Simplification

“ And so simplification has become the motto of the unthinking as well as of the thinking, and is at present the butt of the ridicule of the funny man, and threatens to become as much of a stumbling-block to the mind, if not to the feet, as the passion for decoration was a few years ago. For this reason it seems fitting, in a series of articles which deal with the home problem in relation to the problem of more life for all, to inquire whether simplification can be the means of expanding life by increasing beauty. ”

“ O sancta simplicitas! In what strange simplification and falsification man lives! One can never cease wondering when once one has got eyes for beholding this marvel! How we have made everything around us clear and free and easy and simple! ”

“ Few people will dispute that all the typical movements of our time are upon this road towards simplification. Each system seeks to be more fundamental than the other; each seeks, in the literal sense, to undermine the other. ”

“ The first process therefore in the effectual study of the science must be one of simplification and reduction of the results of previous investigations to a form in which the mind can grasp them. The results of this simplification may take the form of a purely mathematical formula or of a physical hypothesis. ”

“ If we did not conduct our thought on this principle—simplifying by suppression of detail and breadth of treatment—it would take us a twelvemonth to say that it was a fine morning and another for the hearer to apprehend our statement. Any other principle reduces thought to an absurdity.
All painting depends upon simplification. All simplification depends upon a perception of relative importances. All perception of relative importances depends upon a just appreciation of which letters in association’s bond association will most readily dispense with. ”

“ In some cases of induction concerned with objects capable of abstraction and simplification, we have a power of identification, by which, not a priori but in the act of inducing a conclusion, we apprehend that the things signified by its subject and predicate are one and the same thing which cannot exist apart from itself. ”

“ To minds of a certain cast there is nothing so captivating as simplification and generalization. ”

“ The simplification of anything is always sensational. ”

“ It is only when we have seen it for the hundredth time that we see it for the first time. The more consistently things are contemplated, the more they tend to unify themselves and therefore to simplify themselves. The simplification of anything is always sensational. ”

“ Simplification is the great need in all matters of form or style—the easy and scientific conclusion that in all exactly similar instances the one reasoning applies, with the one result. The men who rank as our highest authorities as to spelling, and who should36 be best qualified to lead us, lack one necessary accomplishment—a practical knowledge of the art preservative. ”

“ The experts thus left to themselves in despair of any satisfactory solution, are likely enough to adopt the simplifications most agreeable to their present ideas, and measure the utility of such simplifications by the accidental conveniences of their own science, independently of other considerations. ”

“ Indeed, as we have already noted in passing, simplification is the method of every art. Every artist, in his own way, simplifies life: first by selecting essentials from the helter-skelter of details that life presents to him, and then by arranging these essentials in accordance with a pattern. And we have noted also that the method of the artist in narrative is to select events which bear an essential logical relation 61 to each other and then to arrange them along the lines of a pattern of causation. ”

“ As has been already pointed out, this is all that art can do. To test a generalization, by showing that it either follows from, or conflicts with, some stronger induction, some generalization resting on a broader foundation of experience, is the beginning and end of the logic of induction. ”

“ The problem that confronts you, then, in either kind of analysis, however formal or informal it may be, is, How shall I go to work? The first necessity is the choosing of a basis for division of the subject, whether it be in classification or partition. The necessity for this arises from the demand of the human mind for logical consistency. Life seems often wildly inconsistent, but we demand that explanation of it or any phase of it be arranged according to what seems to us some logical law of progression, some consistent point of view. ”

“ This mode of correcting one generalization by means of another, a narrower generalization by a wider, which common sense suggests and adopts in practice, is the real type of scientific Induction. All that art can do is but to give accuracy and precision to this process, and adapt it to all varieties of cases, without any essential alteration in its principle. ”

“ Bare bald simplicity of statement, concerning things keenly felt but imperfectly known, cannot be perfectly accurate; and yet every effort should be made to combine accuracy and simplicity to the utmost. ”

“ Too often apparent complexities are only the result of an abstruse contemplation of abstract possibilities. Give honest, fearless, practical treatment to each concrete case as it arises, indulge more in inductive reasoning which predicates laws upon facts, not facts upon laws, and complexity gives way to common sense. ”

“ But we think that we shall be able more conveniently to give instances of each kind, when we are furnishing a store of arguments for each kind. For so the system of arguing will be more clear, when it can be at once applied both to the general classification and to the particular instance.
When the statement of the case is once ascertained, then it is proper at once to consider whether the argument be a simple or a complex one; and if it be a complex one, whether it is made up of many subjects of inquiry, or of some comparison. ”

“ If we analyse a judgment, every word in which it is expressed, whether it is a noun or a verb or a preposition or a conjunction, conveys a distinct meaning, indicates a term or a relation, each of which can be made a distinct object to the mind, and all of which are combined in the single meaning the judgment expresses. It is in this complexity that the possibility of error lies, and the possibility increases as the complexity increases. ”

“ But, once more, grant that C is D, and it does not follow that A is B; so neither, if the conclusion of a syllogism be true, does it follow that the premises are. For example:—
Sociology is an exact science;
Mathematics is a branch of Sociology:
∴ Mathematics is an exact science. [Pg 160] Here the conclusion is true although the premises are absurd. Or again:—
Mathematics is an exact science;
Sociology is a branch of Mathematics:
∴ Sociology is an exact science. Here the major premise is true, but the minor is false, and the conclusion is false. ”

“ In the common or Syllogistic Logic, a certain Formula of language is used in stating the reasoning, and is useful in enabling us more readily to apply the Criterion of Form to alleged demonstrations. This formula is the usual Syllogism; with its members, Major Premiss, Minor Premiss, and Conclusion. It may naturally be asked whether in Inductive Logic there is any such Formula? whether there is any standard form of words in which we may most properly express the inference of a general truth from particular facts? ”

“ It has to combine analysis with synthesis, beginning with the dismemberment of the complex whole into simple principles, and passing over to the composition of a complex whole out of the simple principles. ”

“ Let it be considered whether in any science, viewed either as a system of truth or as the foundation of a practical art, there can properly be any other test of the completeness and the fundamental character of its laws, than the completeness of its system of derived truths, and the generality of the methods which it serves to establish. ”

“ In considering any complex matter, we ought to examine every distinct ingredient in the composition, one by one; and reduce everything to the utmost simplicity; since the condition of our nature binds us to a strict law and very narrow limits. ”

“ And so in all cases, the general propositions, whether called definitions, axioms, or laws of nature, which we lay down at the beginning of our reasonings, are merely abridged statements, in a kind of short-hand, of the particular facts, which, as occasion arises, we either think we may proceed on as proved, or intend to assume. In any one demonstration it is enough if we assume for a particular case suitably selected, what by the statement of the definition or principle we announce that we intend to assume in all cases which may arise. ”

“ Doubtless if our means of investigation should become more and more penetrating, we should discover the simple under the complex; then the complex under the simple; then anew the simple under the complex ”

“ Our general ideas, from those immediately bordering on the concrete to those which attain pure symbolism, constitute a hierarchy of ever-increasing simplicity. What value must be assigned to this thinking by concepts, in proportion as it ascends higher in the scale? We are all familiar with the debates upon this question, bearing, as it does, fundamentally upon the objective value of abstraction and generalisation. ”

“ As all modifiers are joined by slanting lines, to the words they modify, you learn from this diagram that who is wise is a modifier of man.
+Oral Analysis+.—This is a complex sentence, because it consists of an independent clause and a dependent clause. A man will be honored is the independent clause; who is wise is the dependent clause. Man is the subject of the independent clause; will be honored is the predicate. The word A and the clause, who is wise, are modifiers of the subject. A points out man, and who is wise tells the kind of man. A man who is wise is the modified subject ”

“ Going further into the matter, we must break up the conception into two parts, and distinguish between the actual production of complexity and the mere transformation of complexity from a condition invisible to us into complexity visible to our senses. ”

“ In the first place, logic, giving primarily the relations between concepts as such, and the relations between natural facts only secondarily or so far as the facts have been already identified with concepts and defined by them, must of course stand or fall with the conceptual method. But the conceptual method is a transformation which the flux of life undergoes at our hands in the interests of practice essentially and only subordinately in the interests of theory. We live forward, we understand backward, said a danish writer ”

“ The mistake is of the more elementary character when the attempt to establish the laws of thought, or a general criterion, is made by help of the reasonings of a special science, for that of course must presuppose the general laws and the criterion. ”

“ If there be necessary and universal truths expressible in propositions of axiomatic simplicity and obviousness, and having for their subject-matter the elements of all our experience and all our knowledge, surely these are the truths which, if experience suggest to us any truths at all, it ought to suggest most readily, clearly, and unceasingly. ”

“ We need only look well to what we have there. Simplicity will be promoted by returning to our previous remark, viz.—that reasoning is asserting a proposition, and then showing why it is true—in other words, adducing the fact or facts, on which the assertion rests. ”

“ The terms of the plan by which we explain the facts, the classes, for instance, daylight and darkness, and their relation of alternation, or the words or symbols which stand for classes and relations are not themselves facts but abstractions. We cannot think in terms of actual facts: the intellectual activity by which we formulate general laws can only work among abstractions, and in order to explain a fact we are obliged to substitute for it either a class or word or other symbol. All description and explanation of facts consists in substitutions of this kind. ”

“ The next division of propositions is into Simple and Complex. A simple proposition is that in which one predicate is affirmed or denied of one subject. A complex proposition is that in which there is more than one predicate, or more than one subject, or both. ”

“ Definition, though belonging still more to the other and larger kind of logic than to this, is a necessary preliminary to this. The end aimed at by Formal Logic, and attained by the observance of its precepts, is not truth, but consistency. It has been seen that this is the only direct purpose of the rules of the syllogism; the intention and effect of which is simply to keep our inferences or conclusions in complete consistency with our general formulæ or directions for drawing them. ”

“ If the simplicity were real and essential, it would resist the increasing precision of our means of measure. If then we believe nature to be essentially simple, we must, from a simplicity that is approximate, infer a simplicity that is rigorous. ”

“ We would like to have a more enduring result than awareness of complexity, and therefor we adopt the Definition & Reality methodology. As said, a proposition - as a statement on reality - can be regarded as a mathematical theorem about/within a model of stylized facts. When there is a tautology, we attain truth by definition. ”