Office of this Power.—We have thus far treated of that power of the mind by which it takes cognizance of objects as directly presented to sense, and also of that by which it represents to itself former objects of cognition in their absence. But a large portion of our knowledge and of our mental activity does not fall under either of these divisions. There is a class of mental operations which differs from the former, in that they do not give us directly sensations or perceptions of things, do not present objects themselves; and from the latter, in that they do not represent to the thought absent objects of perception; which differ from both, in that they deal not with the things themselves, but with the properties and relations of things—not with the concrete, but with the abstract and general. This class of operations, to distinguish it from the preceding classes, we have named, in our analysis, thereflective powerof the mind. It comprises a large part of our mental activity.
Specific Character.—The form of mental activity which is characteristic of this faculty, is the perception of relations, that which Dr. Brown callsrelative suggestion, but which we should prefer to termrelative conception. The mind is so constituted that when distinct objects of thought are presented, it conceives at once the notion of certain relations existing between those objects. One is larger, onesmaller, one is here, the other there, one is a part in relation to a whole, some are like, others unlike each other. The several relations that may exist and fall under the notice of this power of the mind are too many to be easily enumerated. The more important are, position, resemblance, proportion, degree, comprehension. All these may, perhaps, by a sufficiently minute analysis, be resolved into one—that of comprehension, or the relation of a whole to its parts.
Comprehensive of several Processes.—The faculty now under consideration will, on careful investigation, be found to underlie and comprehend several mental processes usually ranked as distinct operations and faculties of the mind, but which are at most only so many forms of the general power of relative conception. Such are the mental operations usually known asjudgment,abstraction,generalization, andreasoning. Of these, and their relation to the general faculty comprehensive of all, we shall have occasion to speak further as we proceed.
Two Modes of Operation.—As the relations of object to object may all be comprised under the general category of comprehension, or the whole and its parts, there are manifestly two modes or processes in which the reflective faculty may put forth its activity. It may combine the several parts or elements to form a complex whole, or it may divide the complex whole into its several parts and elements. In the one case, it works from the parts, as already resolved, to the whole; in the other, from the whole, as already combined, to the parts. The one is the compositive or synthetic, the other, the analytic or divisive process. Each will claim our attention.
THE SYNTHETIC PROCESS—GENERALIZATION.
§ I.—Nature of the Synthetic Process.
Our Conceptions often Complex.—If we examine attentively the various notions or conceptions of the mind, we find that a large part of them are in a sense complex—comprising, in a word, a certain aggregate of properties, which, taken together, constitute our conception of the object. Thus, my notion of table, or chair, or desk, is made up of several conceptions, of form, size, material, color, hardness, weight, use, etc., etc., all which, taken together, constitute my notion of the object thus designated.
Originally given as discrete.—These several elements that enter into the composition of our conceptions of objects, it is further to be noticed, are, in the first instance, given us in perception, not as a complex whole, but as discrete elements. Thus, sight gives us form and color; touch gives us extension, hardness, smoothness, etc.; muscular resistance gives us weight, and so, by the various senses, we gather the several properties which make up our cognizance of the object, and which, taken together, constitute our conception of it.
Conceptions of Classes.—But a large part of our conceptions, if we carefully observe the operations of our own minds, are not particular, but general, not of individual objects, but of classes of objects. Of this, any one may satisfy himself on a little reflection. How are these conceptions formed?
Such Conceptions, how formed.—The process of forming a general conception, I take to be this: The several elements that compose our conception of an individual object,being originally presented, as we have already said, one by one, in the discrete, and not in the concrete, it is of course in our power to conceive of any one of these elements by itself. No new power or faculty is needed for this. By the usual laws of suggestion any one of these elements may be presented to the mind, distinct from those with which, in perception, it is associated, and as such it may be the object of attention and thought. I may thus conceive of the color, the form, the size, or the fragrance of a flower.
Extension of the Process to other Objects.—It is of the form, color, etc., of some particular flower, as yet, however, and not of form and color in general, that I conceive. Suppose, now, that other flowers are presented to my notice, possessing the same form and color, for example, red. Presently I observe other objects, besides flowers, that are of the same color—horses, cows, tables, books, cloths. As the field of observation enlarges, still other objects are added to the list, until that which I first conceived of as the peculiar property of a single flower, the rose, and of a single specimen, no longer is appropriated in my thoughts to any individual object or class of objects, but becomes a general conception. It is an abstraction and also a generalization; an abstraction because it no longer denotes or connotes any individual object, but stands before the mind as simple, pure quality, red, or redness; a generalization inasmuch as it is a quality pertaining equally to a great variety of objects.
The Process carried still further.—Having thus obtained the general conception of red, and, in like manner, of blue, violet, yellow, indigo, orange, etc., etc., I may carry the process still further, and form a conception more general than either, and which shall include all these. These are all varieties denoting the certain peculiarity of appearance which external objects present to the eye. Fixing my thought upon this, their common characteristic, I no longer conceive of red, or blue, or violet, as such, but of color in general.
In like manner, I observe the properties of different triangles—right-angled, obtuse-angled, acute-angled, equilateral, isosceles. I leave out of view whatever is peculiar to each of these varieties, retaining only what is common to them all—the property of three-sidedness; and my conception is now a general one—triangle.
It is in this manner that we form the conceptions expressed by such terms as animal, man, virtue, form, beauty, and the like. A large proportion of the words in ordinary use, are of this sort. They are the names or expressions of abstract, general, conceptions: abstract, in that they do not relate to any individual object; general, in that they comprehend, and are equally applicable to a great variety of objects.
Process of Classification.—The process ofclassificationis essentially the same with that by which we form general abstract conceptions. Observing different objects, I find that they resemble each other in certain respects, while in others they differ. Objects A, B, and C, differ, for instance, in form, and size, and weight, and fragrance, but agree in some other respect, as in color. On the ground of this resemblance, I class them together in my conceptions. In so doing, I leave out of view all other peculiarities, the points in which they differ, and take into account only the one circumstance in which they agree. In the very act of forming a class, I have formed a general conception, which lies at the basis of that classification.
Tendency of the Mind.—The tendency of the mind to group individual objects together on the ground of perceived resemblances, is very strong, and must be regarded as one of the universal and instinctive propensities of our nature, one of the laws of mental action. As we have already remarked, respecting general abstract terms, a large portion of the language of ordinary life is the language of classification. The words which constitute by far the greater part of the names of things, are common nouns, that is, names ofclasses. The names of individual objects are comparatively few. Adjectives, specifying the qualities of objects, denote groups or classes possessing that common quality. Adverbs qualifying verbs or adjectives, designate varieties or classes of action and of quality. Indeed, the very existence of language as a medium of communication, and means of expression, involves and depends upon this tendency of the mind to class together, and then to designate by a common noun, objects diverse in reality, but agreeing in some prominent points of resemblance. In no other way would language be possible to man, since, to designate each individual object by a name peculiar to itself, would be an undertaking altogether impracticable.
Rudeness of the earlier Attempts.—The first efforts of the mind at the process of classification are, doubtless, rude and imperfect. The infancy of the individual, and the infancy of nations and races, are, in this respect, alike; objects are grouped roughly and in the mass, specific differences are overlooked, and individuals differing widely and essentially are thrown into the same class, on the ground of some observed and striking resemblance. As observation becomes more minute, and the mind advances in culture and power of discrimination, these ruder generalizations are either abandoned or subdivided into genera and species, and the process assumes a scientific form. What was at first mere classification, becomes now, in the strictest sense,generalization.
Scientific Classification.—Classification, however scientific, is still essentially the process already described. We observe a number of individuals, for example, of our own species. Certain resemblances and differences strike us. Some have straight hair, and copper complexion, others, woolly hair, and black complexion, others, again, differ from the preceding in both these respects. Neglecting minor and specific differences, we fix our attention on the grand points of resemblance, and thus form a general conception, whichembraces whatever characteristics belong, in common, to the several individuals which thus resemble each other. To this general conception we appropriate the name Indian, Negro, Caucasian, etc., which henceforth represent to us so many classes or varieties of the human race. Bringing these classes again into comparison with each other, we observe certain points of resemblance between them, and form a conception still more general, that of man.
Further Illustration of the same Process.—In this way the genera and species of science are formed. On grounds of observed resemblance, we class together, for example, certain animals. They differ from each other in color, size, and many other respects, but agree in certain characteristics which we find invariable, as, for example, the form of the skeleton, number of vertebræ, number and form of teeth, arrangement of organs of digestion. We give a name to the class thus formed—carnivora, rodentia, etc. The class thus formed and named, we term the genus, while the minor differences mark the subordinate varieties or species included under the genus. In the same way, comparing other animals, we form other genera. Bringing the several genera also into comparison, we find them likewise agreeing in certain broad resemblances. These points of agreement, in turn, constitute the elements of a conception and classification still wider and more comprehensive than the former. Under this new conception I unite the previous genera, and term them all mammalia. And so on to the highest and widest generalizations of science.
Having formed our classification we refer any new specimen to some one of the classes already formed, and the more complete our original survey, the more correct is this process of individual arrangement. It is remarked by Mr. Stewart, that the islanders of the Pacific, who had never seen any species of quadruped, except the hog and the goat, naturally inferred, when they saw a cow, that she must belong to one or the other of these classes. The limitations ofhuman knowledge may lead the wisest philosopher into essentially the same error.
It is in the way now described that we form genera, and species, and the various classes into which, for purposes of science, we divide the multitude of objects which are presented in nature, and which, but for this faculty, would appear to us but a confused and chaotic assemblage without number, order, or arrangement. The individuals exist in nature—not the classes, and orders, and species: these are the creations of the human mind, conceptions of the brain, results of that process of thought now described as the reflective faculty in its synthetic form.
Importance of this Process.—It is evident at a glance that this process lies at the foundation of all science. Had we no power of generalization—had we no power of separating, in our thoughts, the quality from the substance to which it pertains, of going beyond the concrete to the abstract, beyond the particular to the general—could we deal only with individual existences, neither comparison nor classification would be possible; each particular individual object would be a study to us by itself, nor would any amount of diligence ever carry us beyond the very alphabet of knowledge.
Existence of general Conceptions questioned.—Important as this faculty may seem when thus regarded, it has been questioned by some whether, after all, we have, in fact, or can have, any general abstract ideas; whether triangle, man, animal, etc., suggest in reality any thing more to the mind than simply some particular man, or triangle, or animal, which we take to represent the whole class to which the individual belongs.
There can be no question, however, that we do distinguish in our minds the thought of some particular man, as Mr. A, or some particular sort of man, as black man, white man, from the thought suggested by the term man; and the thought of an isosceles or right-angled triangle, fromthe thought suggested by the unqualified term triangle. They do not mean the same thing; they have not the same value to our minds. Now there are a great multitude of such general terms in every language, they have a definite meaning and value, and we knowwhatthey mean. It must be then that we have general abstract ideas, or general conceptions.
Argument of the Nominalist.—But the nominalist replies. The term man, or triangle, awakens in your mind, in reality and directly, only the idea of some particular individual or triangle, and this stands as a sort oftypeorrepresentationof other like individuals of whom you do not definitely think as such and so many. I reply, this cannot be shown; but even if it were so, the very language of the objection implies the power of having general conceptions. If the individual man or triangle thought of stands as a type or representation, as it is said, of a great number of similar men and triangles, then is there not already in my mind, prior to this act of representation, theidea of a class of objects, arranged according to the law of resemblance, in other words, ageneral abstract ideaorconception? If I had not already formed such an idea, the particular object presented to my thoughts could not stand as type or representation of any such thing, or of any thing beyond itself, for the simple reason that there would be nothing of the sort to represent.
Further Reply.—Besides, there is a large class of general terms to which this reasoning of the nominalist would not at all apply—such terms as virtue, vice, knowledge, wisdom, truth, time, space—which manifestly do not awaken in the mind the thought of any particular virtue or vice, any particular truth, any definite time, any definite space, but a general notion under which all particular instances may be included. To this the nominalist will perhaps reply, that in such cases we are really thinking, after all, of merenamesorsigns, as when we use the algebraicformulax-y, a mere term of convenience, having indeed some value, we do not know precisely what,itselfthe terminus and object of our thought for the time being. In such cases the mind stops, he would say, with the term itself, and does not go beyond it to conjure up a general conception for it. So it is with the terms virtue, vice; so with the general terms, class, species, genus, man, animal, triangle; they are mere collective terms,signs, formulas of convenience, to which you attach no more meaning than to the expressionx-y. If you would find their meaning and attach any definite idea to them, you must resolve them into theparticularobjects, the particular vices, virtues, etc., which go to make up the class.
I reply to all this, you are still classifying, still forming a general conception, the expression of which is your so called formula,x-y, alias virtue, man, and the like.
§ II.—Province and Relation of several Terms employed to denote, in Part, or as a Whole, this Power of the Mind.
We are now prepared to consider the proper province and relation of several terms frequently employed, with considerable latitude and diversity of meaning, to denote, in part, or as a whole, the process now described. Such are the termsabstraction,generalization,classification, andjudgment.
I.Abstraction.
Term often used in a Wide Sense.—This term is frequently employed to denote the entire synthetic process as now described—the power of forming abstract general conceptions, and of classifying objects according to those conceptions. It is thus employed by Stewart, Wayland, Mahan, and others. There is, perhaps, no objection to this use of the word, except that it is manifestly a departure from the strict and proper sense of the term.
More limited Sense.—There is another and more common use of the term abstraction, which gives it a more limited sense. As thus employed, it denotes that act of the mind by which we fix our attention on some one of the several parts, properties, or qualities of an object, to the exclusion of all the other parts or properties which go to make up the complex whole. In consequence of this exclusive direction of the thoughts to that one element, the other elements or properties are lost sight of, drop out of the account, and there remains in our present conception only that one item which we have singled out from the rest. This is denominated, in common language,abstraction. Such is the common idea and definition of that term. It is Mr. Upham's definition.
This not really Abstraction.—Whether this, again, is the true idea of abstraction, is, to say the least, questionable. When I think of the cover of a book, the handle of a door, the spring of a watch, in distinction from the other parts which make up a complex whole, I am hardly exercising the power of abstract thought; certainly no new, distinct faculty is requisite for this, but simply attention to one among several items or objects of perception. Hardly ever can it be called analysis, with Wayland. It is the simple direction of the thought to some one out of several objects presented. A red rose is before me. I may think of its color exclusively, in distinction from its form and fragrance; that is, of the redness of this particular rose, this given surface before me. The object of my thought is purely a sensible object. I have not abstracted it from the sensible individual object to which it belongs. It is in no sense an abstract idea, a pure conception. There has been nothing done which is not done in any case where one thing, rather than another of a group or assemblage of objects, is made the object of attention.
The true Nature of Abstraction.—But suppose now that instead of thinking of the redness of this rose inparticular, I think of the color red in general, without reference to the rose or any other substance; or, to carry the process further, of color in general, without specifying in my thought any particular color, evidently I am dealing now with abstractions. I have in my thoughtdrawn away(abstraho) the color from the substance to which it belongs, from all substance, and it stands forth by itself a pure conception, anabstraction, having, as such, no existence save in my mind, but there it does exist a definite object of contemplation. The form of mental activity now described, I should callabstraction. It is not necessary, perhaps, to assign it a place as a distinct faculty of the mind. It is, in reality, a part, and an important part, of the synthetic process already described. But it is not the whole of that process, and the term abstraction should not, therefore, in strict propriety, at least as now defined, be applied as a general term to designate that class of mental operations. The synthetic process involves something more than mere abstraction; viz.:
II.Classification As Distinguished From Generalization.
Classification.—When the general idea or conception has been formed in the mind, we proceed to bring together and arrange, on the basis of that general conception, whatever individual objects seem to us to fall under that general rule. This we call classification. Thus, forming first the abstract, or general conception red, we bring together in our thought a variety of objects to which this conception is applicable, as red horses, red flowers, red books, red tables, etc., etc., thus forming classes of objects on the ground of this common property. The difference betweenclassificationandgeneralization, in so far as they are not synonymous, I take to be simply this, that in the former we group and arrange objects according to no general law, but mere appearance or resemblance, often, therefore, on fanciful or arbitrary grounds while in the latter case, we proceed according tosome general and scientific principle or law of classification, making only those distinctions the basis of our arrangement which are founded in nature, and are at once invariable and essential.
III.Judgment as Related to Classification.
Judgment.—We have already spoken of that specific process by which, having formed a given conception, or a given rule, we bring the individual objects of perception and thought under that rule, or reject them from it, according as they agree or disagree with the conception we have formed. The process itself we have called classification. The mental activity thus employed is technically termedjudgment—the power of subsuming, under a given notion or conception, the particular objects which properly belong there. Thus, the botanist, as he meets with new plants, and the ornithologist, as he discovers new varieties of birds, refers them at once to the family, the genus, the species to which they belong. His mind runs over the generic types of the several classes and orders into which all plants and birds are divided, he perceives that his new specimen answers to the characteristic features of one of these families, or classes, and not to those of the others, and he accordingly assigns it a place under one, and excludes it from the rest. So doing, he exercises judgment. All classification involves and depends upon this power; closely viewed, the action of the mind, in the exercise of this power, amounts simply to this, the perception of agreement or disagreement between two objects of thought. In the case supposed, the genus or species, as described by those who have treated of the particular science, is one of the objects contemplated; the next specimen of plant or bird, as carefully observed and studied, is the other. These two objects of thought are compared; the one is perceived to agree or not to agree with the other; and on the ground of this agreement or disagreement, theclassification is made. This perception of agreement in such a case is an act of judgment, so called.
Not a distinct Faculty.—The form of mental activity now described, is hardly to be ranked as a distinct faculty of the mind, although it has been not unfrequently so treated by writers on mental science. It enters more or less fully into all mental operations; like consciousness and attention, it is, to some extent, involved in the exercise of all the faculties, and cannot, therefore, be ranked, with propriety, as coördinate with them. It is not confined to the investigations of science, but is an activity constantly exercised by all men. We have in our minds a multitude of general conceptions, the result of previous observation and thought. Every moment some new object presents itself. With the quickness of thought, we find its place among the conceptions already in the mind: it agrees with this, it is incompatible with that, it belongs with the one, it is excluded from the other. This is the form of most of our thinking; indeed, no small part of our mental activity consists in this perception of agreements and disagreements, and in the referring of some particular object of experience, some individual conception, to the class or general conception under which it properly belongs. The expression of such a judgment is a proposition. We think in propositions, which are only judgments mentally expressed. We discourse in propositions, which are judgments orally expressed. We cannot frame a proposition which does not affirm, or deny, or call in question, something of something.
Judgment in relation to Knowledge.—Are judgment and knowledge identical? Is all knowledge only some form of judgment? So Kant, Tissot, and other writers of that school, would affirm. "Judgment is the principal operation of the mind, since it is concerned in all knowledge properly so called." "All our knowledges are judgments. To know, is to distinguish, and to distinguish, is at once to affirm, and to deny." Such was also Dr. Reid's doctrine, in oppositionto Locke, who distinguished between knowledge and judgment. Reid, on the contrary, regards knowledge as only one class of judgments, namely, those about which we are most positive and certain. According to this view, judgment seems to cover the whole field of mental activity. Sir William Hamilton thus regards it. We cannot even experience a sensation, he maintains, without the mental affirmation or judgment that we are thus and thus affected.
Common Speech distinguishes them.—It must be admitted, however, that in common use there is a distinction between knowing and judging, the one implying the comparative certainty of the thing known, the other implying some room and ground for doubt, the existence of opinion and belief, rather than of positive knowledge. The word itself, both in its primitive signification, and its derivation, indicating, as it does, the decision by legal tribunal of doubtful cases, favors this usage. That an exercise of judgment is, strictly speaking, involved in all knowledge, is, nevertheless true, since, to know that a thing is thus and thus, and not otherwise, is to distinguish it from other things, and that is to judge.
§ III.—Historical Sketch.
The Realist and Nominalist Controversy.
The Question at Issue.—No question has been more earnestly and even more bitterly discussed, in the whole history of philosophical inquiry, than the point at issue between the Realist and Nominalist, as to what is the precise object of thought when we form an abstract general conception. When I use the termman, for example, is it a merename, and nothing more, or is there areal existencecorresponding to that name, or is it neither a mere name on the one hand, nor, on the other, a real existence, but a conception of my own mind, which is the object of thought?These three answers can be made, these three doctrines held, and essentially only these three. Each has been actually maintained with great ability and acuteness. The names by which the three doctrines are respectively designated are, Realism, Nominalism, and Conceptualism.
Early History of Realism.—Of these doctrines, the former, Realism, was the first to develop itself. To say nothing of the ancients, we find traces of it in modern philosophy, as early as the ninth century. Indeed, it would seem to have been the prevalent doctrine, though not clearly and sharply defined; a belief, as Tissot has well expressed it, "spontaneous, blind, and without self-consciousness." John Scotus Erigena, and St. Anselm, Archbishop of Canterbury, both philosophers of note, together with many others of less distinction, in the ninth, tenth, and eleventh centuries, were prominent Realists. The Platonic view may, in fact, be said to have prevailed down to that period. The early fathers of the Christian Church were strongly tinged with Platonism, and the Realistic theory accordingly very naturally engrafted itself upon the philosophy of the middle ages. The logical and the ontological, existence as mere thought of the mind, and existence as reality, were not distinguished by the leading minds of those centuries. The reality of the thought as thought, and the reality of an actual existence, corresponding to that thought, were confounded the one with the other. As the rose of which I conceive has existence apart from my conception, so man, plant, tree, animal, are realities, and not mere conceptions of the mind.
Rise of Nominalism.—It was not till nearly the close of the eleventh century, that the announcement of the opposite doctrine was distinctly made, in opposition to the prevalent views. This was done by Roscelinus, who maintained that universal and general ideas have no objective reality; that the only reality is that of the individuals comprised under these genera; that there are no such existences asman, animal, beauty, virtue, etc.; that generality is only a pure form given by the mind to the matter of its ideas, a pure abstraction, a mere name.
In this we have the opposite extreme of Realism. If the Realist went too far in affirming the objective reality of his conception, the Nominalist erred on the other in overlooking its subjective reality as a mode or state of the mind, and reducing it to a mere name.
Dispute becomes theological.—The dispute now, unfortunately, but almost inevitably, became theological. The Realist accused the Nominalist of virtually denying the doctrine of the Trinity, inasmuch as, according to him, the idea of Trinity is only an abstraction, and there is no Being corresponding to that idea. To this, Roscelinus replied, with at least equal force and truth, that on the same ground the Realist denied the doctrine of divine unity, by holding a doctrine utterly incompatible with it. Roscelinus, however was defeated, if not in argument, at least by numbers and authority, and was condemned by council at the close of the eleventh century.
Rise of Conceptualism.—It was about this time, that Abelard, pupil of Roscelinus, proposed a modified view of the matter, avoiding the extreme position both of the Realist and the Nominalist party, and allowing thesubjective, but not theobjectivereality, of general ideas. This is substantially the doctrine of Conceptualism. The general abstract idea of man, rose, mountain, etc., has indeed no existence or reality as an external object, nor is there among external objects any thing corresponding to this idea; but it has, nevertheless, a reality and existence as a thought, a conception of my mind.
Prevalence of Realism during the twelfth and thirteenth Centuries.—The doctrine, as thus modified, gained some prevalence, but was condemned by successive councils and by the Pope. Sustained by such authority, as well as by the names of men greatly distinguished for learning and philosophy, Realism prevailed over its antagonists during the latter part of the twelfth and the whole of the thirteenth century. The fourteenth witnessed again the rise and spread of the Conceptualist theory, under the leadership of Occam. The dispute was bitter, leading to strife and even blood.
Later History of the Discussion.—In the seventeenth century we find Hobbes, Hume, and Berkley advocating the doctrine of the Nominalists, while Price maintains the side of Realism. Locke and Reid were Conceptualists, Stewart a Nominalist.
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 itsnature, itsforms, and itsmodes.
§ 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 conceptionwhich 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 conceptionswithout 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 thatlie 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 thatsomehorned 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 thereforecontained 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,dorepresent 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 donot, 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, andcontingent. 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 anyless certainthan 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 oneadmits 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 ofdemonstration, the other admits only that species of reasoning calledprobableormoral. 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 tocertainty, but only todemonstration. That there is such a city as Rome, or London, is just ascertainas 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 nodegreesof 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 mayproceed 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 whichmustbe 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, arepurely 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 uponfactsas 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, certainsuppositionsmade, 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 eitheras 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 thata=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 formulaa=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 iscertain, 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 nomotivefor 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, thatthey 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; theappearancemay 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 towhat it wasthat 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 calledinduction, 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 itintuitive? 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 learnedfrom 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 exceptionsdo 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, thatallthe natives of central Africa are black. In a word, it is onlyunder like circumstancesthat 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 themoralworld. 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 fromanalogy. 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 frominduction. 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 isprobablylike 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, presumptionsagainstthe 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, sofar 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 ofanalogy, 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.