Combination

“ The definite combination of heterogeneous changes, both simultaneous and successive, is a formula which fails to call up an adequate conception. And it fails from omitting the most distinctive peculiarity—the peculiarity of which we have the most familiar experience, and with which our notion of Life is, more than with any other, associated. ”

“ Compounds wherein one element is compound are called decomposites.
§ 370. There are a number of words which are never found by themselves; or, if so found, have never the same sense that they have in combination. Mark the word combination. The terms in question are points of combination, not of composition: since they form not the [271] parts of words, but the parts of phrases. Such are the expressions time and tide—might and main—rede me my riddle—pay your shot—rhyme and reason, &c. ”

“ But a coherent whole made up of definite parts definitely combined, must exhibit more definitely combined changes than a whole made up of parts that are neither definite in themselves nor in their combination. ”

“ Our mental history, says he, is, in its view,
"a perpetual formation of new compounds: and the words 'association,' 'cohesion,' 'fusion,' 'indissoluble connection,' all express the change from plurality of data to some unity of result. An explanation of the process therefore requires two things: a true enumeration of the primary constituents, and a correct statement of their laws of combination: just as, in chemistry, we are furnished with a list of the simple elements, and the with then principles of their synthesis. ”

“ When the set for adding is active, a pair of numbers, seen or heard, together with this internal stimulus of the mental set, arouses the response that gives the sum; but when the multiplying set is active, the same pair of numbers gives the product as the response. All thinking towards any goal is a similar instance of the law of combination. ”

“ 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. ”

“ The solution of a problem may present great difficulties, but once started on the appropriate line, the whole series of combination goes on unfolding, stimulating other moments and aggregates and forming more and more complex combinations. ”

“ The machinery of response by analogy is easily understood by aid of the law of combination. A complex object, presenting a number of parts and characteristics, arouses the response of seeing and perhaps naming the object. This is a unitary response to a collection of stimuli, and each of the parts or characteristics of the object participates in arousing the response, and the linkage of each part with the response is thus strengthened. ”

“ But if we analyze any one of these compound words, Finger-hut, for instance, we shall perceive that while each of the so-called elements of combination, Finger and Hut, has a distinct meaning, which enters into the more specific meaning of the compound, yet they are not, in any true sense, elements, or, in other words, that they are not the ultimate elements of the compound words. ”

“ If the causes of his combination are natural—that is to say, if they arise from his own feelings and from the necessities of his own condition—the combination will end in results mutually beneficial to employers and employed. ”

“ For how, in fact, can we conceive combinations, otherwise than as definite in kind and quantity? If we were to suppose each element ready to combine with any other indifferently, and indifferently in any quantity, we should have a world in 26 which all would be confusion and indefiniteness. ”

“ The reader will see that the numbers which we reach in questions of permutation, increase in a more extraordinary manner even than in combination. Each new object or term doubles the number of combinations, but increases the permutations by a factor continually growing. ”

“ Development by a Combination of Methods.+—A paragraph should have unity of thought, and, so long as this unity of thought is kept, it does not matter what methods of development are used. A dozen paragraphs taken at random will show that combinations are very frequent. Often it will be difficult to determine just how a paragraph has been developed. ”

“ All forms of what we call matter are really but aggregates of spiritual units; and all apparent differences of substance represent only differences of combination among these units. The differences of combination are caused by special tendencies and affinities of the units;—the tendency of each being the necessary result of its particular evolutional history— (using the term “evolu [125] tional” in a purely ethical sense) . ”

“ A combination probably, combinations being the one thing to be taken for granted in any analysis of causes in man or nature. Life for Americans began in a reaction. Form and ceremony had hampered thought and hindered growth, and the earnest Puritan swept both aside once for all. ”

“ So numerous and various, too, are the circumstances which form individual character, that the consequence of any particular combination is hardly ever some definite and strongly marked character, always found where that combination exists, and not otherwise. What is obtained, even after the most extensive and accurate observation, is merely a comparative result ”

“ If thinking is bringing together or combining, addition with its complementary subtraction, the question arises, whether we are to apply the term to the combining into unity which is necessary in every act of knowing, in order to make that presentation of an object to the subject which is cognition itself, or to that combination which we ordinarily designate by the term association. ”

“ Combination and re-combination are principles largely pervading nature. There are few rocks, for example, that are not composed of at least two varieties of matter, each of which is again a compound of elementary substances. ”

“ Now, it often happens that we cannot choose all the combinations of things, without first choosing them subject to the accidental variety of order, and we must then divide by the number of possible variations of order, that we may get to the true number of pure combinations. ”

“ But combinations are of various sorts; there are express combinations entered into by people having the same interest for a particular purpose. Those are done by a sort of an agreement, when the interest of the individual and of the body are the same. ”

“ Those who are accustomed to some of the more modern views of the above subject, will know that a few fundamental relations being true, certain other combinations of relations must of necessity follow; combinations unlimited in variety and extent if the deductions from the primary relations be carried on far enough. ”

“ It certainly will. A hundred objects, combined in twos, threes, and fours, will make over 4 million combinations; so if I made 100 combinations a day, it would take me over 110 years to exhaust them all! ”

“ A thousand subtle combinations are taking place around you, producing the most marvellous transformations—the chemist has a table of substances, and a table of proportions—names and figures both—why these transmutations take place, is a question you should be ashamed to ask. ”

“ It is equally certain, however, that the elements of its composition, if they did not exist in one form, must exist in another; and that the combinations which they would form, must so long as they endured, derive support for their peculiar mode of being from their fitness to the circumstances of their situation. ”

“ But if by myself I am not up to the task, a sizable group of people will be. If 1,000 of us came together to produce the combinations that I have described, then any one person would only have to carry out slightly more than 4,000 combinations. ”

“ If this be true of chemical combinations, it is still more true of those far more complex combinations of elements which constitute organized bodies; and in which those extraordinary new uniformities arise which are called the laws of life. ”

“ The sterile combinations do not even present themselves to the mind of the inventor. Never in the field of his consciousness do combinations appear that are not really useful, except some that he rejects but which have to some extent the characteristics of useful combinations. ”

“ Ideas, of the third class, those which the mind forms arbitrarily, are innumerable; because the combinations capable of being formed of the numerous elements which compose them, exceed computation. All these combinations cannot receive names. ”

“ I felt them collide until pairs interlocked, so to speak, making a stable combination. ”

“ Manifestly the favourable and unfavourable conditions recurring in combinations that are rarely twice alike, cannot be met by any regularly recurring form of heterogenesis; and it is interesting to see how survival of the fittest has established a mixed form. ”

“ Not only do these last differ in having life, but they themselves may appear in numerous combinations, and can combine among themselves to form higher units, whose characters and effectiveness will depend upon these combinations. ”

“ Although in many questions both of art and science we need to calculate the number of permutations on account of their own interest, it far more frequently happens in scientific subjects that they possess but an indirect interest. As I have already pointed out, we almost always deal in the logical and mathematical sciences with combinations, and variety of order enters181 only through the inherent imperfections of our symbols and modes of calculation. ”

“ Synthesis: Conscious Relating.—In the second place all thought is integrating or combining, or, as it is commonly expressed, a process of Synthesis. In thinking we never merely isolate or abstract. We analytically resolve the presentative complexes of our concrete experience only in order to establish certain relations among them. The most appropriate term for all such conscious relating or discernment of relation is Comparison. ”

“ A plurality is therefore a relation of units considered as a sum. Unity is constant only in ultimate particles. Bodies are combined, dissolved again and recombined, making variable units of plurality. ”

“ In illustrating the mode in which repetition makes association more and more easy, I used the process of arithmetical addition as a striking example. Persons little accustomed to the process perform it with great difficulty; persons 328 much accustomed to it, with astonishing facility. In men of the first class, the association is imperfectly formed, and the several antecedent expressions slowly suggest the proper consequent ones; in those of the latter class the association is very perfectly formed, and the expressions suggest one another with the greatest expedition and ease. ”

“ To the foregoing examples from physical science, let us add another from mental. The following is one of the simple laws of mind: Ideas of a pleasurable or painful character form associations more easily and strongly than other ideas, that is, they become associated after fewer repetitions, and the association is more durable. This is an experimental law, grounded on the Method of Difference. ”

“ E.g. the relative product of parent and brother is uncle, but the relative product of brother and parent is parent.
One-one relations give a correlation of two classes, term for term, so that each term in either class has its correlate in the other. Such correlations are simplest to grasp when the two classes have no members in common, like the class of husbands and the class of wives; for in that case we know at once whether a term is to be considered as one from which the correlating relation goes, or as one to which it goes. ”

“ Mass demands that the chief parts of every composition should readily catch the eye. It maintains a harmonious proportion of all the parts. Coherence demands of any composition that the relation of each part to its neighbors should be unmistakable, and that the order, forms, and connections of the parts preserve this relation. ”

“ But this general method of comparison is subdivided into three or four sub-methods. Nature has prepared not only one but three or four series, not identical, not mere duplicates of each other, but varied, yet resembling and illustrating each other. ”

“ This set of facts, which is connoted by both the correlative names, was called by the old logicians the ground of the relation, fundamentum relationis. The fundamentum of any relation is the facts, fully set out, which are the reason of giving to two objects two correlative names. In some cases both objects seem to receive the same name; in the relation of likeness, both objects are said to be like; in the relation of equality, both are said to be equal. ”

“ It is probable, in fact, that this difference—that between the Generalization which uses symbols, and mere Association—is the root of all the differences that follow later on, and give man the magnificent advantage over the animals which he has. ”

“ Connexions of phenomena of a rare, distant, unobtrusive, or intricate kind, which we either suffer from or do not take advantage of, have to be responded to by new connexions of ideas, and acts properly combined and proportioned: there must be increase of knowledge, or skill, or power, or of all these. And to effect this more extensive, more varied, and more accurate, co-ordination of actions, there must be organization of still greater heterogeneity and definiteness. ”

“ The negation of a categorical judgment is not a negative, but a particular judgment. Now the relations between objects are two-fold: either original ones, due to synthesis, or derived from an analysis of other relations. The process of thought which in this way derives relations from given relations is deduction. Induction creates original relations. ”