form of a proposition. Every proposition is, in fact, a species of synthesis, and implies the previous analysis of the conception, or comprehensive whole, whose component parts are thus brought together. Thus, when I say snow is white, man is mortal, the earth is round, I simply affirm of the object designated, one of the qualities which go to make up my conception of that object. Every such statement or proposition involves an analysis of the complex conception which forms the subject of the proposition, while the thing predicated or affirmed is, that the quality designated—the result of such analysis—is one of the parts constituting that complex whole.

Reasoning, what.—Reasoning is simply a series of such propositions following in consecutive order, in which this analysis is carried out more or less minutely. Thus, when I affirm that man is mortal, I resolve my complex notion of man into its component parts, among which I find the attribute of mortality, and this attribute I then proceed to affirm of the subject, man. I simply evolve, and distinctly announce, what was involved in the term man. But this term expresses not merely a complex, but a general notion. Resolving it as such into its individual elements, I find it to comprehend among the rest, a certain person, Socrates, e. g., and the result of this analysis I state in the proposition, Socrates is a man. But on the principle that what is true of a class must be true of the individuals composing it, it follows that the mortality already predicated of the class, man, is an attribute of the individual, Socrates. When I affirm, then, that Socrates is mortal, I announce, in reality, only what was virtually implied in the first proposition—man is mortal. I have analyzed the complex general conception, man, have found involved in it the particular conception, mortal, and the individual conception, Socrates, and by a subsequent synthesis have brought together these results in the proposition, Socrates is mortal, a proposition which sustains to the affirmation, man is mortal, the simple relation of a part to the whole.

Reasoning and Analysis, how related.—This analytic process, as applied to propositions, for the purpose of evolving from a complex general statement, whatever is involved or virtually contained in it, is called reasoning; as applied not to propositions, but to simple conceptions merely, it is known as simple analysis. The psychological process is, in either case, one and the same.

Illustration by Dr. Brown.—Dr. Brown has well illustrated the nature of the reasoning process in its relation to the general proposition with which we set out, by reference to the germ enclosed in the bulb of the plant. "The truths at which we arrive, by repeated intellectual analysis, may be said to resemble the premature plant which is to be found enclosed in that which is itself enclosed in the bulb, or seed which we dissect. We must carry on our dissection more and more minutely to arrive at each new germ; but we do arrive at one after the other, and when our dissection is obliged to stop, we have reason to suppose that still finer instruments, and still finer eyes, might prosecute the discovery almost to infinity. It is the same in the discovery of the truths of reasoning. The stage at which one inquirer stops is not the limit of analysis in reference to the object, but the limit of the analytic power of the individual. Inquirer after inquirer discovers truths which were involved in truths formerly admitted by us, without our being able to perceive what was comprehended in our admission.... There may be races of beings, at least we can conceive of races of beings, whose senses would enable them to perceive the ultimate embryo plant enclosed in its innumerable series of preceding germs; and there may, perhaps, be created powers of some higher order, as we know that there is one Eternal Power, able to feel, in a single comprehensive thought, all those truths, of which the generations of mankind are able, by successive analyses, to discover only a few, that are, perhaps, to the great truths which they contain, only as the flower, which is blossoming before us, is to that infinity of future blossoms enveloped in it, with which, in ever renovated beauty, it is to adorn the summers of other ages."

Inquiry suggested.—But here the inquiry may arise. How happens it that, if the reasonings which conduct to the profoundest and most important truths, are but successive and continued analyses of our previous conceptions, we should have admitted those preceding truths and conceptions without a suspicion of the results involved in them? The reason is probably to be found, as Dr. Brown suggests, in the fact that in the process of generalizing we form classes and orders before distinguishing the minuter varieties; we are struck with some obvious points of agreement which lead us to give a common place and a common term to the objects of such resemblance, and this very circumstance of agreement which we perceive, may involve other circumstances which we do not at the time perceive, but which are disclosed on minute and subsequent attention. "It is as if we knew the situations and bearings of all the great cities in Europe, and could lay down, with most accurate precision, their longitude and latitude. To know thus much, is to know that a certain space must intervene between them, but it is not to know what that space contains. The process of reasoning, in the discoveries which it gives, is like that topographic inquiry which fills up the intervals of our map, placing here a forest, there a long extent of plains, and beyond them a still longer range of mountains, till we see, at last, innumerable objects connected with each other in that space which before presented to us only a few points of mutual bearing."

The Position further argued from the Nature of the Syllogism.—That all deductive reasoning, at least, is essentially what has now been described, an analytic process, is evident from the fact that the syllogism to which all such argument may be reduced, is based upon the admitted principle that whatever is true of the class, is true of all the individuals comprehended under it. Something is affirmed of a given class; an individual or individuals are then affirmed to belong to that class; and on the strength of the principle just stated, it is thereupon affirmed that what was predicated of the class is also true of the individual. Nothing can be plainer than that in this process we are working from the given whole to the comprehended parts, from the complex conception stated at the outset, to the truths that lie hidden and involved in it. In other words, it is a process of analysis which we thus perform, and as all reasoning, when scientifically stated, is brought under this form, it follows that all reasoning is essentially analytic in its nature.

Inductive Reasoning no Exception.—It may be supposed that the inductive method of reasoning is an exception to this rule, inasmuch as we proceed, in that case, not from the general to the particular, but the reverse. Whatever may be true of deduction, is not induction essentially a synthetic process? So it might, at first, appear. I have observed, for example, that several animals of a particular species, sheep, for instance, chew the cud. Having observed this in several instances, I presently conclude that the same is true of the whole class to which these several individuals belong, in other words, that all sheep are ruminant. Extending my observation further, I find other species of animals likewise chewing the cud. I observe, moreover, that every animal, possessing this characteristic, is distinguished by the circumstance of having horns and cloven hoofs; I find, so far as my observation goes, the two things always associated, and hence am led, on observing the one, immediately to infer the other. The proposition that was at the outset particular, now becomes general, viz., all animals that have horns and cloven hoofs are ruminant. Is the conclusion at which I thus arrive, involved in the premiss with which I start? Is the fact that all horned and cloven-footed animals are ruminant, implied and contained in the fact that some horned and cloven-footed animals, that is, so many as I have observed, are so?

Even here the Evidence of the Conclusion lies in the Premiss.—A little reflection will convince us that these questions are to be answered in the affirmative. If the conclusion be itself correct and true, then it is a truth involved in the previous proposition; for whatever evidence I have of the truth of my conclusion, that all animals of this sort are ruminant, is manifestly derived from, and therefore contained in, the fact that such as I have observed are so. I have no other evidence in the case supposed. If this evidence is insufficient, then the conclusion is not established. If it be sufficient, then the conclusion which it establishes, is derived from and involved in it.

The argument fully and scientifically stated, runs thus:

A, B, C, animals observed, are ruminant. But A, B, C, represent the class Z to which they belong.

Therefore, class Z is ruminant.

Admitting now the correctness of my observation in respect to A, B, C, that they are ruminant, the argument turns entirely upon the second proposition that A, B, C, represent the class Z, so that what is true of them in this respect, is true of the whole class. If A, B, C, do represent the class Z, then to say that A, B, C, are ruminant, is to say that Z is so. The one is contained in the other. If they do not, then the conclusion is itself groundless, and there is no occasion to inquire in what it is contained, or whether it is contained in any thing. It is no longer a valid argument and therefore cannot be brought in evidence that some reasoning is not analytic.

What sort of Propositions constitute Reasoning.—It is hardly necessary to state that not any and every series of propositions constitute reasoning. The propositions must be consecutive, following in a certain order, and not only so, but must be in such a manner connected with and related to each other, that the truth of the final proposition shall be manifest from the propositions which precede. To affirm that snow is white, that gold is more valuable than silver, and that virtue is the only sure road to happiness, is to state a series of propositions, each one of which is true, but which have no such relation to each other as to constitute an argument. The truth of the last proposition does not follow from the truth of the preceding ones.

§ II.—Relation of Judgment and Reasoning.

Judgment Synthetic, Reasoning Analytic.—The relation of judgment and reasoning to each other becomes evident from what has been said of the nature of the reasoning process. Judgment is essentially synthetic. Reasoning, essentially analytic. The former combines, affirms one thing to be true of another; the latter divides, declares one truth to be contained in another. All reasoning involves judgment, but all judgment is not reasoning. The several propositions that constitute a chain of reasoning, are so many distinct judgments. Reasoning is the evolution or derivation of one of these judgments, viz., the conclusion, from another, viz., the premiss. It is the process by which we arrive at some of our judgments.

Mr. Stewart's View.—Reasoning is frequently defined as a combination of judgments, in order to reach a result not otherwise obvious. Mr. Stewart compares our several judgments to the separate blocks of stone which the builder has prepared, and which lie upon the ground, upon any one of which a person may elevate himself a slight distance from the ground; while these same judgments, combined in a process of reasoning, he likens to those same blocks converted now, by the builder's art, into a grand staircase leading to the summit of some lofty tower. It is a simple combination of separate judgments, nor is there any thing in the last step of the series differing at all in its nature, says Mr. Stewart, from the first step. Each step is precisely like every other, and the process of reaching the top is simply a repetition of the act by which the first step is reached.

This View called in Question.—It is evident that this position is not in accordance with the general view which we have maintained of the nature of the reasoning process. According to this view, reasoning is not so much a combination as an analysis of judgments; nor is the last of the several propositions in a chain of argument of the same nature precisely as the first. It is, like the first, a judgment, but unlike the first, it is a particular sort of judgment, viz., an inference or conclusion, a judgment involved in and derived from the former.

In the series of propositions, A is B, B is C, therefore A is C, the act of mind by which I perceive that A is B, or that B is C, is not of the same nature with that by which I perceive the consequent truth that A is C; no mere repetition of the former act would amount to the latter. There is a new sort of judgment in the latter case, a deduction from the former. In order to reach it, I must not merely perceive that A is B, and that B is C, but must also perceive the connection of the two propositions, and what is involved in them. It is only by bringing together in the mind these two propositions, that I perceive the new truth, not otherwise obvious, that A is C, and the state or act of mind involved in this latter step seems to me a different one from that by which I reach the former judgments.

§ III.—Different Kinds of Reasoning.

Two Kinds of Truth.—The most natural division is that according to the subject-matter, or the materials of the work. The truths which constitute the material of our reasoning process are of two kinds, necessary, and contingent. That two straight lines cannot enclose a space, that the whole is greater than any one of its parts, are examples of the former. That the earth is an oblate spheroid, moves in an elliptical orbit, and is attended by one satellite, are examples of the latter.

The Difference lies in what.—The difference is not that one is any less certain than the other, but of the one you cannot conceive the opposite, of the other you can. That three times three are nine, is no more true and certain, than that Cæsar invaded Britain, or that the sun will rise to-morrow a few minutes earlier or later than to-day. But the one admits of the contrary supposition without absurdity, the other does not; the one is contingent, the other necessary. Now these two classes of truths, differing as they do, in this important particular, admit of, and require, very different methods of reasoning. The one class is susceptible of demonstration, the other admits only that species of reasoning called probable or moral. It must be remembered, however that when we thus speak we do not mean that this latter class of truths is deficient in proof; the word probable is not, as thus used, opposed to certainty, but only to demonstration. That there is such a city as Rome, or London, is just as certain as that the several angles of a triangle are equal to two right-angles; but the evidence which substantiates the one is of a very different nature from that of the other. The one can be demonstrated, the other cannot. The one is an eternal and necessary truth, subject to no contingence, no possibility of the opposite. The other is of the nature of an event taking place in time, and dependent on the will of man, and might, without any absurdity, be supposed not to be as it is.

I. Demonstrative Reasoning.

Field of Demonstrative Reasoning.—Its field, as we have seen, is necessary truth. It is limited, therefore, in its range, takes in only things abstract, conceptions rather than realities, the relations of things rather than things themselves, as existences. It is confined principally, if not entirely, to mathematical truths.

No degrees of Evidence.—There are no degrees of evidence or certainty in truths of this nature. Every step follows irresistibly from the preceding. Every conclusion is inevitable. One demonstration is as good as another, so far as regards the certainty of the conclusion, and one is as good as a thousand. It is quite otherwise in probable reasoning.

Two Modes of Procedure.—In demonstration, we may proceed directly, or indirectly; as, e. g., in case of two triangles to be proved equal. I may, by super-position, prove this directly; or I may suppose them unequal, and proceed to show the absurdity of such a supposition; or I may make a number of suppositions, one or the other of which must be true, and then show that all but the one which I wish to establish are false.

Force of Mathematical reasoning.—The question arises whence the peculiar force of mathematical, in distinction from other reasoning?—a fact observed by every one, but not easily explained: how happens this, and on what does it depend, this irresistible cogency which compels our assent? Is it owing to the pains taken to define the terms employed, and the strict adherence to those definitions? I think not; for other sciences approximate to mathematics in this, but not to the cogency of its reasoning. The explanation given by Stewart is certainly plausible. He ascribes the peculiar force of demonstrative reasoning to the fact, that the first principles from which it sets out, i. e., its definitions, are purely hypothetical, involving no basis or admixture of facts, and that by simply reasoning strictly upon these assumed hypotheses the conclusions follow irresistibly. The same thing would happen in any other science, could we (as we cannot) construct our definitions to suit ourselves, instead of proceeding upon facts as our data. The same view is ably maintained by other writers.

If this be so, the superior certainty of mathematical, over all other modes of reasoning, if it does not quite vanish, becomes of much less consequence than is generally supposed. Its truths are necessary in no other sense than that certain definitions being assumed, certain suppositions made, then the certain other things follow, which is no more than may be said of any science.

Confirmation of this View.—It may be argued, as a confirmation of this view, that whenever mathematical reasoning comes to be applied to sciences involving facts either as the data, or as objects of investigation, where it is no longer possible to proceed entirely upon hypothesis, as, e. g., when you apply it to mechanics, physics, astronomy, practical geometry, etc., then it ceases to be demonstrative, and becomes merely probable reasoning.

Mathematical reasoning supposed by some to be identical.—It has been much discussed whether all mathematical reasoning is merely identical, asserting, in fact, nothing more than that a=a; that a given thing is equivalent to itself, capable of being resolved at last into merely this. This view has been maintained by Leibnitz, himself one of the greatest mathematicians, and by many others. It was for a long time the prevalent doctrine on the Continent. Condillac applies the same to all reasoning, and Hobbes seems to have had a similar view, i. e., that all reasoning is only so much addition or subtraction. Against this view Stewart contends that even if the propositions themselves might be represented by the formula a=a, it does not follow that the various steps of reasoning leading to the conclusion amount merely to that. A paper written in cipher may be said to be identical with the same paper as interpreted; but the evidence on which the act of deciphering proceeds, amounts to something more than the perception of identity. And further, he denies that the propositions are identical, e. g., even the simple proposition 2×2=4. 2×2 express one set of quantities, and 4 expresses another, and the proposition that asserts their equivalence is not identical; it is not saying that the same quantity is equal to itself, but that two different quantities are equivalent.

II. Probable Reasoning.

Not opposed to Certainty.—It must be borne in mind, as already stated, that the probability now intended is not opposed to certainty. That Cæsar invaded Britain is certain, but the reasoning which goes to establish it, is only probable reasoning, because the thing to be proved is an event in history, contingent therefore, and not capable of demonstration.

Sources of Evidence.—Evidence of this kind of truths is derived from three sources: 1. Testimony; 2. Experience; 3. Analogy.

1. Evidence of Testimony.

In itself probable.—This is, à priori, probable. We are so constituted as to be inclined to believe testimony, and it is only when the incredibility of the witness has been ascertained by sufficient evidence, that we refuse our assent. The child believes whatever is told him. The man, long conversant with human affairs, becomes wary, cautious, suspicious, incredulous. It is remarked by Reid that the evidence of testimony does not depend altogether on the character of the witness. If there be no motive for deception, especially if there be weighty reasons why he should speak truth, or if the narrative be in itself probable and consistent, and tallies with circumstances, it is in such cases to be received even from those not of unimpeachable integrity.

Limits of Belief.—What are the limits of belief in testimony? Suppose the character of witnesses to be good, the narrative self-consistent, the testimony concurrent of various witnesses, explicit, positive, full, no motive for deception; are we to believe in that case whatever may be testified? One thing is certain, we do in fact believe in such cases; we are so constituted. Such is the law of our nature. Nor can it be shown irrational to yield such assent. It has been shown by an eminent mathematician that it is always possible to assign a number of independent witnesses, so great that the falsity of their concurrent testimony shall be mathematically more improbable, and so more incredible, than the truth of their statement, be it what it may.

Case supposed.—Suppose a considerable number of men of undoubted veracity, should, without concert, and agreeing in the main as to particulars, all testify, one by one, that they witnessed, on a given day and hour, some very strange occurrence, as, e. g., a ball of fire, or a form of angelic brightness, hovering in the air, over this building, or any like unwonted and inexplicable phenomenon. Are we to withhold or yield our assent? I reply, if the number of witnesses is large, and the testimony concurrent, and without concert, and no motive exists for deception, and they are men of known integrity, especially if they are sane and sober men, not easily imposed upon, I see not how we can reasonably withhold assent. Their testimony is to be taken as true testimony, i. e., they did really witness the phenomenon described. The proof becomes stronger or weaker in proportion as the circumstances now mentioned coexist to a greater or less extent, i. e.., in proportion as there are more or fewer of these concurring and corroborating circumstances. If there was but a single witness, or if a number of the witnesses were not of the best character, or if there were some possible motive for deception, or if they were not altogether agreed as to important features of the case, so far the testimony would of course be weakened. But we may always suppose a case so strong that the falsity of the witnesses would be a greater miracle than the truth of the story. This is the case with the testimony of the witnesses to our Saviour's miracles.

Distinction to be made.—An important distinction is here to be noticed between the falsity, and the incorrectness, of the witness, between his intention to deceive, and his being himself deceived. He may have seen precisely what he describes; he may be mistaken in thinking it to have been an angel, or a spirit, or a ball of fire. Just as in the case of certain illusions of sense—an oar in the water—the eye correctly reports what it sees, but the judgment is in error, in thinking the oar to be crooked. So the witness may be true, and the testimony true in the case of a supposed miracle or other strange phenomenon; the appearance may have been just as stated, but the question may still be raised, were the witnesses correct, in their inference, or judgment, as to what was the cause of the said appearance, as to what it was that they saw or heard?

This must be decided by the rules that govern the proceedings of sensible men in common affairs of life.

2. Reasoning from Experience.

Induction as distinguished from Deduction.—This is called induction, the peculiar characteristic of which, in distinction from deductive reasoning, is that it begins with individual cases, and from them infers a general conclusion, whereas, the deductive method starts with a general proposition, and infers a particular one. From the proposition all men are mortal, the syllogism infers that Socrates is mortal. From the fact that Socrates, Plato, Aristotle, Pliny, Cæsar, Cicero, and any number of other individuals, are mortal, induction leads you to conclude that all men are so. The premises here are facts occurring within the range of observation and experience, and the reasoning proceeds on the principle of the general uniformity of nature and her laws. Induction, then, is, in other words, the process of inferring that what we know to be true in certain observed cases is also true, and will be found to be true, in other like cases which have not fallen under our observation.

Basis of this Mode of reasoning.—The groundwork of induction, as I have already said, is the axiom or universal proposition of the uniformity of nature. Take this away, and all reasoning from induction or experience fails at once. This is a truth which the human mind is, by its nature and constitution, always disposed to proceed upon. It may not be embodied in the shape of a definite proposition, but it is tacitly assumed and acted upon by all men. How came we by this general truth. Is it intuitive? So say the disciples of certain schools, so says Cousin, and so say the Scotch metaphysicians, and the German. Others, however, contend that it is itself an induction, as truly as any other, a truth learned from experience and observation, and by no means the first, but rather among the latest of our inductions. Without stopping to discuss this question, it is sufficient for our purpose to notice the fact, that this simple truth is universally admitted, and constitutes the basis of all reasoning from experience.

Incorrect Mode of Statement.—The proposition is sometimes incorrectly stated, as, e. g., that the future will resemble the past. This is not an adequate expression of the great truth to which we refer. It is not that the future merely will resemble the past merely, but that the unknown will resemble the known. The idea of time is not properly connected with the subject. That which is unknown may lie in the future, it may lie in the present or the past.

Limits of this Belief.—An important question here arises. What are the limits, if limits there are, to this belief of the uniformity of nature, and to the reasoning based on that belief? Are we warranted, in all cases, in inferring that the unknown will be, in similar circumstances, like the known—that what we have found to be true in five, ten, or fifty cases, and without exception, will be universally true? We do reason thus very generally. Such is the tendency of the mind, its nature. Is it correct procedure? Is it certain that our experience, though it be uniform and unvaried, is the universal experience? If not, if limits there are to this method of reasoning, what are they?

Erroneous Induction.—The inhabitants of Siam have never seen water in any other than a liquid or gaseous form. They conclude that water is never solid. The inhabitants of central Africa may be supposed never to have seen or heard of a white man. They infer that all men are black. Are these correct inductions? No; for they lead to false conclusions. They are built on insufficient foundations. There was not a sufficiently wide observation of facts to justify so wide a conclusion. Evidently, we cannot infer from our own non-observation of exceptions, that exceptions do not exist. We must first know that if there were exceptions we should have known them. In both the cases now supposed, this was overlooked. The African has only seen men who were natives of Africa. There may be in other countries, races that he has not seen, and has had no opportunity to see. The world may be full of exceptions to this general rule, and yet he not know it. Correct induction in his case would be this: I have seen many men, natives of central Africa, and they have all been black men, without exception. I conclude, therefore, that all the natives of central Africa are black. In a word, it is only under like circumstances that we can infer the uniformity of nature, and so reason inductively from the known to the unknown.

Superstitious Belief of the Ancients.—The tendency of men to believe in the universal permanence of nature, and, on that ground, to generalize from insufficient data, is illustrated in the superstitious and widely prevalent idea among the ancients, and some of the moderns also, of grand cycles of events extending both to the natural and the moral world. According to this idea, the changes of the atmosphere, and all other natural phenomena, as observed at any time, would, after a period, return again in the same order of succession as before; storms, and seasons, and times, being subject to some regular law. It was supposed, in fact, "that all the events"—to use the language of one of these theorists—"within the immeasurable circuit of the universe, are the successive evolutions of an extended series, which, at the return of some vast period, repeats its eternal round during the endless flux of time." This is a sufficiently grand induction, startling in its sweep and range of thought, but requiring for its data a somewhat wider observation of facts than can fall to the lot of short-lived and short-sighted man, during the few years of his narrow sojourn, and pilgrimage, in a world like this.

3. Reasoning from Analogy.

Meaning of the term Analogy.—This word, analogy, is used with great variety of meaning, and with much vagueness, therefore. It properly denotes any sort of resemblance, whether of relation or otherwise; and the argument from analogy is an argument from resemblance, an argument of an inductive nature, but not amounting to complete induction. A resembles B in certain respects; therefore it probably resembles it, also, in a certain other respect: such is the argument from analogy. A resembles B in such and such properties, but these are always found connected with a certain other property; therefore A resembles B also in regard to that property: such is the argument from induction. Every resemblance which can be pointed out between A and B creates a further and increased probability that the resemblance holds also in respect to the property which is the object of inquiry. If the two resembled each other in all their properties, there would be no longer any doubt as to this one, but a positive certainty, and the more resemblances in other respects so much the nearer we come to certainty respecting the one that happens to be in question.

Illustration of this Principle.—It was observed by Newton, that the diamond possessed a very high refractive power compared with its density. The same thing he knew to be true of combustible substances. Hence, he conjectured that the diamond was combustible. He conjectured the same thing, and for the same reason, of water, i. e., that it contains a combustible ingredient. In both instances, he guessed right—reasoning from analogy.

Further Illustration of Reasoning from Analogy.—Reasoning from analogy, I might infer that the moon is inhabited, thus: The earth is inhabited—land, sea, and air, are all occupied with life. But the moon resembles the earth in figure, relation to the sun, movement, opacity, etc.; moreover, it has volcanoes as the earth has; therefore, it is probably like the earth in this other respect, that of being inhabited. To make this out by induction, I must show that the moon not only resembles the earth in these several respects, but that these circumstances are in other cases observed to be connected with the one in question; thus, in other cases, bodies that are opaque, spherical, and moving in elliptical orbits, are known to be inhabited. The same thing is probably true then in all cases, and inasmuch as the moon has these marks, it is therefore inhabited.

Counter Probability.—On the other hand, the points of dissimilarity create a counter probability, as, e. g., the moon has no atmosphere, no clouds, and therefore no water; but air and water are, on our planet, essential to life; the presumption is, then, looking at these circumstances merely, that the moon is uninhabited. Nay, more: if life exists, then it must be under very different conditions from those under which it exists here. Evidently, then, the greater the resemblance in other respects between the two planets, the less probability that they differ in this respect (i. e., the mode of sustaining life), so that the resemblances already proved, become, themselves, presumptions against the supposition that the moon is inhabited.

Amount of Probability.—The analogy and diversity, when they come thus into competition and the arguments from the one conflict with those of the other, must be weighed against each other. The extent of the resemblance, compared with the extent of the difference, gives the amount of probability on one side or the other, so far as these elements are known. If any region lies unexplored, we can infer nothing with certainty or probability as to that. Suppose then, that so far as we have had the means of observing, the resemblances are to the differences as four to one; we conclude with a probability of four to one, that any given property of the one will be found to belong to the other. The chances are four out of five.

Value of Analogical Reasoning.—The chief value of analogy, as regards science, however, is as a guide to conjecture and to experiment; and even a faint degree of analogical evidence may be of great service in this way, by directing further inquiries into that channel, and so conducting to eventual probability, or even certainty.

It is well remarked by Stewart, that the tendency of our nature is so to reason from analogy, that we naturally confide in it, as we do in the evidence of testimony.

Liable to mislead.—It must be confessed, however, that it is a species of reasoning likely to mislead in many cases. Its chief value lies not in proving a position, but in rebutting objections; it is good, not for assault, but defence. As thus used it is a powerful weapon in the hands of a skilful master. Such it was in Butler's hands.

§ IV.—Use of Hypotheses and Theories in Reasoning.

Theory, what.—The terms hypothesis and theory are often used interchangeably and loosely. Confusion is the result. It is difficult to define them accurately.

Theory (from the Greek, Τεωρια; Latin, theoria; French, théorie; Italian, teoria; from Τεωρεω, to perceive, see, contemplate) denotes properly any philosophical explanation of phenomena, any connected arrangement and statement of facts according to their bearing on some real or imaginary law. The facts, the phenomena, once known, proved, rest on independent evidence. Theory takes survey of them as such, with special reference to the law which governs and connects them, whether that law be also known or merely conjectured.

Hypothesis, what.—Hypothesis (υπο-τιθημι) denotes a gratuitous supposition or conjecture, in the absence of all positive knowledge as to what the law is that governs and connects the observed phenomena, or as to the cause which will account for them.

Theory may or may not be Hypothesis.—Hypothesis is, in its nature, conjectural, and therefore uncertain; has its degrees of probability—no certainty. The moment the thing supposed is proved true, or verified, if it ever is, it ceases to be hypothesis. Theory, however, is not necessarily a matter of uncertainty. After the law or the cause is ascertained, fully known, and no longer a hypothesis at all, there may be still a theory about it; a survey of the facts and phenomena, as they stand affected by that law, or as accounted for by that cause. The motion of the planets in elliptical orbits, was originally matter of conjecture, of hypothesis. It is still matter of theory.

Probability of Hypothesis.—The probability of a hypothesis is in proportion to the number of facts or phenomena, in the given case, which it will satisfactorily explain, in other words, account for. Of several hypotheses, that is the most probable which will account for the greatest number of the given phenomena—those which, if the hypothesis be true, ought to fall under it as their law. If it accounts for all the phenomena in the case, it is generally regarded as having established its claim to certainty. So Whewell maintains. This, however, is not exactly the case. The hypothesis can be verified only by showing that the facts or phenomena in the case cannot possibly be accounted for on any other supposition, or result from any other cause; not simply that they can be accounted for, or can result from this. This is well stated by Mill in his System of Philosophy. The hypothesis of the undulating movement of a subtle and all-pervading ether will account for many of the known phenomena of light; but it has never been shown, and in the nature of the case never can be, probably, that no other hypothesis possible or supposable will also account for them.

Use of Hypotheses.—As to the use of hypotheses in science, Reid's remarks are altogether too sweeping, and quite incorrect. It is not true that hypotheses lead to no valuable result in philosophy. Almost all discoveries were at first hypotheses, suppositions, lucky guesses, if you please to call them so. The Copernican theory that the earth revolves on its axis was a mere hypothesis at the outset. Kepler's theory of the elliptical orbits of the planets was such; he made and abandoned nineteen false ones before he hit the right. This discovery led to another—that planets describe equal areas in equal times. Newton never framed hypotheses, if we may believe him. But his own grand discovery of the law of gravity as the central force of the system, depends for one of its steps of evidence on his previous discovery that the force of attraction varies as the inverse square of the distance, and this was suggested by him at first as a mere hypothesis; he was able to verify it only by calling in the aid of Kepler's discovery of equal areas in equal times, which latter, as already stated, was itself the result of hypothesis. Had it not been for one hypothesis of Newton, verified by the results of another hypothesis of Kepler Newton could never have made his own discovery.

A hypothesis, it must be remembered, is any supposition, with or without evidence, made in order to deduce from it conclusions agreeable to known facts. If we succeed in doing this, we verify our hypothesis (unless, indeed, it can be shown that some other hypothesis will equally well suit these facts), and our hypothesis, when verified, ceases to be longer a hypothesis, takes its place as known truth, and in turn serves to explain those facts which would, on the supposition of its truth, follow from it as a cause. It is simply a short-hand process of arriving at conclusions in science. Suppose the problem to be the one already named—to prove that the central force of the solar system is one and the same with gravity. Now it may not be easy, or even possible in some cases, to establish the first step or premiss in such a chain of reasoning. The inductions leading to it may not be forthcoming. Hypothesis steps in and supplies the deficiency, by substituting in place of the induction a supposition. Assuming that distant bodies attract each other with a power inversely as the square of the distance, it proceeds on that supposition, and arrives at the desired conclusion.

In what Cases admissible.—Now this method is always allowable, and strictly scientific, whenever it is possible to verify our hypothesis, i. e., in every case in which it is possible to show that no law but the one assumed can lead to these same results; that no other hypothesis can accord with the facts.

In the case supposed, it would not be possible to prove that the same movements might not follow from some other law than the one supposed. It is not certain, therefore, that the moving force of the solar system is identical with gravitation, merely because the latter would, if extended so far, produce the same results. In many other cases it is practicable; indeed, in all cases where the inquiry is not to ascertain the cause, but, the cause being already known, to ascertain the law of its action.

Even in cases where the inquiry is not of this nature, hypothesis is of use in the suggestion of future investigations, and, as such, is frequently indispensable.

View of Mr. Mill.—Nearly every thing which is now theory, was once hypothesis, says Mill. "The process of tracing regularity in any complicated, and, at first sight, confused set of appearances, is necessarily tentative: we begin by making any supposition, even a false one, to see what consequences will follow from it; and by observing how these differ from the real phenomena we learn what corrections to make in our assumption. The simplest supposition which accords with any of the most obvious facts, is the best to begin with, because its consequences are the most easily traced. This rude hypothesis is then rudely corrected, and the operation repeated, until the deductive results are at last made to tally with the phenomena. Let any one watch the manner in which he himself unravels any complicated mass of evidence; let him observe how, for instance, he elicits the true history of any occurrence from the involved statements of one or of many witnesses. He will find that he does not take all the items of evidence into his mind at once, and attempt to weave them together; the human faculties are not equal to such an undertaking; he extemporizes, from a few of the particulars, a first rude theory of the mode in which the facts took place, and then looks at the other statements, one by one, to try whether they can be reconciled with the provisional theory, or what corrections or additions it requires to make it square with them. In this way, which, as M. Comte remarks, has some resemblance to the methods of approximation of mathematicians, we arrive by means of hypothesis at conclusions not hypothetical."

§ V.—Different Forms of Reasoning.

It remains to treat briefly of the different forms of reasoning, as founded in the laws of thought.

How far these Forms fall within the Province of Psychology.—As there are different kinds or modes of reasoning, according to the difference of the subject-matter or material about which our reasoning is employed, so there are certain general forms into which all reasoning may be cast, and which, according to the laws of thought, it naturally assumes. To treat specifically of these forms, their nature, use, and value, is the business of logic; but, in so far as they depend upon the laws of thought, and are merely modes of mental activity as exercised in reasoning, they are to be considered, in connection with other phenomena of the mind, by the psychologist. Briefly to describe these forms, and then to consider their value, is all that I now propose. I begin with the proposition, as the starting point in every process of reasoning.

I. Analysis of the Proposition.

What constitutes a Proposition.—All reasoning deals with propositions, which are judgments expressed. Every proposition involves two distinct conceptions, and expresses the relation between them; affirms the agreement or disagreement of the one with the other. As when I say, Snow is white, the conception of snow is before my mind, and also of whiteness; I perceive that the latter element enters into my notion of snow, and constitutes one of the qualities of the substance so called; I affirm the relation of the two, accordingly, and this gives the proposition enunciated. Every proposition then consists of these several parts, a word or words expressing some conception, a word or words expressing some other conception, a word or words expressing the relation of the two. The words which designate these two conceptions are called the terms of the proposition, and, according to the above analysis, there are, in every proposition, always two terms. That term or conception of which something is affirmed, is called the subject, that which is affirmed of the same, the predicate, and the word which expresses the relation of the two, the copula. In the above proposition, snow is the subject, white, the predicate, and is, the copula.

Quality and Quantity.—Propositions are distinguished as to quality and quantity. The former has reference to the affirmative or negative character of the proposition, the latter to its comprehensiveness. Every proposition is either affirmative or negative, which is called its quality. As to quantity, every proposition is either universal, affirming something of the whole of the subject—as, All men are mortal; or else particular, affirming something of only a part of the subject—as, Some tyrants are miserable.

Four kinds of categorical Propositions.—We have, then, four kinds of categorical propositions, viz., universal affirmative, universal negative, particular affirmative, particular negative. That is, with the same subject and predicate, it is always possible to state four distinct propositions; as, every A is B, no A is B, some A is B, some A is not B. For the sake of convenience, logicians designate these different kinds of propositions severally by the letters A, E, I, O. Propositions that thus differ in quantity and quality are said to be opposed to each other. Of these, the two universals, A and E, are called contraries; the two particulars, I and O, sub-contraries; the universal affirmative, and the particular affirmative, A and I, also the universal negative and the particular negative, E and O, are respectively subalterns; while the universal affirmative and the particular negative, A and O, as also the universal negative and particular affirmative, E and I, are contradictories.

Rules of Opposition.—The following rules will be found universally applicable to propositions as opposed to each other. If the universal is true, so is the particular. If the particular is false, so is the universal. Contraries are never both true, but may be both false. Sub-contraries are never both false, but may be both true. Contradictories are never both true, or both false, but always one is true, the other false. The truth of these maxims will be evident on applying them to any proposition and its opposites, as for example, to the affirmation, Every man is mortal.

Categorical and hypothetical Propositions.—Propositions may be further distinguished as categorical or hypothetical; the one asserting or denying directly, as, e. g., The earth is round; the other conditionally,—as, If the earth is round, it is not oblong.

Pure, and Modal.—The proposition, moreover, may be either pure or modal, the former asserting or denying without qualification,—as, Man is liable to err; the latter qualifying the statement,—as, Man is extremely or unquestionably liable to err.

II. Analysis of the Syllogism.

Proposition the Link, Syllogism the Chain.—All reasoning admits of being reduced to the form of a syllogism. Having discussed the proposition which forms the material or groundwork of every connected chain of argument, we are prepared now to examine the syllogism, or chain itself, into which the several propositions, as so many links, are wrought.

Syllogism defined.—A syllogism is an argument so expressed that the conclusiveness of it is manifest from the mere form of expression. When, for example, I affirm that all A is B, that all B is C, and that, consequently, all A is C, it is impossible that any one who is able to reason at all, and who comprehends the force of these several propositions taken singly, should fail to perceive that the conclusion follows inevitably from the premises. That which is affirmed, may or may not be true, but it is conclusive. If the premises are true, so is the conclusion; but whether they are true or not, the argument, as such, is conclusive; nay, even if they are false, the conclusion may possibly be true. For example, Every tyrant is a good man; Washington was a tyrant; therefore, Washington was a good man, Both the premises are false, but the argument, as regards the form, is valid, and the conclusion is not only correctly drawn, but is, moreover, a true proposition. In a word, the syllogism concerns itself not at all with the truth or falsity of the thing stated, but only with the form of stating, and that form must be such, that the premises being conceded, the conclusion shall be obvious and inevitable. All valid reasoning admits of such statement.

Composition of a Syllogism.—Every syllogism contains three propositions, of which two state the grounds or reasons, and are called the premises, the other states the inference from those positions, and is called the conclusion. These three propositions contain three, and only three, distinct terms, of which one is common to both premises, and is called the middle term; the others are the extremes, one of which is the subject of the conclusion, and is called the minor term; the other the predicate of the conclusion, and is called the major term, from the fact that it denotes the class to which the subject or minor term belongs. In the syllogism,—Every man is mortal; Socrates is a man; therefore, Socrates is mortal,—the three terms are, man, mortal, and Socrates: of these, Socrates, or the subject of the conclusion, is the minor; mortal, or the predicate of the conclusion, is the major; and man, with which both the others are compared, is the middle term.

Major and minor Premiss.—The premiss which contains the major term, and compares it with the middle, is called the major premiss; that which, in like manner, compares the minor term with the middle, is called the minor premiss. In the syllogism already given, 'Every man is mortal' is the major premiss; 'Socrates is a man' is the minor premiss.

The Order variable.—The order of the terms in the respective propositions, and even the order of the propositions themselves, is not invariable, but depends on circumstances. In the above proposition, it is immaterial whether I say, Every man is mortal, or, Mortal is every man; it is immaterial whether I state first the major or the minor premiss; nay, it is allowable even to state the conclusion first, and then the grounds and reasons for the same.

III. Laws of Syllogism.

The following rules or maxims will be found applicable to all cases, and may be regarded as laws of the syllogism.

Middle Term unequivocal.—The middle term must not be equivocal.—This rule is violated in the following syllogism. Nothing is heavier than lead; feathers are heavier than nothing; therefore, feathers are heavier than lead. The middle term, nothing, is here used in different senses in the two premises.

Middle Term to be distributed.—Essentially the same thing occurs when the middle term is not, at least once, in the premises, used in its most complete and comprehensive sense, or, as the logicians express it, distributed. As, for example, when I say, White is a color, the term color is not here distributed, for it properly includes many things besides white. If now I introduce into another proposition the same term in a similar manner, as Black is a color, I evidently include under the term, as now used, some part of the class of things denoted by the general word color, which was not included under the same term as first used. The color which is affirmed to agree with black, is not the same color which is affirmed to agree with white. The term, in fact, denotes one thing in the one proposition, and another in the other. A syllogism thus constructed, is invalid. Hence the rule, that the middle term must be distributed, or taken in its completeness, to include the whole class which it properly denotes, at least once in the premises. This is done either by making it the subject of an affirmative, or the predicate of a negative proposition; as, All men are mortal, or, No vice is useful. Here the term man in the one case, and the term useful in the other, are each distributed or taken in their completeness. There is no individual to whom the term man can properly be applied, who is not included in the expression, all men, nor is there any useful thing which is not here denied of vice.

What distributed in the Conclusion.—On the same principle, no term must be distributed in the conclusion which was not distributed in one of the premises. This rule is violated in the following syllogism, All birds are bipeds; no man is a bird; therefore, no man is a biped. Here the term biped, in the major premiss, is not taken in its completeness, since many creatures besides birds are bipeds. Birds are only one sort of bipeds. In the conclusion, however, the term biped, being the predicate of a negative proposition, is distributed, the whole class of bipeds is spoken of, and man is excluded from the whole class. The syllogism is, of course, invalid.

Law of negative Premiss.—It is further a law of the syllogism, that from negative premises nothing can be inferred. Also, that if one premiss is negative, the conclusion will be negative.

Law of particular Premiss.—From two particular premises nothing follows, but if one premiss is particular, the conclusion will be so.

These rules are too obvious, and too easily verified, to require illustration.

IV. Different Kinds of Syllogism.

Syllogisms differ.—We have mentioned as yet only those properties of the syllogism which universally belong to it. There are differences, however, which require to be noticed, and which constitute a distinction of some importance, presenting, in fact, two distinct kinds of syllogism.

Two Modes of procedure.—There are manifestly two entirely distinct modes of procedure in reasoning. We may infer from the whole to the parts, or from the parts to the whole. The former is called deductive, the latter inductive reasoning. The one is precisely the reverse of the other in method of procedure. Each is a perfectly valid method of reasoning, and each is, in itself, a distinct and valid kind of syllogism. Each requires the other. The deductive is wholly dependent on the inductive for its major premiss, which is only the conclusion of a previous induction, while, on the other hand, the induction is valuable chiefly as preparing the way for subsequent deduction. Each has equal claims with the other to be regarded as a distinct and independent form of syllogism. They have not, however, been so treated by logicians, but, on the contrary, the inductive method has been regarded, almost universally, as a mere appendage of the deductive, an imperfect form of one or another of the several figures of the syllogism deductive. Of this we shall have occasion to speak more fully in the historical sketch.

The two Modes compared.—The precise relation of the two modes will best appear by the comparison of the following syllogisms. The inductive syllogism runs thus: x, y, z, are A; x, y, z, constitute B; therefore, B is A.

The deductive runs thus: B is A; x, y, z, constitute B; therefore, x, y, z, are A.

The latter, it will be seen at a glance, is the precise counterpart of the other, beginning where the former ends, and exactly reversing the several steps in their order.

The Law of each.—The general law or rule which governs the former, is, What belongs (or does not belong) to all the constituent parts, belongs (or does not belong) to the constituted whole. The law of the latter is, What belongs (or not) to the containing whole, belongs (or not) to all the contained parts.

Application of the inductive Method.—Applying the inductive method to a particular case, we reason thus: Magnets x, y, z, etc., including so many as I have observed, attract iron. But it is fair to presume that what I have observed as true of x, y, z, is equally true of e, f, g, and all other magnets; in other words, x, y, z, do represent, and may fairly be taken as constituting the whole class of magnets; consequently, I conclude that all magnets attract iron. Thus stated, the truth which was at first observed and affirmed only of particular instances, becomes a general proposition, and may, in turn, become the premiss of a process of deduction. Thus, from the general proposition, obtained as now explained by the inductive mode, that all horned animals ruminate, I may proceed, by the deductive mode, to infer that this is true of deer or goats, or any particular species or individual whose habits I have not as yet observed.

V. Different Forms of Syllogism.

The Form of Statement not invariable.—As there are different kinds of syllogism, so also there are different forms in which any kind of syllogism may be stated. These forms are not essential, pertaining to the nature of the syllogism itself, but accidental, pertaining merely to the order of announcing the several propositions. It has already been remarked, in speaking of the general structure of the syllogism, that the order of propositions is not essential. Either premiss may precede, either follow. Nay, we may state first the conclusion, and then the reasons, or grounds. This latter method, as Hamilton has shown in his New Analytic of Logical forms, is perfectly valid, though usually neglected by writers on logic. It is not only valid, but the more natural of the two methods. When asked if Socrates is mortal, it is more natural to say, He is mortal, for he is a man, and all men are mortal, than to say, All men are mortal, he is a man, and therefore, he is mortal. In fact, most of our reasoning takes the first of these forms. The two are designated by Hamilton, respectively, as the analytic and synthetic syllogism.

Order of Premises may vary.—As to the order of the premises, which shall precede the other, this, too, is quite unessential and accidental. The earlier method, practised by Greek, Arabian, Jewish and Latin schools, was to state first the minor premiss, precisely the reverse of our modern custom.

Order of Terms not essential.—The order of the terms, in the several propositions, is also accidental rather than essential. There are several possible and allowable arrangements of these terms with reference to the order of precedence and succession, giving rise to what are called figures of the syllogism. These arrangements and figures have usually been reckoned as four; three only are admitted by Hamilton, the fourth being abolished. The first figure occurs when the middle term is the subject of one premiss and the predicate of the other. The second figure gives the middle term the place of predicate in both premises. The third makes it the subject of both.

A further Variation.—There is still another form of statement, in which the terms compared are not, as above, severally subject and predicate, but, in the same proposition, are both subject, or both predicate, as when we say, A and B are equal; B and C are equal; therefore, A and C are equal. This is a valid synthetic syllogism, though not recognized by logicians previously to the New Analytic of Hamilton. It is termed by him the unfigured syllogism.

Hypothetical reasoning not syllogistic.—It has been customary to treat of hypothetical reasoning, in its two forms of conditional and disjunctive, as forms or kinds of syllogism. As when we say, if A is B, C is D; but A is B, therefore C is D; or, disjunctively, either A is B, or C is D; but A is not B, therefore C is D. These, however, are not properly syllogisms. The inference is not mediate, through comparison with a common or middle term, but immediate, whereas the syllogism is, in all its forms, a process of mediate inference.

Summary of Distinctions.—To sum up the distinctions now pointed out. All inference is either immediate, as in the case of hypothetical reasoning, whether conjunctive or disjunctive, or else mediate, as in the syllogism. The latter may be inductive or deductive; and, as to form, analytic or synthetic, figured or unfigured.

VI. Laws of Thought on which the Syllogism depends.

Statement.—There are certain universal laws of thought on which all reasoning, and, of course, all syllogisms, depend. These laws, according to Hamilton, are the principles of identity, of contradiction, and of excluded middle; from which primary laws results a fourth, that of reason and consequent.

Law of Identity, what.—The principle of identity compels us to recognize the equivalence of a whole and its several parts taken together, as applied to any conception and its distinctive characters. As, for example, the sameness or equivalence of the notion man with the aggregate of qualities or characters that constitute that notion.

Law of Contradiction, what.—The law of contradiction is the principle that what is contradictory is unthinkable: as, for example, that A has, and yet has not, a given quality, B.

Law of excluded Middle.—The principle of excluded middle is this, that of two contradictory notions, we must think one or the other to be true; as, that A either has or has not the quality B.

Law of Reason and Consequent.—From these primary principles results the law of reason and consequent. All logical inference is based on that law of our nature, that one notion shall always depend on another. This inference is of two kinds, from the whole to the parts, or from the parts to the whole, respectively called deductive and inductive, as already explained.

Certain Points not included in the preceding Synopsis.—I have presented, as was proposed, in brief outline, a synopsis of the forms of reasoning. For a full treatment of these forms, and the laws which govern them, the treatises on logic must be consulted.

Some things usually considered essential to logical forms, as the modality of propositions and syllogisms, and the conversion of the other figures of the syllogism into the first, I have not included in the above outline, for the reason that the former does not properly fall within the province of logic, which has to do only with the form and not with the matter of a proposition or an argument, while, as to the latter, it is only an accidental, and not an essential circumstance, what may be the figure of a syllogism, and it is, therefore, of no importance to reduce the second and third figures to the first.

VII. Use and Value of the Syllogism.

Having considered the various forms which the syllogism may assume, as also the laws or canons which govern it, we proceed to inquire, finally, as to its use and value in reasoning.

All mediate reasoning syllogistic.—It must be conceded, I think, that all mediate reasoning, all inference, which is not immediate and direct, but which, in order to reach its conclusion, compares one thing with another, is essentially syllogistic. The greater part of our reasoning processes are of this sort. When fully and explicitly stated, such reasoning resolves itself into some form of syllogism. It is not, as sometimes stated, a mode of reasoning, but the mode which all reasoning, except such as is direct and immediate, tends to assume. Not always, indeed, is this reasoning fully drawn out and explicitly stated, but all valid reasoning admits of being thus stated; nay, it is not, as to form at least, complete until it is so expressed.

Not always syllogistically expressed.—In ordinary conversation, and even in public address, we omit many intermediate steps in the trains and processes of our arguments, for the reason that their statement is not essential to our being understood, the hearer's mind supplying, for itself, the connecting links as we proceed; just as in speaking or writing, we make many abbreviations, drop out some letters and syllables here and there, in our hasty utterance, and yet all such short-hand processes imply and are based upon the full form; and it would be as correct and as reasonable to say that the fully written or fully spoken word is merely a mode of speaking and writing, which, when the grammarian and rhetorician come into contact with common people, they lay aside for the ordinary forms of speech, as to say that syllogism is merely a mode of reasoning, which the logician lays aside when he comes out of his study, and reasons with other men.

Chief Value of the Syllogism.—The chief use of the syllogism, I apprehend, however, to be, not in presenting a train of argument for the purpose of convincing and persuading others; for the laws of thought do not require us in such a case to state every thing that is even essential to the argument, but only so much as shall clearly indicate our meaning, and enable the hearer or reader to follow us; but rather in testing the soundness or detecting the unsoundness of an argument, whether our own, or that of an opponent. For this purpose, an acquaintance with the forms and laws of syllogism may be of great service to the writer and to the orator.

Objection to the Syllogism.—But it is objected to the syllogism that it is of no value in the discovery and establishment of truth, inasmuch as, by the very laws of the syllogism, there can be nothing more in the conclusion than was assumed in the premises. There is, and can be, in this way, no progress from the known to the unknown. The very construction of the syllogism, it is said, involves a petitio principii. When I say, All men are mortal; Socrates is a man; therefore, Socrates is mortal; the major premiss, it is said, affirms the very thing to be proved; that Socrates is mortal is virtually affirmed in the proposition that all men are so. Either, then, the syllogism proves nothing which was not known before, or else the general proposition, with which it sets out, is unwarranted, as asserting more than we know to be true, and, in that case, the conclusion is equally unreliable; in either case nothing is gained by the process; the syllogism is worthless.

Lies equally against all reasoning.—This objection, if valid against the syllogism, is valid against and overthrows not the syllogism merely, but all reasoning of whatever kind, and in whatever form. It is an objection which really applies, not to the form which an argument may happen to assume, but to the essential nature of reasoning itself. As was shown in discussing the nature of the reasoning process, all reasoning is, in its nature, essentially analytic. It is the evolution of a truth that lies involved in some already admitted truth. It simply develops, draws out, what was therein contained. Its starting-point must always be some admitted position, its conclusions must always be some inevitable necessary consequence of that admission. The mortality of Socrates is, indeed, involved and contained in the general proposition which affirms the mortality of all men, and so, also, is every inferred truth contained in that from which it is inferred.

Conclusion not affirmed in the Premiss.—But while contained, it is not affirmed, in the premiss. To say that all men are mortal, is not to say that Socrates is so, but only to say what implies that. The conclusion which draws out and affirms what was involved, but not affirmed, in the premiss, is an advance in the order of thought, a step of progress, and not merely an idle repetition, and the syllogism, as a whole, moves the mind onward from the starting-point to a position not otherwise explicitly and positively reached. It is a movement onward, and not merely a rotation of the wheel about its own axis.

The Form accidental.—In so far as the objection of petitio principii relates, not to the nature of reasoning, but only to its form, this is entirely a matter of accident, and does not pertain to the syllogism as such. As was shown in treating of the different forms of syllogism, the order of the propositions is not essential. We may, if we like, state the conclusion first, and then the reasons, as, All A is C, for all A is B, and all B is C; or we may state the same thing in a different form, as, A and B are equal; B and C are equal; therefore, A and C are equal. Both are syllogisms, the former analytic, the latter unfigured, but to neither does the objection of petitio principii apply so far as regards the mere form of statement. Nor does it apply to that form of syllogism in which the major premiss is a singular proposition, as, e. g., Cæsar was fortunate; Cæsar was a tyrant; therefore, a tyrant may be fortunate. Here the subject of the conclusion is not formally contained in that of the major premiss, as Socrates is contained in the expression, all men, a part of the whole.

Objection inapplicable to the inductive Syllogism.—Nor does the objection apply again to the inductive syllogism, in which the conclusion is more comprehensive than the premiss. The objection applies, in fact, only to the deductive syllogism, and to that only in its synthetic form, and to that only as figured, and as presenting, in its major premiss, other than a singular proposition.

Major Premiss, whence derived.—But whence, it may still be asked, comes the general proposition which every deductive syllogism contains, whether analytic or synthetic, the proposition e. g., that all men are mortal? Whether this be stated before or after the conclusion is a mere matter of form; but what is our authority for stating such a proposition at all? How do we know that which is here affirmed?

I reply, it is a truth reached by previous induction. Every deduction implies previous induction. I observe the mortality of individuals, x, y, z. I find no exceptions. My observation extends to a great number of cases, insomuch that I am authorized to take those cases as fairly representing the whole class to which they belong. I conclude, therefore, that what I have observed of the many is true of the whole. So comes the general proposition, All men are mortal.

Authority for this Belief.—But what reason have I to believe that what is true of the many is true of the whole, and how do I know this? I reply, I do not know it by observation, nor by demonstration; my belief of it rests upon, and resolves itself into, that general law or constitution of the mind according to which I am led to expect, under like circumstances, like results, in other words, that nature acts uniformly. This is my warrant, and my only warrant, for the inference, that what I have observed in many cases is true in others that I have not observed.

A Difficulty suggested.—But in what manner, now, shall this mere belief of mine, for it is nothing more, come to take its place as a general proposition, as positive categorical affirmation in the syllogism whose major premiss reads, All men are mortal?

A law of the mind may be a sufficient explanation of my belief; but the science of syllogisms cannot take cognizance of laws of the mind, as such, and has nothing to do with beliefs, but is concerned only with the forms in which an argument shall be presented. Those forms must be conclusive. How shall I convert, then, my conjecture, my plausible belief, in the present case, into that general positive affirmation which alone will answer the demands of the syllogism?

The Process explained.—The process is this: The precise result of my observation stands thus—x, y, z, are mortal. But I know that x, y, z, are so numerous as fairly to represent the class to which they belong. On the strength of this position, the inductive syllogism takes its stand, and overlooking the fact that there are some cases which have not fallen under my observation, positively affirms what I only believe and presume to be true, and the argument then reads, x, y, z, are mortal. But x, y, z, are all men, therefore, all men are mortal.

The general proposition thus reached by induction becomes, in turn, the major premiss of the deductive syllogism, which concludes, from the mortality of all men, that of Socrates in particular.

Position of Mill.—An able and ingenious writer, Mr. Mill, in his treatise on logic, takes the ground that we have no need to embody the result of our observations in the form of a general proposition, from which again to descend to the particular conclusion, but that, dispensing with the general proposition altogether, and with the syllogism of every kind and form, we may, and virtually do, reason directly from one particular instance to another, as, e. g., x, y, z, are mortal; therefore, f, g, h, are so. "If from our experience of John, Thomas, etc., who were once living, but are now dead, we are entitled to conclude that all human beings are mortal, we might surely, without any logical inconsequence, have concluded at once, from those instances, that the Duke of Wellington is mortal. The mortality of John, Thomas, and company, is, after all, the whole evidence we have of the mortality of the Duke of Wellington. Not one iota is added to the proof by interpolating a general proposition." Our earliest inferences, he contends, are precisely of this sort. The child burning his fingers, reasons thus: "That fire burnt me, therefore this will." He does not generalize, "All fire burns; this is fire; therefore, this will burn." The only use of a general proposition, Mill contends, is simply to furnish collateral security for the correctness of our inference.

Remarks upon this View.—This view sweeps away at once, and forever, all mediate reasoning, and shuts us up to the narrow limits of such inference alone as proceeds from a given instance directly to a conclusion therefrom. No doubt we do sometimes reason thus. But it is a reasoning, the conclusiveness of which is not, and cannot be made, apparent by any form of statement. If called in question, we can only say, I think so, or, I believe so. The mortality of John does not prove the mortality of Thomas. It may not even render it probable; it is only when I have observed such and so many cases as to leave no reasonable doubt that the property in question is a law of the class as such, and not a mere accident of the individual, that I am really warranted in the belief that any individual, not as yet observed, will come under the same law, because belonging to the same class. To reason in this way is to generalize; whatever process stops short of this, stops so far short of any and all conclusive evidence of the truth of what it affirms.

VIII. Historical Sketch of the Science of Logic.

Indian Logic earlier than that of Aristotle.—It is of the Greek logic, that of Aristotle, that we usually speak when we have occasion to refer to this science. It is usually attributed to Aristotle, indeed, as his peculiar glory, that he should at once have originated, and brought to perfection, a science which, for more than two thousand years, has received few alterations, found few minds capable of suggesting improvements. Recent labors of Orientalists have, however, brought to light the fact that in India, long before the palmy days of Grecian philosophy, logic was pursued with vigor as a study and science. The Nyàya of Gotama holds, in the Indian systems of philosophy, much the same place that the Organon of Aristotle holds with us. The two, however, are quite independent of each other. Aristotle was no disciple of Gotama.

Aristotle's Logic not perfect.—Nor, on the other hand, was the logic of Aristotle by any means perfect, as it is often represented. Its imperfections are many, and have been, for the most part, faithfully copied by his disciples.

Aristotle the first Greek Logician.—Previous to Aristotle there had been nothing worthy the name of science in this department of philosophy. The Sophists had made some attempts at logic, but of no great value. Plato had not devoted much attention to it. Aristotle himself says, in the close of his Organon, that he had worked without models or predecessors to guide him.

Subsequent Writers.—The work of Aristotle is in six parts, the first four treating of logic pure, the remaining two of its application. The school of Aristotle carried the cultivation and study of logic to a high degree. Theophrastus and Eudemus labored assiduously as commentators on their master, but made no change in the essential principles of the system. The Stoics, however, gave logic more attention and honor, more time and care, than did any other of the rival schools of philosophy. They sought to enlarge its boundaries and make it an instrument for the discovery of truth. It held the first place in their system, ethics and physics ranking after it.

St. Hilaire is wrong in saying that with Epicurus logic was of little consideration, that sensation was the source and criterion of thought with that school. The Epicurean logic was a peculiar system, differing from the Aristotelian, and very little known in the subsequent centuries.

In Alexandria the logic of Aristotle was in great honor, and had numerous commentators in the first centuries of the Christian era.

Introduced into Rome.—For a time the original works of Aristotle were lost. They lay buried in an obscure retreat whither they had been carried for safe preservation, and no one knew what they were. Sylla, capturing the city, brought them to Rome, where they were discovered to be the works of the great master, and Cicero gives them, with some labor and learning, to the public. But the Roman mind never mastered the logic of Aristotle. In all Roman philosophy, says St. Hilaire, there is scarcely a logician worthy of the name.

For several centuries, if not in Rome, yet in Alexandria and Athens, in Greece and in Egypt, the logic of Aristotle continued to be assiduously cultivated.

Logic in the Middle Ages.—It was in the middle ages, however, that logic received its chief cultivation and its highest honors. Aristotle was for some six centuries almost the only teacher of the human mind, and the Organon was the foundation of his knowledge. Nor during the irruption of the northern hordes, and the revolutions of society, and empire, and human manners, which followed, did the philosophy and logic of Aristotle pass out of sight or out of mind. It seemed impossible for any revolution of empire or of time to shake its foundations or break its sceptre over the human mind. In the seventh century, Isidore of Seville, and Bede the Venerable, gave it their labors and renown. In the eighth, Alcuin introduced it into the court of Charlemagne. In the twelfth, Abelard, and the controversy between the Realists and Nominalists, gave this science still more importance.

Logic in the Arabian Schools.—Meanwhile, the Mohammedans had been in advance of the Christians in the study of this science. The Arabs had inherited the learning of antiquity, and had carried the cultivation of the peripatetic philosophy to a high degree of perfection more than a century before it had received the homage of the West. From Arabia it passed, with the march of conquest, into Spain, and some of the ablest commentators Europe has produced, on the works of Aristotle, have been the Moors of Spain.

Continuance of Aristotle's Dominion.—The Crusades tended only to enlarge the sphere of this influence. Such men as Albert the Great, and Thomas Aquinas, became, in the thirteenth century, expounders of Aristotle. Not till the sixteenth century did this long dominion over the human mind show symptoms of decadence.

The Reformers.—Luther, among the Protestant reformers, sought to banish logic from the schools; but it was retained, and in the Protestant universities was still professed.

Attacks upon Aristotle.—It now became the fashion, however, in certain quarters, especially among the mystics in the Catholic communion, to decry Aristotle, and each original genius took this way to show his independence. Ramus is noted among these. Bacon followed in this track, and did little more than repeat the invectives of his predecessors. He attempted to set aside the syllogism, and put in its place induction.

Induction, however, in some form, is as old as the syllogism. From Plato and Aristotle downward, a thousand philosophers had availed themselves of this method of reasoning and had also stated and defended it.

The Moderns.—From Bacon and Descartes till our day logic has been in process of decadence. Locke condemns it. Reid and the Scotch school ridicule its pretensions. Kant and Hegel, on the other hand, give it a due place in their systems—the latter especially; while in France, it has admirers in St. Hilaire, Cousin, and others of like genius; and in Edinburgh, the great Hamilton devoted to it the powers of his unrivalled intellect.

Logic of Hamilton.—As no writer, since the days of Aristotle, has done more to complete and perfect the science of reasoning, than Sir William Hamilton, it seems due that even so brief a sketch of the history of logic as the present, should indicate, at least, the more important changes which his system introduces. Whatever may be thought of some of his views and proposed reforms in this ancient science and sanctuary of past learning, it is not too much to say, that no writer on logic can henceforth present a claim to be considered, who has not, at least, thoroughly mastered and carefully weighed these views and proposed changes, even if he do not adopt them. They are, moreover, for the most part, changes so obviously demanded in order to the completeness of the science, and so thorough-going withal, that they are destined, it would seem, to be sooner or later adopted, and if adopted, to work a radical change in the whole structure of this ancient and time-honored science.

I shall attempt nothing more, in this connection, than, in the briefest manner, to enumerate some of the more important of these improvements.

Assigns Induction its true Place.—Hamilton is the first, so far as I know, to elevate to its true place the inductive method of reasoning, making it coördinate with the deductive, and assigning its true character and value as a form of syllogism.

Recognizes the analytic Syllogism.—He is the first to bring to notice the claims of the analytic syllogism to a distinctive place and recognition in logic; a form of reasoning, which, however natural and necessary, and in use almost universal, had been strangely overlooked by logicians from Aristotle down.

Rejects Modality.—He strenuously and consistently rejects the modality of the proposition and the syllogism, on the ground that logic is not concerned with the character of the matter, whether it be true or false, necessary or contingent, but only with the form of statement, and consequently, all distinctions founded on the truth or falsity, the necessity or contingence of the matter, are utterly irrelevant to the science—a principle admitted by others, but not previously carried out to its true results.

Doctrine of Figure.—He shows that the figure of the syllogism is a matter accidental, rather than essential, that it may be even entirely unfigured; abolishes the fourth figure as superfluous; and sets aside, as quite useless and unnecessary, the old laborious processes of reducing and connecting the several figures to the first.

Rejects hypothetical Syllogism.—He throws out of the syllogism entirely, the so-called hypothetical forms, both conjunctive and disjunctive, as reducible to immediate inference, and not, therefore, to be included under syllogistic reasoning, which is always mediate.

The single Canon.—He reduces the several laws and canons of the figured syllogism to a single comprehensive canon.

Quantification of the Predicate.—But the most important discovery made by Hamilton in this science, is the quantification of the predicate. The predicate is always a given quantity in relation to the subject, and that quantity should be stated. This, logicians have always overlooked, quantifying only the subject, as, All men, Some men, etc., but never the predicate. Fully quantified, the proposition reads, All man is some animal, no animal, etc., i. e., some sort or species of animal. This doubles the number of possible propositions, giving eight in place of four, and gives a corresponding increase in the number of words. These eight propositions are shown to be, not only possible, but admissible and valid. They are thus enumerated and named:

		AFFIRMATIVE.	NEGATIVE.
I.	Toto-total;	All A is all B.	Any A is not any B.
II.	Toto-partial:	All A is some B.	Any A is not some B.
III.	Parti-total:	Some A is some B.	Some A is not some B.
IV.	Parti-partial:	Some A is some B.	Some A is not some B.

Reference.—For a more full and exact account of Hamilton's system, the reader is referred to the article on logic in the volume of Discussions on Philosophy and Literature, by Sir W. Hamilton; also, to "An Essay on the New Analytic of Logical Forms," by Thomas Spencer Baynes, L. L. B. On the history of logic in general, see Dictionnaire des Sciences Philosophiques—Article Logique, by Barthèleme St. Hilaire, Professor of Philosophy to the College of France, member of the Institute, etc., etc.; also, Blakey's History of Logic. The Memoir of St. Hilaire, on the logic of Aristotle, is one of the best works of modern times on the subject of which it treats.

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