Chapter II: The Analytic Process--Reasoning (1)

_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, [Greek: Theôria]; Latin, theoria; French, théorie; Italian, teoria; from [Greek: Theôreô], 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_ ([Greek: hypo-tithêmi]) 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.