The Online Library of Liberty

A project of Liberty Fund, Inc.

• Preface.
• Part I.: Special Analysis.
• Chapter I.: A Datum Wanted.
• Chapter II.: The Universal Postulate.
• Chapter III.: Its Corollaries.
• Chapter IV.: Our Present Position.
• Part II.: Special Analysis.
• Chapter I.: Compound Quantitative Reasoning.
• Chapter II.: Compound Quantitative Reasoning (continued).
• Chapter III.: Imperfect and Simple Quantitative Reasoning.
• Chapter IV.: Quantitative Reasoning In General.
• Chapter V.: Perfect Qualitative Reasoning.
• Chapter VI.: Imperfect Qualitative Reasoning.
• Chapter VII.: Reasoning In General.
• Chapter VIII.: Classification, Naming, and Recognition.
• Chapter IX.: The Perception of Special Objects.
• Chapter X.: The Perception of Body As Presenting Dynamical, Statico-dynamical, and Statical Attributes. ∗
• Chapter XI.: The Perception of Body As Presenting Statico-dynamical and Statical Attributes.
• Chapter XII.: The Perception of Body As Presenting Statical Attributes.
• Chapter XIII.: The Perception of Space.
• Chapter XIV.: The Perception of Time.
• Chapter XV.: The Perception of Motion.
• Chapter XVI.: The Perception of Resistance.
• Chapter XVII.: Perception In General.
• Chapter XVIII.: The Relations of Similarity and Dissimilarity.
• Chapter XIX.: The Relations of Cointension and Non-cointension.
• Chapter XX.: The Relations of Coextension and Non-coextension.
• Chapter XXI.: The Relations of Coexistence and Non-coexistence.
• Chapter XXII.: The Relations of Connature and Non-connature.
• Chapter XXIII.: The Relations of Likeness and Unlikeness.
• Chapter XXIV.: The Relation of Sequence.
• Chapter XXV.: Consciousness In General.
• Chapter XXVI.: Results.
• Part III.: General Synthesis.
• Chapter I.: Method.
• Chapter II.: Connexion of Mind and Life.
• Chapter III.: Proximate Definition of Life.
• Chapter IV.: The Correspondence Between Life and Its Circumstances.
• Chapter V.: The Degree of Life Varies As the Degree of Correspondence.
• Chapter VI.: The Correspondence As Direct and Homogeneous.
• Chapter VII.: The Correspondence As Direct But Heterogeneous.
• Chapter VIII.: The Correspondence As Extending In Space.
• Chapter IX.: The Correspondence As Extending In Time.
• Chapter X.: The Correspondence As Increasing In Speciality.
• Chapter XI.: The Correspondence As Increasing In Generality.
• Chapter XII.: The Correspondence As Increasing In Complexity.
• Chapter XIII.: The Co-ordination of Correspondences.
• Chapter XIV.: The Integration of Correspondences.
• Chapter XV.: The Correspondences In Their Totality.
• Part IV.: Special Synthesis.
• Chapter I.: The Nature of Intelligence.
• Chapter II.: The Law of Intelligence.
• Chapter III.: The Growth of Intelligence.
• Chapter IV.: Reflex Action.
• Chapter V.: Instinct.
• Chapter VI.: Memory.
• Chapter VII.: Reason.
• Chapter VIII.: The Feelings.
• Chapter IX.: The Will.

CHAPTER XVIII.

THE RELATIONS OF SIMILARITY AND DISSIMILARITY.

§ 82. Of all relations the most complex is that of Similarity—that in virtue of which we range together objects of the same species, notwithstanding their differences of magnitude; and in virtue of which we put into the same class, phenomena of causation that are widely contrasted in degree. Already, in treating of Reasoning and of Classification, much has been said of this relation which forms their common basis. Here it needs only to state what it is when considered under its most general aspect.

The similarity which we predicate of natural objects belonging to the same class, is made up of many component similarities. Two animals identical in kind but unlike in size, are similar not only as wholes, but are also similar in their parts. The head of one is similar to the head of the other; the leg to the leg; the hoof to the hoof; the eye to the eye. Even the parts of the parts will be found more or less similar; as, on comparing two teeth, the crown to the crown, and the fangs to the fangs. And even such minute components as the hairs, show in their structure this same parallelism. One of these ordinary similarities therefore, consisting of an intricate plexus of similarities held together in similar ways, and resolvable as it consequently is into simple similarities, will, by implication, be analyzed in analyzing one of these simple similarities.

Though similarities of sequence do not admit of a complication parallel to that which similarities of coexistence admit of—seeing that, as known by us, a sequence is in its nature single—yet, they admit of another species of complication: namely, that arising from composition of causes and composition of effects. While, by the gravitation of a weight, the string to which it hangs may be elongated, and no other appreciable result be produced; by the joint action of a certain temperature, a certain amount of moisture, and a certain miasm, upon an individual of a particular diathesis, who happens to be in a particular state, there may be produced the immense complication of effects constituting a disease. Each of these sequences is classed with others which we call similar; and in conjunction with them may form a premiss for future conclusions. And though, in the first case, there is a single antecedent and a single consequent, while, in the second case, there is a group of antecedents and a group of consequents—though in this second case the antecedent is not a force, but a variety of forces united in a special plexus of relations, and the consequent is not an effect, but a variety of effects united in a special plexus of relations; yet, we so obviously think of a composite cause and a composite effect, as related in the same way that a simple cause and a simple effect are related, that in treating of similar sequences we may confine our attention to the simple ones, as those out of which the othersarise by complication of the terms.

Thus, then, choosing some primitive type of each, we have to consider what there is in common between similar coexistences and similar sequences.

§ 83. Of the one class, similar triangles furnish the most convenient example: and as an example of the other, we may take the uniform sequence of heat upon compression.

After all that was before said, it is needless to do more than remind the reader, that in both of these cases the similarity resolves itself into either equality or likeness of relations—that triangles are similar when any two sides of the one bear to each other a relation like that which the homologous sides of the other bear to each other; and that when classing as similar, the various cases in which compression produces heat, the likeness of the relations between compression and heat in those various cases, is the sole thing meant. Here it concerns us, not to dwell upon the fact that similarity is likeness of relations, but to consider what this likeness of relations implies.

In the first place, it is to be observed, that while it implies likeness in nature between the two antecedents and between the two consequents, it does not imply likeness in their amounts; but that, in nearly all cases, though not necessarily, the two antecedents are quantitatively unlike, and the two consequents are quantitatively unlike. Two triangles may be similar, though the sides of the one are severally a score times as great as the homologous sides of the other; and though in one case a small evolution of heat results from the pressure of a hundred pounds, and in another case a greater evolution from the pressure of a hundred tons, the cases are classed as similar. So that thus regarded, similarity may be described as the likeness of relations whose antecedents are like in kind, but mostly unlike in degree, and whose consequents are like in kind, but mostly unlike in degree.

This likeness of relations has itself two phases. It may be both qualitative and quantitative; or it may be qualitative only. It may be a likeness both in the kind of the relations and their degree; or it may be a likeness in kind only. And hence arise the two orders of similarity—perfect and imperfect: the similarity on which mathematical reasoning proceeds; and the similarity on which the reasoning of daily life proceeds. Thus, in the case of the triangles, the intuition of similarity implies, first, that the relations of extension between the sides of the one, are compared in thought with the like kind of relations between the sides of the other. There can be no idea of similarity if a relation of coexistence between two sides of one triangle, is presented in consciousness along with some relation of extension between two sides of the other. Evidently, therefore, the primary element in the intuition of perfect similarity, is—likeness of nature between relations. And then, joined to this, is the secondary element—likeness of degree between these connatural relations. The relations must be of the same order; and each antecedent must bear to its consequent a contrast of the same strength. In imperfect similarity however, the only implication is, likeness of nature in the relations. When, in any new case, we predicate heat as a result of compression, the implied similarity between such new case and previous cases, is simply a consciousness of connate relations, of which the two antecedents are connate and the two consequents are connate. Nothing is said of degree. The new relation between compression and heat, is simply thought of as a sequence like in kind to certain foreknown sequences; and though there may be a vague idea of the quantity of heat as varying with the quantity of compression, this is not included in the predication. Hence then, while imperfect similarity involves the connature of relations whose antecedents are connatural and whose consequents are connatural; perfect similarity involves the cointension of such connatural relations.

§ 84. So much for the elements into which the relation of similarity is resolvable, objectively considered. Subjectively considered, it may be defined as a consciousness that two successive states of consciousness are severally composed of like states of consciousness arranged in like ways: or more specifically—it is a consciousness of the cointension of two connatural relations between states of consciousness, which are themselves like in kind but commonly unlike in degree. And this being the consciousness of similarity in its simplest form, it results that when, as in ordinary cases, the similarity consists of many component similarities, each of the compared states of consciousness contains many relations that are severally connatural and cointense with the corresponding relations in the other.

Respecting dissimilarity it needs only to be said that—neglecting all those ordinary applications or rather misapplications of the word in which it is used to describe any kind of unlikeness, and confining our attention to dissimilarity proper, as existing between two geometrical figures—it is a consciousness of the non-cointension of two connatural relations between states of consciousness which are themselves like in kind, but commonly unlike in degree.

The relations of similarity and dissimilarity being thus proximately decomposed into certain more general relations, the further analysis of them is involved in the analysis of these more general relations: to which let us now proceed.