Schema

“ But all Actual Knowledge brings with it, by its formal nature, its schematized apposition;—although I now know of the Schema of God, yet I am not yet immediately this Schema, but I am only a Schema of the Schema. The required Being is not yet realized.
I shall be. Who is this I? Evidently that which is,—the Ego given in Intuition,—the Individual. This shall be.
What does its Being signify? It is given as a Principle in the World of Sense. Blind Instinct is indeed annihilated, and in its place there now stands the clearly perceived Shall. ”

“ In Kantian philosophy, “ Schema ” is used of “ the product of the exercise of the transcendental imagination in giving generality to sense and particularity to thought,” and “ schematism of the theory, in the Kantian analysis of knowledge, of the use of the transcendental imagination as mediating between sense and understanding ” (Baldwin, Dictionary of Philosophy and Psychology, 1902, vol. ii.) ”

“ Categories as modes of understanding, schemata as modes of productive imagination, data of sense as modes of affection, are linked together, and appear to have a nature and existence independently of one another, and of the synthesis in which they are combined. ”

“ In the presentation of a theme the speaker or writer is prone to arrange his material in a scheme which may be very wise for the purpose intended for distinct presentation and clear understanding. Such a piece of valuable literature may live, and the schematization may be taken as a classification with disastrous results. ”

“ Names are developed before classes are logically distinguished, and, although naming involves a mode of classification, many devices of naming are very illogical methods of classification, but still convenient in schematization ”

“ The schemata, therefore, are nothing but a priori determinations of time according to rules, and these, in regard to all possible objects, following the arrangement of the categories, relate to the series in time, the content in time, the order in time, and finally, to the complex or totality in time. ”

“ Just these natural attitudes resist all schematization as yet; nevertheless they are, on the one hand, the chief material of biographical-historical studies, and, on the other, in the case of psychographing a living individual who can be subjected to experiment, indispensable for completeness. In view of this, the Scheme must try to formulate more exactly the data with reference to natural attitudes in such a manner that they may appear as reactions to definite stimuli occurring in the course of life, e. ”

“ The formation of a morphological classification is therefore a logical process, the purpose of which is to throw the facts of structure into the smallest possible number of general propositions, which propositions constitute the definitions of the respective groups. ”

“ Since the common properties of a true Kind, and consequently the general assertions which can be made respecting it, or which are certain to be made hereafter as our knowledge extends, are indefinite and inexhaustible; and since the very first principle of natural classification is that of forming the classes so that the objects composing each may have the greatest number of properties in common; this principle prescribes that every such classification shall recognize and adopt into itself all distinctions of Kind, which exist among the objects it professes to classify. ”

“ Thus, a scheme is any statement, theory, model, formula, taxonomy, concept, categorization, classification, or other representational or linguistic structure which identifies the recurring characteristics of particular environments. ”

“ When we think of the infinite variety of the physical objects around us, and of the small number of classes in which they are at present arranged, it would seem to us, if we were ignorant of the history of philosophy, that the regular progress of classification must have been to simplify, more and more, the general circumstances of agreement, on which arrangement depends ”

“ Now, however, when it is known that a class, a universal, a genus or species, is not an entity _per se_, but neither more nor less than the individual substances themselves which are placed in the class, and that there is nothing real in the matter except those objects, a common name given to them, and common attributes indicated by the name; what, I should be glad to know, do we learn by being told, that whatever can be affirmed of a class, may be affirmed of every object contained in the class? ”

“ The object of classification is clear. We understand things if we can comprehend them; that is to say, if we can grasp and hold together single facts, connect isolated impressions, distinguish between what is essential and what is merely accidental, and thus predicate the general of the individual, and class the individual under the general. This is the secret of all scientific knowledge. Many sciences, while passing through this second or classificatory stage, assume the title of comparative. ”

“ In Book I, Chapter II, I have adopted a new definition of ‘Classification’, which enables me to regard the whole Universe as a ‘Class,’ and thus to dispense with the very awkward phrase ‘a Set of Things.’
In the Chapter on ‘Propositions of Existence’ I have adopted a new ‘normal form,’ in which the Class, whose existence is affirmed or denied, is regarded as the Predicate, instead of the Subject, of the Proposition, thus evading a very subtle difficulty which besets the other form. ”

“ What we usually do is first to frame some system of concepts mentally classified, serialized, or connected in some intellectual way, and then to use this as a tally by which we 'keep tab' on the impressions that present themselves. When each is referred to some possible place in the conceptual system, it is thereby 'understood.' This notion of parallel 'manifolds' with their elements standing reciprocally in 'one-to-one relations,' is proving so convenient nowadays in mathematics and logic as to supersede more and more the older classificatory conceptions. ”

“ The apperceptive process of interpreting the new by selecting and relating elements of former experience, or the process of analysis-synthesis, is universal in learning. Expressed in another form, what is at first indistinct and indefinite becomes clear and defined through attention selecting, for the interpretation of the new presentation, suitable old ideas and setting up relationships among them. Analysis, or selection, is incomplete without an accompanying unification, or synthesis; synthesis, or organization, is impossible without analysis, or selection. ”

“ The phrase Natural Classification seems most peculiarly appropriate to such arrangements as correspond, in the groups which they form, to the spontaneous tendencies of the mind, by placing together the objects most similar in their general aspect; in opposition to those technical systems which, arranging things according to their agreement in some circumstance arbitrarily selected, often throw into the same group objects which in the general aggregate of their properties present no resemblance, and into different and remote groups, others which have the closest similarity. ”

“ The two former we infer from the testimony adduced, or from the traces of those past occurrences which still exist; the latter, from the premises laid down in books of geometry, under the title of definitions and axioms. Whatever we are capable of knowing must belong to the one class or to the other; must be in the number of the primitive data, or of the conclusions which can be drawn from these. ”

“ We commence our present division—and shall follow the like course with the others—with its higher forms, and, proceeding in descending order, shall in each conclude with those humble rudimentary forms in which the rigid divisions of classification are obliterated, and the only differences which can be assigned are, at best, but little more than arbitrary. ”

“ A scheme that distributes marks on anything but a rational and intelligent system; a scheme that excludes the Natural History Sciences, mineralogy and Geology, as well as Psychology and Moral Philosophy from its scope altogether; a scheme that prescribes only Elements and Outlines of such important subjects as Natural Science (Chemistry, Electricity and Magnetism, &c.) and Political Economy—stands self-condemned. ”

“ This discovery is made by means of comparison and classification. We cease to study each flower for its own sake; and by continually enlarging the sphere of our observation, we try to discover what is common to many and offers those essential points on which groups or natural classes may be established. These classes again, in their more general features, are mutually compared; new points of difference, or of similarity of a more general and higher character, spring to view, and enable us to discover classes of classes, or families. ”

“ The Classification thus obtained, depends neither upon the faculties of the mind to which the separate parts of our knowledge owe their origin, nor upon the objects which each science contemplates; but upon a more 137 natural and fundamental element;—namely, the Ideas which each science involves. The Ideas regulate and connect the facts, and are the foundations of the reasoning, in each science: and having in another work more fully examined these Ideas, we are now prepared to state here the classification to which they lead. ”

“ That orderly arrangement of objects called Classification has two purposes, which, though not absolutely distinct, are distinct in great part. It may be employed to facilitate identification, or it may be employed to organize our knowledge. If a librarian places his books in the alphabetical succession of the author's names, he places them in such way that any particular book may easily be found, but not in such way that books of a given nature stand together. ”

“ Every new quality or circumstance which can belong to an object, subdivides each combination or class, so that the number of such combinations, when unrestricted by logical conditions, is represented by an infinitely high power of two. The extremely rapid increase in the number of subdivisions obliges us to confine our attention to a few qualities at a time. ”

“ It is also to be borne in mind that a classification is a system whose parts are arranged according to a hierarchy. There are dominating members and others which are subordinate to the first; species and their distinctive properties depend upon classes and the attributes which characterize them; again, the different species of a single class are conceived as all placed on the same level in regard to each other. ”

“ The production of a scheme is a major effort of the speculative Reason. It involves imagination far outrunning the direct observations. The interwoven group of categoreal notions which constitute the scheme allow of derivative extension by the constructive power of deductive logic. Throughout the whole range of these propositions respecting the interrelations of the forms of things, some of them allow of direct comparison with experience. In this way, the scheme as a whole has contact with experience. ”

“ The principles of Division are often given in Formal Logic, and the principles of Classification in Inductive Logic, but there is no valid reason for the separation. The classification of objects in the Natural Sciences, of animals, plants, and stones, with a view to the thorough study of them in form, structure, and function, is more complex than classifications for more limited purposes, and the tendency is to restrict the word classification to these elaborate systems. ”

“ What interpretation is to be put on these truths of classification? We find that organic forms admit of an arrangement everywhere indicating the fact, that along with certain attributes, certain other attributes, which are not directly connected with them, always exist. How are we to account for this fact? And how are we to account for the fact that the attributes possessed in common by the largest assemblages of forms, are the most vitally-important attributes? ”

“ Nothing can be more superficial than such a mode of classification; and if these groups actually exist in Nature, they must be based, like all the other divisions, upon some combination of structural characters peculiar to them. We have seen that Branches are founded upon the general plan of structure, Classes on the mode of executing the plan, Orders upon the greater or less complication of a given mode of execution, and we shall find that form, as determined by structure, characterizes Families. ”

“ A classification system is a schedule or chart of knowledge arranged in some logical order according to a definite and invariable principle. It may arrange knowledge by the historical, evolutionary or some other and arbitrary principle, the choice of which is governed by the rule that the order must be that which is likely to be most serviceable to the users of the system. ”

“ In the concrete individuality, where the mere unanalysed quality of the definition is regarded as a correlation of elements, the object is a synthetical nexus of distinct characteristics. It is a Theorem. Being different, these characteristics possess but a mediated identity. To supply the materials, which form the middle terms, is the office of Construction: and the process of mediation itself, from which cognition derives the necessity of that nexus, is the Demonstration. ”

“ Every scheme is an idea; every scheme, more or less new, implies an idea more or less original; every scheme proceeded with, implies an idea vivid enough to prompt action; and every scheme which succeeds, implies an idea so accurate and exhaustive that the results correspond with it. ”