Exact sciences

“ I do not mean the mechanical sciences alone, physical astronomy and the like, though these undoubtedly have a prerogative value as the instruments of such a culture; but the like effect will be promoted by the exact and solid study of any portion of the circle of natural sciences; botany, comparative anatomy, geology, chemistry, for instance. But I say the exact and solid knowledge; not a mere verbal knowledge, but a knowledge which is real in its character, though it may be elementary and limited in its extent. ”

“ There is no science apart from the general.
It may even be said the very object of the exact sciences is to spare us these direct verifications. ”

“ Biology, which not long ago was purely descriptive and speculative, has begun to adopt the methods of the exact sciences, recognizing that for permanent progress not only experiments are required but quantitative experiments. ”

“ This scientific conception of causation has been developed and rendered definite by the investigations of those physical sciences that can avail themselves of exact experiments and mathematical calculation; and it is there, in Chemistry and Physics, that it is most at home. The conception can indeed be carried into the Biological and Social Sciences, even in its quantitative form, by making the proper allowances. For the limbs of animals are levers, and act upon mechanical principles ”

“ INTRODUCTION. IN order to the acquisition of any such exact and real knowledge of nature as that which we properly call Physical Science, it is requisite, as has already been said, that men should possess Ideas both distinct and appropriate, and should apply them to ascertained Facts. ”

“ In classifying our existing Knowledge, then, on our present basis of Scientific acquisition, we must draw a distinct line between Mathematics, Astronomy, and Physics, on the one side, and all remaining departments of Thought, on the other, and set these three Sciences apart as the Exact or Infallible ones, occupying a rank superior to the others, by virtue of the Certainty and Exactitude with which we are able, through the operation of the true Deductive Method, to ascertain their Principles and Phenomena. ”

“ He denominated as Positive Sciences those systems of Principles and correlated Facts, comprising Math [Pg 615] ematics, Astronomy, Physics, Chemistry, Biology, Sociology, and their derivative domains, which were founded on the exact Observation of Phenomena, and set aside all other realms of the universe of thought as departments in which exact knowledge was impossible, and whose intellectual examination was therefore fruitless. ”

“ The same distinction could very easily be shown to be the foundation of every other science. All the physical sciences have this in common, that they are researches into what is real as distinguished from what is apparent, that is, from what lies exposed and obvious on the very surface of things. ”

“ It may be a task, not hopeless, to extract from the past progress of science the elements of an effectual and substantial method of Scientific Discovery. The advances which have, during the last three centuries, been made in the physical sciences;—in Astronomy, in Physics, in Chemistry, in Natural History, in Physiology;—these are allowed by all to be real, to be great, to be striking ”

“ It is a general truth that the physical sciences of light and heat are based upon mechanical conditions of the particles of matter; that the science of chemistry is founded upon physics; that biological phenomena are dependent upon physical and chemical conditions; that psychological subjects are based upon biology; and that biological science cannot progress excepting in proportion to the advance of the sciences on which it is based. ”

“ I shall thus have to trace some of the most remarkable branches of human knowledge, from their first germ to their growth into a vast and varied assemblage of undisputed truths; from the acute, but fruitless, essays of the early Greek Philosophy, to the comprehensive systems, and demonstrated generalizations, which compose such sciences as the Mechanics, Astronomy, and Chemistry, of modern times. ”

“ Thus chemistry uses the characteristic ideas and methods of physics and mathematics, but especially of physics. Biology, besides its own characteristic ideas and methods, uses freely the methods and ideas of chemistry—physics and mathematics—but especially those of chemistry. If there be any other still higher science, it must use with the greatest advantage the ideas and methods of all lower sciences, but especially those of biology. ”

“ Hence, while Chemistry and Biology, even apart from the possibility of their conversion into branches of applied Mechanics, are essentially descriptive sciences, the task fulfilled by them, so far as they use qualitative and teleological categories, is one of æsthetic and historical rather than of properly scientific description. ”

“ We cannot expect men who work with books chiefly to have much in common with men whose lives are passed in laboratories. But, after differences of this kind, the next most important are differences in the modes of reasoning. Of the natural sciences, we have, first, the classificatory sciences, which are purely inductive—systematic botany 153and zoölogy, mineralogy, and chemistry. Then, we have the sciences of theory, as above explained—astronomy, pure physics, etc. Then, we have sciences of hypothesis—geology, biology, etc. ”

“ The definitions which those works furnish of the sciences, for the most part either do not fit them—some being too wide, some too narrow—or do not go deep enough into them, but define a science by its accidents, not its essentials; by some one of its properties which may, indeed, serve the purpose of a distinguishing mark, but which is of too little importance to have ever of itself led mankind to give the science a name and rank as a separate object of study. ”

“ There is, if we will but reflect and understand that the course of procedure proper to the physical sciences, namely, the assumption that their, objects and the facts appertaining to these objects lie before them ready-made—is utterly inadmissible in true philosophy—is totally at variance with the scope and spirit of a science which professes to deal fairly with the phenomena of man. ”

“ Indeed, if at the present moment we run over the names distinguished in the several sciences into which Natural Knowledge may be divided—in Physics, in Chemistry, in Botany, in Zoology—we find but few investigators who can be said to have thoroughly mastered the whole range of any one of them. ”

“ According to the notions of scientific order and completeness in the present day, a full course of the primary sciences would comprise mathematics, natural philosophy, chemistry, physiology or biology, and mental philosophy. The natural history branches are not looked upon as primary sciences; they give no laws, but repeat the laws of the primary sciences while classifying the kingdoms of Nature. ”

“ The processes by which truth is attained, reasoning and observation, have been carried to their greatest known perfection in the physical sciences. As classical literature furnishes the most perfect types of the art of expression, so do the physical sciences those of the art of thinking. Mathematics, and its application to astronomy and natural philosophy, are the most complete example of the discovery of truths by reasoning; experimental science, of their discovery by direct observation. ”

“ Measure, weight, and proportion were applied to all celestial and terrestrial phenomena, and physics, chemistry, and all the organic sciences became the manifestation of facts, of observed and calculated laws, arranged in a natural order, and in this way an immense advance was made in all branches of science. ”

“ It is in the essence of any modern method of inquiry that we should be first sure of our facts, and it is on this account that all philosophical research worthy of the name must begin with the physical sciences. For the last few weeks I have illustrated my lectures with chemical experiments and occasionally with large coloured diagrams, which, especially to young people like yourselves have done not a little to enliven what might at first appear a very dull subject. ”

“ Such sciences there must be, not only having reference to the bodies with which chemistry deals, but also to all things respecting which we aspire to obtain any general knowledge, as, for instance, plants and animals. ”

“ And in this series or ramification of the sciences, the more general science will not suffice to solve the problems of the more special. Chemistry embraces phenomena which are not explicable by Physics; Biology embraces phenomena which are not explicable by Chemistry ”

“ I shall confine myself almost wholly to the effect of science in enabling us to gratify our passions more freely, which8 has hitherto been far the more important of the two.
From our point of view, we may divide the sciences into three groups: physical, biological, and anthropological. In the physical group I include chemistry, and broadly speaking any science concerned with the properties of matter apart from life. ”

“ The surest way to acquire this qualification is to study the sciences. The dazzling array of facts which science has accumulated, owe half their value to the systematization they have received at the hands of her greatest savants.
It is impossible to take a step in scientific study without coming face to face with her grand classifications. At the very beginning science divides the universe into two parts, the inorganic and the organic. The inorganic is studied under the head of “physics”; the organic, under “biology.” ”

“ The Study of the Biological and Physical Sciences.—The last century is marked by scientific development along several {466} rather distinct lines as follows: the study of the earth, or geology; animal and vegetable life, or biology; atomic analysis, or chemistry; biochemistry; physics, especially that part relating to electricity and radioactivity; and more recently it might be stated that investigations are carried on in psychology and sociology, while mathematics and astronomy have made progress. ”

“ The sciences of chemistry, physics, and astronomy, based as they are on mathematics, allow precise statement and accurate experiment. In geology and biology, on the other hand, the factors are so complex that these sciences take on the nature of historical sciences, with all the difficulties which such a statement implies. ”

“ Further, it ought to be pointed out, as specially applicable to our present subject, that the best attainable knowledge on anything is due to a combination of general principles obtained from the sciences, with well-conducted observations and experiments made in actual practice. ”

“ As a treatise on any science usually commences with an attempt to express, in a brief formula, what the science is, and wherein it differs from other sciences, so, it might be supposed, did the framing of such a formula naturally precede the successful cultivation of the science. ”

“ Science: the Knowledge of the Laws of Nature obtained by Observation, Experiment, and Reasoning. No line can be drawn between common knowledge of things and scientific knowledge; nor between common reasoning and scientific reasoning. In strictness all accurate knowledge is Science; and all exact reasoning is scientific reasoning. The method of observation and experiment by which such great results are obtained in science, is identically the same as that which is employed by every one, every day of his life, but refined and rendered precise. ”

“ In addition to this, each science, to establish its own truths, needs those of all the sciences anterior to it. The only means, for example, by which the physiological laws of life could have been ascertained, was by distinguishing, among the multifarious and complicated facts of life, the portion which physical and chemical laws cannot account for. ”

“ For example, the physical sciences deal only with those universal phenomena produced by physical forces; chemistry, in addition to these, deals also with a higher but more limited and special group of phenomena, determined by a peculiar force—chemical affinity; biology, in addition to all the preceding, deals also with a still higher and far more limited and special group of phenomena produced by a still more characteristic force—life. ”

“ For the classification of the sciences it is convenient to prepare the way by distinguishing between theoretical sciences which are the sciences properly so called, and practical science. A theoretical science embraces a distinct department of nature, and is so arranged as to give in the most compact form the entire body of ascertained (scientific) knowledge in that department, such as mathematics, chemistry, physiology, and zoology. ”

“ So long as we select our examples in this arbitrary and limited manner, we lose the best part of that philosophical instruction, which the sciences are fitted to afford when we consider them as all members of one series, and as governed by rules which are the same for all. Mathematical and chemical truths, physical and physiological doctrines, the sciences of 10 classification and of causation, must alike be taken into our account, in order that we may learn what are the general characters of real knowledge. ”

“ If this view seems at first sight disappointing, we may remind ourselves that a similar change has been found necessary in all the other sciences. The physicist or chemist is not now required to prove the ethical importance of his ions or atoms; the biologist is not expected to prove the utility of the plants or animals [30] which he dissects. ”

“ There requires, first, the discipline yielded by Physics and Chemistry, to make definite the ideas of forces and actions as necessarily related in their kinds and amounts; and then the study of organic phenomena may be carried on with a clear consciousness that while the processes of causation are so involved as often to be inexplicable, yet there is causation, no less necessary and no less exact than causation of simpler kinds. ”